From 098bc46c2a6dac1a95e5834319aa5b4a38b43709 Mon Sep 17 00:00:00 2001 From: adigitoleo Date: Thu, 3 Aug 2023 06:36:09 +0000 Subject: [PATCH] deploy: 946c29ef130637c5296be687d9dad1581d4ffa04 --- pydrex/minerals.html | 1932 +++++++-------- search.js | 2 +- tests/test_simple_shear_2d.html | 3905 ++++++++++++++++--------------- 3 files changed, 3009 insertions(+), 2830 deletions(-) diff --git a/pydrex/minerals.html b/pydrex/minerals.html index cc952d6d..059ce21c 100644 --- a/pydrex/minerals.html +++ b/pydrex/minerals.html @@ -98,6 +98,12 @@

API Documentation

  • seed
    • +
  • + lband +
    • +
  • + uband +
  • update_orientations
    • @@ -357,344 +363,360 @@

    217 fractions: list = field(default_factory=list) 218 orientations: list = field(default_factory=list) 219 seed: int = None -220 -221 def __str__(self): -222 # String output, used for str(self) and f"{self}", etc. -223 if hasattr(self.fractions[0], "shape"): -224 shape_of_fractions = str(self.fractions[0].shape) -225 else: -226 shape_of_fractions = "(?)" -227 -228 if hasattr(self.orientations[0], "shape"): -229 shape_of_orientations = str(self.orientations[0].shape) -230 else: -231 shape_of_orientations = "(?)" -232 -233 return ( -234 self.__class__.__qualname__ -235 + f"(phase={self.phase!s}, " -236 + f"fabric={self.fabric!s}, " -237 + f"regime={self.regime!s}, " -238 + f"n_grains={self.n_grains!s}, " -239 + f"fractions=<{self.fractions.__class__.__qualname__}" -240 + f" of {self.fractions[0].__class__.__qualname__} {shape_of_fractions}>, " -241 + f"orientations=<{self.orientations.__class__.__qualname__}" -242 + f" of {self.orientations[0].__class__.__qualname__} {shape_of_orientations}>)" -243 ) -244 -245 def _repr_pretty_(self, p, cycle): -246 # Format to use when printing to IPython or other interactive console. -247 p.text(self.__str__() if not cycle else self.__class__.__qualname__ + "(...)") -248 -249 def __post_init__(self): -250 """Initialise random orientations and grain volume fractions.""" -251 if self.fractions_init is None: -252 self.fractions_init = np.full(self.n_grains, 1.0 / self.n_grains) -253 if self.orientations_init is None: -254 self.orientations_init = Rotation.random( -255 self.n_grains, random_state=self.seed -256 ).as_matrix() -257 -258 # Copy the initial values to the storage lists. -259 self.fractions.append(self.fractions_init) -260 self.orientations.append(self.orientations_init) -261 -262 # Delete the initial value duplicates to avoid confusion. -263 del self.fractions_init -264 del self.orientations_init -265 -266 _log.info("created %s", self) -267 -268 def update_orientations( -269 self, -270 config, -271 deformation_gradient, -272 get_velocity_gradient, -273 pathline, -274 **kwargs, -275 ): -276 """Update orientations and volume distribution for the `Mineral`. -277 -278 Update crystalline orientations and grain volume distribution -279 for minerals undergoing plastic deformation. -280 -281 Args: -282 - `config` (dict) — PyDRex configuration dictionary -283 - `deformation_gradient` (array) — 3x3 initial deformation gradient tensor -284 - `get_velocity_gradient` (function) — callable with signature f(x) that returns -285 a 3x3 velocity gradient matrix at position x (vector) -286 - `pathline` (tuple) — tuple consisting of: -287 1. the time at which to start the CPO integration (t_start) -288 2. the time at which to stop the CPO integration (t_end) -289 3. callable with signature f(t) that returns the position of the mineral at -290 time t ∈ [t_start, t_end] +220 lband: int = None +221 uband: int = None +222 +223 def __str__(self): +224 # String output, used for str(self) and f"{self}", etc. +225 if hasattr(self.fractions[0], "shape"): +226 shape_of_fractions = str(self.fractions[0].shape) +227 else: +228 shape_of_fractions = "(?)" +229 +230 if hasattr(self.orientations[0], "shape"): +231 shape_of_orientations = str(self.orientations[0].shape) +232 else: +233 shape_of_orientations = "(?)" +234 +235 return ( +236 self.__class__.__qualname__ +237 + f"(phase={self.phase!s}, " +238 + f"fabric={self.fabric!s}, " +239 + f"regime={self.regime!s}, " +240 + f"n_grains={self.n_grains!s}, " +241 + f"fractions=<{self.fractions.__class__.__qualname__}" +242 + f" of {self.fractions[0].__class__.__qualname__} {shape_of_fractions}>, " +243 + f"orientations=<{self.orientations.__class__.__qualname__}" +244 + f" of {self.orientations[0].__class__.__qualname__} {shape_of_orientations}>)" +245 ) +246 +247 def _repr_pretty_(self, p, cycle): +248 # Format to use when printing to IPython or other interactive console. +249 p.text(self.__str__() if not cycle else self.__class__.__qualname__ + "(...)") +250 +251 def __post_init__(self): +252 """Initialise random orientations and grain volume fractions.""" +253 if self.fractions_init is None: +254 self.fractions_init = np.full(self.n_grains, 1.0 / self.n_grains) +255 if self.orientations_init is None: +256 self.orientations_init = Rotation.random( +257 self.n_grains, random_state=self.seed +258 ).as_matrix() +259 # For large numbers of grains, the number of ODE's exceeds what LSODA can +260 # handle. Therefore, we specify the Jacobian matrix as banded. +261 # By default, we use a bandwidth o f 12000 with lband = uband = 6000. +262 # This should work for up to 10000 grains. +263 if self.lband is None and self.uband is None and self.n_grains > 4632: +264 _log.warning( +265 "using a banded Jacobian because of the large number of grains." +266 + " To manually control the bandwidth, set `lband` and/or `uband`" +267 + f" in calls to `{self.__class__.__qualname__}.update_orientations`." +268 ) +269 self.lband = 6000 +270 self.uband = 6000 +271 +272 # Copy the initial values to the storage lists. +273 self.fractions.append(self.fractions_init) +274 self.orientations.append(self.orientations_init) +275 +276 # Delete the initial value duplicates to avoid confusion. +277 del self.fractions_init +278 del self.orientations_init +279 +280 _log.info("created %s", self) +281 +282 def update_orientations( +283 self, +284 config, +285 deformation_gradient, +286 get_velocity_gradient, +287 pathline, +288 **kwargs, +289 ): +290 """Update orientations and volume distribution for the `Mineral`. 291 -292 Any additional (optional) keyword arguments are passed to -293 `scipy.integrate.LSODA`. +292 Update crystalline orientations and grain volume distribution +293 for minerals undergoing plastic deformation. 294 -295 Array values must provide a NumPy-compatible interface: -296 <https://numpy.org/doc/stable/user/whatisnumpy.html> -297 -298 """ -299 -300 # ===== Set up callables for the ODE solver and internal processing ===== -301 -302 def extract_vars(y): -303 # TODO: Check if we can avoid .copy() here. -304 deformation_gradient = y[:9].copy().reshape((3, 3)) -305 orientations = ( -306 y[9 : self.n_grains * 9 + 9] -307 .copy() -308 .reshape((self.n_grains, 3, 3)) -309 .clip(-1, 1) -310 ) -311 # TODO: Check if we can avoid .copy() here. -312 fractions = ( -313 y[self.n_grains * 9 + 9 : self.n_grains * 10 + 9].copy().clip(0, None) -314 ) -315 fractions /= fractions.sum() -316 return deformation_gradient, orientations, fractions -317 -318 def eval_rhs(t, y): -319 """Evaluate right hand side of the D-Rex PDE.""" -320 # assert not np.any(np.isnan(y)), y[np.isnan(y)].shape -321 position = get_position(t) -322 velocity_gradient = get_velocity_gradient(position) -323 # _log.debug( -324 # "calculating CPO at %s (t=%e) with velocity gradient %s", -325 # position, -326 # t, -327 # velocity_gradient.flatten(), -328 # ) -329 -330 strain_rate = (velocity_gradient + velocity_gradient.transpose()) / 2 -331 strain_rate_max = np.abs(la.eigvalsh(strain_rate)).max() -332 deformation_gradient, orientations, fractions = extract_vars(y) -333 # Uses nondimensional values of strain rate and velocity gradient. -334 orientations_diff, fractions_diff = _core.derivatives( -335 phase=self.phase, -336 fabric=self.fabric, -337 n_grains=self.n_grains, -338 orientations=orientations, -339 fractions=fractions, -340 strain_rate=strain_rate / strain_rate_max, -341 velocity_gradient=velocity_gradient / strain_rate_max, -342 stress_exponent=config["stress_exponent"], -343 deformation_exponent=config["deformation_exponent"], -344 nucleation_efficiency=config["nucleation_efficiency"], -345 gbm_mobility=config["gbm_mobility"], -346 volume_fraction=volume_fraction, -347 ) -348 return np.hstack( -349 ( -350 (velocity_gradient @ deformation_gradient).flatten(), -351 orientations_diff.flatten() * strain_rate_max, -352 fractions_diff * strain_rate_max, -353 ) -354 ) -355 -356 def apply_gbs(orientations, fractions, config): -357 """Apply grain boundary sliding for small grains.""" -358 mask = fractions < (config["gbs_threshold"] / self.n_grains) -359 # _log.debug( -360 # "grain boundary sliding activity (volume percentage): %s", -361 # len(np.nonzero(mask)) / len(fractions), -362 # ) -363 # No rotation: carry over previous orientations. -364 orientations[mask, :, :] = self.orientations[-1][mask, :, :] -365 fractions[mask] = config["gbs_threshold"] / self.n_grains -366 fractions /= fractions.sum() -367 # _log.debug( -368 # "grain volume fractions: median=%e, min=%e, max=%e, sum=%e", -369 # np.median(fractions), -370 # np.min(fractions), -371 # np.max(fractions), -372 # np.sum(fractions), -373 # ) -374 return orientations, fractions -375 -376 def perform_step(solver): -377 """Perform SciPy solver step and appropriate processing.""" -378 message = solver.step() -379 if message is not None and solver.status == "failed": -380 raise _err.IterationError(message) +295 Args: +296 - `config` (dict) — PyDRex configuration dictionary +297 - `deformation_gradient` (array) — 3x3 initial deformation gradient tensor +298 - `get_velocity_gradient` (function) — callable with signature f(x) that returns +299 a 3x3 velocity gradient matrix at position x (vector) +300 - `pathline` (tuple) — tuple consisting of: +301 1. the time at which to start the CPO integration (t_start) +302 2. the time at which to stop the CPO integration (t_end) +303 3. callable with signature f(t) that returns the position of the mineral at +304 time t ∈ [t_start, t_end] +305 +306 Any additional (optional) keyword arguments are passed to +307 `scipy.integrate.LSODA`. +308 +309 Array values must provide a NumPy-compatible interface: +310 <https://numpy.org/doc/stable/user/whatisnumpy.html> +311 +312 """ +313 +314 # ===== Set up callables for the ODE solver and internal processing ===== +315 +316 def extract_vars(y): +317 # TODO: Check if we can avoid .copy() here. +318 deformation_gradient = y[:9].copy().reshape((3, 3)) +319 orientations = ( +320 y[9 : self.n_grains * 9 + 9] +321 .copy() +322 .reshape((self.n_grains, 3, 3)) +323 .clip(-1, 1) +324 ) +325 # TODO: Check if we can avoid .copy() here. +326 fractions = ( +327 y[self.n_grains * 9 + 9 : self.n_grains * 10 + 9].copy().clip(0, None) +328 ) +329 fractions /= fractions.sum() +330 return deformation_gradient, orientations, fractions +331 +332 def eval_rhs(t, y): +333 """Evaluate right hand side of the D-Rex PDE.""" +334 # assert not np.any(np.isnan(y)), y[np.isnan(y)].shape +335 position = get_position(t) +336 velocity_gradient = get_velocity_gradient(position) +337 # _log.debug( +338 # "calculating CPO at %s (t=%e) with velocity gradient %s", +339 # position, +340 # t, +341 # velocity_gradient.flatten(), +342 # ) +343 +344 strain_rate = (velocity_gradient + velocity_gradient.transpose()) / 2 +345 strain_rate_max = np.abs(la.eigvalsh(strain_rate)).max() +346 deformation_gradient, orientations, fractions = extract_vars(y) +347 # Uses nondimensional values of strain rate and velocity gradient. +348 orientations_diff, fractions_diff = _core.derivatives( +349 phase=self.phase, +350 fabric=self.fabric, +351 n_grains=self.n_grains, +352 orientations=orientations, +353 fractions=fractions, +354 strain_rate=strain_rate / strain_rate_max, +355 velocity_gradient=velocity_gradient / strain_rate_max, +356 stress_exponent=config["stress_exponent"], +357 deformation_exponent=config["deformation_exponent"], +358 nucleation_efficiency=config["nucleation_efficiency"], +359 gbm_mobility=config["gbm_mobility"], +360 volume_fraction=volume_fraction, +361 ) +362 return np.hstack( +363 ( +364 (velocity_gradient @ deformation_gradient).flatten(), +365 orientations_diff.flatten() * strain_rate_max, +366 fractions_diff * strain_rate_max, +367 ) +368 ) +369 +370 def apply_gbs(orientations, fractions, config): +371 """Apply grain boundary sliding for small grains.""" +372 mask = fractions < (config["gbs_threshold"] / self.n_grains) +373 # _log.debug( +374 # "grain boundary sliding activity (volume percentage): %s", +375 # len(np.nonzero(mask)) / len(fractions), +376 # ) +377 # No rotation: carry over previous orientations. +378 orientations[mask, :, :] = self.orientations[-1][mask, :, :] +379 fractions[mask] = config["gbs_threshold"] / self.n_grains +380 fractions /= fractions.sum() 381 # _log.debug( -382 # "%s step_size=%e", solver.__class__.__qualname__, solver.step_size -383 # ) -384 -385 deformation_gradient, orientations, fractions = extract_vars(solver.y) -386 orientations, fractions = apply_gbs(orientations, fractions, config) -387 solver.y[9:] = np.hstack((orientations.flatten(), fractions)) -388 -389 # ===== Initialise and run the solver using the above callables ===== -390 -391 time_start, time_end, get_position = pathline -392 if not callable(get_velocity_gradient): -393 raise ValueError( -394 "unable to evaluate velocity gradient callable." -395 + " You must provide a callable with signature f(x)" -396 + " that returns a 3x3 matrix." -397 ) -398 if not callable(get_position): -399 raise ValueError( -400 "unable to evaluate position callable." -401 + " You must provide a callable with signature f(t)" -402 + " that returns a 3-component array." -403 ) +382 # "grain volume fractions: median=%e, min=%e, max=%e, sum=%e", +383 # np.median(fractions), +384 # np.min(fractions), +385 # np.max(fractions), +386 # np.sum(fractions), +387 # ) +388 return orientations, fractions +389 +390 def perform_step(solver): +391 """Perform SciPy solver step and appropriate processing.""" +392 message = solver.step() +393 if message is not None and solver.status == "failed": +394 raise _err.IterationError(message) +395 # _log.debug( +396 # "%s step_size=%e", solver.__class__.__qualname__, solver.step_size +397 # ) +398 +399 deformation_gradient, orientations, fractions = extract_vars(solver.y) +400 orientations, fractions = apply_gbs(orientations, fractions, config) +401 solver.y[9:] = np.hstack((orientations.flatten(), fractions)) +402 +403 # ===== Initialise and run the solver using the above callables ===== 404 -405 if self.phase == _core.MineralPhase.olivine: -406 volume_fraction = config["olivine_fraction"] -407 elif self.phase == _core.MineralPhase.enstatite: -408 volume_fraction = config["enstatite_fraction"] -409 else: -410 assert False # Should never happen. -411 -412 y_start = np.hstack( -413 ( -414 deformation_gradient.flatten(), -415 self.orientations[-1].flatten(), -416 self.fractions[-1], +405 time_start, time_end, get_position = pathline +406 if not callable(get_velocity_gradient): +407 raise ValueError( +408 "unable to evaluate velocity gradient callable." +409 + " You must provide a callable with signature f(x)" +410 + " that returns a 3x3 matrix." +411 ) +412 if not callable(get_position): +413 raise ValueError( +414 "unable to evaluate position callable." +415 + " You must provide a callable with signature f(t)" +416 + " that returns a 3-component array." 417 ) -418 ) -419 solver = LSODA( -420 eval_rhs, -421 time_start, -422 y_start, -423 time_end, -424 atol=kwargs.pop("atol", np.abs(y_start * 1e-6) + 1e-12), -425 rtol=kwargs.pop("rtol", 1e-6), -426 first_step=kwargs.pop("first_step", np.abs(time_end - time_start) * 1e-1), -427 # max_step=kwargs.pop("max_step", np.abs(time_end - time_start)), -428 **kwargs, -429 ) -430 perform_step(solver) -431 while solver.status == "running": -432 perform_step(solver) -433 -434 # Extract final values for this simulation step, append to storage. -435 deformation_gradient, orientations, fractions = extract_vars(solver.y.squeeze()) -436 self.orientations.append(orientations) -437 self.fractions.append(fractions) -438 return deformation_gradient -439 -440 def save(self, filename, postfix=None): -441 """Save CPO data for all stored timesteps to a `numpy` NPZ file. -442 -443 If `postfix` is not `None`, the data is appended to the NPZ file -444 in fields ending with "`_postfix`". -445 -446 Raises a `ValueError` if the data shapes are not compatible. -447 -448 See also: `numpy.savez`, `Mineral.load`, `Mineral.from_file`. +418 +419 if self.phase == _core.MineralPhase.olivine: +420 volume_fraction = config["olivine_fraction"] +421 elif self.phase == _core.MineralPhase.enstatite: +422 volume_fraction = config["enstatite_fraction"] +423 else: +424 assert False # Should never happen. +425 +426 y_start = np.hstack( +427 ( +428 deformation_gradient.flatten(), +429 self.orientations[-1].flatten(), +430 self.fractions[-1], +431 ) +432 ) +433 solver = LSODA( +434 eval_rhs, +435 time_start, +436 y_start, +437 time_end, +438 atol=kwargs.pop("atol", np.abs(y_start * 1e-6) + 1e-12), +439 rtol=kwargs.pop("rtol", 1e-6), +440 first_step=kwargs.pop("first_step", np.abs(time_end - time_start) * 1e-1), +441 # max_step=kwargs.pop("max_step", np.abs(time_end - time_start)), +442 lband=self.lband, +443 uband=self.uband, +444 **kwargs, +445 ) +446 perform_step(solver) +447 while solver.status == "running": +448 perform_step(solver) 449 -450 """ -451 if len(self.fractions) != len(self.orientations): -452 raise ValueError( -453 "Length of stored results must match." -454 + " You've supplied currupted data with:\n" -455 + f"- {len(self.fractions)} grain size results, and\n" -456 + f"- {len(self.orientations)} orientation results." -457 ) -458 if self.fractions[0].shape[0] == self.orientations[0].shape[0] == self.n_grains: -459 data = { -460 "meta": np.array( -461 [self.phase, self.fabric, self.regime], dtype=np.uint8 -462 ), -463 "fractions": np.stack(self.fractions), -464 "orientations": np.stack(self.orientations), -465 } -466 # Create parent directories, resolve relative paths. -467 _io.resolve_path(filename) -468 # Append to file, requires postfix (unique name). -469 if postfix is not None: -470 archive = ZipFile(filename, mode="a", allowZip64=True) -471 for key in data.keys(): -472 with archive.open( -473 f"{key}_{postfix}", "w", force_zip64=True -474 ) as file: -475 buffer = io.BytesIO() -476 np.save(buffer, data[key]) -477 file.write(buffer.getvalue()) -478 buffer.close() -479 else: -480 np.savez(filename, **data) -481 else: -482 raise ValueError( -483 "Size of CPO data arrays must match number of grains." -484 + " You've supplied corrupted data with:\n" -485 + f"- `n_grains = {self.n_grains}`,\n" -486 + f"- `fractions[0].shape = {self.fractions[0].shape}`, and\n" -487 + f"- `orientations[0].shape = {self.orientations[0].shape}`." -488 ) -489 -490 def load(self, filename, postfix=None): -491 """Load CPO data from a `numpy` NPZ file. -492 -493 If `postfix` is not `None`, data is read from fields ending with "`_postfix`". -494 -495 See also: `Mineral.save`, `Mineral.from_file`. -496 -497 """ -498 if not filename.endswith(".npz"): -499 raise ValueError( -500 f"Must only load from numpy NPZ format. Cannot load from {filename}." -501 ) -502 data = np.load(filename) -503 if postfix is not None: -504 phase, fabric, regime = data[f"meta_{postfix}"] -505 self.fractions = list(data[f"fractions_{postfix}"]) -506 self.orientations = list(data[f"orientations_{postfix}"]) -507 else: -508 phase, fabric, regime = data["meta"] -509 self.fractions = list(data["fractions"]) -510 self.orientations = list(data["orientations"]) -511 -512 self.phase = phase -513 self.fabric = fabric -514 self.regime = regime -515 self.orientations_init = self.orientations[0] -516 self.fractions_init = self.fractions[0] -517 -518 @classmethod -519 def from_file(cls, filename, postfix=None): -520 """Construct a `Mineral` instance using data from a `numpy` NPZ file. -521 -522 If `postfix` is not `None`, data is read from fields ending with “`_postfix`”. -523 -524 See also: `Mineral.save`, `Mineral.load`. -525 -526 """ -527 if not filename.endswith(".npz"): -528 raise ValueError( -529 f"Must only load from numpy NPZ format. Cannot load from {filename}." -530 ) -531 data = np.load(filename) -532 if postfix is not None: -533 phase, fabric, regime = data[f"meta_{postfix}"] -534 fractions = list(data[f"fractions_{postfix}"]) -535 orientations = list(data[f"orientations_{postfix}"]) -536 else: -537 phase, fabric, regime = data["meta"] -538 fractions = list(data["fractions"]) -539 orientations = list(data["orientations"]) -540 -541 mineral = cls( -542 phase, -543 fabric, -544 regime, -545 n_grains=len(fractions[0]), -546 fractions_init=fractions[0], -547 orientations_init=orientations[0], -548 ) -549 mineral.fractions = fractions -550 mineral.orientations = orientations -551 return mineral -552 -553 -554def __run_doctests(): -555 import doctest +450 # Extract final values for this simulation step, append to storage. +451 deformation_gradient, orientations, fractions = extract_vars(solver.y.squeeze()) +452 self.orientations.append(orientations) +453 self.fractions.append(fractions) +454 return deformation_gradient +455 +456 def save(self, filename, postfix=None): +457 """Save CPO data for all stored timesteps to a `numpy` NPZ file. +458 +459 If `postfix` is not `None`, the data is appended to the NPZ file +460 in fields ending with "`_postfix`". +461 +462 Raises a `ValueError` if the data shapes are not compatible. +463 +464 See also: `numpy.savez`, `Mineral.load`, `Mineral.from_file`. +465 +466 """ +467 if len(self.fractions) != len(self.orientations): +468 raise ValueError( +469 "Length of stored results must match." +470 + " You've supplied currupted data with:\n" +471 + f"- {len(self.fractions)} grain size results, and\n" +472 + f"- {len(self.orientations)} orientation results." +473 ) +474 if self.fractions[0].shape[0] == self.orientations[0].shape[0] == self.n_grains: +475 data = { +476 "meta": np.array( +477 [self.phase, self.fabric, self.regime], dtype=np.uint8 +478 ), +479 "fractions": np.stack(self.fractions), +480 "orientations": np.stack(self.orientations), +481 } +482 # Create parent directories, resolve relative paths. +483 _io.resolve_path(filename) +484 # Append to file, requires postfix (unique name). +485 if postfix is not None: +486 archive = ZipFile(filename, mode="a", allowZip64=True) +487 for key in data.keys(): +488 with archive.open( +489 f"{key}_{postfix}", "w", force_zip64=True +490 ) as file: +491 buffer = io.BytesIO() +492 np.save(buffer, data[key]) +493 file.write(buffer.getvalue()) +494 buffer.close() +495 else: +496 np.savez(filename, **data) +497 else: +498 raise ValueError( +499 "Size of CPO data arrays must match number of grains." +500 + " You've supplied corrupted data with:\n" +501 + f"- `n_grains = {self.n_grains}`,\n" +502 + f"- `fractions[0].shape = {self.fractions[0].shape}`, and\n" +503 + f"- `orientations[0].shape = {self.orientations[0].shape}`." +504 ) +505 +506 def load(self, filename, postfix=None): +507 """Load CPO data from a `numpy` NPZ file. +508 +509 If `postfix` is not `None`, data is read from fields ending with "`_postfix`". +510 +511 See also: `Mineral.save`, `Mineral.from_file`. +512 +513 """ +514 if not filename.endswith(".npz"): +515 raise ValueError( +516 f"Must only load from numpy NPZ format. Cannot load from {filename}." +517 ) +518 data = np.load(filename) +519 if postfix is not None: +520 phase, fabric, regime = data[f"meta_{postfix}"] +521 self.fractions = list(data[f"fractions_{postfix}"]) +522 self.orientations = list(data[f"orientations_{postfix}"]) +523 else: +524 phase, fabric, regime = data["meta"] +525 self.fractions = list(data["fractions"]) +526 self.orientations = list(data["orientations"]) +527 +528 self.phase = phase +529 self.fabric = fabric +530 self.regime = regime +531 self.orientations_init = self.orientations[0] +532 self.fractions_init = self.fractions[0] +533 +534 @classmethod +535 def from_file(cls, filename, postfix=None): +536 """Construct a `Mineral` instance using data from a `numpy` NPZ file. +537 +538 If `postfix` is not `None`, data is read from fields ending with “`_postfix`”. +539 +540 See also: `Mineral.save`, `Mineral.load`. +541 +542 """ +543 if not filename.endswith(".npz"): +544 raise ValueError( +545 f"Must only load from numpy NPZ format. Cannot load from {filename}." +546 ) +547 data = np.load(filename) +548 if postfix is not None: +549 phase, fabric, regime = data[f"meta_{postfix}"] +550 fractions = list(data[f"fractions_{postfix}"]) +551 orientations = list(data[f"orientations_{postfix}"]) +552 else: +553 phase, fabric, regime = data["meta"] +554 fractions = list(data["fractions"]) +555 orientations = list(data["orientations"]) 556 -557 return doctest.testmod() +557 mineral = cls( +558 phase, +559 fabric, +560 regime, +561 n_grains=len(fractions[0]), +562 fractions_init=fractions[0], +563 orientations_init=orientations[0], +564 ) +565 mineral.fractions = fractions +566 mineral.orientations = orientations +567 return mineral +568 +569 +570def __run_doctests(): +571 import doctest +572 +573 return doctest.testmod() @@ -960,338 +982,354 @@

    218 fractions: list = field(default_factory=list) 219 orientations: list = field(default_factory=list) 220 seed: int = None -221 -222 def __str__(self): -223 # String output, used for str(self) and f"{self}", etc. -224 if hasattr(self.fractions[0], "shape"): -225 shape_of_fractions = str(self.fractions[0].shape) -226 else: -227 shape_of_fractions = "(?)" -228 -229 if hasattr(self.orientations[0], "shape"): -230 shape_of_orientations = str(self.orientations[0].shape) -231 else: -232 shape_of_orientations = "(?)" -233 -234 return ( -235 self.__class__.__qualname__ -236 + f"(phase={self.phase!s}, " -237 + f"fabric={self.fabric!s}, " -238 + f"regime={self.regime!s}, " -239 + f"n_grains={self.n_grains!s}, " -240 + f"fractions=<{self.fractions.__class__.__qualname__}" -241 + f" of {self.fractions[0].__class__.__qualname__} {shape_of_fractions}>, " -242 + f"orientations=<{self.orientations.__class__.__qualname__}" -243 + f" of {self.orientations[0].__class__.__qualname__} {shape_of_orientations}>)" -244 ) -245 -246 def _repr_pretty_(self, p, cycle): -247 # Format to use when printing to IPython or other interactive console. -248 p.text(self.__str__() if not cycle else self.__class__.__qualname__ + "(...)") -249 -250 def __post_init__(self): -251 """Initialise random orientations and grain volume fractions.""" -252 if self.fractions_init is None: -253 self.fractions_init = np.full(self.n_grains, 1.0 / self.n_grains) -254 if self.orientations_init is None: -255 self.orientations_init = Rotation.random( -256 self.n_grains, random_state=self.seed -257 ).as_matrix() -258 -259 # Copy the initial values to the storage lists. -260 self.fractions.append(self.fractions_init) -261 self.orientations.append(self.orientations_init) -262 -263 # Delete the initial value duplicates to avoid confusion. -264 del self.fractions_init -265 del self.orientations_init -266 -267 _log.info("created %s", self) -268 -269 def update_orientations( -270 self, -271 config, -272 deformation_gradient, -273 get_velocity_gradient, -274 pathline, -275 **kwargs, -276 ): -277 """Update orientations and volume distribution for the `Mineral`. -278 -279 Update crystalline orientations and grain volume distribution -280 for minerals undergoing plastic deformation. -281 -282 Args: -283 - `config` (dict) — PyDRex configuration dictionary -284 - `deformation_gradient` (array) — 3x3 initial deformation gradient tensor -285 - `get_velocity_gradient` (function) — callable with signature f(x) that returns -286 a 3x3 velocity gradient matrix at position x (vector) -287 - `pathline` (tuple) — tuple consisting of: -288 1. the time at which to start the CPO integration (t_start) -289 2. the time at which to stop the CPO integration (t_end) -290 3. callable with signature f(t) that returns the position of the mineral at -291 time t ∈ [t_start, t_end] +221 lband: int = None +222 uband: int = None +223 +224 def __str__(self): +225 # String output, used for str(self) and f"{self}", etc. +226 if hasattr(self.fractions[0], "shape"): +227 shape_of_fractions = str(self.fractions[0].shape) +228 else: +229 shape_of_fractions = "(?)" +230 +231 if hasattr(self.orientations[0], "shape"): +232 shape_of_orientations = str(self.orientations[0].shape) +233 else: +234 shape_of_orientations = "(?)" +235 +236 return ( +237 self.__class__.__qualname__ +238 + f"(phase={self.phase!s}, " +239 + f"fabric={self.fabric!s}, " +240 + f"regime={self.regime!s}, " +241 + f"n_grains={self.n_grains!s}, " +242 + f"fractions=<{self.fractions.__class__.__qualname__}" +243 + f" of {self.fractions[0].__class__.__qualname__} {shape_of_fractions}>, " +244 + f"orientations=<{self.orientations.__class__.__qualname__}" +245 + f" of {self.orientations[0].__class__.__qualname__} {shape_of_orientations}>)" +246 ) +247 +248 def _repr_pretty_(self, p, cycle): +249 # Format to use when printing to IPython or other interactive console. +250 p.text(self.__str__() if not cycle else self.__class__.__qualname__ + "(...)") +251 +252 def __post_init__(self): +253 """Initialise random orientations and grain volume fractions.""" +254 if self.fractions_init is None: +255 self.fractions_init = np.full(self.n_grains, 1.0 / self.n_grains) +256 if self.orientations_init is None: +257 self.orientations_init = Rotation.random( +258 self.n_grains, random_state=self.seed +259 ).as_matrix() +260 # For large numbers of grains, the number of ODE's exceeds what LSODA can +261 # handle. Therefore, we specify the Jacobian matrix as banded. +262 # By default, we use a bandwidth o f 12000 with lband = uband = 6000. +263 # This should work for up to 10000 grains. +264 if self.lband is None and self.uband is None and self.n_grains > 4632: +265 _log.warning( +266 "using a banded Jacobian because of the large number of grains." +267 + " To manually control the bandwidth, set `lband` and/or `uband`" +268 + f" in calls to `{self.__class__.__qualname__}.update_orientations`." +269 ) +270 self.lband = 6000 +271 self.uband = 6000 +272 +273 # Copy the initial values to the storage lists. +274 self.fractions.append(self.fractions_init) +275 self.orientations.append(self.orientations_init) +276 +277 # Delete the initial value duplicates to avoid confusion. +278 del self.fractions_init +279 del self.orientations_init +280 +281 _log.info("created %s", self) +282 +283 def update_orientations( +284 self, +285 config, +286 deformation_gradient, +287 get_velocity_gradient, +288 pathline, +289 **kwargs, +290 ): +291 """Update orientations and volume distribution for the `Mineral`. 292 -293 Any additional (optional) keyword arguments are passed to -294 `scipy.integrate.LSODA`. +293 Update crystalline orientations and grain volume distribution +294 for minerals undergoing plastic deformation. 295 -296 Array values must provide a NumPy-compatible interface: -297 <https://numpy.org/doc/stable/user/whatisnumpy.html> -298 -299 """ -300 -301 # ===== Set up callables for the ODE solver and internal processing ===== -302 -303 def extract_vars(y): -304 # TODO: Check if we can avoid .copy() here. -305 deformation_gradient = y[:9].copy().reshape((3, 3)) -306 orientations = ( -307 y[9 : self.n_grains * 9 + 9] -308 .copy() -309 .reshape((self.n_grains, 3, 3)) -310 .clip(-1, 1) -311 ) -312 # TODO: Check if we can avoid .copy() here. -313 fractions = ( -314 y[self.n_grains * 9 + 9 : self.n_grains * 10 + 9].copy().clip(0, None) -315 ) -316 fractions /= fractions.sum() -317 return deformation_gradient, orientations, fractions -318 -319 def eval_rhs(t, y): -320 """Evaluate right hand side of the D-Rex PDE.""" -321 # assert not np.any(np.isnan(y)), y[np.isnan(y)].shape -322 position = get_position(t) -323 velocity_gradient = get_velocity_gradient(position) -324 # _log.debug( -325 # "calculating CPO at %s (t=%e) with velocity gradient %s", -326 # position, -327 # t, -328 # velocity_gradient.flatten(), -329 # ) -330 -331 strain_rate = (velocity_gradient + velocity_gradient.transpose()) / 2 -332 strain_rate_max = np.abs(la.eigvalsh(strain_rate)).max() -333 deformation_gradient, orientations, fractions = extract_vars(y) -334 # Uses nondimensional values of strain rate and velocity gradient. -335 orientations_diff, fractions_diff = _core.derivatives( -336 phase=self.phase, -337 fabric=self.fabric, -338 n_grains=self.n_grains, -339 orientations=orientations, -340 fractions=fractions, -341 strain_rate=strain_rate / strain_rate_max, -342 velocity_gradient=velocity_gradient / strain_rate_max, -343 stress_exponent=config["stress_exponent"], -344 deformation_exponent=config["deformation_exponent"], -345 nucleation_efficiency=config["nucleation_efficiency"], -346 gbm_mobility=config["gbm_mobility"], -347 volume_fraction=volume_fraction, -348 ) -349 return np.hstack( -350 ( -351 (velocity_gradient @ deformation_gradient).flatten(), -352 orientations_diff.flatten() * strain_rate_max, -353 fractions_diff * strain_rate_max, -354 ) -355 ) -356 -357 def apply_gbs(orientations, fractions, config): -358 """Apply grain boundary sliding for small grains.""" -359 mask = fractions < (config["gbs_threshold"] / self.n_grains) -360 # _log.debug( -361 # "grain boundary sliding activity (volume percentage): %s", -362 # len(np.nonzero(mask)) / len(fractions), -363 # ) -364 # No rotation: carry over previous orientations. -365 orientations[mask, :, :] = self.orientations[-1][mask, :, :] -366 fractions[mask] = config["gbs_threshold"] / self.n_grains -367 fractions /= fractions.sum() -368 # _log.debug( -369 # "grain volume fractions: median=%e, min=%e, max=%e, sum=%e", -370 # np.median(fractions), -371 # np.min(fractions), -372 # np.max(fractions), -373 # np.sum(fractions), -374 # ) -375 return orientations, fractions -376 -377 def perform_step(solver): -378 """Perform SciPy solver step and appropriate processing.""" -379 message = solver.step() -380 if message is not None and solver.status == "failed": -381 raise _err.IterationError(message) +296 Args: +297 - `config` (dict) — PyDRex configuration dictionary +298 - `deformation_gradient` (array) — 3x3 initial deformation gradient tensor +299 - `get_velocity_gradient` (function) — callable with signature f(x) that returns +300 a 3x3 velocity gradient matrix at position x (vector) +301 - `pathline` (tuple) — tuple consisting of: +302 1. the time at which to start the CPO integration (t_start) +303 2. the time at which to stop the CPO integration (t_end) +304 3. callable with signature f(t) that returns the position of the mineral at +305 time t ∈ [t_start, t_end] +306 +307 Any additional (optional) keyword arguments are passed to +308 `scipy.integrate.LSODA`. +309 +310 Array values must provide a NumPy-compatible interface: +311 <https://numpy.org/doc/stable/user/whatisnumpy.html> +312 +313 """ +314 +315 # ===== Set up callables for the ODE solver and internal processing ===== +316 +317 def extract_vars(y): +318 # TODO: Check if we can avoid .copy() here. +319 deformation_gradient = y[:9].copy().reshape((3, 3)) +320 orientations = ( +321 y[9 : self.n_grains * 9 + 9] +322 .copy() +323 .reshape((self.n_grains, 3, 3)) +324 .clip(-1, 1) +325 ) +326 # TODO: Check if we can avoid .copy() here. +327 fractions = ( +328 y[self.n_grains * 9 + 9 : self.n_grains * 10 + 9].copy().clip(0, None) +329 ) +330 fractions /= fractions.sum() +331 return deformation_gradient, orientations, fractions +332 +333 def eval_rhs(t, y): +334 """Evaluate right hand side of the D-Rex PDE.""" +335 # assert not np.any(np.isnan(y)), y[np.isnan(y)].shape +336 position = get_position(t) +337 velocity_gradient = get_velocity_gradient(position) +338 # _log.debug( +339 # "calculating CPO at %s (t=%e) with velocity gradient %s", +340 # position, +341 # t, +342 # velocity_gradient.flatten(), +343 # ) +344 +345 strain_rate = (velocity_gradient + velocity_gradient.transpose()) / 2 +346 strain_rate_max = np.abs(la.eigvalsh(strain_rate)).max() +347 deformation_gradient, orientations, fractions = extract_vars(y) +348 # Uses nondimensional values of strain rate and velocity gradient. +349 orientations_diff, fractions_diff = _core.derivatives( +350 phase=self.phase, +351 fabric=self.fabric, +352 n_grains=self.n_grains, +353 orientations=orientations, +354 fractions=fractions, +355 strain_rate=strain_rate / strain_rate_max, +356 velocity_gradient=velocity_gradient / strain_rate_max, +357 stress_exponent=config["stress_exponent"], +358 deformation_exponent=config["deformation_exponent"], +359 nucleation_efficiency=config["nucleation_efficiency"], +360 gbm_mobility=config["gbm_mobility"], +361 volume_fraction=volume_fraction, +362 ) +363 return np.hstack( +364 ( +365 (velocity_gradient @ deformation_gradient).flatten(), +366 orientations_diff.flatten() * strain_rate_max, +367 fractions_diff * strain_rate_max, +368 ) +369 ) +370 +371 def apply_gbs(orientations, fractions, config): +372 """Apply grain boundary sliding for small grains.""" +373 mask = fractions < (config["gbs_threshold"] / self.n_grains) +374 # _log.debug( +375 # "grain boundary sliding activity (volume percentage): %s", +376 # len(np.nonzero(mask)) / len(fractions), +377 # ) +378 # No rotation: carry over previous orientations. +379 orientations[mask, :, :] = self.orientations[-1][mask, :, :] +380 fractions[mask] = config["gbs_threshold"] / self.n_grains +381 fractions /= fractions.sum() 382 # _log.debug( -383 # "%s step_size=%e", solver.__class__.__qualname__, solver.step_size -384 # ) -385 -386 deformation_gradient, orientations, fractions = extract_vars(solver.y) -387 orientations, fractions = apply_gbs(orientations, fractions, config) -388 solver.y[9:] = np.hstack((orientations.flatten(), fractions)) -389 -390 # ===== Initialise and run the solver using the above callables ===== -391 -392 time_start, time_end, get_position = pathline -393 if not callable(get_velocity_gradient): -394 raise ValueError( -395 "unable to evaluate velocity gradient callable." -396 + " You must provide a callable with signature f(x)" -397 + " that returns a 3x3 matrix." -398 ) -399 if not callable(get_position): -400 raise ValueError( -401 "unable to evaluate position callable." -402 + " You must provide a callable with signature f(t)" -403 + " that returns a 3-component array." -404 ) +383 # "grain volume fractions: median=%e, min=%e, max=%e, sum=%e", +384 # np.median(fractions), +385 # np.min(fractions), +386 # np.max(fractions), +387 # np.sum(fractions), +388 # ) +389 return orientations, fractions +390 +391 def perform_step(solver): +392 """Perform SciPy solver step and appropriate processing.""" +393 message = solver.step() +394 if message is not None and solver.status == "failed": +395 raise _err.IterationError(message) +396 # _log.debug( +397 # "%s step_size=%e", solver.__class__.__qualname__, solver.step_size +398 # ) +399 +400 deformation_gradient, orientations, fractions = extract_vars(solver.y) +401 orientations, fractions = apply_gbs(orientations, fractions, config) +402 solver.y[9:] = np.hstack((orientations.flatten(), fractions)) +403 +404 # ===== Initialise and run the solver using the above callables ===== 405 -406 if self.phase == _core.MineralPhase.olivine: -407 volume_fraction = config["olivine_fraction"] -408 elif self.phase == _core.MineralPhase.enstatite: -409 volume_fraction = config["enstatite_fraction"] -410 else: -411 assert False # Should never happen. -412 -413 y_start = np.hstack( -414 ( -415 deformation_gradient.flatten(), -416 self.orientations[-1].flatten(), -417 self.fractions[-1], +406 time_start, time_end, get_position = pathline +407 if not callable(get_velocity_gradient): +408 raise ValueError( +409 "unable to evaluate velocity gradient callable." +410 + " You must provide a callable with signature f(x)" +411 + " that returns a 3x3 matrix." +412 ) +413 if not callable(get_position): +414 raise ValueError( +415 "unable to evaluate position callable." +416 + " You must provide a callable with signature f(t)" +417 + " that returns a 3-component array." 418 ) -419 ) -420 solver = LSODA( -421 eval_rhs, -422 time_start, -423 y_start, -424 time_end, -425 atol=kwargs.pop("atol", np.abs(y_start * 1e-6) + 1e-12), -426 rtol=kwargs.pop("rtol", 1e-6), -427 first_step=kwargs.pop("first_step", np.abs(time_end - time_start) * 1e-1), -428 # max_step=kwargs.pop("max_step", np.abs(time_end - time_start)), -429 **kwargs, -430 ) -431 perform_step(solver) -432 while solver.status == "running": -433 perform_step(solver) -434 -435 # Extract final values for this simulation step, append to storage. -436 deformation_gradient, orientations, fractions = extract_vars(solver.y.squeeze()) -437 self.orientations.append(orientations) -438 self.fractions.append(fractions) -439 return deformation_gradient -440 -441 def save(self, filename, postfix=None): -442 """Save CPO data for all stored timesteps to a `numpy` NPZ file. -443 -444 If `postfix` is not `None`, the data is appended to the NPZ file -445 in fields ending with "`_postfix`". -446 -447 Raises a `ValueError` if the data shapes are not compatible. -448 -449 See also: `numpy.savez`, `Mineral.load`, `Mineral.from_file`. +419 +420 if self.phase == _core.MineralPhase.olivine: +421 volume_fraction = config["olivine_fraction"] +422 elif self.phase == _core.MineralPhase.enstatite: +423 volume_fraction = config["enstatite_fraction"] +424 else: +425 assert False # Should never happen. +426 +427 y_start = np.hstack( +428 ( +429 deformation_gradient.flatten(), +430 self.orientations[-1].flatten(), +431 self.fractions[-1], +432 ) +433 ) +434 solver = LSODA( +435 eval_rhs, +436 time_start, +437 y_start, +438 time_end, +439 atol=kwargs.pop("atol", np.abs(y_start * 1e-6) + 1e-12), +440 rtol=kwargs.pop("rtol", 1e-6), +441 first_step=kwargs.pop("first_step", np.abs(time_end - time_start) * 1e-1), +442 # max_step=kwargs.pop("max_step", np.abs(time_end - time_start)), +443 lband=self.lband, +444 uband=self.uband, +445 **kwargs, +446 ) +447 perform_step(solver) +448 while solver.status == "running": +449 perform_step(solver) 450 -451 """ -452 if len(self.fractions) != len(self.orientations): -453 raise ValueError( -454 "Length of stored results must match." -455 + " You've supplied currupted data with:\n" -456 + f"- {len(self.fractions)} grain size results, and\n" -457 + f"- {len(self.orientations)} orientation results." -458 ) -459 if self.fractions[0].shape[0] == self.orientations[0].shape[0] == self.n_grains: -460 data = { -461 "meta": np.array( -462 [self.phase, self.fabric, self.regime], dtype=np.uint8 -463 ), -464 "fractions": np.stack(self.fractions), -465 "orientations": np.stack(self.orientations), -466 } -467 # Create parent directories, resolve relative paths. -468 _io.resolve_path(filename) -469 # Append to file, requires postfix (unique name). -470 if postfix is not None: -471 archive = ZipFile(filename, mode="a", allowZip64=True) -472 for key in data.keys(): -473 with archive.open( -474 f"{key}_{postfix}", "w", force_zip64=True -475 ) as file: -476 buffer = io.BytesIO() -477 np.save(buffer, data[key]) -478 file.write(buffer.getvalue()) -479 buffer.close() -480 else: -481 np.savez(filename, **data) -482 else: -483 raise ValueError( -484 "Size of CPO data arrays must match number of grains." -485 + " You've supplied corrupted data with:\n" -486 + f"- `n_grains = {self.n_grains}`,\n" -487 + f"- `fractions[0].shape = {self.fractions[0].shape}`, and\n" -488 + f"- `orientations[0].shape = {self.orientations[0].shape}`." -489 ) -490 -491 def load(self, filename, postfix=None): -492 """Load CPO data from a `numpy` NPZ file. -493 -494 If `postfix` is not `None`, data is read from fields ending with "`_postfix`". -495 -496 See also: `Mineral.save`, `Mineral.from_file`. -497 -498 """ -499 if not filename.endswith(".npz"): -500 raise ValueError( -501 f"Must only load from numpy NPZ format. Cannot load from {filename}." -502 ) -503 data = np.load(filename) -504 if postfix is not None: -505 phase, fabric, regime = data[f"meta_{postfix}"] -506 self.fractions = list(data[f"fractions_{postfix}"]) -507 self.orientations = list(data[f"orientations_{postfix}"]) -508 else: -509 phase, fabric, regime = data["meta"] -510 self.fractions = list(data["fractions"]) -511 self.orientations = list(data["orientations"]) -512 -513 self.phase = phase -514 self.fabric = fabric -515 self.regime = regime -516 self.orientations_init = self.orientations[0] -517 self.fractions_init = self.fractions[0] -518 -519 @classmethod -520 def from_file(cls, filename, postfix=None): -521 """Construct a `Mineral` instance using data from a `numpy` NPZ file. -522 -523 If `postfix` is not `None`, data is read from fields ending with “`_postfix`”. -524 -525 See also: `Mineral.save`, `Mineral.load`. -526 -527 """ -528 if not filename.endswith(".npz"): -529 raise ValueError( -530 f"Must only load from numpy NPZ format. Cannot load from {filename}." -531 ) -532 data = np.load(filename) -533 if postfix is not None: -534 phase, fabric, regime = data[f"meta_{postfix}"] -535 fractions = list(data[f"fractions_{postfix}"]) -536 orientations = list(data[f"orientations_{postfix}"]) -537 else: -538 phase, fabric, regime = data["meta"] -539 fractions = list(data["fractions"]) -540 orientations = list(data["orientations"]) -541 -542 mineral = cls( -543 phase, -544 fabric, -545 regime, -546 n_grains=len(fractions[0]), -547 fractions_init=fractions[0], -548 orientations_init=orientations[0], -549 ) -550 mineral.fractions = fractions -551 mineral.orientations = orientations -552 return mineral +451 # Extract final values for this simulation step, append to storage. +452 deformation_gradient, orientations, fractions = extract_vars(solver.y.squeeze()) +453 self.orientations.append(orientations) +454 self.fractions.append(fractions) +455 return deformation_gradient +456 +457 def save(self, filename, postfix=None): +458 """Save CPO data for all stored timesteps to a `numpy` NPZ file. +459 +460 If `postfix` is not `None`, the data is appended to the NPZ file +461 in fields ending with "`_postfix`". +462 +463 Raises a `ValueError` if the data shapes are not compatible. +464 +465 See also: `numpy.savez`, `Mineral.load`, `Mineral.from_file`. +466 +467 """ +468 if len(self.fractions) != len(self.orientations): +469 raise ValueError( +470 "Length of stored results must match." +471 + " You've supplied currupted data with:\n" +472 + f"- {len(self.fractions)} grain size results, and\n" +473 + f"- {len(self.orientations)} orientation results." +474 ) +475 if self.fractions[0].shape[0] == self.orientations[0].shape[0] == self.n_grains: +476 data = { +477 "meta": np.array( +478 [self.phase, self.fabric, self.regime], dtype=np.uint8 +479 ), +480 "fractions": np.stack(self.fractions), +481 "orientations": np.stack(self.orientations), +482 } +483 # Create parent directories, resolve relative paths. +484 _io.resolve_path(filename) +485 # Append to file, requires postfix (unique name). +486 if postfix is not None: +487 archive = ZipFile(filename, mode="a", allowZip64=True) +488 for key in data.keys(): +489 with archive.open( +490 f"{key}_{postfix}", "w", force_zip64=True +491 ) as file: +492 buffer = io.BytesIO() +493 np.save(buffer, data[key]) +494 file.write(buffer.getvalue()) +495 buffer.close() +496 else: +497 np.savez(filename, **data) +498 else: +499 raise ValueError( +500 "Size of CPO data arrays must match number of grains." +501 + " You've supplied corrupted data with:\n" +502 + f"- `n_grains = {self.n_grains}`,\n" +503 + f"- `fractions[0].shape = {self.fractions[0].shape}`, and\n" +504 + f"- `orientations[0].shape = {self.orientations[0].shape}`." +505 ) +506 +507 def load(self, filename, postfix=None): +508 """Load CPO data from a `numpy` NPZ file. +509 +510 If `postfix` is not `None`, data is read from fields ending with "`_postfix`". +511 +512 See also: `Mineral.save`, `Mineral.from_file`. +513 +514 """ +515 if not filename.endswith(".npz"): +516 raise ValueError( +517 f"Must only load from numpy NPZ format. Cannot load from {filename}." +518 ) +519 data = np.load(filename) +520 if postfix is not None: +521 phase, fabric, regime = data[f"meta_{postfix}"] +522 self.fractions = list(data[f"fractions_{postfix}"]) +523 self.orientations = list(data[f"orientations_{postfix}"]) +524 else: +525 phase, fabric, regime = data["meta"] +526 self.fractions = list(data["fractions"]) +527 self.orientations = list(data["orientations"]) +528 +529 self.phase = phase +530 self.fabric = fabric +531 self.regime = regime +532 self.orientations_init = self.orientations[0] +533 self.fractions_init = self.fractions[0] +534 +535 @classmethod +536 def from_file(cls, filename, postfix=None): +537 """Construct a `Mineral` instance using data from a `numpy` NPZ file. +538 +539 If `postfix` is not `None`, data is read from fields ending with “`_postfix`”. +540 +541 See also: `Mineral.save`, `Mineral.load`. +542 +543 """ +544 if not filename.endswith(".npz"): +545 raise ValueError( +546 f"Must only load from numpy NPZ format. Cannot load from {filename}." +547 ) +548 data = np.load(filename) +549 if postfix is not None: +550 phase, fabric, regime = data[f"meta_{postfix}"] +551 fractions = list(data[f"fractions_{postfix}"]) +552 orientations = list(data[f"orientations_{postfix}"]) +553 else: +554 phase, fabric, regime = data["meta"] +555 fractions = list(data["fractions"]) +556 orientations = list(data["orientations"]) +557 +558 mineral = cls( +559 phase, +560 fabric, +561 regime, +562 n_grains=len(fractions[0]), +563 fractions_init=fractions[0], +564 orientations_init=orientations[0], +565 ) +566 mineral.fractions = fractions +567 mineral.orientations = orientations +568 return mineral @@ -1372,7 +1410,7 @@

    - Mineral( phase: int = <MineralPhase.olivine: 0>, fabric: int = <MineralFabric.olivine_A: 0>, regime: int = <DeformationRegime.dislocation: 1>, n_grains: int = 1000, fractions_init: numpy.ndarray = None, orientations_init: numpy.ndarray = None, fractions: list = <factory>, orientations: list = <factory>, seed: int = None) + Mineral( phase: int = <MineralPhase.olivine: 0>, fabric: int = <MineralFabric.olivine_A: 0>, regime: int = <DeformationRegime.dislocation: 1>, n_grains: int = 1000, fractions_init: numpy.ndarray = None, orientations_init: numpy.ndarray = None, fractions: list = <factory>, orientations: list = <factory>, seed: int = None, lband: int = None, uband: int = None)
    @@ -1486,6 +1524,30 @@

    +

    +
    +
    + lband: int = +None + + +
    + + + + +
    +
    +
    + uband: int = +None + + +
    + + + +
    @@ -1498,177 +1560,179 @@

    - 
    269    def update_orientations(
-270        self,
-271        config,
-272        deformation_gradient,
-273        get_velocity_gradient,
-274        pathline,
-275        **kwargs,
-276    ):
-277        """Update orientations and volume distribution for the `Mineral`.
-278
-279        Update crystalline orientations and grain volume distribution
-280        for minerals undergoing plastic deformation.
-281
-282        Args:
-283        - `config` (dict) — PyDRex configuration dictionary
-284        - `deformation_gradient` (array) — 3x3 initial deformation gradient tensor
-285        - `get_velocity_gradient` (function) — callable with signature f(x) that returns
-286          a 3x3 velocity gradient matrix at position x (vector)
-287        - `pathline` (tuple) — tuple consisting of:
-288            1. the time at which to start the CPO integration (t_start)
-289            2. the time at which to stop the CPO integration (t_end)
-290            3. callable with signature f(t) that returns the position of the mineral at
-291                time t ∈ [t_start, t_end]
+            
    283    def update_orientations(
+284        self,
+285        config,
+286        deformation_gradient,
+287        get_velocity_gradient,
+288        pathline,
+289        **kwargs,
+290    ):
+291        """Update orientations and volume distribution for the `Mineral`.
 292
-293        Any additional (optional) keyword arguments are passed to
-294        `scipy.integrate.LSODA`.
+293        Update crystalline orientations and grain volume distribution
+294        for minerals undergoing plastic deformation.
 295
-296        Array values must provide a NumPy-compatible interface:
-297        <https://numpy.org/doc/stable/user/whatisnumpy.html>
-298
-299        """
-300
-301        # ===== Set up callables for the ODE solver and internal processing =====
-302
-303        def extract_vars(y):
-304            # TODO: Check if we can avoid .copy() here.
-305            deformation_gradient = y[:9].copy().reshape((3, 3))
-306            orientations = (
-307                y[9 : self.n_grains * 9 + 9]
-308                .copy()
-309                .reshape((self.n_grains, 3, 3))
-310                .clip(-1, 1)
-311            )
-312            # TODO: Check if we can avoid .copy() here.
-313            fractions = (
-314                y[self.n_grains * 9 + 9 : self.n_grains * 10 + 9].copy().clip(0, None)
-315            )
-316            fractions /= fractions.sum()
-317            return deformation_gradient, orientations, fractions
-318
-319        def eval_rhs(t, y):
-320            """Evaluate right hand side of the D-Rex PDE."""
-321            # assert not np.any(np.isnan(y)), y[np.isnan(y)].shape
-322            position = get_position(t)
-323            velocity_gradient = get_velocity_gradient(position)
-324            # _log.debug(
-325            #     "calculating CPO at %s (t=%e) with velocity gradient %s",
-326            #     position,
-327            #     t,
-328            #     velocity_gradient.flatten(),
-329            # )
-330
-331            strain_rate = (velocity_gradient + velocity_gradient.transpose()) / 2
-332            strain_rate_max = np.abs(la.eigvalsh(strain_rate)).max()
-333            deformation_gradient, orientations, fractions = extract_vars(y)
-334            # Uses nondimensional values of strain rate and velocity gradient.
-335            orientations_diff, fractions_diff = _core.derivatives(
-336                phase=self.phase,
-337                fabric=self.fabric,
-338                n_grains=self.n_grains,
-339                orientations=orientations,
-340                fractions=fractions,
-341                strain_rate=strain_rate / strain_rate_max,
-342                velocity_gradient=velocity_gradient / strain_rate_max,
-343                stress_exponent=config["stress_exponent"],
-344                deformation_exponent=config["deformation_exponent"],
-345                nucleation_efficiency=config["nucleation_efficiency"],
-346                gbm_mobility=config["gbm_mobility"],
-347                volume_fraction=volume_fraction,
-348            )
-349            return np.hstack(
-350                (
-351                    (velocity_gradient @ deformation_gradient).flatten(),
-352                    orientations_diff.flatten() * strain_rate_max,
-353                    fractions_diff * strain_rate_max,
-354                )
-355            )
-356
-357        def apply_gbs(orientations, fractions, config):
-358            """Apply grain boundary sliding for small grains."""
-359            mask = fractions < (config["gbs_threshold"] / self.n_grains)
-360            # _log.debug(
-361            #     "grain boundary sliding activity (volume percentage): %s",
-362            #     len(np.nonzero(mask)) / len(fractions),
-363            # )
-364            # No rotation: carry over previous orientations.
-365            orientations[mask, :, :] = self.orientations[-1][mask, :, :]
-366            fractions[mask] = config["gbs_threshold"] / self.n_grains
-367            fractions /= fractions.sum()
-368            # _log.debug(
-369            #     "grain volume fractions: median=%e, min=%e, max=%e, sum=%e",
-370            #     np.median(fractions),
-371            #     np.min(fractions),
-372            #     np.max(fractions),
-373            #     np.sum(fractions),
-374            # )
-375            return orientations, fractions
-376
-377        def perform_step(solver):
-378            """Perform SciPy solver step and appropriate processing."""
-379            message = solver.step()
-380            if message is not None and solver.status == "failed":
-381                raise _err.IterationError(message)
+296        Args:
+297        - `config` (dict) — PyDRex configuration dictionary
+298        - `deformation_gradient` (array) — 3x3 initial deformation gradient tensor
+299        - `get_velocity_gradient` (function) — callable with signature f(x) that returns
+300          a 3x3 velocity gradient matrix at position x (vector)
+301        - `pathline` (tuple) — tuple consisting of:
+302            1. the time at which to start the CPO integration (t_start)
+303            2. the time at which to stop the CPO integration (t_end)
+304            3. callable with signature f(t) that returns the position of the mineral at
+305                time t ∈ [t_start, t_end]
+306
+307        Any additional (optional) keyword arguments are passed to
+308        `scipy.integrate.LSODA`.
+309
+310        Array values must provide a NumPy-compatible interface:
+311        <https://numpy.org/doc/stable/user/whatisnumpy.html>
+312
+313        """
+314
+315        # ===== Set up callables for the ODE solver and internal processing =====
+316
+317        def extract_vars(y):
+318            # TODO: Check if we can avoid .copy() here.
+319            deformation_gradient = y[:9].copy().reshape((3, 3))
+320            orientations = (
+321                y[9 : self.n_grains * 9 + 9]
+322                .copy()
+323                .reshape((self.n_grains, 3, 3))
+324                .clip(-1, 1)
+325            )
+326            # TODO: Check if we can avoid .copy() here.
+327            fractions = (
+328                y[self.n_grains * 9 + 9 : self.n_grains * 10 + 9].copy().clip(0, None)
+329            )
+330            fractions /= fractions.sum()
+331            return deformation_gradient, orientations, fractions
+332
+333        def eval_rhs(t, y):
+334            """Evaluate right hand side of the D-Rex PDE."""
+335            # assert not np.any(np.isnan(y)), y[np.isnan(y)].shape
+336            position = get_position(t)
+337            velocity_gradient = get_velocity_gradient(position)
+338            # _log.debug(
+339            #     "calculating CPO at %s (t=%e) with velocity gradient %s",
+340            #     position,
+341            #     t,
+342            #     velocity_gradient.flatten(),
+343            # )
+344
+345            strain_rate = (velocity_gradient + velocity_gradient.transpose()) / 2
+346            strain_rate_max = np.abs(la.eigvalsh(strain_rate)).max()
+347            deformation_gradient, orientations, fractions = extract_vars(y)
+348            # Uses nondimensional values of strain rate and velocity gradient.
+349            orientations_diff, fractions_diff = _core.derivatives(
+350                phase=self.phase,
+351                fabric=self.fabric,
+352                n_grains=self.n_grains,
+353                orientations=orientations,
+354                fractions=fractions,
+355                strain_rate=strain_rate / strain_rate_max,
+356                velocity_gradient=velocity_gradient / strain_rate_max,
+357                stress_exponent=config["stress_exponent"],
+358                deformation_exponent=config["deformation_exponent"],
+359                nucleation_efficiency=config["nucleation_efficiency"],
+360                gbm_mobility=config["gbm_mobility"],
+361                volume_fraction=volume_fraction,
+362            )
+363            return np.hstack(
+364                (
+365                    (velocity_gradient @ deformation_gradient).flatten(),
+366                    orientations_diff.flatten() * strain_rate_max,
+367                    fractions_diff * strain_rate_max,
+368                )
+369            )
+370
+371        def apply_gbs(orientations, fractions, config):
+372            """Apply grain boundary sliding for small grains."""
+373            mask = fractions < (config["gbs_threshold"] / self.n_grains)
+374            # _log.debug(
+375            #     "grain boundary sliding activity (volume percentage): %s",
+376            #     len(np.nonzero(mask)) / len(fractions),
+377            # )
+378            # No rotation: carry over previous orientations.
+379            orientations[mask, :, :] = self.orientations[-1][mask, :, :]
+380            fractions[mask] = config["gbs_threshold"] / self.n_grains
+381            fractions /= fractions.sum()
 382            # _log.debug(
-383            #     "%s step_size=%e", solver.__class__.__qualname__, solver.step_size
-384            # )
-385
-386            deformation_gradient, orientations, fractions = extract_vars(solver.y)
-387            orientations, fractions = apply_gbs(orientations, fractions, config)
-388            solver.y[9:] = np.hstack((orientations.flatten(), fractions))
-389
-390        # ===== Initialise and run the solver using the above callables =====
-391
-392        time_start, time_end, get_position = pathline
-393        if not callable(get_velocity_gradient):
-394            raise ValueError(
-395                "unable to evaluate velocity gradient callable."
-396                + " You must provide a callable with signature f(x)"
-397                + " that returns a 3x3 matrix."
-398            )
-399        if not callable(get_position):
-400            raise ValueError(
-401                "unable to evaluate position callable."
-402                + " You must provide a callable with signature f(t)"
-403                + " that returns a 3-component array."
-404            )
+383            #     "grain volume fractions: median=%e, min=%e, max=%e, sum=%e",
+384            #     np.median(fractions),
+385            #     np.min(fractions),
+386            #     np.max(fractions),
+387            #     np.sum(fractions),
+388            # )
+389            return orientations, fractions
+390
+391        def perform_step(solver):
+392            """Perform SciPy solver step and appropriate processing."""
+393            message = solver.step()
+394            if message is not None and solver.status == "failed":
+395                raise _err.IterationError(message)
+396            # _log.debug(
+397            #     "%s step_size=%e", solver.__class__.__qualname__, solver.step_size
+398            # )
+399
+400            deformation_gradient, orientations, fractions = extract_vars(solver.y)
+401            orientations, fractions = apply_gbs(orientations, fractions, config)
+402            solver.y[9:] = np.hstack((orientations.flatten(), fractions))
+403
+404        # ===== Initialise and run the solver using the above callables =====
 405
-406        if self.phase == _core.MineralPhase.olivine:
-407            volume_fraction = config["olivine_fraction"]
-408        elif self.phase == _core.MineralPhase.enstatite:
-409            volume_fraction = config["enstatite_fraction"]
-410        else:
-411            assert False  # Should never happen.
-412
-413        y_start = np.hstack(
-414            (
-415                deformation_gradient.flatten(),
-416                self.orientations[-1].flatten(),
-417                self.fractions[-1],
+406        time_start, time_end, get_position = pathline
+407        if not callable(get_velocity_gradient):
+408            raise ValueError(
+409                "unable to evaluate velocity gradient callable."
+410                + " You must provide a callable with signature f(x)"
+411                + " that returns a 3x3 matrix."
+412            )
+413        if not callable(get_position):
+414            raise ValueError(
+415                "unable to evaluate position callable."
+416                + " You must provide a callable with signature f(t)"
+417                + " that returns a 3-component array."
 418            )
-419        )
-420        solver = LSODA(
-421            eval_rhs,
-422            time_start,
-423            y_start,
-424            time_end,
-425            atol=kwargs.pop("atol", np.abs(y_start * 1e-6) + 1e-12),
-426            rtol=kwargs.pop("rtol", 1e-6),
-427            first_step=kwargs.pop("first_step", np.abs(time_end - time_start) * 1e-1),
-428            # max_step=kwargs.pop("max_step", np.abs(time_end - time_start)),
-429            **kwargs,
-430        )
-431        perform_step(solver)
-432        while solver.status == "running":
-433            perform_step(solver)
-434
-435        # Extract final values for this simulation step, append to storage.
-436        deformation_gradient, orientations, fractions = extract_vars(solver.y.squeeze())
-437        self.orientations.append(orientations)
-438        self.fractions.append(fractions)
-439        return deformation_gradient
+419
+420        if self.phase == _core.MineralPhase.olivine:
+421            volume_fraction = config["olivine_fraction"]
+422        elif self.phase == _core.MineralPhase.enstatite:
+423            volume_fraction = config["enstatite_fraction"]
+424        else:
+425            assert False  # Should never happen.
+426
+427        y_start = np.hstack(
+428            (
+429                deformation_gradient.flatten(),
+430                self.orientations[-1].flatten(),
+431                self.fractions[-1],
+432            )
+433        )
+434        solver = LSODA(
+435            eval_rhs,
+436            time_start,
+437            y_start,
+438            time_end,
+439            atol=kwargs.pop("atol", np.abs(y_start * 1e-6) + 1e-12),
+440            rtol=kwargs.pop("rtol", 1e-6),
+441            first_step=kwargs.pop("first_step", np.abs(time_end - time_start) * 1e-1),
+442            # max_step=kwargs.pop("max_step", np.abs(time_end - time_start)),
+443            lband=self.lband,
+444            uband=self.uband,
+445            **kwargs,
+446        )
+447        perform_step(solver)
+448        while solver.status == "running":
+449            perform_step(solver)
+450
+451        # Extract final values for this simulation step, append to storage.
+452        deformation_gradient, orientations, fractions = extract_vars(solver.y.squeeze())
+453        self.orientations.append(orientations)
+454        self.fractions.append(fractions)
+455        return deformation_gradient
 
    
 
 
@@ -1713,55 +1777,55 @@
    - 
    441    def save(self, filename, postfix=None):
-442        """Save CPO data for all stored timesteps to a `numpy` NPZ file.
-443
-444        If `postfix` is not `None`, the data is appended to the NPZ file
-445        in fields ending with "`_postfix`".
-446
-447        Raises a `ValueError` if the data shapes are not compatible.
-448
-449        See also: `numpy.savez`, `Mineral.load`, `Mineral.from_file`.
-450
-451        """
-452        if len(self.fractions) != len(self.orientations):
-453            raise ValueError(
-454                "Length of stored results must match."
-455                + " You've supplied currupted data with:\n"
-456                + f"- {len(self.fractions)} grain size results, and\n"
-457                + f"- {len(self.orientations)} orientation results."
-458            )
-459        if self.fractions[0].shape[0] == self.orientations[0].shape[0] == self.n_grains:
-460            data = {
-461                "meta": np.array(
-462                    [self.phase, self.fabric, self.regime], dtype=np.uint8
-463                ),
-464                "fractions": np.stack(self.fractions),
-465                "orientations": np.stack(self.orientations),
-466            }
-467            # Create parent directories, resolve relative paths.
-468            _io.resolve_path(filename)
-469            # Append to file, requires postfix (unique name).
-470            if postfix is not None:
-471                archive = ZipFile(filename, mode="a", allowZip64=True)
-472                for key in data.keys():
-473                    with archive.open(
-474                        f"{key}_{postfix}", "w", force_zip64=True
-475                    ) as file:
-476                        buffer = io.BytesIO()
-477                        np.save(buffer, data[key])
-478                        file.write(buffer.getvalue())
-479                        buffer.close()
-480            else:
-481                np.savez(filename, **data)
-482        else:
-483            raise ValueError(
-484                "Size of CPO data arrays must match number of grains."
-485                + " You've supplied corrupted data with:\n"
-486                + f"- `n_grains = {self.n_grains}`,\n"
-487                + f"- `fractions[0].shape = {self.fractions[0].shape}`, and\n"
-488                + f"- `orientations[0].shape = {self.orientations[0].shape}`."
-489            )
+            
    457    def save(self, filename, postfix=None):
+458        """Save CPO data for all stored timesteps to a `numpy` NPZ file.
+459
+460        If `postfix` is not `None`, the data is appended to the NPZ file
+461        in fields ending with "`_postfix`".
+462
+463        Raises a `ValueError` if the data shapes are not compatible.
+464
+465        See also: `numpy.savez`, `Mineral.load`, `Mineral.from_file`.
+466
+467        """
+468        if len(self.fractions) != len(self.orientations):
+469            raise ValueError(
+470                "Length of stored results must match."
+471                + " You've supplied currupted data with:\n"
+472                + f"- {len(self.fractions)} grain size results, and\n"
+473                + f"- {len(self.orientations)} orientation results."
+474            )
+475        if self.fractions[0].shape[0] == self.orientations[0].shape[0] == self.n_grains:
+476            data = {
+477                "meta": np.array(
+478                    [self.phase, self.fabric, self.regime], dtype=np.uint8
+479                ),
+480                "fractions": np.stack(self.fractions),
+481                "orientations": np.stack(self.orientations),
+482            }
+483            # Create parent directories, resolve relative paths.
+484            _io.resolve_path(filename)
+485            # Append to file, requires postfix (unique name).
+486            if postfix is not None:
+487                archive = ZipFile(filename, mode="a", allowZip64=True)
+488                for key in data.keys():
+489                    with archive.open(
+490                        f"{key}_{postfix}", "w", force_zip64=True
+491                    ) as file:
+492                        buffer = io.BytesIO()
+493                        np.save(buffer, data[key])
+494                        file.write(buffer.getvalue())
+495                        buffer.close()
+496            else:
+497                np.savez(filename, **data)
+498        else:
+499            raise ValueError(
+500                "Size of CPO data arrays must match number of grains."
+501                + " You've supplied corrupted data with:\n"
+502                + f"- `n_grains = {self.n_grains}`,\n"
+503                + f"- `fractions[0].shape = {self.fractions[0].shape}`, and\n"
+504                + f"- `orientations[0].shape = {self.orientations[0].shape}`."
+505            )
 
    
 
 
@@ -1788,33 +1852,33 @@
    - 
    491    def load(self, filename, postfix=None):
-492        """Load CPO data from a `numpy` NPZ file.
-493
-494        If `postfix` is not `None`, data is read from fields ending with "`_postfix`".
-495
-496        See also: `Mineral.save`, `Mineral.from_file`.
-497
-498        """
-499        if not filename.endswith(".npz"):
-500            raise ValueError(
-501                f"Must only load from numpy NPZ format. Cannot load from {filename}."
-502            )
-503        data = np.load(filename)
-504        if postfix is not None:
-505            phase, fabric, regime = data[f"meta_{postfix}"]
-506            self.fractions = list(data[f"fractions_{postfix}"])
-507            self.orientations = list(data[f"orientations_{postfix}"])
-508        else:
-509            phase, fabric, regime = data["meta"]
-510            self.fractions = list(data["fractions"])
-511            self.orientations = list(data["orientations"])
-512
-513        self.phase = phase
-514        self.fabric = fabric
-515        self.regime = regime
-516        self.orientations_init = self.orientations[0]
-517        self.fractions_init = self.fractions[0]
+            
    507    def load(self, filename, postfix=None):
+508        """Load CPO data from a `numpy` NPZ file.
+509
+510        If `postfix` is not `None`, data is read from fields ending with "`_postfix`".
+511
+512        See also: `Mineral.save`, `Mineral.from_file`.
+513
+514        """
+515        if not filename.endswith(".npz"):
+516            raise ValueError(
+517                f"Must only load from numpy NPZ format. Cannot load from {filename}."
+518            )
+519        data = np.load(filename)
+520        if postfix is not None:
+521            phase, fabric, regime = data[f"meta_{postfix}"]
+522            self.fractions = list(data[f"fractions_{postfix}"])
+523            self.orientations = list(data[f"orientations_{postfix}"])
+524        else:
+525            phase, fabric, regime = data["meta"]
+526            self.fractions = list(data["fractions"])
+527            self.orientations = list(data["orientations"])
+528
+529        self.phase = phase
+530        self.fabric = fabric
+531        self.regime = regime
+532        self.orientations_init = self.orientations[0]
+533        self.fractions_init = self.fractions[0]
 
    
 
 
@@ -1839,40 +1903,40 @@
    - 
    519    @classmethod
-520    def from_file(cls, filename, postfix=None):
-521        """Construct a `Mineral` instance using data from a `numpy` NPZ file.
-522
-523        If `postfix` is not `None`, data is read from fields ending with “`_postfix`”.
-524
-525        See also: `Mineral.save`, `Mineral.load`.
-526
-527        """
-528        if not filename.endswith(".npz"):
-529            raise ValueError(
-530                f"Must only load from numpy NPZ format. Cannot load from {filename}."
-531            )
-532        data = np.load(filename)
-533        if postfix is not None:
-534            phase, fabric, regime = data[f"meta_{postfix}"]
-535            fractions = list(data[f"fractions_{postfix}"])
-536            orientations = list(data[f"orientations_{postfix}"])
-537        else:
-538            phase, fabric, regime = data["meta"]
-539            fractions = list(data["fractions"])
-540            orientations = list(data["orientations"])
-541
-542        mineral = cls(
-543            phase,
-544            fabric,
-545            regime,
-546            n_grains=len(fractions[0]),
-547            fractions_init=fractions[0],
-548            orientations_init=orientations[0],
-549        )
-550        mineral.fractions = fractions
-551        mineral.orientations = orientations
-552        return mineral
+            
    535    @classmethod
+536    def from_file(cls, filename, postfix=None):
+537        """Construct a `Mineral` instance using data from a `numpy` NPZ file.
+538
+539        If `postfix` is not `None`, data is read from fields ending with “`_postfix`”.
+540
+541        See also: `Mineral.save`, `Mineral.load`.
+542
+543        """
+544        if not filename.endswith(".npz"):
+545            raise ValueError(
+546                f"Must only load from numpy NPZ format. Cannot load from {filename}."
+547            )
+548        data = np.load(filename)
+549        if postfix is not None:
+550            phase, fabric, regime = data[f"meta_{postfix}"]
+551            fractions = list(data[f"fractions_{postfix}"])
+552            orientations = list(data[f"orientations_{postfix}"])
+553        else:
+554            phase, fabric, regime = data["meta"]
+555            fractions = list(data["fractions"])
+556            orientations = list(data["orientations"])
+557
+558        mineral = cls(
+559            phase,
+560            fabric,
+561            regime,
+562            n_grains=len(fractions[0]),
+563            fractions_init=fractions[0],
+564            orientations_init=orientations[0],
+565        )
+566        mineral.fractions = fractions
+567        mineral.orientations = orientations
+568        return mineral
 
    
 
 
diff --git a/search.js b/search.js
index 923ade9b..de6790a4 100644
--- a/search.js
+++ b/search.js
@@ -1,6 +1,6 @@
 window.pdocSearch = (function(){
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this.config},t.Configuration.prototype.reset=function(){this.config={}},lunr.SortedSet=function(){this.length=0,this.elements=[]},lunr.SortedSet.load=function(e){var t=new this;return t.elements=e,t.length=e.length,t},lunr.SortedSet.prototype.add=function(){var e,t;for(e=0;e1;){if(r===e)return o;e>r&&(t=o),r>e&&(n=o),i=n-t,o=t+Math.floor(i/2),r=this.elements[o]}return r===e?o:-1},lunr.SortedSet.prototype.locationFor=function(e){for(var t=0,n=this.elements.length,i=n-t,o=t+Math.floor(i/2),r=this.elements[o];i>1;)e>r&&(t=o),r>e&&(n=o),i=n-t,o=t+Math.floor(i/2),r=this.elements[o];return r>e?o:e>r?o+1:void 0},lunr.SortedSet.prototype.intersect=function(e){for(var t=new lunr.SortedSet,n=0,i=0,o=this.length,r=e.length,s=this.elements,u=e.elements;;){if(n>o-1||i>r-1)break;s[n]!==u[i]?s[n]u[i]&&i++:(t.add(s[n]),n++,i++)}return t},lunr.SortedSet.prototype.clone=function(){var e=new lunr.SortedSet;return e.elements=this.toArray(),e.length=e.elements.length,e},lunr.SortedSet.prototype.union=function(e){var t,n,i;this.length>=e.length?(t=this,n=e):(t=e,n=this),i=t.clone();for(var o=0,r=n.toArray();oSimulate crystallographic preferred orientation evolution in polycrystals

    \n\n
    \n\n
    \n\n

    This software is currently in early development.\nOnly modules that have tests are anywhere close to being stable.

    \n\n
    \n\n

    About

    \n\n

    The core routines are based on the original implementation by \u00c9douard Kaminski,\nwhich can be downloaded from this link (~90KB).\nThe reference paper is Kaminski & Ribe 2001,\nand an open-access paper which discusses the model is Fraters & Billen 2021. [TODO: Add our paper]

    \n\n

    The package is currently not available on PyPi,\nand must be installed by cloning the source code.\nand using pip install . (with the dot) in the top-level folder.\nMultiprocessing is not yet available in the packaged version.\nRunning the tests requires pytest,\nand the custom pytest flag --outdir=\"OUT\" can be used to save output figures\nto the folder called OUT (or the current folder, using \".\").

    \n\n

    The submodule sidebar on the left can be used\nto discover the public API of this package.\nSome of the tests are also documented and can serve as usage examples.\nThey can be viewed in the module index (modules starting with test_).

    \n\n

    The D-Rex kinematic CPO model

    \n\n

    The D-Rex model is used to compute crystallographic preferred orientation (CPO)\nfor polycrystals deforming by dislocation creep and dynamic recrystallization.\nPolycrystals are discretized into \"grains\" which represent fractional volumes\nof the total crystal that are characterised by a particular crystal lattice\norientation. For numerical efficiency, the number of grains in the model does\nnot change, and should only be interpreted as an approximation of the number\nof physical grains. Dynamic recrystallization is modelled using statistical\nexpressions which approximate the interaction of each grain with an effective\nmedium based on the averaged dislocation energy of all other grains.\nNote that the model is not suited to situations where static recrystallization\nprocesses are significant.

    \n\n

    The primary microphysical mechanism for plastic deformation of the polycrystal\nis dislocation creep, which involves dislocation glide (\"slip\") along symmetry\nplanes of the mineral and dislocation climb, which allows for dislocations to\nannihilate each other so that the number of dislocations reaches a steady-state.\nThe D-Rex model does not simulate dislocation climb, but implicitly assumes that\nthe dislocations are in steady-state so that the dislocation density of the\ncrystal can be described by

    \n\n

    $$\n\u03c1 \u221d b^{-2} \\left(\\frac{\u03c3}{\u03bc}\\right)^{p}\n$$

    \n\n

    where $b$ is the length of the Burgers' vector, $\u03c3$ is the stress\nand $\u03bc$ is the shear modulus. The value of the exponent $p$ is given by the\nstress_exponent input parameter. For an overview of available parameters,\nsee [the tests/conftest.py source code, for now...]

    \n\n

    The effects of dynamic recrystallization are twofold. Grains with a higher than\naverage dislocation density may be affected by either grain nucleation, which is\nthe formation of initially small, strain-free sub-grains, or grain boundary\nmigration, by which process other grains of lower strain energy annex a portion\nof its volume. Nucleation occurs mostly in grains oriented favourably for\ndislocation glide, and the new grains also grow by grain boundary migration.\nIf nucleation is too inefficient, the dislocation density in deformation-aligned\ngrains will remain high and these grains will therefore shrink in volume. On the\nother hand, if grain boundaries are too immobile, then nucleated grains will take\nlonger to grow, reducing the speed of CPO development and re-orientation.\nBecause nucleated grains are assumed to inherit the orientation of the parent,\nthey do not affect the model except by reducing the average dislocation density.\nA grain boundary mobility parameter of $M^{\u2217} = 0$ will therefore disable any\nrecrystallization effects. Finally, the process of grain boundary sliding can\nalso be included, which simply disallows rotation of grains with very small volume.\nThis only affects CPO evolution by introducing a latency for the onset of grain\nboundary migration in nucleated grains. It also manifests as an upper bound on\ntexture strength.

    \n\n

    Parameter reference

    \n\n

    Model parameters will eventually be provided in an .ini file.\n[For now just pass a dictionary to config in the Mineral.update_orientations method]\nThe file must contain section headers enclosed by square braces\nand key-value assignments, for example:

    \n\n
    [Output]\nolivine = volume_distribution, orientations\n\n[D-Rex]\nolivine_fraction = 1\nstress_exponent = 1.5\n...\n
    \n\n

    The following reference describes the available sections and their parameters.

    \n\n

    Geometry

    \n\n

    This section allows for specifying the geometry of the model domain,\nincluding any interpolation meshes.

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    ParameterDescription
    meshfile[not implemented]
    \n\n

    Output

    \n\n

    Parameters in the output section control which variables are stored to files,\nas well as any options for automatic postprocessing.

    \n\n\n\n\n \n \n \n\n\n\n\n \n \n \n\n\n \n \n \n\n\n \n \n \n\n\n
    ParameterDescriptionDefault
    simulation_namea short name (without spaces) used for the output folder and metadatapydrex_example
    olivinethe choice of olivine mineral outputs, from {volume_distribution, orientations} with multiple choices separated by a commavolume_distribution,orientations
    enstatitethe choice of enstatite mineral outputs, from {volume_distribution, orientations} with multiple choices separated by a commavolume_distribution,orientations
    \n\n

    D-Rex

    \n\n

    Parameters in the D-Rex section specify the runtime configuration for the D-Rex model.\nRead the D-Rex introduction section for more details.

    \n\n\n\n\n \n \n \n\n\n\n\n \n \n \n\n\n \n \n \n\n\n \n \n \n\n\n \n \n \n\n\n \n \n \n\n\n \n \n \n\n\n \n \n \n\n\n \n \n \n\n\n \n \n \n\n\n \n \n \n\n\n
    ParameterDescriptionDefault
    stress_exponentthe stress exponent $p$ that characterises the relationship between dislocation density and stress1.5
    deformation_exponentthe exponent $n$ that characterises the relationship between stress and rate of deformation3.5
    gbm_mobilitythe dimensionless grain boundary mobility $M^{\u2217}$ which controls the chance for growth of grains with lower than average dislocation energy125
    gbs_thresholda threshold ratio of current to original volume below which small grains move by sliding rather than rotation0.3
    nucleation_efficiencythe dimensionless nucleation efficiency which controls the chance for new, small, strain-free sub-grains to be created inside high dislocation energy grains5
    number_of_grainsthe number of initial grains per crystal2500
    olivine_fabric[not implemented]A
    mineralsa tuple of mineral phase names that specify the composition of the polycrystal(\"olivine\",)
    olivine_fractionthe volume fraction of olivine compared to other phases (1 for pure olivine)1
    <phase>_fractionthe volume fraction of any other phases (sum of all volume fractions must sum to 1)N/A
    \n"}, "pydrex.axes": {"fullname": "pydrex.axes", "modulename": "pydrex.axes", "kind": "module", "doc": "
    \n

    PyDRex: Custom Matplotlib Axes subclasses.

    \n
    \n"}, "pydrex.axes.PoleFigureAxes": {"fullname": "pydrex.axes.PoleFigureAxes", "modulename": "pydrex.axes", "qualname": "PoleFigureAxes", "kind": "class", "doc": "

    Axes class designed for crystallographic pole figures.

    \n\n

    Thin matplotlib Axes wrapper for crystallographic pole figures.

    \n\n
    \n\n

    Projections are not performed automatically using default methods like\nscatter or plot. To actually plot the pole figures, use polefigure.

    \n\n
    \n", "bases": "matplotlib.axes._axes.Axes"}, "pydrex.axes.PoleFigureAxes.name": {"fullname": "pydrex.axes.PoleFigureAxes.name", "modulename": "pydrex.axes", "qualname": "PoleFigureAxes.name", "kind": "variable", "doc": "

    \n", "default_value": "'pydrex.polefigure'"}, "pydrex.axes.PoleFigureAxes.polefigure": {"fullname": "pydrex.axes.PoleFigureAxes.polefigure", "modulename": "pydrex.axes", "qualname": "PoleFigureAxes.polefigure", "kind": "function", "doc": "

    Plot pole figure of crystallographic texture.

    \n\n

    Args:

    \n\n\n\n

    Any additional keyword arguments are passed to either tripcolor if\ndensity=True or scatter if density=False

    \n", "signature": "(\tself,\tdata,\tdensity=False,\tref_axes='xz',\thkl=[1, 0, 0],\tdensity_kwargs=None,\t**kwargs):", "funcdef": "def"}, "pydrex.axes.PoleFigureAxes.set": {"fullname": "pydrex.axes.PoleFigureAxes.set", "modulename": "pydrex.axes", "qualname": "PoleFigureAxes.set", "kind": "function", "doc": "

    Set multiple properties at once.

    \n\n

    Supported properties are

    \n\n

    Properties:\n adjustable: {'box', 'datalim'}\n agg_filter: a filter function, which takes a (m, n, 3) float array and a dpi value, and returns a (m, n, 3) array and two offsets from the bottom left corner of the image\n alpha: scalar or None\n anchor: (float, float) or {'C', 'SW', 'S', 'SE', 'E', 'NE', ...}\n animated: bool\n aspect: {'auto', 'equal'} or float\n autoscale_on: bool\n autoscalex_on: unknown\n autoscaley_on: unknown\n axes_locator: Callable[[Axes, Renderer], Bbox]\n axisbelow: bool or 'line'\n box_aspect: float or None\n clip_box: .Bbox\n clip_on: bool\n clip_path: Patch or (Path, Transform) or None\n facecolor or fc: color\n figure: .Figure\n frame_on: bool\n gid: str\n in_layout: bool\n label: object\n mouseover: bool\n navigate: bool\n navigate_mode: unknown\n path_effects: .AbstractPathEffect\n picker: None or bool or float or callable\n position: [left, bottom, width, height] or ~matplotlib.transforms.Bbox\n prop_cycle: unknown\n rasterization_zorder: float or None\n rasterized: bool\n sketch_params: (scale: float, length: float, randomness: float)\n snap: bool or None\n subplotspec: unknown\n title: str\n transform: .Transform\n url: str\n visible: bool\n xbound: unknown\n xlabel: str\n xlim: (bottom: float, top: float)\n xmargin: float greater than -0.5\n xscale: unknown\n xticklabels: unknown\n xticks: unknown\n ybound: unknown\n ylabel: str\n ylim: (bottom: float, top: float)\n ymargin: float greater than -0.5\n yscale: unknown\n yticklabels: unknown\n yticks: unknown\n zorder: float

    \n", "signature": "(\tself,\t*,\tadjustable=<UNSET>,\tagg_filter=<UNSET>,\talpha=<UNSET>,\tanchor=<UNSET>,\tanimated=<UNSET>,\taspect=<UNSET>,\tautoscale_on=<UNSET>,\tautoscalex_on=<UNSET>,\tautoscaley_on=<UNSET>,\taxes_locator=<UNSET>,\taxisbelow=<UNSET>,\tbox_aspect=<UNSET>,\tclip_box=<UNSET>,\tclip_on=<UNSET>,\tclip_path=<UNSET>,\tfacecolor=<UNSET>,\tframe_on=<UNSET>,\tgid=<UNSET>,\tin_layout=<UNSET>,\tlabel=<UNSET>,\tmouseover=<UNSET>,\tnavigate=<UNSET>,\tpath_effects=<UNSET>,\tpicker=<UNSET>,\tposition=<UNSET>,\tprop_cycle=<UNSET>,\trasterization_zorder=<UNSET>,\trasterized=<UNSET>,\tsketch_params=<UNSET>,\tsnap=<UNSET>,\tsubplotspec=<UNSET>,\ttitle=<UNSET>,\ttransform=<UNSET>,\turl=<UNSET>,\tvisible=<UNSET>,\txbound=<UNSET>,\txlabel=<UNSET>,\txlim=<UNSET>,\txmargin=<UNSET>,\txscale=<UNSET>,\txticklabels=<UNSET>,\txticks=<UNSET>,\tybound=<UNSET>,\tylabel=<UNSET>,\tylim=<UNSET>,\tymargin=<UNSET>,\tyscale=<UNSET>,\tyticklabels=<UNSET>,\tyticks=<UNSET>,\tzorder=<UNSET>):", "funcdef": "def"}, "pydrex.cli": {"fullname": "pydrex.cli", "modulename": "pydrex.cli", "kind": "module", "doc": "
    \n

    PyDRex: Entry points for command line tools.

    \n
    \n"}, "pydrex.cli.PoleFigureVisualiser": {"fullname": "pydrex.cli.PoleFigureVisualiser", "modulename": "pydrex.cli", "qualname": "PoleFigureVisualiser", "kind": "class", "doc": "

    PyDRex script to plot pole figures of serialized CPO data.

    \n\n

    Produces [100], [010] and [001] pole figures for serialized pydrex.Minerals.\nIf the range of indices is not specified,\na maximum of 25 of each pole figure will be produced.

    \n"}, "pydrex.cli.CLI_HANDLERS": {"fullname": "pydrex.cli.CLI_HANDLERS", "modulename": "pydrex.cli", "qualname": "CLI_HANDLERS", "kind": "variable", "doc": "

    \n", "default_value": "CLI_HANDLERS(pole_figure_visualiser=PoleFigureVisualiser())"}, "pydrex.core": {"fullname": "pydrex.core", "modulename": "pydrex.core", "kind": "module", "doc": "
    \n

    PyDRex: Core D-Rex functions and enums.

    \n
    \n\n

    The function derivatives implements the core D-Rex solver, which computes the\ncrystallographic rotation rate and changes in fractional grain volumes.

    \n\n

    Acronyms:

    \n\n\n"}, "pydrex.core.PERMUTATION_SYMBOL": {"fullname": "pydrex.core.PERMUTATION_SYMBOL", "modulename": "pydrex.core", "qualname": "PERMUTATION_SYMBOL", "kind": "variable", "doc": "

    \n", "default_value": "array([[[0.e+00, 0.e+00, 0.e+00],\n [0.e+00, 0.e+00, 1.e+00],\n [0.e+00, -1.e+00, 0.e+00]],\n\n [[0.e+00, 0.e+00, -1.e+00],\n [0.e+00, 0.e+00, 0.e+00],\n [1.e+00, 0.e+00, 0.e+00]],\n\n [[0.e+00, 1.e+00, 0.e+00],\n [-1.e+00, 0.e+00, 0.e+00],\n [0.e+00, 0.e+00, 0.e+00]]])"}, "pydrex.core.MineralPhase": {"fullname": "pydrex.core.MineralPhase", "modulename": "pydrex.core", "qualname": "MineralPhase", "kind": "class", "doc": "

    Supported mineral phases.

    \n", "bases": "enum.IntEnum"}, "pydrex.core.MineralPhase.olivine": {"fullname": "pydrex.core.MineralPhase.olivine", "modulename": "pydrex.core", "qualname": "MineralPhase.olivine", "kind": "variable", "doc": "

    \n", "default_value": "<MineralPhase.olivine: 0>"}, "pydrex.core.MineralPhase.enstatite": {"fullname": "pydrex.core.MineralPhase.enstatite", "modulename": "pydrex.core", "qualname": "MineralPhase.enstatite", "kind": "variable", "doc": "

    \n", "default_value": "<MineralPhase.enstatite: 1>"}, "pydrex.core.DeformationRegime": {"fullname": "pydrex.core.DeformationRegime", "modulename": "pydrex.core", "qualname": "DeformationRegime", "kind": "class", "doc": "

    Deformation mechanism regimes.

    \n", "bases": "enum.IntEnum"}, "pydrex.core.DeformationRegime.diffusion": {"fullname": "pydrex.core.DeformationRegime.diffusion", "modulename": "pydrex.core", "qualname": "DeformationRegime.diffusion", "kind": "variable", "doc": "

    \n", "default_value": "<DeformationRegime.diffusion: 0>"}, "pydrex.core.DeformationRegime.dislocation": {"fullname": "pydrex.core.DeformationRegime.dislocation", "modulename": "pydrex.core", "qualname": "DeformationRegime.dislocation", "kind": "variable", "doc": "

    \n", "default_value": "<DeformationRegime.dislocation: 1>"}, "pydrex.core.DeformationRegime.byerlee": {"fullname": "pydrex.core.DeformationRegime.byerlee", "modulename": "pydrex.core", "qualname": "DeformationRegime.byerlee", "kind": "variable", "doc": "

    \n", "default_value": "<DeformationRegime.byerlee: 2>"}, "pydrex.core.DeformationRegime.max_viscosity": {"fullname": "pydrex.core.DeformationRegime.max_viscosity", "modulename": "pydrex.core", "qualname": "DeformationRegime.max_viscosity", "kind": "variable", "doc": "

    \n", "default_value": "<DeformationRegime.max_viscosity: 3>"}, "pydrex.core.MineralFabric": {"fullname": "pydrex.core.MineralFabric", "modulename": "pydrex.core", "qualname": "MineralFabric", "kind": "class", "doc": "

    Supported mineral fabrics.

    \n\n

    The following fabric types are supported:

    \n\n\n", "bases": "enum.IntEnum"}, "pydrex.core.MineralFabric.olivine_A": {"fullname": "pydrex.core.MineralFabric.olivine_A", "modulename": "pydrex.core", "qualname": "MineralFabric.olivine_A", "kind": "variable", "doc": "

    \n", "default_value": "<MineralFabric.olivine_A: 0>"}, "pydrex.core.MineralFabric.olivine_B": {"fullname": "pydrex.core.MineralFabric.olivine_B", "modulename": "pydrex.core", "qualname": "MineralFabric.olivine_B", "kind": "variable", "doc": "

    \n", "default_value": "<MineralFabric.olivine_B: 1>"}, "pydrex.core.MineralFabric.olivine_C": {"fullname": "pydrex.core.MineralFabric.olivine_C", "modulename": "pydrex.core", "qualname": "MineralFabric.olivine_C", "kind": "variable", "doc": "

    \n", "default_value": "<MineralFabric.olivine_C: 2>"}, "pydrex.core.MineralFabric.olivine_D": {"fullname": "pydrex.core.MineralFabric.olivine_D", "modulename": "pydrex.core", "qualname": "MineralFabric.olivine_D", "kind": "variable", "doc": "

    \n", "default_value": "<MineralFabric.olivine_D: 3>"}, "pydrex.core.MineralFabric.olivine_E": {"fullname": "pydrex.core.MineralFabric.olivine_E", "modulename": "pydrex.core", "qualname": "MineralFabric.olivine_E", "kind": "variable", "doc": "

    \n", "default_value": "<MineralFabric.olivine_E: 4>"}, "pydrex.core.MineralFabric.enstatite_AB": {"fullname": "pydrex.core.MineralFabric.enstatite_AB", "modulename": "pydrex.core", "qualname": "MineralFabric.enstatite_AB", "kind": "variable", "doc": "

    \n", "default_value": "<MineralFabric.enstatite_AB: 5>"}, "pydrex.core.get_crss": {"fullname": "pydrex.core.get_crss", "modulename": "pydrex.core", "qualname": "get_crss", "kind": "function", "doc": "

    Get Critical Resolved Shear Stress for the mineral phase and fabric.

    \n\n

    Returns an array of the normalised threshold stresses required to activate slip on\neach slip system. Olivine slip systems are ordered according to the convention used\nfor pydrex.minerals.OLIVINE_SLIP_SYSTEMS.

    \n", "signature": "(phase, fabric):", "funcdef": "def"}, "pydrex.core.derivatives": {"fullname": "pydrex.core.derivatives", "modulename": "pydrex.core", "qualname": "derivatives", "kind": "function", "doc": "

    Get derivatives of orientation and volume distribution.

    \n\n

    Args:

    \n\n\n\n

    Returns a tuple with the rotation rates and grain volume fraction changes.

    \n", "signature": "(\tphase,\tfabric,\tn_grains,\torientations,\tfractions,\tstrain_rate,\tvelocity_gradient,\tstress_exponent,\tdeformation_exponent,\tnucleation_efficiency,\tgbm_mobility,\tvolume_fraction):", "funcdef": "def"}, "pydrex.diagnostics": {"fullname": "pydrex.diagnostics", "modulename": "pydrex.diagnostics", "kind": "module", "doc": "
    \n

    PyDRex: Methods to calculate texture and strain diagnostics.

    \n
    \n\n
    \n\n

    Calculations expect orientation matrices $a$ to represent passive\n(i.e. alias) rotations, which are defined in terms of the extrinsic ZXZ\neuler angles $\u03d5, \u03b8, \u03c6$ as\n$$\na = \\begin{bmatrix}\n \\cos\u03c6\\cos\u03d5 - \\cos\u03b8\\sin\u03d5\\sin\u03c6 & \\cos\u03b8\\cos\u03d5\\sin\u03c6 + \\cos\u03c6\\sin\u03d5 & \\sin\u03c6\\sin\u03b8 \\cr\n -\\sin\u03c6\\cos\u03d5 - \\cos\u03b8\\sin\u03d5\\cos\u03c6 & \\cos\u03b8\\cos\u03d5\\cos\u03c6 - \\sin\u03c6\\sin\u03d5 & \\cos\u03c6\\sin\u03b8 \\cr\n \\sin\u03b8\\sin\u03d5 & -\\sin\u03b8\\cos\u03d5 & \\cos\u03b8\n \\end{bmatrix}\n$$\nsuch that a[i, j] gives the direction cosine of the angle between the i-th\ngrain axis and the j-th external axis (in the global Eulerian frame).

    \n\n
    \n"}, "pydrex.diagnostics.anisotropy": {"fullname": "pydrex.diagnostics.anisotropy", "modulename": "pydrex.diagnostics", "qualname": "anisotropy", "kind": "function", "doc": "

    Calculate anisotropy diagnostics for the given elasticity tensor.

    \n\n

    Args:

    \n\n\n\n

    Returns the percent anisotropy, a matrix containing the axes of the Symmetry\nCartesian Coordinate System (rows), and the elasticity tensor in the SCCS frame\n(Voigt vector representation).

    \n", "signature": "(voigt_matrix, proj='hex'):", "funcdef": "def"}, "pydrex.diagnostics.bingham_average": {"fullname": "pydrex.diagnostics.bingham_average", "modulename": "pydrex.diagnostics", "qualname": "bingham_average", "kind": "function", "doc": "

    Compute Bingham averages from olivine orientation matrices.

    \n\n

    Returns the antipodally symmetric average orientation\nof the given crystallographic axis, or the a-axis by default.\nValid axis specifiers are \"a\" for [100], \"b\" for [010] and \"c\" for [001].

    \n\n

    See also: Watson 1966,\nMardia & Jupp, \u201cDirectional Statistics\u201d.

    \n", "signature": "(orientations, axis='a'):", "funcdef": "def"}, "pydrex.diagnostics.finite_strain": {"fullname": "pydrex.diagnostics.finite_strain", "modulename": "pydrex.diagnostics", "qualname": "finite_strain", "kind": "function", "doc": "

    Extract measures of finite strain from the deformation gradient.

    \n\n

    Extracts the vector defining the axis of maximum extension (longest semiaxis of the\nfinite strain ellipsoid) and the largest principal strain value from the 3x3\ndeformation gradient tensor.

    \n", "signature": "(deformation_gradient, **kwargs):", "funcdef": "def"}, "pydrex.diagnostics.symmetry": {"fullname": "pydrex.diagnostics.symmetry", "modulename": "pydrex.diagnostics", "qualname": "symmetry", "kind": "function", "doc": "

    Compute texture symmetry eigenvalue diagnostics from olivine orientation matrices.

    \n\n

    Compute Point, Girdle and Random symmetry diagnostics\nfor ternary texture classification.\nReturns the tuple (P, G, R) where\n$$\n\\begin{align*}\nP &= (\u03bb_{1} - \u03bb_{2}) / N \\cr\nG &= 2 (\u03bb_{2} - \u03bb_{3}) / N \\cr\nR &= 3 \u03bb_{3} / N\n\\end{align*}\n$$\nwith $N$ the sum of the eigenvalues $\u03bb_{1} \u2265 \u03bb_{2} \u2265 \u03bb_{3}$\nof the scatter (inertia) matrix.

    \n\n

    See e.g. Vollmer 1990.

    \n", "signature": "(orientations, axis='a'):", "funcdef": "def"}, "pydrex.diagnostics.misorientation_index": {"fullname": "pydrex.diagnostics.misorientation_index", "modulename": "pydrex.diagnostics", "qualname": "misorientation_index", "kind": "function", "doc": "

    Calculate M-index for polycrystal orientations.

    \n\n

    The bins argument is passed to numpy.histogram.\nIf left as None, 1\u00b0 bins will be used as recommended by the reference paper.\nThe symmetry system can be specified using the system argument.\nThe default system is orthorhombic.

    \n\n

    See Skemer et al. 2005.

    \n", "signature": "(orientations, bins=None, system=(2, 4)):", "funcdef": "def"}, "pydrex.diagnostics.coaxial_index": {"fullname": "pydrex.diagnostics.coaxial_index", "modulename": "pydrex.diagnostics", "qualname": "coaxial_index", "kind": "function", "doc": "

    Calculate coaxial \u201cBA\u201d index for a combination of two crystal axes.

    \n\n

    The BA index of Mainprice et al. 2015\nis derived from the eigenvalue symmetry diagnostics and measures point vs girdle\nsymmetry in the aggregate. $BA \u2208 [0, 1]$ where $BA = 0$ corresponds to a perfect\naxial girdle texture and $BA = 1$ represents a point symmetry texture assuming that\nthe random component $R$ is negligible. May be less susceptible to random\nfluctuations compared to the raw eigenvalue diagnostics.

    \n", "signature": "(orientations, axis1='b', axis2='a'):", "funcdef": "def"}, "pydrex.diagnostics.misorientation_angles": {"fullname": "pydrex.diagnostics.misorientation_angles", "modulename": "pydrex.diagnostics", "qualname": "misorientation_angles", "kind": "function", "doc": "

    Calculate the misorientation angles for pairs of rotation quaternions.

    \n\n

    Calculate the angular distance between the rotations combinations[:, 0]\nand combinations[:, 1], which are expected to be 1x4 passive (alias)\nrotation quaternions.

    \n\n

    Uses ~25% less memory than the same operation with rotation matrices.

    \n\n

    See also:

    \n\n\n", "signature": "(combinations):", "funcdef": "def"}, "pydrex.diagnostics.smallest_angle": {"fullname": "pydrex.diagnostics.smallest_angle", "modulename": "pydrex.diagnostics", "qualname": "smallest_angle", "kind": "function", "doc": "

    Get smallest angle between a unit vector and a bidirectional axis.

    \n\n

    The axis is specified using either of its two parallel unit vectors.

    \n", "signature": "(vector, axis):", "funcdef": "def"}, "pydrex.exceptions": {"fullname": "pydrex.exceptions", "modulename": "pydrex.exceptions", "kind": "module", "doc": "
    \n

    PyDRex: Custom exceptions (subclasses of pydrex.Error).

    \n
    \n"}, "pydrex.exceptions.Error": {"fullname": "pydrex.exceptions.Error", "modulename": "pydrex.exceptions", "qualname": "Error", "kind": "class", "doc": "

    Base class for exceptions in PyDRex.

    \n", "bases": "builtins.Exception"}, "pydrex.exceptions.ConfigError": {"fullname": "pydrex.exceptions.ConfigError", "modulename": "pydrex.exceptions", "qualname": "ConfigError", "kind": "class", "doc": "

    Exception raised for errors in the input configuration.

    \n\n

    Attributes:\n message \u2014 explanation of the error

    \n", "bases": "Error"}, "pydrex.exceptions.ConfigError.__init__": {"fullname": "pydrex.exceptions.ConfigError.__init__", "modulename": "pydrex.exceptions", "qualname": "ConfigError.__init__", "kind": "function", "doc": "

    \n", "signature": "(message)"}, "pydrex.exceptions.ConfigError.message": {"fullname": "pydrex.exceptions.ConfigError.message", "modulename": "pydrex.exceptions", "qualname": "ConfigError.message", "kind": "variable", "doc": "

    \n"}, "pydrex.exceptions.MeshError": {"fullname": "pydrex.exceptions.MeshError", "modulename": "pydrex.exceptions", "qualname": "MeshError", "kind": "class", "doc": "

    Exception raised for errors in the input mesh.

    \n\n

    Attributes:\n message \u2014 explanation of the error

    \n", "bases": "Error"}, "pydrex.exceptions.MeshError.__init__": {"fullname": "pydrex.exceptions.MeshError.__init__", "modulename": "pydrex.exceptions", "qualname": "MeshError.__init__", "kind": "function", "doc": "

    \n", "signature": "(message)"}, "pydrex.exceptions.MeshError.message": {"fullname": "pydrex.exceptions.MeshError.message", "modulename": "pydrex.exceptions", "qualname": "MeshError.message", "kind": "variable", "doc": "

    \n"}, "pydrex.exceptions.IterationError": {"fullname": "pydrex.exceptions.IterationError", "modulename": "pydrex.exceptions", "qualname": "IterationError", "kind": "class", "doc": "

    Exception raised for errors in numerical iteration schemes.

    \n\n

    Attributes:\n message \u2014 explanation of the error

    \n", "bases": "Error"}, "pydrex.exceptions.IterationError.__init__": {"fullname": "pydrex.exceptions.IterationError.__init__", "modulename": "pydrex.exceptions", "qualname": "IterationError.__init__", "kind": "function", "doc": "

    \n", "signature": "(message)"}, "pydrex.exceptions.IterationError.message": {"fullname": "pydrex.exceptions.IterationError.message", "modulename": "pydrex.exceptions", "qualname": "IterationError.message", "kind": "variable", "doc": "

    \n"}, "pydrex.exceptions.SCSVError": {"fullname": "pydrex.exceptions.SCSVError", "modulename": "pydrex.exceptions", "qualname": "SCSVError", "kind": "class", "doc": "

    Exception raised for errors in SCSV file I/O.

    \n\n

    Attributes:

    \n\n\n", "bases": "Error"}, "pydrex.exceptions.SCSVError.__init__": {"fullname": "pydrex.exceptions.SCSVError.__init__", "modulename": "pydrex.exceptions", "qualname": "SCSVError.__init__", "kind": "function", "doc": "

    \n", "signature": "(message)"}, "pydrex.exceptions.SCSVError.message": {"fullname": "pydrex.exceptions.SCSVError.message", "modulename": "pydrex.exceptions", "qualname": "SCSVError.message", "kind": "variable", "doc": "

    \n"}, "pydrex.geometry": {"fullname": "pydrex.geometry", "modulename": "pydrex.geometry", "kind": "module", "doc": "
    \n

    PyDRex: Functions for geometric coordinate conversions and projections.

    \n
    \n"}, "pydrex.geometry.to_cartesian": {"fullname": "pydrex.geometry.to_cartesian", "modulename": "pydrex.geometry", "qualname": "to_cartesian", "kind": "function", "doc": "

    Convert spherical to cartesian coordinates in \u211d\u00b3.

    \n\n

    Spherical coordinate convention:

    \n\n\n\n

    By default, a radius of r = 1 is used for the sphere.\nReturns a tuple containing arrays of x, y, and z values.

    \n", "signature": "(\u03c6, \u03b8, r=1):", "funcdef": "def"}, "pydrex.geometry.to_spherical": {"fullname": "pydrex.geometry.to_spherical", "modulename": "pydrex.geometry", "qualname": "to_spherical", "kind": "function", "doc": "

    Convert cartesian coordinates in \u211d\u00b3 to spherical coordinates.

    \n\n

    Spherical coordinate convention:

    \n\n\n\n

    Returns a tuple containing arrays of r, \u03d5 and \u03b8 values.

    \n", "signature": "(x, y, z):", "funcdef": "def"}, "pydrex.geometry.poles": {"fullname": "pydrex.geometry.poles", "modulename": "pydrex.geometry", "qualname": "poles", "kind": "function", "doc": "

    Extract 3D vectors of crystallographic directions from orientation matrices.

    \n\n

    Expects orientations to be an array with shape (N, 3, 3).\nThe optional arguments ref_axes and hkl can be used to change\nthe global reference axes and the crystallographic direction respectively.\nThe reference axes should be given as a string of two letters,\ne.g. \"xz\" (default), which specify the second and third axes\nof the global right-handed reference frame. The third letter in the set \"xyz\"\ndetermines the first axis. The ref_axes will therefore become the\nhorizontal and vertical axes of pole figures used to plot the directions.

    \n", "signature": "(orientations, ref_axes='xz', hkl=[1, 0, 0]):", "funcdef": "def"}, "pydrex.geometry.lambert_equal_area": {"fullname": "pydrex.geometry.lambert_equal_area", "modulename": "pydrex.geometry", "qualname": "lambert_equal_area", "kind": "function", "doc": "

    Project axial data from a 3D sphere onto a 2D disk.

    \n\n

    Project points from a 3D sphere of radius 1, given in Cartesian coordinates,\nto points on a 2D disk using a Lambert equal area azimuthal projection.\nReturns arrays of the X and Y coordinates in the unit disk.

    \n\n

    This implementation first maps all points onto the same hemisphere,\nand then projects that hemisphere onto the disk.

    \n", "signature": "(xvals, yvals, zvals):", "funcdef": "def"}, "pydrex.geometry.shirley_concentric_squaredisk": {"fullname": "pydrex.geometry.shirley_concentric_squaredisk", "modulename": "pydrex.geometry", "qualname": "shirley_concentric_squaredisk", "kind": "function", "doc": "

    Project points from a square onto a disk using the concentric Shirley method.

    \n\n

    The concentric method of Shirley & Chiu 1997 is optimised to preserve area.\nSee also: http://marc-b-reynolds.github.io/math/2017/01/08/SquareDisc.html.

    \n\n

    This can be used to set up uniform grids on a disk, e.g.

    \n\n
    \n
    >>> a = [x / 5.0 for x in range(-5, 6)]\n>>> x = [[x] * len(a) for x in a]\n>>> y = [a for _ in a]\n>>> x_flat = [j for i in x for j in i]\n>>> y_flat = [j for i in y for j in i]\n>>> x_disk, y_disk = shirley_concentric_squaredisk(x_flat, y_flat)\n>>> r = x_disk**2 + y_disk**2\n>>> r\narray([1.  , 1.  , 1.  , 1.  , 1.  , 1.  , 1.  , 1.  , 1.  , 1.  , 1.  ,\n       1.  , 0.64, 0.64, 0.64, 0.64, 0.64, 0.64, 0.64, 0.64, 0.64, 1.  ,\n       1.  , 0.64, 0.36, 0.36, 0.36, 0.36, 0.36, 0.36, 0.36, 0.64, 1.  ,\n       1.  , 0.64, 0.36, 0.16, 0.16, 0.16, 0.16, 0.16, 0.36, 0.64, 1.  ,\n       1.  , 0.64, 0.36, 0.16, 0.04, 0.04, 0.04, 0.16, 0.36, 0.64, 1.  ,\n       1.  , 0.64, 0.36, 0.16, 0.04, 0.  , 0.04, 0.16, 0.36, 0.64, 1.  ,\n       1.  , 0.64, 0.36, 0.16, 0.04, 0.04, 0.04, 0.16, 0.36, 0.64, 1.  ,\n       1.  , 0.64, 0.36, 0.16, 0.16, 0.16, 0.16, 0.16, 0.36, 0.64, 1.  ,\n       1.  , 0.64, 0.36, 0.36, 0.36, 0.36, 0.36, 0.36, 0.36, 0.64, 1.  ,\n       1.  , 0.64, 0.64, 0.64, 0.64, 0.64, 0.64, 0.64, 0.64, 0.64, 1.  ,\n       1.  , 1.  , 1.  , 1.  , 1.  , 1.  , 1.  , 1.  , 1.  , 1.  , 1.  ])\n>>> from math import atan2\n>>> \u03b8 = [atan2(y, x) for y, x in zip(y_disk, x_disk)]\n>>> max(\u03b8)\n3.141592653589793\n>>> min(\u03b8)\n-2.9845130209101467\n
    \n
    \n", "signature": "(xvals, yvals):", "funcdef": "def"}, "pydrex.interpolations": {"fullname": "pydrex.interpolations", "modulename": "pydrex.interpolations", "kind": "module", "doc": "
    \n

    PyDRex: Interpolation callbacks and helpers.

    \n
    \n"}, "pydrex.interpolations.default_interpolators": {"fullname": "pydrex.interpolations.default_interpolators", "modulename": "pydrex.interpolations", "qualname": "default_interpolators", "kind": "function", "doc": "

    Create a dictionary of default interpolator callbacks for PyDRex input.

    \n\n

    Args:

    \n\n\n\n

    Optionaly pass a string to mpl_interp to use\nmatplotlib.tri.CubicTriInterpolator with the chosen smoothing algorithm.\nOnly valid for 2D data with pre-existing triangulations.

    \n\n

    See also create_interpolators.

    \n", "signature": "(config, coords, vtk_output, mpl_interp=None):", "funcdef": "def"}, "pydrex.interpolations.create_interpolators": {"fullname": "pydrex.interpolations.create_interpolators", "modulename": "pydrex.interpolations", "qualname": "create_interpolators", "kind": "function", "doc": "

    Create interpolator callbacks for data arrays.

    \n\n

    Args:

    \n\n\n\n

    Optional kwargs will be passed to the interpolation constructor.

    \n\n

    Returns a list of interpolator callbacks, one for each data vector component.

    \n\n

    The triangles arg is required only for matplotlib.tri.CubicTriInterpolator.\nSee the documentation of that constructor for details.

    \n", "signature": "(interpolator, coords, data, triangles=None, **kwargs):", "funcdef": "def"}, "pydrex.interpolations.get_velocity": {"fullname": "pydrex.interpolations.get_velocity", "modulename": "pydrex.interpolations", "qualname": "get_velocity", "kind": "function", "doc": "

    Interpolates the velocity at a given point.

    \n", "signature": "(point, interpolators):", "funcdef": "def"}, "pydrex.interpolations.get_velocity_gradient": {"fullname": "pydrex.interpolations.get_velocity_gradient", "modulename": "pydrex.interpolations", "qualname": "get_velocity_gradient", "kind": "function", "doc": "

    Return the interpolated velocity gradient tensor at a given point.

    \n", "signature": "(point, interpolators):", "funcdef": "def"}, "pydrex.interpolations.get_deformation_mechanism": {"fullname": "pydrex.interpolations.get_deformation_mechanism", "modulename": "pydrex.interpolations", "qualname": "get_deformation_mechanism", "kind": "function", "doc": "

    Return the interpolated deformation mechanism ID at the given point.

    \n", "signature": "(point, interpolators):", "funcdef": "def"}, "pydrex.io": {"fullname": "pydrex.io", "modulename": "pydrex.io", "kind": "module", "doc": "
    \n

    PyDRex: Mesh, configuration and supporting data Input/Output functions.

    \n
    \n\n

    PyDRex can read/write three kinds of plain text files:

    \n\n\n\n

    SCSV files are our custom CSV files with a YAML header. The header is used for data\nattribution and metadata, as well as a column type spec. There is no official spec for\nSCSV files at the moment but they should follow the format of existing SCSV files in\nthe data/ folder of the source repository. For supported cell types, see\nSCSV_TYPEMAP.

    \n"}, "pydrex.io.DEFAULT_PARAMS": {"fullname": "pydrex.io.DEFAULT_PARAMS", "modulename": "pydrex.io", "qualname": "DEFAULT_PARAMS", "kind": "variable", "doc": "

    Default simulation parameters.

    \n", "default_value": "{'olivine_fraction': 1.0, 'enstatite_fraction': 0.0, 'stress_exponent': 1.5, 'deformation_exponent': 3.5, 'gbm_mobility': 125, 'gbs_threshold': 0.3, 'nucleation_efficiency': 5.0, 'number_of_grains': 2500, 'initial_olivine_fabric': 'A'}"}, "pydrex.io.SCSV_TYPEMAP": {"fullname": "pydrex.io.SCSV_TYPEMAP", "modulename": "pydrex.io", "qualname": "SCSV_TYPEMAP", "kind": "variable", "doc": "

    Mapping of supported SCSV field types to corresponding Python types.

    \n", "default_value": "{'string': <class 'str'>, 'integer': <class 'int'>, 'float': <class 'float'>, 'boolean': <class 'bool'>, 'complex': <class 'complex'>}"}, "pydrex.io.read_scsv": {"fullname": "pydrex.io.read_scsv", "modulename": "pydrex.io", "qualname": "read_scsv", "kind": "function", "doc": "

    Read data from an SCSV file.

    \n\n

    See also save_scsv, read_scsv_header.

    \n", "signature": "(file):", "funcdef": "def"}, "pydrex.io.write_scsv_header": {"fullname": "pydrex.io.write_scsv_header", "modulename": "pydrex.io", "qualname": "write_scsv_header", "kind": "function", "doc": "

    Write YAML header to an SCSV stream.

    \n\n

    Args:

    \n\n\n\n

    See also read_scsv, save_scsv.

    \n", "signature": "(stream, schema, comments=None):", "funcdef": "def"}, "pydrex.io.save_scsv": {"fullname": "pydrex.io.save_scsv", "modulename": "pydrex.io", "qualname": "save_scsv", "kind": "function", "doc": "

    Save data to SCSV file.

    \n\n

    Args:

    \n\n\n\n

    Optional keyword arguments are passed to write_scsv_header. See also read_scsv.

    \n", "signature": "(file, schema, data, **kwargs):", "funcdef": "def"}, "pydrex.io.parse_config": {"fullname": "pydrex.io.parse_config", "modulename": "pydrex.io", "qualname": "parse_config", "kind": "function", "doc": "

    Parse a TOML file containing PyDRex configuration.

    \n", "signature": "(path):", "funcdef": "def"}, "pydrex.io.read_mesh": {"fullname": "pydrex.io.read_mesh", "modulename": "pydrex.io", "qualname": "read_mesh", "kind": "function", "doc": "

    Wrapper of meshio.read, see https://github.com/nschloe/meshio.

    \n", "signature": "(meshfile, *args, **kwargs):", "funcdef": "def"}, "pydrex.io.resolve_path": {"fullname": "pydrex.io.resolve_path", "modulename": "pydrex.io", "qualname": "resolve_path", "kind": "function", "doc": "

    Resolve relative paths and create parent directories if necessary.

    \n\n

    Relative paths are interpreted with respect to the current working directory,\ni.e. the directory from whith the current Python process was executed,\nunless a specific reference directory is provided with refdir.

    \n", "signature": "(path, refdir=None):", "funcdef": "def"}, "pydrex.io.stringify": {"fullname": "pydrex.io.stringify", "modulename": "pydrex.io", "qualname": "stringify", "kind": "function", "doc": "

    Return a cleaned version of a string for use in filenames, etc.

    \n", "signature": "(s):", "funcdef": "def"}, "pydrex.io.data": {"fullname": "pydrex.io.data", "modulename": "pydrex.io", "qualname": "data", "kind": "function", "doc": "

    Get resolved path to a pydrex data folder.

    \n", "signature": "(folder):", "funcdef": "def"}, "pydrex.logger": {"fullname": "pydrex.logger", "modulename": "pydrex.logger", "kind": "module", "doc": "
    \n

    PyDRex: logger settings and boilerplate.

    \n
    \n\n

    Python's logging module is weird and its methods don't allow us to specify\nwhich logger to use, so just using logging.debug for example always uses\nthe \"root\" logger, which spams a bunch of messages from other imports/modules.\nInstead, the methods in this module are thin wrappers that use custom\nlogging objects (pydrex.logger.LOGGER and pydrex.logger.CONSOLE_LOGGER).\nThe method quiet_aliens can be invoked to suppress most messages\nfrom third-party modules, except critical errors and warnings from Numba.

    \n\n

    By default, PyDRex emits INFO level messages to the console.\nThis can be changed globally by setting the new level with CONSOLE_LOGGER.setLevel:

    \n\n
    \n
    from pydrex import logger as _log\n_log.info("this message will be printed to the console")\n\n_log.CONSOLE_LOGGER.setLevel("ERROR")\n_log.info("this message will NOT be printed to the console")\n_log.error("this message will be printed to the console")\n
    \n
    \n\n

    To change the console logging level for a particular local context,\nuse the handler_level context manager:

    \n\n
    \n
    _log.CONSOLE_LOGGER.setLevel("INFO")\n_log.info("this message will be printed to the console")\n\nwith handler_level("ERROR"):\n    _log.info("this message will NOT be printed to the console")\n\n_log.info("this message will be printed to the console")\n
    \n
    \n\n

    To save debug logs to a file, the logfile_enable context manager is recommended.\nAlways use the old printf style formatting for log messages, not fstrings,\notherwise compute time will be wasted on string conversions when logging is disabled:

    \n\n
    \n
    _log.quiet_aliens()  # Suppress third-party log messages except CRITICAL from Numba.\nwith _log.logfile_enable("my_log_file.log"):  # Overwrite existing file unless mode="a".\n    value = 42\n    _log.critical("critical error with value: %s", value)\n    _log.error("runtime error with value: %s", value)\n    _log.warning("warning with value: %s", value)\n    _log.info("information message with value: %s", value)\n    _log.debug("verbose debugging message with value: %s", value)\n    ... # Construct Minerals, update orientations, etc.\n
    \n
    \n"}, "pydrex.logger.ConsoleFormatter": {"fullname": "pydrex.logger.ConsoleFormatter", "modulename": "pydrex.logger", "qualname": "ConsoleFormatter", "kind": "class", "doc": "

    Log formatter that uses terminal color codes.

    \n", "bases": "logging.Formatter"}, "pydrex.logger.ConsoleFormatter.colorfmt": {"fullname": "pydrex.logger.ConsoleFormatter.colorfmt", "modulename": "pydrex.logger", "qualname": "ConsoleFormatter.colorfmt", "kind": "function", "doc": "

    \n", "signature": "(self, code):", "funcdef": "def"}, "pydrex.logger.ConsoleFormatter.format": {"fullname": "pydrex.logger.ConsoleFormatter.format", "modulename": "pydrex.logger", "qualname": "ConsoleFormatter.format", "kind": "function", "doc": "

    Format the specified record as text.

    \n\n

    The record's attribute dictionary is used as the operand to a\nstring formatting operation which yields the returned string.\nBefore formatting the dictionary, a couple of preparatory steps\nare carried out. The message attribute of the record is computed\nusing LogRecord.getMessage(). If the formatting string uses the\ntime (as determined by a call to usesTime(), formatTime() is\ncalled to format the event time. If there is exception information,\nit is formatted using formatException() and appended to the message.

    \n", "signature": "(self, record):", "funcdef": "def"}, "pydrex.logger.LOGGER": {"fullname": "pydrex.logger.LOGGER", "modulename": "pydrex.logger", "qualname": "LOGGER", "kind": "variable", "doc": "

    \n", "default_value": "<Logger pydrex (DEBUG)>"}, "pydrex.logger.LOGGER_CONSOLE": {"fullname": "pydrex.logger.LOGGER_CONSOLE", "modulename": "pydrex.logger", "qualname": "LOGGER_CONSOLE", "kind": "variable", "doc": "

    \n", "default_value": "<StreamHandler (INFO)>"}, "pydrex.logger.handler_level": {"fullname": "pydrex.logger.handler_level", "modulename": "pydrex.logger", "qualname": "handler_level", "kind": "function", "doc": "

    Set logging handler level for current context.

    \n\n

    Args:

    \n\n\n", "signature": "(level, handler=<StreamHandler (INFO)>):", "funcdef": "def"}, "pydrex.logger.logfile_enable": {"fullname": "pydrex.logger.logfile_enable", "modulename": "pydrex.logger", "qualname": "logfile_enable", "kind": "function", "doc": "

    Enable logging to a file at path with given level.

    \n", "signature": "(path, level=10, mode='w'):", "funcdef": "def"}, "pydrex.logger.critical": {"fullname": "pydrex.logger.critical", "modulename": "pydrex.logger", "qualname": "critical", "kind": "function", "doc": "

    Log a CRITICAL message in PyDRex.

    \n", "signature": "(msg, *args, **kwargs):", "funcdef": "def"}, "pydrex.logger.error": {"fullname": "pydrex.logger.error", "modulename": "pydrex.logger", "qualname": "error", "kind": "function", "doc": "

    Log an ERROR message in PyDRex.

    \n", "signature": "(msg, *args, **kwargs):", "funcdef": "def"}, "pydrex.logger.warning": {"fullname": "pydrex.logger.warning", "modulename": "pydrex.logger", "qualname": "warning", "kind": "function", "doc": "

    Log a WARNING message in PyDRex.

    \n", "signature": "(msg, *args, **kwargs):", "funcdef": "def"}, "pydrex.logger.info": {"fullname": "pydrex.logger.info", "modulename": "pydrex.logger", "qualname": "info", "kind": "function", "doc": "

    Log an INFO message in PyDRex.

    \n", "signature": "(msg, *args, **kwargs):", "funcdef": "def"}, "pydrex.logger.debug": {"fullname": "pydrex.logger.debug", "modulename": "pydrex.logger", "qualname": "debug", "kind": "function", "doc": "

    Log a DEBUG message in PyDRex.

    \n", "signature": "(msg, *args, **kwargs):", "funcdef": "def"}, "pydrex.logger.exception": {"fullname": "pydrex.logger.exception", "modulename": "pydrex.logger", "qualname": "exception", "kind": "function", "doc": "

    Log a message with level ERROR but retain exception information.

    \n\n

    This function should only be called from an exception handler.

    \n", "signature": "(msg, *args, **kwargs):", "funcdef": "def"}, "pydrex.logger.quiet_aliens": {"fullname": "pydrex.logger.quiet_aliens", "modulename": "pydrex.logger", "qualname": "quiet_aliens", "kind": "function", "doc": "

    Restrict alien loggers \ud83d\udc7d because I'm trying to find MY bugs, thanks.

    \n", "signature": "():", "funcdef": "def"}, "pydrex.minerals": {"fullname": "pydrex.minerals", "modulename": "pydrex.minerals", "kind": "module", "doc": "
    \n

    PyDRex: Computations of mineral texture and elasticity.

    \n
    \n"}, "pydrex.minerals.OLIVINE_STIFFNESS": {"fullname": "pydrex.minerals.OLIVINE_STIFFNESS", "modulename": "pydrex.minerals", "qualname": "OLIVINE_STIFFNESS", "kind": "variable", "doc": "

    Stiffness tensor for olivine (Voigt representation), with units of GPa.

    \n\n

    The source of the values used here is unknown, but they are copied\nfrom the original DRex code: http://www.ipgp.fr/~kaminski/web_doudoud/DRex.tar.gz [88K download]

    \n", "default_value": "array([[3.2071e+02, 6.984e+01, 7.122e+01, 0.e+00, 0.e+00, 0.e+00],\n [6.984e+01, 1.9725e+02, 7.48e+01, 0.e+00, 0.e+00, 0.e+00],\n [7.122e+01, 7.48e+01, 2.3432e+02, 0.e+00, 0.e+00, 0.e+00],\n [0.e+00, 0.e+00, 0.e+00, 6.377e+01, 0.e+00, 0.e+00],\n [0.e+00, 0.e+00, 0.e+00, 0.e+00, 7.767e+01, 0.e+00],\n [0.e+00, 0.e+00, 0.e+00, 0.e+00, 0.e+00, 7.836e+01]])"}, "pydrex.minerals.ENSTATITE_STIFFNESS": {"fullname": "pydrex.minerals.ENSTATITE_STIFFNESS", "modulename": "pydrex.minerals", "qualname": "ENSTATITE_STIFFNESS", "kind": "variable", "doc": "

    Stiffness tensor for enstatite (Voigt representation), with units of GPa.

    \n\n

    The source of the values used here is unknown, but they are copied\nfrom the original DRex code: http://www.ipgp.fr/~kaminski/web_doudoud/DRex.tar.gz [88K download]

    \n", "default_value": "array([[2.369e+02, 7.96e+01, 6.32e+01, 0.e+00, 0.e+00, 0.e+00],\n [7.96e+01, 1.805e+02, 5.68e+01, 0.e+00, 0.e+00, 0.e+00],\n [6.32e+01, 5.68e+01, 2.304e+02, 0.e+00, 0.e+00, 0.e+00],\n [0.e+00, 0.e+00, 0.e+00, 8.43e+01, 0.e+00, 0.e+00],\n [0.e+00, 0.e+00, 0.e+00, 0.e+00, 7.94e+01, 0.e+00],\n [0.e+00, 0.e+00, 0.e+00, 0.e+00, 0.e+00, 8.01e+01]])"}, "pydrex.minerals.OLIVINE_PRIMARY_AXIS": {"fullname": "pydrex.minerals.OLIVINE_PRIMARY_AXIS", "modulename": "pydrex.minerals", "qualname": "OLIVINE_PRIMARY_AXIS", "kind": "variable", "doc": "

    Primary slip axis name for for the given olivine fabric.

    \n", "default_value": "{<MineralFabric.olivine_A: 0>: 'a', <MineralFabric.olivine_B: 1>: 'c', <MineralFabric.olivine_C: 2>: 'c', <MineralFabric.olivine_D: 3>: 'a', <MineralFabric.olivine_E: 4>: 'a'}"}, "pydrex.minerals.OLIVINE_SLIP_SYSTEMS": {"fullname": "pydrex.minerals.OLIVINE_SLIP_SYSTEMS", "modulename": "pydrex.minerals", "qualname": "OLIVINE_SLIP_SYSTEMS", "kind": "variable", "doc": "

    Slip systems for olivine in conventional order.

    \n\n

    Tuples contain the slip plane normal and slip direction vectors.\nThe order of slip systems returned matches the order of critical shear stresses\nreturned by pydrex.core.get_crss.

    \n", "default_value": "(([0, 1, 0], [1, 0, 0]), ([0, 0, 1], [1, 0, 0]), ([0, 1, 0], [0, 0, 1]), ([1, 0, 0], [0, 0, 1]))"}, "pydrex.minerals.voigt_averages": {"fullname": "pydrex.minerals.voigt_averages", "modulename": "pydrex.minerals", "qualname": "voigt_averages", "kind": "function", "doc": "

    Calculate elastic tensors as the Voigt averages of a collection of minerals.

    \n\n

    Args:

    \n\n\n\n

    Raises a ValueError if the minerals contain an unequal number of grains or stored\ntexture results.

    \n", "signature": "(minerals, weights):", "funcdef": "def"}, "pydrex.minerals.Mineral": {"fullname": "pydrex.minerals.Mineral", "modulename": "pydrex.minerals", "qualname": "Mineral", "kind": "class", "doc": "

    Class for storing polycrystal texture for a single mineral phase.

    \n\n

    A Mineral stores texture data for an aggregate of grains*.\nAdditionally, mineral fabric type and deformation regime are also tracked.\nTo provide an initial texture for the mineral, use the constructor arguments\nfractions_init and orientations_init. By default,\na uniform volume distribution of random orientations is generated.

    \n\n

    The update_orientations method computes new orientations and grain volumes\nfor a given velocity gradient. These results are stored in the .orientations and\n.fractions attributes of the Mineral instance. The method also returns the\nupdated macroscopic deformation gradient based on the provided initial deformation\ngradient.

    \n\n

    *Note that the \"number of grains\" is a static integer value that\ndoes not track the actual number of physical grains in the deforming polycrystal.\nInstead, this number acts as a \"number of bins\" for the statistical resolution of\nthe crystallographic orientation distribution. The value is roughly equivalent to\n(a multiple of) the number of initial, un-recrystallised grains in the polycrystal.\nIt is assumed that recrystallised grains do not grow large enough to require\nrotation tracking.

    \n\n

    Examples:

    \n\n

    Mineral with isotropic initial texture:

    \n\n
    \n
    >>> import pydrex\n>>> pydrex.Mineral(\n>>>     phase=pydrex.MineralPhase.olivine,\n>>>     fabric=pydrex.MineralFabric.olivine_A,\n>>>     regime=pydrex.DeformationRegime.dislocation,\n>>>     n_grains=2000,\n>>> )\nMineral(phase=0, fabric=0, regime=1, n_grains=2000, fractions=<list of ndarray (2000,)>, orientations=<list of ndarray (2000, 3, 3)>)\n
    \n
    \n\n

    Mineral with specified initial texture and default phase, fabric and regime settings\nwhich are for an olivine A-type mineral in the dislocation creep regime.\nThe initial grain volume fractions should be normalised.

    \n\n
    \n
    >>> import numpy as np\n>>> from scipy.spatial.transform import Rotation\n>>> import pydrex\n>>> rng = np.random.default_rng()\n>>> n_grains = 2000\n>>> pydrex.Mineral(\n>>>     n_grains=n_grains,\n>>>     fractions_init=np.full(n_grains, 1 / n_grains),\n>>>     orientations_init=Rotation.from_euler(\n>>>         "zxz", [[x * np.pi / 2, np.pi / /2, np.pi / 2] for x in rng.random(n_grains)]\n>>>     ).inv().as_matrix(),\n>>> )\nMineral(phase=0, fabric=0, regime=1, n_grains=2000, fractions=<list of ndarray (2000,)>, orientations=<list of ndarray (2000, 3, 3)>)\n
    \n
    \n\n

    Attributes:

    \n\n\n"}, "pydrex.minerals.Mineral.__init__": {"fullname": "pydrex.minerals.Mineral.__init__", "modulename": "pydrex.minerals", "qualname": "Mineral.__init__", "kind": "function", "doc": "

    \n", "signature": "(\tphase: int = <MineralPhase.olivine: 0>,\tfabric: int = <MineralFabric.olivine_A: 0>,\tregime: int = <DeformationRegime.dislocation: 1>,\tn_grains: int = 1000,\tfractions_init: numpy.ndarray = None,\torientations_init: numpy.ndarray = None,\tfractions: list = <factory>,\torientations: list = <factory>,\tseed: int = None)"}, "pydrex.minerals.Mineral.phase": {"fullname": "pydrex.minerals.Mineral.phase", "modulename": "pydrex.minerals", "qualname": "Mineral.phase", "kind": "variable", "doc": "

    \n", "annotation": ": int", "default_value": "<MineralPhase.olivine: 0>"}, "pydrex.minerals.Mineral.fabric": {"fullname": "pydrex.minerals.Mineral.fabric", "modulename": "pydrex.minerals", "qualname": "Mineral.fabric", "kind": "variable", "doc": "

    \n", "annotation": ": int", "default_value": "<MineralFabric.olivine_A: 0>"}, "pydrex.minerals.Mineral.regime": {"fullname": "pydrex.minerals.Mineral.regime", "modulename": "pydrex.minerals", "qualname": "Mineral.regime", "kind": "variable", "doc": "

    \n", "annotation": ": int", "default_value": "<DeformationRegime.dislocation: 1>"}, "pydrex.minerals.Mineral.n_grains": {"fullname": "pydrex.minerals.Mineral.n_grains", "modulename": "pydrex.minerals", "qualname": "Mineral.n_grains", "kind": "variable", "doc": "

    \n", "annotation": ": int", "default_value": "1000"}, "pydrex.minerals.Mineral.fractions_init": {"fullname": "pydrex.minerals.Mineral.fractions_init", "modulename": "pydrex.minerals", "qualname": "Mineral.fractions_init", "kind": "variable", "doc": "

    \n", "annotation": ": numpy.ndarray", "default_value": "None"}, "pydrex.minerals.Mineral.orientations_init": {"fullname": "pydrex.minerals.Mineral.orientations_init", "modulename": "pydrex.minerals", "qualname": "Mineral.orientations_init", "kind": "variable", "doc": "

    \n", "annotation": ": numpy.ndarray", "default_value": "None"}, "pydrex.minerals.Mineral.fractions": {"fullname": "pydrex.minerals.Mineral.fractions", "modulename": "pydrex.minerals", "qualname": "Mineral.fractions", "kind": "variable", "doc": "

    \n", "annotation": ": list"}, "pydrex.minerals.Mineral.orientations": {"fullname": "pydrex.minerals.Mineral.orientations", "modulename": "pydrex.minerals", "qualname": "Mineral.orientations", "kind": "variable", "doc": "

    \n", "annotation": ": list"}, "pydrex.minerals.Mineral.seed": {"fullname": "pydrex.minerals.Mineral.seed", "modulename": "pydrex.minerals", "qualname": "Mineral.seed", "kind": "variable", "doc": "

    \n", "annotation": ": int", "default_value": "None"}, "pydrex.minerals.Mineral.update_orientations": {"fullname": "pydrex.minerals.Mineral.update_orientations", "modulename": "pydrex.minerals", "qualname": "Mineral.update_orientations", "kind": "function", "doc": "

    Update orientations and volume distribution for the Mineral.

    \n\n

    Update crystalline orientations and grain volume distribution\nfor minerals undergoing plastic deformation.

    \n\n

    Args:

    \n\n\n\n

    Any additional (optional) keyword arguments are passed to\nscipy.integrate.LSODA.

    \n\n

    Array values must provide a NumPy-compatible interface:\nhttps://numpy.org/doc/stable/user/whatisnumpy.html

    \n", "signature": "(\tself,\tconfig,\tdeformation_gradient,\tget_velocity_gradient,\tpathline,\t**kwargs):", "funcdef": "def"}, "pydrex.minerals.Mineral.save": {"fullname": "pydrex.minerals.Mineral.save", "modulename": "pydrex.minerals", "qualname": "Mineral.save", "kind": "function", "doc": "

    Save CPO data for all stored timesteps to a numpy NPZ file.

    \n\n

    If postfix is not None, the data is appended to the NPZ file\nin fields ending with \"_postfix\".

    \n\n

    Raises a ValueError if the data shapes are not compatible.

    \n\n

    See also: numpy.savez, Mineral.load, Mineral.from_file.

    \n", "signature": "(self, filename, postfix=None):", "funcdef": "def"}, "pydrex.minerals.Mineral.load": {"fullname": "pydrex.minerals.Mineral.load", "modulename": "pydrex.minerals", "qualname": "Mineral.load", "kind": "function", "doc": "

    Load CPO data from a numpy NPZ file.

    \n\n

    If postfix is not None, data is read from fields ending with \"_postfix\".

    \n\n

    See also: Mineral.save, Mineral.from_file.

    \n", "signature": "(self, filename, postfix=None):", "funcdef": "def"}, "pydrex.minerals.Mineral.from_file": {"fullname": "pydrex.minerals.Mineral.from_file", "modulename": "pydrex.minerals", "qualname": "Mineral.from_file", "kind": "function", "doc": "

    Construct a Mineral instance using data from a numpy NPZ file.

    \n\n

    If postfix is not None, data is read from fields ending with \u201c_postfix\u201d.

    \n\n

    See also: Mineral.save, Mineral.load.

    \n", "signature": "(cls, filename, postfix=None):", "funcdef": "def"}, "pydrex.mock": {"fullname": "pydrex.mock", "modulename": "pydrex.mock", "kind": "module", "doc": "
    \n

    PyDRex: Mock objects for testing and reproducibility.

    \n
    \n"}, "pydrex.mock.PARAMS_FRATERS2021": {"fullname": "pydrex.mock.PARAMS_FRATERS2021", "modulename": "pydrex.mock", "qualname": "PARAMS_FRATERS2021", "kind": "variable", "doc": "

    Values used for tests 1, 2 and 4 in https://doi.org/10.1029/2021gc009846.

    \n", "default_value": "{'olivine_fraction': 0.7, 'enstatite_fraction': 0.3, 'initial_olivine_fabric': <MineralFabric.olivine_A: 0>, 'stress_exponent': 1.5, 'deformation_exponent': 3.5, 'gbm_mobility': 125, 'gbs_threshold': 0.3, 'nucleation_efficiency': 5, 'number_of_grains': 500}"}, "pydrex.mock.PARAMS_KAMINSKI2001_FIG5_SOLID": {"fullname": "pydrex.mock.PARAMS_KAMINSKI2001_FIG5_SOLID", "modulename": "pydrex.mock", "qualname": "PARAMS_KAMINSKI2001_FIG5_SOLID", "kind": "variable", "doc": "

    Values used for the M*=0 test in https://doi.org/10.1016/s0012-821x(01)00356-9.

    \n", "default_value": "{'olivine_fraction': 1, 'enstatite_fraction': 0, 'initial_olivine_fabric': <MineralFabric.olivine_A: 0>, 'stress_exponent': 1.5, 'deformation_exponent': 3.5, 'gbm_mobility': 0, 'gbs_threshold': 0, 'nucleation_efficiency': 5, 'number_of_grains': 3375}"}, "pydrex.mock.PARAMS_KAMINSKI2001_FIG5_SHORTDASH": {"fullname": "pydrex.mock.PARAMS_KAMINSKI2001_FIG5_SHORTDASH", "modulename": "pydrex.mock", "qualname": "PARAMS_KAMINSKI2001_FIG5_SHORTDASH", "kind": "variable", "doc": "

    Values used for the M*=50 test in https://doi.org/10.1016/s0012-821x(01)00356-9.

    \n", "default_value": "{'olivine_fraction': 1, 'enstatite_fraction': 0, 'initial_olivine_fabric': <MineralFabric.olivine_A: 0>, 'stress_exponent': 1.5, 'deformation_exponent': 3.5, 'gbm_mobility': 50, 'gbs_threshold': 0, 'nucleation_efficiency': 5, 'number_of_grains': 3375}"}, "pydrex.mock.PARAMS_KAMINSKI2001_FIG5_LONGDASH": {"fullname": "pydrex.mock.PARAMS_KAMINSKI2001_FIG5_LONGDASH", "modulename": "pydrex.mock", "qualname": "PARAMS_KAMINSKI2001_FIG5_LONGDASH", "kind": "variable", "doc": "

    Values used for the M*=200 test in https://doi.org/10.1016/s0012-821x(01)00356-9.

    \n", "default_value": "{'olivine_fraction': 1, 'enstatite_fraction': 0, 'initial_olivine_fabric': <MineralFabric.olivine_A: 0>, 'stress_exponent': 1.5, 'deformation_exponent': 3.5, 'gbm_mobility': 200, 'gbs_threshold': 0, 'nucleation_efficiency': 5, 'number_of_grains': 3375}"}, "pydrex.mock.PARAMS_KAMINSKI2004_FIG4_TRIANGLES": {"fullname": "pydrex.mock.PARAMS_KAMINSKI2004_FIG4_TRIANGLES", "modulename": "pydrex.mock", "qualname": "PARAMS_KAMINSKI2004_FIG4_TRIANGLES", "kind": "variable", "doc": "

    Values used for the \u03c7=0.4 test in https://doi.org/10.1111/j.1365-246x.2004.02308.x.

    \n", "default_value": "{'olivine_fraction': 1, 'enstatite_fraction': 0, 'initial_olivine_fabric': <MineralFabric.olivine_A: 0>, 'stress_exponent': 1.5, 'deformation_exponent': 3.5, 'gbm_mobility': 125, 'gbs_threshold': 0.4, 'nucleation_efficiency': 5, 'number_of_grains': 4394}"}, "pydrex.mock.PARAMS_KAMINSKI2004_FIG4_SQUARES": {"fullname": "pydrex.mock.PARAMS_KAMINSKI2004_FIG4_SQUARES", "modulename": "pydrex.mock", "qualname": "PARAMS_KAMINSKI2004_FIG4_SQUARES", "kind": "variable", "doc": "

    Values used for the \u03c7=0.2 test in https://doi.org/10.1111/j.1365-246x.2004.02308.x.

    \n", "default_value": "{'olivine_fraction': 1, 'enstatite_fraction': 0, 'initial_olivine_fabric': <MineralFabric.olivine_A: 0>, 'stress_exponent': 1.5, 'deformation_exponent': 3.5, 'gbm_mobility': 125, 'gbs_threshold': 0.2, 'nucleation_efficiency': 5, 'number_of_grains': 4394}"}, "pydrex.mock.PARAMS_KAMINSKI2004_FIG4_CIRCLES": {"fullname": "pydrex.mock.PARAMS_KAMINSKI2004_FIG4_CIRCLES", "modulename": "pydrex.mock", "qualname": "PARAMS_KAMINSKI2004_FIG4_CIRCLES", "kind": "variable", "doc": "

    Values used for the \u03c7=0 test in https://doi.org/10.1111/j.1365-246x.2004.02308.x.

    \n", "default_value": "{'olivine_fraction': 1, 'enstatite_fraction': 0, 'initial_olivine_fabric': <MineralFabric.olivine_A: 0>, 'stress_exponent': 1.5, 'deformation_exponent': 3.5, 'gbm_mobility': 125, 'gbs_threshold': 0, 'nucleation_efficiency': 5, 'number_of_grains': 4394}"}, "pydrex.mock.PARAMS_HEDJAZIAN2017": {"fullname": "pydrex.mock.PARAMS_HEDJAZIAN2017", "modulename": "pydrex.mock", "qualname": "PARAMS_HEDJAZIAN2017", "kind": "variable", "doc": "

    Values used for the MOR model in https://doi.org/10.1016/j.epsl.2016.12.004.

    \n", "default_value": "{'olivine_fraction': 0.7, 'enstatite_fraction': 0.3, 'initial_olivine_fabric': <MineralFabric.olivine_A: 0>, 'stress_exponent': 1.5, 'deformation_exponent': 3.5, 'gbm_mobility': 10, 'gbs_threshold': 0.2, 'nucleation_efficiency': 5, 'number_of_grains': 2197}"}, "pydrex.pathlines": {"fullname": "pydrex.pathlines", "modulename": "pydrex.pathlines", "kind": "module", "doc": "
    \n

    PyDRex: Functions for pathline construction.

    \n
    \n"}, "pydrex.pathlines.get_pathline": {"fullname": "pydrex.pathlines.get_pathline", "modulename": "pydrex.pathlines", "qualname": "get_pathline", "kind": "function", "doc": "

    Determine the pathline for a particle in a steady state flow.

    \n\n

    The pathline will intersect the given point and follow a curve determined by\nthe interpolated velocity gradient.

    \n\n

    Args:\n point (NumPy array) \u2014 coordinates of the point\n interp_velocity (interpolator) \u2014 returns velocity vector at a point\n interp_velocity_gradient (interpolator) \u2014 returns \u2207v (3x3 matrix) at a point\n min_coords (iterable) \u2014 lower bound coordinate of the interpolation grid\n max_coords (iterable) \u2014 upper bound coordinate of the interpolation grid

    \n\n

    Returns a tuple containing the time points and an interpolant that can be used\nto evaluate the pathline position (see scipy.integrate.OdeSolution).

    \n", "signature": "(\tpoint,\tinterp_velocity,\tinterp_velocity_gradient,\tmin_coords,\tmax_coords):", "funcdef": "def"}, "pydrex.stats": {"fullname": "pydrex.stats", "modulename": "pydrex.stats", "kind": "module", "doc": "
    \n

    PyDRex: Statistical methods for orientation and elasticity data.

    \n
    \n"}, "pydrex.stats.resample_orientations": {"fullname": "pydrex.stats.resample_orientations", "modulename": "pydrex.stats", "qualname": "resample_orientations", "kind": "function", "doc": "

    Generate new samples from orientations weighed by the volume distribution.

    \n\n

    If the optional number of samples n_samples is not specified,\nit will be set to the number of original \"grains\" (length of fractions).\nThe argument seed can be used to seed the random number generator.

    \n", "signature": "(orientations, fractions, n_samples=None, seed=None):", "funcdef": "def"}, "pydrex.stats.misorientations_random": {"fullname": "pydrex.stats.misorientations_random", "modulename": "pydrex.stats", "qualname": "misorientations_random", "kind": "function", "doc": "

    Get expected count of misorientation angles for an isotropic aggregate.

    \n\n

    Estimate the expected number of misorientation angles between grains\nthat would fall within $($low, high$)$ in degrees for an aggregate\nwith randomly oriented grains, where low $\u2208 [0, $high$)$,\nand high is bounded by the maximum theoretical misorientation angle\nfor the given symmetry system.

    \n\n

    The optional argument system accepts a tuple of integers (a, b)\nthat specifies the crystal symmetry system according to:

    \n\n
    system  triclinic  monoclinic  orthorhombic  rhombohedral tetragonal hexagonal\n------------------------------------------------------------------------------\na       1          2           2             3            4          6\nb       1          2           4             6            8          12\n\u03b8max    180\u00b0       180\u00b0        120\u00b0          120\u00b0         90\u00b0        90\u00b0\n
    \n\n

    This is identically Table 1 in Grimmer 1979.\nThe orthorhombic system (olivine) is selected by default.

    \n", "signature": "(low, high, system=(2, 4)):", "funcdef": "def"}, "pydrex.stats.point_density": {"fullname": "pydrex.stats.point_density", "modulename": "pydrex.stats", "qualname": "point_density", "kind": "function", "doc": "

    Estimate point density of orientation data on the unit sphere.

    \n\n

    Estimates the density of orientations on the unit sphere by counting the input data\nthat falls within small areas around a uniform grid of spherical counting locations.\nThe input data is expected in cartesian coordinates, and the contouring is performed\nusing kernel functions defined in Vollmer 1995.\nThe following optional parameters control the contouring method:

    \n\n\n\n

    Any other keyword arguments are passed to the kernel function calls.\nMost kernels accept a parameter \u03c3 to control the degree of smoothing.

    \n", "signature": "(\tx_data,\ty_data,\tz_data,\tgridsteps=101,\tweights=1,\tkernel='linear_inverse_kamb',\taxial=True,\t**kwargs):", "funcdef": "def"}, "pydrex.stats.exponential_kamb": {"fullname": "pydrex.stats.exponential_kamb", "modulename": "pydrex.stats", "qualname": "exponential_kamb", "kind": "function", "doc": "

    Kernel function from Vollmer 1995 for exponential smoothing.

    \n", "signature": "(cos_dist, \u03c3=10, axial=True):", "funcdef": "def"}, "pydrex.stats.linear_inverse_kamb": {"fullname": "pydrex.stats.linear_inverse_kamb", "modulename": "pydrex.stats", "qualname": "linear_inverse_kamb", "kind": "function", "doc": "

    Kernel function from Vollmer 1995 for linear smoothing.

    \n", "signature": "(cos_dist, \u03c3=10, axial=True):", "funcdef": "def"}, "pydrex.stats.square_inverse_kamb": {"fullname": "pydrex.stats.square_inverse_kamb", "modulename": "pydrex.stats", "qualname": "square_inverse_kamb", "kind": "function", "doc": "

    Kernel function from Vollmer 1995 for inverse square smoothing.

    \n", "signature": "(cos_dist, \u03c3=10, axial=True):", "funcdef": "def"}, "pydrex.stats.kamb_count": {"fullname": "pydrex.stats.kamb_count", "modulename": "pydrex.stats", "qualname": "kamb_count", "kind": "function", "doc": "

    Original Kamb 1959 kernel function (raw count within radius).

    \n", "signature": "(cos_dist, \u03c3=10, axial=True):", "funcdef": "def"}, "pydrex.stats.schmidt_count": {"fullname": "pydrex.stats.schmidt_count", "modulename": "pydrex.stats", "qualname": "schmidt_count", "kind": "function", "doc": "

    Schmidt (a.k.a. 1%) counting kernel function.

    \n", "signature": "(cos_dist, axial=None):", "funcdef": "def"}, "pydrex.stats.SPHERICAL_COUNTING_KERNELS": {"fullname": "pydrex.stats.SPHERICAL_COUNTING_KERNELS", "modulename": "pydrex.stats", "qualname": "SPHERICAL_COUNTING_KERNELS", "kind": "variable", "doc": "

    Kernel functions that return an un-summed distribution and a normalization factor.

    \n\n

    Supported kernel functions are based on the discussion in\nVollmer 1995.\nKamb methods accept the parameter \u03c3 (default: 10) to control the degree of smoothing.\nValues lower than 3 and higher than 20 are not recommended.

    \n", "default_value": "{'kamb_count': <function kamb_count>, 'schmidt_count': <function schmidt_count>, 'exponential_kamb': <function exponential_kamb>, 'linear_inverse_kamb': <function linear_inverse_kamb>, 'square_inverse_kamb': <function square_inverse_kamb>}"}, "pydrex.tensors": {"fullname": "pydrex.tensors", "modulename": "pydrex.tensors", "kind": "module", "doc": "
    \n

    PyDRex: Tensor operation functions and helpers.

    \n
    \n\n

    For Voigt notation, the symmetric 6x6 matrix representation is used,\nwhich assumes that the fourth order tensor being represented as such is also symmetric.\nThe vectorial notation uses 21 components which are the independent components of the\nsymmetric 6x6 matrix.

    \n"}, "pydrex.tensors.PERMUTATION_SYMBOL": {"fullname": "pydrex.tensors.PERMUTATION_SYMBOL", "modulename": "pydrex.tensors", "qualname": "PERMUTATION_SYMBOL", "kind": "variable", "doc": "

    \n", "default_value": "array([[[0.e+00, 0.e+00, 0.e+00],\n [0.e+00, 0.e+00, 1.e+00],\n [0.e+00, -1.e+00, 0.e+00]],\n\n [[0.e+00, 0.e+00, -1.e+00],\n [0.e+00, 0.e+00, 0.e+00],\n [1.e+00, 0.e+00, 0.e+00]],\n\n [[0.e+00, 1.e+00, 0.e+00],\n [-1.e+00, 0.e+00, 0.e+00],\n [0.e+00, 0.e+00, 0.e+00]]])"}, "pydrex.tensors.voigt_decompose": {"fullname": "pydrex.tensors.voigt_decompose", "modulename": "pydrex.tensors", "qualname": "voigt_decompose", "kind": "function", "doc": "

    Decompose elastic tensor (as 6x6 Voigt matrix) into distinct contractions.

    \n\n

    Return the only two independent contractions of the elastic tensor, given as a 6x6\nVoigt matrix. For the equivalent 4-th order elastic tensor, the contractions are:

    \n\n\n\n

    See Equations 3.4 & 3.5 in Browaeys & Chevrot.

    \n", "signature": "(matrix):", "funcdef": "def"}, "pydrex.tensors.hex_projector": {"fullname": "pydrex.tensors.hex_projector", "modulename": "pydrex.tensors", "qualname": "hex_projector", "kind": "function", "doc": "

    Projector p\u2084 onto hexagonal (a.k.a. transverse isotropy) symmetry.

    \n\n

    See Browaeys & Chevrot.

    \n", "signature": "(x):", "funcdef": "def"}, "pydrex.tensors.upper_tri_to_symmetric": {"fullname": "pydrex.tensors.upper_tri_to_symmetric", "modulename": "pydrex.tensors", "qualname": "upper_tri_to_symmetric", "kind": "function", "doc": "

    Create symmetric array using upper triangle of input array.

    \n\n
    \n
    >>> import numpy as np\n>>> upper_tri_to_symmetric(np.array([\n>>>         [ 1.,  2.,  3.,  4.],\n>>>         [ 0.,  5.,  6.,  7.],\n>>>         [ 0.,  0.,  8.,  9.],\n>>>         [ 9.,  0.,  0., 10.]\n>>> ]))\narray([[ 1.,  2.,  3.,  4.],\n       [ 2.,  5.,  6.,  7.],\n       [ 3.,  6.,  8.,  9.],\n       [ 4.,  7.,  9., 10.]])\n
    \n
    \n", "signature": "(arr):", "funcdef": "def"}, "pydrex.tensors.voigt_to_elastic_tensor": {"fullname": "pydrex.tensors.voigt_to_elastic_tensor", "modulename": "pydrex.tensors", "qualname": "voigt_to_elastic_tensor", "kind": "function", "doc": "

    Create 4-th order elastic tensor from an equivalent Voigt matrix.

    \n\n

    See also: elastic_tensor_to_voigt.

    \n", "signature": "(matrix):", "funcdef": "def"}, "pydrex.tensors.elastic_tensor_to_voigt": {"fullname": "pydrex.tensors.elastic_tensor_to_voigt", "modulename": "pydrex.tensors", "qualname": "elastic_tensor_to_voigt", "kind": "function", "doc": "

    Create a 6x6 Voigt matrix from an equivalent 4-th order elastic tensor.

    \n", "signature": "(tensor):", "funcdef": "def"}, "pydrex.tensors.voigt_matrix_to_vector": {"fullname": "pydrex.tensors.voigt_matrix_to_vector", "modulename": "pydrex.tensors", "qualname": "voigt_matrix_to_vector", "kind": "function", "doc": "

    Create the 21-component Voigt vector equivalent to the 6x6 Voigt matrix.

    \n", "signature": "(matrix):", "funcdef": "def"}, "pydrex.tensors.voigt_vector_to_matrix": {"fullname": "pydrex.tensors.voigt_vector_to_matrix", "modulename": "pydrex.tensors", "qualname": "voigt_vector_to_matrix", "kind": "function", "doc": "

    Create the 6x6 matrix representation of the 21-component Voigt vector.

    \n\n

    See also: voigt_matrix_to_vector.

    \n", "signature": "(vector):", "funcdef": "def"}, "pydrex.tensors.rotate": {"fullname": "pydrex.tensors.rotate", "modulename": "pydrex.tensors", "qualname": "rotate", "kind": "function", "doc": "

    Rotate 4-th order tensor using a 3x3 rotation matrix.

    \n", "signature": "(tensor, rotation):", "funcdef": "def"}, "pydrex.utils": {"fullname": "pydrex.utils", "modulename": "pydrex.utils", "kind": "module", "doc": "
    \n

    PyDRex: Miscellaneous utility methods.

    \n
    \n"}, "pydrex.utils.remove_nans": {"fullname": "pydrex.utils.remove_nans", "modulename": "pydrex.utils", "qualname": "remove_nans", "kind": "function", "doc": "

    Remove NaN values from array.

    \n", "signature": "(a):", "funcdef": "def"}, "pydrex.utils.readable_timestamp": {"fullname": "pydrex.utils.readable_timestamp", "modulename": "pydrex.utils", "qualname": "readable_timestamp", "kind": "function", "doc": "

    Convert timestamp in fractional seconds to human readable format.

    \n", "signature": "(timestamp, tformat='%H:%M:%S'):", "funcdef": "def"}, "pydrex.utils.angle_fse_simpleshear": {"fullname": "pydrex.utils.angle_fse_simpleshear", "modulename": "pydrex.utils", "qualname": "angle_fse_simpleshear", "kind": "function", "doc": "

    Get angle of FSE long axis anticlockwise from the X axis in simple shear.

    \n", "signature": "(strain):", "funcdef": "def"}, "pydrex.velocity_gradients": {"fullname": "pydrex.velocity_gradients", "modulename": "pydrex.velocity_gradients", "kind": "module", "doc": "
    \n

    PyDRex: Steady-state solutions of velocity gradients for various flows.

    \n
    \n"}, "pydrex.velocity_gradients.simple_shear_2d": {"fullname": "pydrex.velocity_gradients.simple_shear_2d", "modulename": "pydrex.velocity_gradients", "qualname": "simple_shear_2d", "kind": "function", "doc": "

    Return simple shear velocity gradient callable f(x) for the given parameters.

    \n", "signature": "(direction, deformation_plane, strain_rate):", "funcdef": "def"}, "pydrex.visualisation": {"fullname": "pydrex.visualisation", "modulename": "pydrex.visualisation", "kind": "module", "doc": "
    \n

    PyDRex: Visualisation functions for test outputs and examples.

    \n
    \n"}, "pydrex.visualisation.polefigures": {"fullname": "pydrex.visualisation.polefigures", "modulename": "pydrex.visualisation", "qualname": "polefigures", "kind": "function", "doc": "

    Plot pole figures of a series of (Nx3x3) orientation matrix stacks.

    \n\n

    Produces [100], [010] and [001] pole figures for (resampled) orientations.\nFor the argument specification, check the output of pydrex-polefigures --help\non the command line.

    \n", "signature": "(\torientations,\tref_axes,\ti_range,\tdensity=False,\tsavefile='polefigures.png',\tstrains=None,\t**kwargs):", "funcdef": "def"}, "pydrex.visualisation.simple_shear_stationary_2d": {"fullname": "pydrex.visualisation.simple_shear_stationary_2d", "modulename": "pydrex.visualisation", "qualname": "simple_shear_stationary_2d", "kind": "function", "doc": "

    Plot diagnostics for stationary A-type olivine 2D simple shear box tests.

    \n", "signature": "(\tstrains,\tangles,\tpoint100_symmetry,\ttarget_angles=None,\tangles_err=None,\tsavefile='pydrex_simple_shear_stationary_2d.png',\tmarkers='.',\t\u03b8_fse=None,\tlabels=None,\ta_type=True):", "funcdef": "def"}, "pydrex.visualisation.corner_flow_2d": {"fullname": "pydrex.visualisation.corner_flow_2d", "modulename": "pydrex.visualisation", "qualname": "corner_flow_2d", "kind": "function", "doc": "

    Plot diagnostics for prescribed path 2D corner flow tests.

    \n", "signature": "(\tx_paths,\tz_paths,\tangles,\tindices,\tdirections,\ttimestamps,\txlabel,\tsavefile='pydrex_corner_2d.png',\tmarkers='.',\tlabels=None,\txlims=None,\tzlims=None,\tcpo_threshold=0.33,\t\u03a0_levels=(0.1, 0.5, 1, 2, 3),\ttick_formatter=<function <lambda>>):", "funcdef": "def"}, "pydrex.visualisation.single_olivineA_simple_shear": {"fullname": "pydrex.visualisation.single_olivineA_simple_shear", "modulename": "pydrex.visualisation", "qualname": "single_olivineA_simple_shear", "kind": "function", "doc": "

    \n", "signature": "(\tinitial_angles,\trotation_rates,\ttarget_rotation_rates,\tsavefile='single_olivineA_simple_shear.png'):", "funcdef": "def"}, "pydrex.vtk_helpers": {"fullname": "pydrex.vtk_helpers", "modulename": "pydrex.vtk_helpers", "kind": "module", "doc": "
    \n

    PyDRex: VTK wrappers and helper functions.

    \n
    \n"}, "pydrex.vtk_helpers.get_output": {"fullname": "pydrex.vtk_helpers.get_output", "modulename": "pydrex.vtk_helpers", "qualname": "get_output", "kind": "function", "doc": "

    Get a reference to an unstructured (XML) VTK grid stored in filename.

    \n\n

    Only supports modern vtk formats, i.e. .vtu and .pvtu files.

    \n", "signature": "(filename):", "funcdef": "def"}, "pydrex.vtk_helpers.read_tuple_array": {"fullname": "pydrex.vtk_helpers.read_tuple_array", "modulename": "pydrex.vtk_helpers", "qualname": "read_tuple_array", "kind": "function", "doc": "

    Read tuples from VTK points into a numpy array.

    \n\n

    Create a numpy array from tuples extracted from a vtkPointData object.\nThe returned array has a shape of either (N, d) for vector data,\nor (N, d, d) for matrix data, where N is the number of VTK nodes\nand d is the dimension (3 by default, or 2 if skip3 is True).

    \n\n

    If skip3 is True, the domain is assumed to be two-dimensional,\nand any values corresponding to a third dimension are skipped.

    \n\n

    Throws a LookupError if the fieldname string does not match any data.

    \n", "signature": "(points, fieldname, skip3=False):", "funcdef": "def"}, "pydrex.vtk_helpers.read_coord_array": {"fullname": "pydrex.vtk_helpers.read_coord_array", "modulename": "pydrex.vtk_helpers", "qualname": "read_coord_array", "kind": "function", "doc": "

    Read coordinates from vtkgrid into a numpy array.

    \n\n

    Create a numpy array with coordinates extracted from a vtk{Uns,S}tructuredGrid\nobject.

    \n\n

    If skip_empty is True (default), columns full of zeros are skipped.\nThese are often present in VTK output files from 2D simulations.

    \n\n

    If depth_conversion is True (default), the last nonzero column is assumed\nto contain height values which are converted to depth values by subtraction\nfrom the maximum value.

    \n", "signature": "(vtkgrid, skip_empty=True, convert_depth=True):", "funcdef": "def"}, "pydrex.vtk_helpers.get_steps": {"fullname": "pydrex.vtk_helpers.get_steps", "modulename": "pydrex.vtk_helpers", "qualname": "get_steps", "kind": "function", "doc": "

    Get forward difference of 2D array a, with repeated last elements.

    \n\n

    The repeated last elements ensure that output and input arrays have equal shape.

    \n\n

    Examples:

    \n\n
    \n
    >>> _get_steps(np.array([1, 2, 3, 4, 5]))\narray([[1, 1, 1, 1, 1]])\n
    \n
    \n\n
    \n
    >>> _get_steps(np.array([[1, 2, 3, 4, 5], [1, 3, 6, 9, 10]]))\narray([[1, 1, 1, 1, 1],\n       [2, 3, 3, 1, 1]])\n
    \n
    \n\n
    \n
    >>> _get_steps(np.array([[1, 2, 3, 4, 5], [1, 3, 6, 9, 10], [1, 0, 0, 0, np.inf]]))\narray([[ 1.,  1.,  1.,  1.,  1.],\n       [ 2.,  3.,  3.,  1.,  1.],\n       [-1.,  0.,  0., inf, nan]])\n
    \n
    \n", "signature": "(a):", "funcdef": "def"}, "tests": {"fullname": "tests", "modulename": "tests", "kind": "module", "doc": "

    PyDRex tests

    \n\n

    Running the tests requires pytest.\nFrom the root of the source tree, run pytest.\nTo print more verbose information (including INFO level logging),\nuse the flag pytest -v.\nThe custom optional flag --outdir=\"OUT\" can be used\nto produce output figures, data dumps and logs and save them in the directory \"OUT\".\nThe value \".\" can be used to save these in the current directory.\nLong tests/examples are disabled by default to prevent clogging up the CI,\nthey can be enabled with --runslow.\nTo mark a test as slow,\nadd the @pytest.mark.slow decorator above its method definition.

    \n\n

    Tests should not produce persistent output by default.\nIf a test method can produce such output for debugging, it should accept the outdir\npositional argument, and check if its value is not None.\nIf outdir is None then no persistent output should be produced.\nIf outdir is a directory path (string):

    \n\n\n"}, "tests.conftest": {"fullname": "tests.conftest", "modulename": "tests.conftest", "kind": "module", "doc": "
    \n

    Configuration and fixtures for PyDRex tests.

    \n
    \n"}, "tests.conftest.pytest_addoption": {"fullname": "tests.conftest.pytest_addoption", "modulename": "tests.conftest", "qualname": "pytest_addoption", "kind": "function", "doc": "

    \n", "signature": "(parser):", "funcdef": "def"}, "tests.conftest.PytestConsoleLogger": {"fullname": "tests.conftest.PytestConsoleLogger", "modulename": "tests.conftest", "qualname": "PytestConsoleLogger", "kind": "class", "doc": "

    Pytest plugin that allows linking up a custom console logger.

    \n", "bases": "_pytest.logging.LoggingPlugin"}, "tests.conftest.PytestConsoleLogger.__init__": {"fullname": "tests.conftest.PytestConsoleLogger.__init__", "modulename": "tests.conftest", "qualname": "PytestConsoleLogger.__init__", "kind": "function", "doc": "

    Create a new plugin to capture log messages.

    \n\n

    The formatter can be safely shared across all handlers so\ncreate a single one for the entire test session here.

    \n", "signature": "(config, *args, **kwargs)"}, "tests.conftest.PytestConsoleLogger.name": {"fullname": "tests.conftest.PytestConsoleLogger.name", "modulename": "tests.conftest", "qualname": "PytestConsoleLogger.name", "kind": "variable", "doc": "

    \n", "default_value": "'pytest-console-logger'"}, "tests.conftest.PytestConsoleLogger.log_cli_handler": {"fullname": "tests.conftest.PytestConsoleLogger.log_cli_handler", "modulename": "tests.conftest", "qualname": "PytestConsoleLogger.log_cli_handler", "kind": "variable", "doc": "

    \n"}, "tests.conftest.PytestConsoleLogger.pytest_runtest_teardown": {"fullname": "tests.conftest.PytestConsoleLogger.pytest_runtest_teardown", "modulename": "tests.conftest", "qualname": "PytestConsoleLogger.pytest_runtest_teardown", "kind": "function", "doc": "

    \n", "signature": "(self, item):", "funcdef": "def"}, "tests.conftest.pytest_configure": {"fullname": "tests.conftest.pytest_configure", "modulename": "tests.conftest", "qualname": "pytest_configure", "kind": "function", "doc": "

    \n", "signature": "(config):", "funcdef": "def"}, "tests.conftest.pytest_collection_modifyitems": {"fullname": "tests.conftest.pytest_collection_modifyitems", "modulename": "tests.conftest", "qualname": "pytest_collection_modifyitems", "kind": "function", "doc": "

    \n", "signature": "(config, items):", "funcdef": "def"}, "tests.conftest.outdir": {"fullname": "tests.conftest.outdir", "modulename": "tests.conftest", "qualname": "outdir", "kind": "function", "doc": "

    \n", "signature": "(request):", "funcdef": "def"}, "tests.conftest.ncpus": {"fullname": "tests.conftest.ncpus", "modulename": "tests.conftest", "qualname": "ncpus", "kind": "function", "doc": "

    \n", "signature": "(request):", "funcdef": "def"}, "tests.conftest.console_handler": {"fullname": "tests.conftest.console_handler", "modulename": "tests.conftest", "qualname": "console_handler", "kind": "function", "doc": "

    \n", "signature": "(request):", "funcdef": "def"}, "tests.conftest.params_Fraters2021": {"fullname": "tests.conftest.params_Fraters2021", "modulename": "tests.conftest", "qualname": "params_Fraters2021", "kind": "function", "doc": "

    \n", "signature": "():", "funcdef": "def"}, "tests.conftest.params_Kaminski2001_fig5_solid": {"fullname": "tests.conftest.params_Kaminski2001_fig5_solid", "modulename": "tests.conftest", "qualname": "params_Kaminski2001_fig5_solid", "kind": "function", "doc": "

    \n", "signature": "():", "funcdef": "def"}, "tests.conftest.params_Kaminski2001_fig5_shortdash": {"fullname": "tests.conftest.params_Kaminski2001_fig5_shortdash", "modulename": "tests.conftest", "qualname": "params_Kaminski2001_fig5_shortdash", "kind": "function", "doc": "

    \n", "signature": "():", "funcdef": "def"}, "tests.conftest.params_Kaminski2001_fig5_longdash": {"fullname": "tests.conftest.params_Kaminski2001_fig5_longdash", "modulename": "tests.conftest", "qualname": "params_Kaminski2001_fig5_longdash", "kind": "function", "doc": "

    \n", "signature": "():", "funcdef": "def"}, "tests.conftest.params_Kaminski2004_fig4_triangles": {"fullname": "tests.conftest.params_Kaminski2004_fig4_triangles", "modulename": "tests.conftest", "qualname": "params_Kaminski2004_fig4_triangles", "kind": "function", "doc": "

    \n", "signature": "():", "funcdef": "def"}, "tests.conftest.params_Kaminski2004_fig4_squares": {"fullname": "tests.conftest.params_Kaminski2004_fig4_squares", "modulename": "tests.conftest", "qualname": "params_Kaminski2004_fig4_squares", "kind": "function", "doc": "

    \n", "signature": "():", "funcdef": "def"}, "tests.conftest.params_Kaminski2004_fig4_circles": {"fullname": "tests.conftest.params_Kaminski2004_fig4_circles", "modulename": "tests.conftest", "qualname": "params_Kaminski2004_fig4_circles", "kind": "function", "doc": "

    \n", "signature": "():", "funcdef": "def"}, "tests.conftest.params_Hedjazian2017": {"fullname": "tests.conftest.params_Hedjazian2017", "modulename": "tests.conftest", "qualname": "params_Hedjazian2017", "kind": "function", "doc": "

    \n", "signature": "():", "funcdef": "def"}, "tests.conftest.hkl": {"fullname": "tests.conftest.hkl", "modulename": "tests.conftest", "qualname": "hkl", "kind": "function", "doc": "

    \n", "signature": "(request):", "funcdef": "def"}, "tests.conftest.ref_axes": {"fullname": "tests.conftest.ref_axes", "modulename": "tests.conftest", "qualname": "ref_axes", "kind": "function", "doc": "

    \n", "signature": "(request):", "funcdef": "def"}, "tests.conftest.seeds": {"fullname": "tests.conftest.seeds", "modulename": "tests.conftest", "qualname": "seeds", "kind": "function", "doc": "

    1000 unique seeds for ensemble runs that need an RNG seed.

    \n", "signature": "():", "funcdef": "def"}, "tests.conftest.seed": {"fullname": "tests.conftest.seed", "modulename": "tests.conftest", "qualname": "seed", "kind": "function", "doc": "

    Default seed for test RNG.

    \n", "signature": "():", "funcdef": "def"}, "tests.conftest.seeds_nearX45": {"fullname": "tests.conftest.seeds_nearX45", "modulename": "tests.conftest", "qualname": "seeds_nearX45", "kind": "function", "doc": "

    41 seeds which have the initial hexagonal symmetry axis near 45\u00b0 from X.

    \n", "signature": "():", "funcdef": "def"}, "tests.test_config": {"fullname": "tests.test_config", "modulename": "tests.test_config", "kind": "module", "doc": "
    \n

    PyDRex: tests for configuration file format.

    \n
    \n"}, "tests.test_config.test_specfile": {"fullname": "tests.test_config.test_specfile", "modulename": "tests.test_config", "qualname": "test_specfile", "kind": "function", "doc": "

    Test TOML spec file parsing.

    \n", "signature": "():", "funcdef": "def"}, "tests.test_core": {"fullname": "tests.test_core", "modulename": "tests.test_core", "kind": "module", "doc": "
    \n

    PyDRex: tests for core D-Rex routines.

    \n
    \n"}, "tests.test_core.SUBDIR": {"fullname": "tests.test_core.SUBDIR", "modulename": "tests.test_core", "qualname": "SUBDIR", "kind": "variable", "doc": "

    \n", "default_value": "'core'"}, "tests.test_core.TestSimpleShearOPX": {"fullname": "tests.test_core.TestSimpleShearOPX", "modulename": "tests.test_core", "qualname": "TestSimpleShearOPX", "kind": "class", "doc": "

    Single-grain orthopyroxene crystallographic rotation rate tests.

    \n"}, "tests.test_core.TestSimpleShearOPX.class_id": {"fullname": "tests.test_core.TestSimpleShearOPX.class_id", "modulename": "tests.test_core", "qualname": "TestSimpleShearOPX.class_id", "kind": "variable", "doc": "

    \n", "default_value": "'simple_shear_OPX'"}, "tests.test_core.TestSimpleShearOPX.test_shear_dudz": {"fullname": "tests.test_core.TestSimpleShearOPX.test_shear_dudz", "modulename": "tests.test_core", "qualname": "TestSimpleShearOPX.test_shear_dudz", "kind": "function", "doc": "

    \n", "signature": "(self, outdir):", "funcdef": "def"}, "tests.test_core.TestSimpleShearOPX.test_shear_dvdx": {"fullname": "tests.test_core.TestSimpleShearOPX.test_shear_dvdx", "modulename": "tests.test_core", "qualname": "TestSimpleShearOPX.test_shear_dvdx", "kind": "function", "doc": "

    \n", "signature": "(self, outdir):", "funcdef": "def"}, "tests.test_core.TestSimpleShearOlivineA": {"fullname": "tests.test_core.TestSimpleShearOlivineA", "modulename": "tests.test_core", "qualname": "TestSimpleShearOlivineA", "kind": "class", "doc": "

    Single-grain A-type olivine analytical rotation rate tests.

    \n"}, "tests.test_core.TestSimpleShearOlivineA.class_id": {"fullname": "tests.test_core.TestSimpleShearOlivineA.class_id", "modulename": "tests.test_core", "qualname": "TestSimpleShearOlivineA.class_id", "kind": "variable", "doc": "

    \n", "default_value": "'simple_shear_Ol'"}, "tests.test_core.TestSimpleShearOlivineA.test_shear_dvdx_slip_010_100": {"fullname": "tests.test_core.TestSimpleShearOlivineA.test_shear_dvdx_slip_010_100", "modulename": "tests.test_core", "qualname": "TestSimpleShearOlivineA.test_shear_dvdx_slip_010_100", "kind": "function", "doc": "

    Single grain of olivine A-type, simple shear on (010)[100].

    \n\n

    Velocity gradient:\n$$\\bm{L} = \\begin{bmatrix} 0 & 0 & 0 \\cr 2 & 0 & 0 \\cr 0 & 0 & 0 \\end{bmatrix}$$

    \n", "signature": "(self, outdir):", "funcdef": "def"}, "tests.test_core.TestSimpleShearOlivineA.test_shear_dudz_slip_001_100": {"fullname": "tests.test_core.TestSimpleShearOlivineA.test_shear_dudz_slip_001_100", "modulename": "tests.test_core", "qualname": "TestSimpleShearOlivineA.test_shear_dudz_slip_001_100", "kind": "function", "doc": "

    Single grain of olivine A-type, simple shear on (001)[100].

    \n\n

    Velocity gradient:\n$$\\bm{L} = \\begin{bmatrix} 0 & 0 & 2 \\cr 0 & 0 & 0 \\cr 0 & 0 & 0 \\end{bmatrix}$$

    \n", "signature": "(self, outdir):", "funcdef": "def"}, "tests.test_core.TestSimpleShearOlivineA.test_shear_dwdx_slip_001_100": {"fullname": "tests.test_core.TestSimpleShearOlivineA.test_shear_dwdx_slip_001_100", "modulename": "tests.test_core", "qualname": "TestSimpleShearOlivineA.test_shear_dwdx_slip_001_100", "kind": "function", "doc": "

    Single grain of olivine A-type, simple shear on (001)[100].

    \n\n

    Velocity gradient:\n$$\\bm{L} = \\begin{bmatrix} 0 & 0 & 0 \\cr 0 & 0 & 0 \\cr 2 & 0 & 0 \\end{bmatrix}$$

    \n", "signature": "(self, outdir):", "funcdef": "def"}, "tests.test_core.TestSimpleShearOlivineA.test_shear_dvdz_slip_010_001": {"fullname": "tests.test_core.TestSimpleShearOlivineA.test_shear_dvdz_slip_010_001", "modulename": "tests.test_core", "qualname": "TestSimpleShearOlivineA.test_shear_dvdz_slip_010_001", "kind": "function", "doc": "

    Single grain of olivine A-type, simple shear on (010)[001].

    \n\n

    Velocity gradient:\n$$\\bm{L} = \\begin{bmatrix} 0 & 0 & 0 \\cr 0 & 0 & 2 \\cr 0 & 0 & 0 \\end{bmatrix}$$

    \n", "signature": "(self, outdir):", "funcdef": "def"}, "tests.test_corner_flow_2d": {"fullname": "tests.test_corner_flow_2d", "modulename": "tests.test_corner_flow_2d", "kind": "module", "doc": "
    \n

    PyDRex: 2D corner flow tests

    \n
    \n\n

    The flow field is defined by:\n$$\n\\bm{u} = \\frac{dr}{dt} \\bm{\\hat{r}} + r \\frac{d\u03b8}{dt} \\bm{\\hat{\u03b8}}\n= \\frac{2 U}{\u03c0}(\u03b8\\sin\u03b8 - \\cos\u03b8) \u22c5 \\bm{\\hat{r}} + \\frac{2 U}{\u03c0}\u03b8\\cos\u03b8 \u22c5 \\bm{\\hat{\u03b8}}\n$$\nwhere $\u03b8 = 0$ points vertically downwards along the ridge axis\nand $\u03b8 = \u03c0/2$ points along the surface. $U$ is the half spreading velocity.\nStreamlines for the flow obey:\n$$\n\u03c8 = \\frac{2 U r}{\u03c0}\u03b8\\cos\u03b8\n$$\nand are related to the velocity through:\n$$\n\\bm{u} = -\\frac{1}{r} \u22c5 \\frac{d\u03c8}{d\u03b8} \u22c5 \\bm{\\hat{r}} + \\frac{d\u03c8}{dr}\\bm{\\hat{\u03b8}}\n$$\nConversion to Cartesian ($x,y,z$) coordinates yields:\n$$\n\\bm{u} = \\frac{2U}{\u03c0} \\left[\n\\tan^{-1}\\left(\\frac{x}{-z}\\right) + \\frac{xz}{x^{2} + z^{2}} \\right] \\bm{\\hat{x}} +\n\\frac{2U}{\u03c0} \\frac{z^{2}}{x^{2} + z^{2}} \\bm{\\hat{z}}\n$$\nwhere\n\\begin{align*}\nx &= r \\sin\u03b8 \\cr\nz &= -r \\cos\u03b8\n\\end{align*}\nand the velocity gradient is:\n$$\nL = \\frac{4 U}{\u03c0{(x^{2}+z^{2})}^{2}} \u22c5\n\\begin{bmatrix}\n -x^{2}z & 0 & x^{3} \\cr\n 0 & 0 & 0 \\cr\n -xz^{2} & 0 & x^{2}z\n\\end{bmatrix}\n$$

    \n\n

    See also Fig. 5 in Kaminski & Ribe, 2002.

    \n"}, "tests.test_corner_flow_2d.get_velocity": {"fullname": "tests.test_corner_flow_2d.get_velocity", "modulename": "tests.test_corner_flow_2d", "qualname": "get_velocity", "kind": "function", "doc": "

    Return velocity in a corner flow (Cartesian coordinate basis).

    \n", "signature": "(x, z, plate_velocity):", "funcdef": "def"}, "tests.test_corner_flow_2d.get_velocity_gradient": {"fullname": "tests.test_corner_flow_2d.get_velocity_gradient", "modulename": "tests.test_corner_flow_2d", "qualname": "get_velocity_gradient", "kind": "function", "doc": "

    Return velocity gradient in a corner flow (Cartesian coordinate basis).

    \n", "signature": "(x, z, plate_velocity):", "funcdef": "def"}, "tests.test_corner_flow_2d.TestOlivineA": {"fullname": "tests.test_corner_flow_2d.TestOlivineA", "modulename": "tests.test_corner_flow_2d", "qualname": "TestOlivineA", "kind": "class", "doc": "

    Tests for pure A-type olivine polycrystals in 2D corner flows.

    \n"}, "tests.test_corner_flow_2d.TestOlivineA.test_corner_prescribed_init_isotropic": {"fullname": "tests.test_corner_flow_2d.TestOlivineA.test_corner_prescribed_init_isotropic", "modulename": "tests.test_corner_flow_2d", "qualname": "TestOlivineA.test_corner_prescribed_init_isotropic", "kind": "function", "doc": "

    Test CPO evolution in prescribed 2D corner flow.

    \n\n

    Initial condition: random orientations and uniform volumes in all Minerals.

    \n\n

    Plate velocity: 2 cm/yr

    \n", "signature": "(self, params_Kaminski2001_fig5_shortdash, seed, outdir):", "funcdef": "def"}, "tests.test_diagnostics": {"fullname": "tests.test_diagnostics", "modulename": "tests.test_diagnostics", "kind": "module", "doc": "
    \n

    PyDRex: tests for texture diagnostics.

    \n
    \n"}, "tests.test_diagnostics.TestSymmetryPGR": {"fullname": "tests.test_diagnostics.TestSymmetryPGR", "modulename": "tests.test_diagnostics", "qualname": "TestSymmetryPGR", "kind": "class", "doc": "

    Test Point-Girdle-Random (eigenvalue) symmetry diagnostics.

    \n"}, "tests.test_diagnostics.TestSymmetryPGR.test_pointX": {"fullname": "tests.test_diagnostics.TestSymmetryPGR.test_pointX", "modulename": "tests.test_diagnostics", "qualname": "TestSymmetryPGR.test_pointX", "kind": "function", "doc": "

    Test diagnostics of point symmetry aligned to the X axis.

    \n", "signature": "(self):", "funcdef": "def"}, "tests.test_diagnostics.TestSymmetryPGR.test_random": {"fullname": "tests.test_diagnostics.TestSymmetryPGR.test_random", "modulename": "tests.test_diagnostics", "qualname": "TestSymmetryPGR.test_random", "kind": "function", "doc": "

    Test diagnostics of random grain orientations.

    \n", "signature": "(self):", "funcdef": "def"}, "tests.test_diagnostics.TestSymmetryPGR.test_girdle": {"fullname": "tests.test_diagnostics.TestSymmetryPGR.test_girdle", "modulename": "tests.test_diagnostics", "qualname": "TestSymmetryPGR.test_girdle", "kind": "function", "doc": "

    Test diagnostics of girdled orientations.

    \n", "signature": "(self):", "funcdef": "def"}, "tests.test_diagnostics.TestVolumeWeighting": {"fullname": "tests.test_diagnostics.TestVolumeWeighting", "modulename": "tests.test_diagnostics", "qualname": "TestVolumeWeighting", "kind": "class", "doc": "

    Tests for volumetric resampling of orientation data.

    \n"}, "tests.test_diagnostics.TestVolumeWeighting.test_upsample": {"fullname": "tests.test_diagnostics.TestVolumeWeighting.test_upsample", "modulename": "tests.test_diagnostics", "qualname": "TestVolumeWeighting.test_upsample", "kind": "function", "doc": "

    Test upsampling of the raw orientation data.

    \n", "signature": "(self):", "funcdef": "def"}, "tests.test_diagnostics.TestVolumeWeighting.test_downsample": {"fullname": "tests.test_diagnostics.TestVolumeWeighting.test_downsample", "modulename": "tests.test_diagnostics", "qualname": "TestVolumeWeighting.test_downsample", "kind": "function", "doc": "

    Test downsampling of orientation data.

    \n", "signature": "(self):", "funcdef": "def"}, "tests.test_diagnostics.TestBinghamStats": {"fullname": "tests.test_diagnostics.TestBinghamStats", "modulename": "tests.test_diagnostics", "qualname": "TestBinghamStats", "kind": "class", "doc": "

    Tests for antipodally symmetric (bingham) statistics.

    \n"}, "tests.test_diagnostics.TestBinghamStats.test_average_0": {"fullname": "tests.test_diagnostics.TestBinghamStats.test_average_0", "modulename": "tests.test_diagnostics", "qualname": "TestBinghamStats.test_average_0", "kind": "function", "doc": "

    Test bingham average of vectors aligned to the reference frame.

    \n", "signature": "(self):", "funcdef": "def"}, "tests.test_diagnostics.TestBinghamStats.test_average_twopoles90Z": {"fullname": "tests.test_diagnostics.TestBinghamStats.test_average_twopoles90Z", "modulename": "tests.test_diagnostics", "qualname": "TestBinghamStats.test_average_twopoles90Z", "kind": "function", "doc": "

    Test bingham average of vectors rotated by \u00b190\u00b0 around Z.

    \n", "signature": "(self):", "funcdef": "def"}, "tests.test_diagnostics.TestBinghamStats.test_average_spread10X": {"fullname": "tests.test_diagnostics.TestBinghamStats.test_average_spread10X", "modulename": "tests.test_diagnostics", "qualname": "TestBinghamStats.test_average_spread10X", "kind": "function", "doc": "

    Test bingham average of vectors spread within 10\u00b0 of the \u00b1X-axis.

    \n", "signature": "(self):", "funcdef": "def"}, "tests.test_diagnostics.TestMIndex": {"fullname": "tests.test_diagnostics.TestMIndex", "modulename": "tests.test_diagnostics", "qualname": "TestMIndex", "kind": "class", "doc": "

    Tests for the M-index texture strength diagnostic.

    \n"}, "tests.test_diagnostics.TestMIndex.test_texture_uniform": {"fullname": "tests.test_diagnostics.TestMIndex.test_texture_uniform", "modulename": "tests.test_diagnostics", "qualname": "TestMIndex.test_texture_uniform", "kind": "function", "doc": "

    Test M-index for random (uniform distribution) grain orientations.

    \n", "signature": "(self):", "funcdef": "def"}, "tests.test_diagnostics.TestMIndex.test_texture_spread10X": {"fullname": "tests.test_diagnostics.TestMIndex.test_texture_spread10X", "modulename": "tests.test_diagnostics", "qualname": "TestMIndex.test_texture_spread10X", "kind": "function", "doc": "

    Test M-index for grains spread within 10\u00b0 of the \u00b1X axis.

    \n", "signature": "(self):", "funcdef": "def"}, "tests.test_diagnostics.TestMIndex.test_texture_spread30X": {"fullname": "tests.test_diagnostics.TestMIndex.test_texture_spread30X", "modulename": "tests.test_diagnostics", "qualname": "TestMIndex.test_texture_spread30X", "kind": "function", "doc": "

    Test M-index for grains spread within 45\u00b0 of the \u00b1X axis.

    \n", "signature": "(self):", "funcdef": "def"}, "tests.test_diagnostics.TestMIndex.test_textures_increasing": {"fullname": "tests.test_diagnostics.TestMIndex.test_textures_increasing", "modulename": "tests.test_diagnostics", "qualname": "TestMIndex.test_textures_increasing", "kind": "function", "doc": "

    Test M-index for textures of increasing strength.

    \n", "signature": "(self):", "funcdef": "def"}, "tests.test_diagnostics.TestMIndex.test_texture_girdle": {"fullname": "tests.test_diagnostics.TestMIndex.test_texture_girdle", "modulename": "tests.test_diagnostics", "qualname": "TestMIndex.test_texture_girdle", "kind": "function", "doc": "

    Test M-index for girdled texture.

    \n", "signature": "(self):", "funcdef": "def"}, "tests.test_doctests": {"fullname": "tests.test_doctests", "modulename": "tests.test_doctests", "kind": "module", "doc": "
    \n

    PyDRex: Run doctests for applicable modules.

    \n
    \n"}, "tests.test_doctests.test_doctests": {"fullname": "tests.test_doctests.test_doctests", "modulename": "tests.test_doctests", "qualname": "test_doctests", "kind": "function", "doc": "

    Run doctests as well.

    \n", "signature": "():", "funcdef": "def"}, "tests.test_geometry": {"fullname": "tests.test_geometry", "modulename": "tests.test_geometry", "kind": "module", "doc": "
    \n

    PyDRex: Tests for geometric conversions and projections.

    \n
    \n"}, "tests.test_geometry.test_poles_example": {"fullname": "tests.test_geometry.test_poles_example", "modulename": "tests.test_geometry", "qualname": "test_poles_example", "kind": "function", "doc": "

    Test poles (directions of crystallographic axes) of example data.

    \n", "signature": "(hkl, ref_axes):", "funcdef": "def"}, "tests.test_geometry.test_lambert_equal_area": {"fullname": "tests.test_geometry.test_lambert_equal_area", "modulename": "tests.test_geometry", "qualname": "test_lambert_equal_area", "kind": "function", "doc": "

    Test Lambert equal area projection.

    \n", "signature": "(seed):", "funcdef": "def"}, "tests.test_scsv": {"fullname": "tests.test_scsv", "modulename": "tests.test_scsv", "kind": "module", "doc": "
    \n

    PyDRex: tests for the SCSV plain text file format.

    \n
    \n"}, "tests.test_scsv.test_validate_schema": {"fullname": "tests.test_scsv.test_validate_schema", "modulename": "tests.test_scsv", "qualname": "test_validate_schema", "kind": "function", "doc": "

    Test SCSV schema validation.

    \n", "signature": "(console_handler):", "funcdef": "def"}, "tests.test_scsv.test_read_specfile": {"fullname": "tests.test_scsv.test_read_specfile", "modulename": "tests.test_scsv", "qualname": "test_read_specfile", "kind": "function", "doc": "

    Test SCSV spec file parsing.

    \n", "signature": "():", "funcdef": "def"}, "tests.test_scsv.test_save_specfile": {"fullname": "tests.test_scsv.test_save_specfile", "modulename": "tests.test_scsv", "qualname": "test_save_specfile", "kind": "function", "doc": "

    Test SCSV spec file reproduction.

    \n", "signature": "(outdir):", "funcdef": "def"}, "tests.test_scsv.test_read_Kaminski2002": {"fullname": "tests.test_scsv.test_read_Kaminski2002", "modulename": "tests.test_scsv", "qualname": "test_read_Kaminski2002", "kind": "function", "doc": "

    \n", "signature": "():", "funcdef": "def"}, "tests.test_scsv.test_read_Kaminski2004": {"fullname": "tests.test_scsv.test_read_Kaminski2004", "modulename": "tests.test_scsv", "qualname": "test_read_Kaminski2004", "kind": "function", "doc": "

    \n", "signature": "():", "funcdef": "def"}, "tests.test_scsv.test_read_Skemer2016": {"fullname": "tests.test_scsv.test_read_Skemer2016", "modulename": "tests.test_scsv", "qualname": "test_read_Skemer2016", "kind": "function", "doc": "

    \n", "signature": "():", "funcdef": "def"}, "tests.test_simple_shear_2d": {"fullname": "tests.test_simple_shear_2d", "modulename": "tests.test_simple_shear_2d", "kind": "module", "doc": "
    \n

    PyDRex: 2D simple shear tests.

    \n
    \n"}, "tests.test_simple_shear_2d.SUBDIR": {"fullname": "tests.test_simple_shear_2d.SUBDIR", "modulename": "tests.test_simple_shear_2d", "qualname": "SUBDIR", "kind": "variable", "doc": "

    \n", "default_value": "'2d_simple_shear'"}, "tests.test_simple_shear_2d.TestOlivineA": {"fullname": "tests.test_simple_shear_2d.TestOlivineA", "modulename": "tests.test_simple_shear_2d", "qualname": "TestOlivineA", "kind": "class", "doc": "

    Tests for A-type olivine polycrystals in 2D simple shear.

    \n"}, "tests.test_simple_shear_2d.TestOlivineA.class_id": {"fullname": "tests.test_simple_shear_2d.TestOlivineA.class_id", "modulename": "tests.test_simple_shear_2d", "qualname": "TestOlivineA.class_id", "kind": "variable", "doc": "

    \n", "default_value": "'olivineA'"}, "tests.test_simple_shear_2d.TestOlivineA.get_position": {"fullname": "tests.test_simple_shear_2d.TestOlivineA.get_position", "modulename": "tests.test_simple_shear_2d", "qualname": "TestOlivineA.get_position", "kind": "function", "doc": "

    \n", "signature": "(cls, t):", "funcdef": "def"}, "tests.test_simple_shear_2d.TestOlivineA.run": {"fullname": "tests.test_simple_shear_2d.TestOlivineA.run", "modulename": "tests.test_simple_shear_2d", "qualname": "TestOlivineA.run", "kind": "function", "doc": "

    Reusable logic for 2D olivine simple shear tests.

    \n\n

    Always returns a tuple with 4 elements\n(mineral, mean_angles, texture_symmetry, \u03b8_fse),\nbut if return_fse is None then the last tuple element is also None.

    \n", "signature": "(\tcls,\tparams,\ttimestamps,\tstrain_rate,\tget_velocity_gradient,\tshear_direction,\tseed=None,\tlog_param=None,\tuse_bingham_average=False,\treturn_fse=True):", "funcdef": "def"}, "tests.test_simple_shear_2d.TestOlivineA.postprocess": {"fullname": "tests.test_simple_shear_2d.TestOlivineA.postprocess", "modulename": "tests.test_simple_shear_2d", "qualname": "TestOlivineA.postprocess", "kind": "function", "doc": "

    Reusable postprocessing routine for olivine 2D simple shear simulations.

    \n", "signature": "(\tcls,\tstrains,\tangles,\tpoint100_symmetry,\t\u03b8_fse,\tlabels,\tmarkers,\toutdir,\tout_basepath,\ttarget_interpolator=None):", "funcdef": "def"}, "tests.test_simple_shear_2d.TestOlivineA.interp_GBM_Kaminski2001": {"fullname": "tests.test_simple_shear_2d.TestOlivineA.interp_GBM_Kaminski2001", "modulename": "tests.test_simple_shear_2d", "qualname": "TestOlivineA.interp_GBM_Kaminski2001", "kind": "function", "doc": "

    Interpolate Kaminski & Ribe, 2001 data to get target angles at strains.

    \n", "signature": "(cls, strains):", "funcdef": "def"}, "tests.test_simple_shear_2d.TestOlivineA.interp_GBS_Kaminski2004": {"fullname": "tests.test_simple_shear_2d.TestOlivineA.interp_GBS_Kaminski2004", "modulename": "tests.test_simple_shear_2d", "qualname": "TestOlivineA.interp_GBS_Kaminski2004", "kind": "function", "doc": "

    Interpolate Kaminski & Ribe, 2001 data to get target angles at strains.

    \n", "signature": "(cls, strains):", "funcdef": "def"}, "tests.test_simple_shear_2d.TestOlivineA.test_dvdx_GBM_ensemble": {"fullname": "tests.test_simple_shear_2d.TestOlivineA.test_dvdx_GBM_ensemble", "modulename": "tests.test_simple_shear_2d", "qualname": "TestOlivineA.test_dvdx_GBM_ensemble", "kind": "function", "doc": "

    Test a-axis alignment to shear in Y direction (init. SCCS near 45\u00b0 from X).

    \n\n

    Velocity gradient:\n$$\\bm{L} = \\begin{bmatrix} 0 & 0 & 0 \\cr 2 & 0 & 0 \\cr 0 & 0 & 0 \\end{bmatrix}$$

    \n\n

    Tests the effect of grain boundary migration, similar to Fig. 5 in\nKaminski 2001.

    \n", "signature": "(\tself,\tparams_Kaminski2001_fig5_solid,\tparams_Kaminski2001_fig5_shortdash,\tparams_Kaminski2001_fig5_longdash,\tseeds_nearX45,\toutdir,\tncpus):", "funcdef": "def"}, "tests.test_simple_shear_2d.TestOlivineA.test_dudz_GBS_ensemble": {"fullname": "tests.test_simple_shear_2d.TestOlivineA.test_dudz_GBS_ensemble", "modulename": "tests.test_simple_shear_2d", "qualname": "TestOlivineA.test_dudz_GBS_ensemble", "kind": "function", "doc": "

    Test a-axis alignment to shear in X direction (init. SCCS near 45\u00b0 from X).

    \n\n

    Velocity gradient:\n$$\\bm{L} = \\begin{bmatrix} 0 & 0 & 2 \\cr 0 & 0 & 0 \\cr 0 & 0 & 0 \\end{bmatrix}$$

    \n", "signature": "(\tself,\tparams_Kaminski2004_fig4_circles,\tparams_Kaminski2004_fig4_squares,\tparams_Kaminski2004_fig4_triangles,\tseeds_nearX45,\toutdir,\tncpus):", "funcdef": "def"}, "tests.test_simple_shear_2d.TestOlivineA.test_boundary_mobility": {"fullname": "tests.test_simple_shear_2d.TestOlivineA.test_boundary_mobility", "modulename": "tests.test_simple_shear_2d", "qualname": "TestOlivineA.test_boundary_mobility", "kind": "function", "doc": "

    Test that the grain boundary mobility parameter has an effect.

    \n", "signature": "(self, seed, outdir):", "funcdef": "def"}, "tests.test_simple_shear_2d.TestOlivineA.test_boudary_sliding": {"fullname": "tests.test_simple_shear_2d.TestOlivineA.test_boudary_sliding", "modulename": "tests.test_simple_shear_2d", "qualname": "TestOlivineA.test_boudary_sliding", "kind": "function", "doc": "

    Test that the grain boundary sliding parameter has an effect.

    \n", "signature": "(self, seed, outdir):", "funcdef": "def"}, "tests.test_tensors": {"fullname": "tests.test_tensors", "modulename": "tests.test_tensors", "kind": "module", "doc": "
    \n

    PyDRex: Tests for tensor operations.

    \n
    \n"}, "tests.test_tensors.test_voigt_decompose": {"fullname": "tests.test_tensors.test_voigt_decompose", "modulename": "tests.test_tensors", "qualname": "test_voigt_decompose", "kind": "function", "doc": "

    Test decomposition of Voigt 6x6 matrix into distinct contractions.

    \n", "signature": "():", "funcdef": "def"}, "tests.test_tensors.test_voigt_tensor": {"fullname": "tests.test_tensors.test_voigt_tensor", "modulename": "tests.test_tensors", "qualname": "test_voigt_tensor", "kind": "function", "doc": "

    Test elasticity tensor <-> 6x6 Voigt matrix conversions.

    \n", "signature": "():", "funcdef": "def"}, "tests.test_tensors.test_voigt_to_vector": {"fullname": "tests.test_tensors.test_voigt_to_vector", "modulename": "tests.test_tensors", "qualname": "test_voigt_to_vector", "kind": "function", "doc": "

    Test Voigt vector construction.

    \n", "signature": "():", "funcdef": "def"}, "tests.test_vtk_helpers": {"fullname": "tests.test_vtk_helpers", "modulename": "tests.test_vtk_helpers", "kind": "module", "doc": "
    \n

    PyDRex: Tests for VTK readers and helpers.

    \n
    \n"}, "tests.test_vtk_helpers.test_vtk_2d_array_shapes": {"fullname": "tests.test_vtk_helpers.test_vtk_2d_array_shapes", "modulename": "tests.test_vtk_helpers", "qualname": "test_vtk_2d_array_shapes", "kind": "function", "doc": "

    \n", "signature": "():", "funcdef": "def"}}, "docInfo": {"pydrex": {"qualname": 0, "fullname": 1, "annotation": 0, "default_value": 0, "signature": 0, "bases": 0, "doc": 1384}, "pydrex.axes": {"qualname": 0, "fullname": 2, "annotation": 0, "default_value": 0, "signature": 0, "bases": 0, "doc": 12}, "pydrex.axes.PoleFigureAxes": {"qualname": 1, "fullname": 3, "annotation": 0, "default_value": 0, "signature": 0, "bases": 4, "doc": 54}, "pydrex.axes.PoleFigureAxes.name": {"qualname": 2, "fullname": 4, "annotation": 0, "default_value": 6, "signature": 0, "bases": 0, "doc": 3}, "pydrex.axes.PoleFigureAxes.polefigure": {"qualname": 2, "fullname": 4, "annotation": 0, "default_value": 0, "signature": 92, "bases": 0, "doc": 148}, "pydrex.axes.PoleFigureAxes.set": {"qualname": 2, "fullname": 4, "annotation": 0, "default_value": 0, "signature": 833, "bases": 0, "doc": 251}, "pydrex.cli": {"qualname": 0, "fullname": 2, "annotation": 0, "default_value": 0, "signature": 0, "bases": 0, "doc": 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1}}}}}}}}}, "i": {"docs": {}, "df": 0, "e": {"docs": {}, "df": 0, "t": {"docs": {"pydrex.logger": {"tf": 1.4142135623730951}}, "df": 1}}}, "o": {"docs": {}, "df": 0, "t": {"docs": {"pydrex.logger": {"tf": 5.656854249492381}, "pydrex.minerals.Mineral": {"tf": 1.4142135623730951}}, "df": 2}}}}}}}, "pipeline": ["trimmer"], "_isPrebuiltIndex": true}; + /** pdoc search index */const docs = {"version": "0.9.5", "fields": ["qualname", "fullname", "annotation", "default_value", "signature", "bases", "doc"], "ref": "fullname", "documentStore": {"docs": {"pydrex": {"fullname": "pydrex", "modulename": "pydrex", "kind": "module", "doc": "

    Simulate crystallographic preferred orientation evolution in polycrystals

    \n\n
    \n\n
    \n\n

    This software is currently in early development.\nOnly modules that have tests are anywhere close to being stable.

    \n\n
    \n\n

    About

    \n\n

    The core routines are based on the original implementation by \u00c9douard Kaminski,\nwhich can be downloaded from this link (~90KB).\nThe reference paper is Kaminski & Ribe 2001,\nand an open-access paper which discusses the model is Fraters & Billen 2021. [TODO: Add our paper]

    \n\n

    The package is currently not available on PyPi,\nand must be installed by cloning the source code.\nand using pip install . (with the dot) in the top-level folder.\nMultiprocessing is not yet available in the packaged version.\nRunning the tests requires pytest,\nand the custom pytest flag --outdir=\"OUT\" can be used to save output figures\nto the folder called OUT (or the current folder, using \".\").

    \n\n

    The submodule sidebar on the left can be used\nto discover the public API of this package.\nSome of the tests are also documented and can serve as usage examples.\nThey can be viewed in the module index (modules starting with test_).

    \n\n

    The D-Rex kinematic CPO model

    \n\n

    The D-Rex model is used to compute crystallographic preferred orientation (CPO)\nfor polycrystals deforming by dislocation creep and dynamic recrystallization.\nPolycrystals are discretized into \"grains\" which represent fractional volumes\nof the total crystal that are characterised by a particular crystal lattice\norientation. For numerical efficiency, the number of grains in the model does\nnot change, and should only be interpreted as an approximation of the number\nof physical grains. Dynamic recrystallization is modelled using statistical\nexpressions which approximate the interaction of each grain with an effective\nmedium based on the averaged dislocation energy of all other grains.\nNote that the model is not suited to situations where static recrystallization\nprocesses are significant.

    \n\n

    The primary microphysical mechanism for plastic deformation of the polycrystal\nis dislocation creep, which involves dislocation glide (\"slip\") along symmetry\nplanes of the mineral and dislocation climb, which allows for dislocations to\nannihilate each other so that the number of dislocations reaches a steady-state.\nThe D-Rex model does not simulate dislocation climb, but implicitly assumes that\nthe dislocations are in steady-state so that the dislocation density of the\ncrystal can be described by

    \n\n

    $$\n\u03c1 \u221d b^{-2} \\left(\\frac{\u03c3}{\u03bc}\\right)^{p}\n$$

    \n\n

    where $b$ is the length of the Burgers' vector, $\u03c3$ is the stress\nand $\u03bc$ is the shear modulus. The value of the exponent $p$ is given by the\nstress_exponent input parameter. For an overview of available parameters,\nsee [the tests/conftest.py source code, for now...]

    \n\n

    The effects of dynamic recrystallization are twofold. Grains with a higher than\naverage dislocation density may be affected by either grain nucleation, which is\nthe formation of initially small, strain-free sub-grains, or grain boundary\nmigration, by which process other grains of lower strain energy annex a portion\nof its volume. Nucleation occurs mostly in grains oriented favourably for\ndislocation glide, and the new grains also grow by grain boundary migration.\nIf nucleation is too inefficient, the dislocation density in deformation-aligned\ngrains will remain high and these grains will therefore shrink in volume. On the\nother hand, if grain boundaries are too immobile, then nucleated grains will take\nlonger to grow, reducing the speed of CPO development and re-orientation.\nBecause nucleated grains are assumed to inherit the orientation of the parent,\nthey do not affect the model except by reducing the average dislocation density.\nA grain boundary mobility parameter of $M^{\u2217} = 0$ will therefore disable any\nrecrystallization effects. Finally, the process of grain boundary sliding can\nalso be included, which simply disallows rotation of grains with very small volume.\nThis only affects CPO evolution by introducing a latency for the onset of grain\nboundary migration in nucleated grains. It also manifests as an upper bound on\ntexture strength.

    \n\n

    Parameter reference

    \n\n

    Model parameters will eventually be provided in an .ini file.\n[For now just pass a dictionary to config in the Mineral.update_orientations method]\nThe file must contain section headers enclosed by square braces\nand key-value assignments, for example:

    \n\n
    [Output]\nolivine = volume_distribution, orientations\n\n[D-Rex]\nolivine_fraction = 1\nstress_exponent = 1.5\n...\n
    \n\n

    The following reference describes the available sections and their parameters.

    \n\n

    Geometry

    \n\n

    This section allows for specifying the geometry of the model domain,\nincluding any interpolation meshes.

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    ParameterDescription
    meshfile[not implemented]
    \n\n

    Output

    \n\n

    Parameters in the output section control which variables are stored to files,\nas well as any options for automatic postprocessing.

    \n\n\n\n\n \n \n \n\n\n\n\n \n \n \n\n\n \n \n \n\n\n \n \n \n\n\n
    ParameterDescriptionDefault
    simulation_namea short name (without spaces) used for the output folder and metadatapydrex_example
    olivinethe choice of olivine mineral outputs, from {volume_distribution, orientations} with multiple choices separated by a commavolume_distribution,orientations
    enstatitethe choice of enstatite mineral outputs, from {volume_distribution, orientations} with multiple choices separated by a commavolume_distribution,orientations
    \n\n

    D-Rex

    \n\n

    Parameters in the D-Rex section specify the runtime configuration for the D-Rex model.\nRead the D-Rex introduction section for more details.

    \n\n\n\n\n \n \n \n\n\n\n\n \n \n \n\n\n \n \n \n\n\n \n \n \n\n\n \n \n \n\n\n \n \n \n\n\n \n \n \n\n\n \n \n \n\n\n \n \n \n\n\n \n \n \n\n\n \n \n \n\n\n
    ParameterDescriptionDefault
    stress_exponentthe stress exponent $p$ that characterises the relationship between dislocation density and stress1.5
    deformation_exponentthe exponent $n$ that characterises the relationship between stress and rate of deformation3.5
    gbm_mobilitythe dimensionless grain boundary mobility $M^{\u2217}$ which controls the chance for growth of grains with lower than average dislocation energy125
    gbs_thresholda threshold ratio of current to original volume below which small grains move by sliding rather than rotation0.3
    nucleation_efficiencythe dimensionless nucleation efficiency which controls the chance for new, small, strain-free sub-grains to be created inside high dislocation energy grains5
    number_of_grainsthe number of initial grains per crystal2500
    olivine_fabric[not implemented]A
    mineralsa tuple of mineral phase names that specify the composition of the polycrystal(\"olivine\",)
    olivine_fractionthe volume fraction of olivine compared to other phases (1 for pure olivine)1
    <phase>_fractionthe volume fraction of any other phases (sum of all volume fractions must sum to 1)N/A
    \n"}, "pydrex.axes": {"fullname": "pydrex.axes", "modulename": "pydrex.axes", "kind": "module", "doc": "
    \n

    PyDRex: Custom Matplotlib Axes subclasses.

    \n
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    Axes class designed for crystallographic pole figures.

    \n\n

    Thin matplotlib Axes wrapper for crystallographic pole figures.

    \n\n
    \n\n

    Projections are not performed automatically using default methods like\nscatter or plot. To actually plot the pole figures, use polefigure.

    \n\n
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    Plot pole figure of crystallographic texture.

    \n\n

    Args:

    \n\n\n\n

    Any additional keyword arguments are passed to either tripcolor if\ndensity=True or scatter if density=False

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    Set multiple properties at once.

    \n\n

    Supported properties are

    \n\n

    Properties:\n adjustable: {'box', 'datalim'}\n agg_filter: a filter function, which takes a (m, n, 3) float array and a dpi value, and returns a (m, n, 3) array and two offsets from the bottom left corner of the image\n alpha: scalar or None\n anchor: (float, float) or {'C', 'SW', 'S', 'SE', 'E', 'NE', ...}\n animated: bool\n aspect: {'auto', 'equal'} or float\n autoscale_on: bool\n autoscalex_on: unknown\n autoscaley_on: unknown\n axes_locator: Callable[[Axes, Renderer], Bbox]\n axisbelow: bool or 'line'\n box_aspect: float or None\n clip_box: .Bbox\n clip_on: bool\n clip_path: Patch or (Path, Transform) or None\n facecolor or fc: color\n figure: .Figure\n frame_on: bool\n gid: str\n in_layout: bool\n label: object\n mouseover: bool\n navigate: bool\n navigate_mode: unknown\n path_effects: .AbstractPathEffect\n picker: None or bool or float or callable\n position: [left, bottom, width, height] or ~matplotlib.transforms.Bbox\n prop_cycle: unknown\n rasterization_zorder: float or None\n rasterized: bool\n sketch_params: (scale: float, length: float, randomness: float)\n snap: bool or None\n subplotspec: unknown\n title: str\n transform: .Transform\n url: str\n visible: bool\n xbound: unknown\n xlabel: str\n xlim: (bottom: float, top: float)\n xmargin: float greater than -0.5\n xscale: unknown\n xticklabels: unknown\n xticks: unknown\n ybound: unknown\n ylabel: str\n ylim: (bottom: float, top: float)\n ymargin: float greater than -0.5\n yscale: unknown\n yticklabels: unknown\n yticks: unknown\n zorder: float

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    \n

    PyDRex: Entry points for command line tools.

    \n
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    PyDRex script to plot pole figures of serialized CPO data.

    \n\n

    Produces [100], [010] and [001] pole figures for serialized pydrex.Minerals.\nIf the range of indices is not specified,\na maximum of 25 of each pole figure will be produced.

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    \n

    PyDRex: Core D-Rex functions and enums.

    \n
    \n\n

    The function derivatives implements the core D-Rex solver, which computes the\ncrystallographic rotation rate and changes in fractional grain volumes.

    \n\n

    Acronyms:

    \n\n\n"}, "pydrex.core.PERMUTATION_SYMBOL": {"fullname": "pydrex.core.PERMUTATION_SYMBOL", "modulename": "pydrex.core", "qualname": "PERMUTATION_SYMBOL", "kind": "variable", "doc": "

    \n", "default_value": "array([[[0.e+00, 0.e+00, 0.e+00],\n [0.e+00, 0.e+00, 1.e+00],\n [0.e+00, -1.e+00, 0.e+00]],\n\n [[0.e+00, 0.e+00, -1.e+00],\n [0.e+00, 0.e+00, 0.e+00],\n [1.e+00, 0.e+00, 0.e+00]],\n\n [[0.e+00, 1.e+00, 0.e+00],\n [-1.e+00, 0.e+00, 0.e+00],\n [0.e+00, 0.e+00, 0.e+00]]])"}, "pydrex.core.MineralPhase": {"fullname": "pydrex.core.MineralPhase", "modulename": "pydrex.core", "qualname": "MineralPhase", "kind": "class", "doc": "

    Supported mineral phases.

    \n", "bases": "enum.IntEnum"}, "pydrex.core.MineralPhase.olivine": {"fullname": "pydrex.core.MineralPhase.olivine", "modulename": "pydrex.core", "qualname": "MineralPhase.olivine", "kind": "variable", "doc": "

    \n", "default_value": "<MineralPhase.olivine: 0>"}, "pydrex.core.MineralPhase.enstatite": {"fullname": "pydrex.core.MineralPhase.enstatite", "modulename": "pydrex.core", "qualname": "MineralPhase.enstatite", "kind": "variable", "doc": "

    \n", "default_value": "<MineralPhase.enstatite: 1>"}, "pydrex.core.DeformationRegime": {"fullname": "pydrex.core.DeformationRegime", "modulename": "pydrex.core", "qualname": "DeformationRegime", "kind": "class", "doc": "

    Deformation mechanism regimes.

    \n", "bases": "enum.IntEnum"}, "pydrex.core.DeformationRegime.diffusion": {"fullname": "pydrex.core.DeformationRegime.diffusion", "modulename": "pydrex.core", "qualname": "DeformationRegime.diffusion", "kind": "variable", "doc": "

    \n", "default_value": "<DeformationRegime.diffusion: 0>"}, "pydrex.core.DeformationRegime.dislocation": {"fullname": "pydrex.core.DeformationRegime.dislocation", "modulename": "pydrex.core", "qualname": "DeformationRegime.dislocation", "kind": "variable", "doc": "

    \n", "default_value": "<DeformationRegime.dislocation: 1>"}, "pydrex.core.DeformationRegime.byerlee": {"fullname": "pydrex.core.DeformationRegime.byerlee", "modulename": "pydrex.core", "qualname": "DeformationRegime.byerlee", "kind": "variable", "doc": "

    \n", "default_value": "<DeformationRegime.byerlee: 2>"}, "pydrex.core.DeformationRegime.max_viscosity": {"fullname": "pydrex.core.DeformationRegime.max_viscosity", "modulename": "pydrex.core", "qualname": "DeformationRegime.max_viscosity", "kind": "variable", "doc": "

    \n", "default_value": "<DeformationRegime.max_viscosity: 3>"}, "pydrex.core.MineralFabric": {"fullname": "pydrex.core.MineralFabric", "modulename": "pydrex.core", "qualname": "MineralFabric", "kind": "class", "doc": "

    Supported mineral fabrics.

    \n\n

    The following fabric types are supported:

    \n\n\n", "bases": "enum.IntEnum"}, "pydrex.core.MineralFabric.olivine_A": {"fullname": "pydrex.core.MineralFabric.olivine_A", "modulename": "pydrex.core", "qualname": "MineralFabric.olivine_A", "kind": "variable", "doc": "

    \n", "default_value": "<MineralFabric.olivine_A: 0>"}, "pydrex.core.MineralFabric.olivine_B": {"fullname": "pydrex.core.MineralFabric.olivine_B", "modulename": "pydrex.core", "qualname": "MineralFabric.olivine_B", "kind": "variable", "doc": "

    \n", "default_value": "<MineralFabric.olivine_B: 1>"}, "pydrex.core.MineralFabric.olivine_C": {"fullname": "pydrex.core.MineralFabric.olivine_C", "modulename": "pydrex.core", "qualname": "MineralFabric.olivine_C", "kind": "variable", "doc": "

    \n", "default_value": "<MineralFabric.olivine_C: 2>"}, "pydrex.core.MineralFabric.olivine_D": {"fullname": "pydrex.core.MineralFabric.olivine_D", "modulename": "pydrex.core", "qualname": "MineralFabric.olivine_D", "kind": "variable", "doc": "

    \n", "default_value": "<MineralFabric.olivine_D: 3>"}, "pydrex.core.MineralFabric.olivine_E": {"fullname": "pydrex.core.MineralFabric.olivine_E", "modulename": "pydrex.core", "qualname": "MineralFabric.olivine_E", "kind": "variable", "doc": "

    \n", "default_value": "<MineralFabric.olivine_E: 4>"}, "pydrex.core.MineralFabric.enstatite_AB": {"fullname": "pydrex.core.MineralFabric.enstatite_AB", "modulename": "pydrex.core", "qualname": "MineralFabric.enstatite_AB", "kind": "variable", "doc": "

    \n", "default_value": "<MineralFabric.enstatite_AB: 5>"}, "pydrex.core.get_crss": {"fullname": "pydrex.core.get_crss", "modulename": "pydrex.core", "qualname": "get_crss", "kind": "function", "doc": "

    Get Critical Resolved Shear Stress for the mineral phase and fabric.

    \n\n

    Returns an array of the normalised threshold stresses required to activate slip on\neach slip system. Olivine slip systems are ordered according to the convention used\nfor pydrex.minerals.OLIVINE_SLIP_SYSTEMS.

    \n", "signature": "(phase, fabric):", "funcdef": "def"}, "pydrex.core.derivatives": {"fullname": "pydrex.core.derivatives", "modulename": "pydrex.core", "qualname": "derivatives", "kind": "function", "doc": "

    Get derivatives of orientation and volume distribution.

    \n\n

    Args:

    \n\n\n\n

    Returns a tuple with the rotation rates and grain volume fraction changes.

    \n", "signature": "(\tphase,\tfabric,\tn_grains,\torientations,\tfractions,\tstrain_rate,\tvelocity_gradient,\tstress_exponent,\tdeformation_exponent,\tnucleation_efficiency,\tgbm_mobility,\tvolume_fraction):", "funcdef": "def"}, "pydrex.diagnostics": {"fullname": "pydrex.diagnostics", "modulename": "pydrex.diagnostics", "kind": "module", "doc": "
    \n

    PyDRex: Methods to calculate texture and strain diagnostics.

    \n
    \n\n
    \n\n

    Calculations expect orientation matrices $a$ to represent passive\n(i.e. alias) rotations, which are defined in terms of the extrinsic ZXZ\neuler angles $\u03d5, \u03b8, \u03c6$ as\n$$\na = \\begin{bmatrix}\n \\cos\u03c6\\cos\u03d5 - \\cos\u03b8\\sin\u03d5\\sin\u03c6 & \\cos\u03b8\\cos\u03d5\\sin\u03c6 + \\cos\u03c6\\sin\u03d5 & \\sin\u03c6\\sin\u03b8 \\cr\n -\\sin\u03c6\\cos\u03d5 - \\cos\u03b8\\sin\u03d5\\cos\u03c6 & \\cos\u03b8\\cos\u03d5\\cos\u03c6 - \\sin\u03c6\\sin\u03d5 & \\cos\u03c6\\sin\u03b8 \\cr\n \\sin\u03b8\\sin\u03d5 & -\\sin\u03b8\\cos\u03d5 & \\cos\u03b8\n \\end{bmatrix}\n$$\nsuch that a[i, j] gives the direction cosine of the angle between the i-th\ngrain axis and the j-th external axis (in the global Eulerian frame).

    \n\n
    \n"}, "pydrex.diagnostics.anisotropy": {"fullname": "pydrex.diagnostics.anisotropy", "modulename": "pydrex.diagnostics", "qualname": "anisotropy", "kind": "function", "doc": "

    Calculate anisotropy diagnostics for the given elasticity tensor.

    \n\n

    Args:

    \n\n\n\n

    Returns the percent anisotropy, a matrix containing the axes of the Symmetry\nCartesian Coordinate System (rows), and the elasticity tensor in the SCCS frame\n(Voigt vector representation).

    \n", "signature": "(voigt_matrix, proj='hex'):", "funcdef": "def"}, "pydrex.diagnostics.bingham_average": {"fullname": "pydrex.diagnostics.bingham_average", "modulename": "pydrex.diagnostics", "qualname": "bingham_average", "kind": "function", "doc": "

    Compute Bingham averages from olivine orientation matrices.

    \n\n

    Returns the antipodally symmetric average orientation\nof the given crystallographic axis, or the a-axis by default.\nValid axis specifiers are \"a\" for [100], \"b\" for [010] and \"c\" for [001].

    \n\n

    See also: Watson 1966,\nMardia & Jupp, \u201cDirectional Statistics\u201d.

    \n", "signature": "(orientations, axis='a'):", "funcdef": "def"}, "pydrex.diagnostics.finite_strain": {"fullname": "pydrex.diagnostics.finite_strain", "modulename": "pydrex.diagnostics", "qualname": "finite_strain", "kind": "function", "doc": "

    Extract measures of finite strain from the deformation gradient.

    \n\n

    Extracts the vector defining the axis of maximum extension (longest semiaxis of the\nfinite strain ellipsoid) and the largest principal strain value from the 3x3\ndeformation gradient tensor.

    \n", "signature": "(deformation_gradient, **kwargs):", "funcdef": "def"}, "pydrex.diagnostics.symmetry": {"fullname": "pydrex.diagnostics.symmetry", "modulename": "pydrex.diagnostics", "qualname": "symmetry", "kind": "function", "doc": "

    Compute texture symmetry eigenvalue diagnostics from olivine orientation matrices.

    \n\n

    Compute Point, Girdle and Random symmetry diagnostics\nfor ternary texture classification.\nReturns the tuple (P, G, R) where\n$$\n\\begin{align*}\nP &= (\u03bb_{1} - \u03bb_{2}) / N \\cr\nG &= 2 (\u03bb_{2} - \u03bb_{3}) / N \\cr\nR &= 3 \u03bb_{3} / N\n\\end{align*}\n$$\nwith $N$ the sum of the eigenvalues $\u03bb_{1} \u2265 \u03bb_{2} \u2265 \u03bb_{3}$\nof the scatter (inertia) matrix.

    \n\n

    See e.g. Vollmer 1990.

    \n", "signature": "(orientations, axis='a'):", "funcdef": "def"}, "pydrex.diagnostics.misorientation_index": {"fullname": "pydrex.diagnostics.misorientation_index", "modulename": "pydrex.diagnostics", "qualname": "misorientation_index", "kind": "function", "doc": "

    Calculate M-index for polycrystal orientations.

    \n\n

    The bins argument is passed to numpy.histogram.\nIf left as None, 1\u00b0 bins will be used as recommended by the reference paper.\nThe symmetry system can be specified using the system argument.\nThe default system is orthorhombic.

    \n\n

    See Skemer et al. 2005.

    \n", "signature": "(orientations, bins=None, system=(2, 4)):", "funcdef": "def"}, "pydrex.diagnostics.coaxial_index": {"fullname": "pydrex.diagnostics.coaxial_index", "modulename": "pydrex.diagnostics", "qualname": "coaxial_index", "kind": "function", "doc": "

    Calculate coaxial \u201cBA\u201d index for a combination of two crystal axes.

    \n\n

    The BA index of Mainprice et al. 2015\nis derived from the eigenvalue symmetry diagnostics and measures point vs girdle\nsymmetry in the aggregate. $BA \u2208 [0, 1]$ where $BA = 0$ corresponds to a perfect\naxial girdle texture and $BA = 1$ represents a point symmetry texture assuming that\nthe random component $R$ is negligible. May be less susceptible to random\nfluctuations compared to the raw eigenvalue diagnostics.

    \n", "signature": "(orientations, axis1='b', axis2='a'):", "funcdef": "def"}, "pydrex.diagnostics.misorientation_angles": {"fullname": "pydrex.diagnostics.misorientation_angles", "modulename": "pydrex.diagnostics", "qualname": "misorientation_angles", "kind": "function", "doc": "

    Calculate the misorientation angles for pairs of rotation quaternions.

    \n\n

    Calculate the angular distance between the rotations combinations[:, 0]\nand combinations[:, 1], which are expected to be 1x4 passive (alias)\nrotation quaternions.

    \n\n

    Uses ~25% less memory than the same operation with rotation matrices.

    \n\n

    See also:

    \n\n\n", "signature": "(combinations):", "funcdef": "def"}, "pydrex.diagnostics.smallest_angle": {"fullname": "pydrex.diagnostics.smallest_angle", "modulename": "pydrex.diagnostics", "qualname": "smallest_angle", "kind": "function", "doc": "

    Get smallest angle between a unit vector and a bidirectional axis.

    \n\n

    The axis is specified using either of its two parallel unit vectors.

    \n", "signature": "(vector, axis):", "funcdef": "def"}, "pydrex.exceptions": {"fullname": "pydrex.exceptions", "modulename": "pydrex.exceptions", "kind": "module", "doc": "
    \n

    PyDRex: Custom exceptions (subclasses of pydrex.Error).

    \n
    \n"}, "pydrex.exceptions.Error": {"fullname": "pydrex.exceptions.Error", "modulename": "pydrex.exceptions", "qualname": "Error", "kind": "class", "doc": "

    Base class for exceptions in PyDRex.

    \n", "bases": "builtins.Exception"}, "pydrex.exceptions.ConfigError": {"fullname": "pydrex.exceptions.ConfigError", "modulename": "pydrex.exceptions", "qualname": "ConfigError", "kind": "class", "doc": "

    Exception raised for errors in the input configuration.

    \n\n

    Attributes:\n message \u2014 explanation of the error

    \n", "bases": "Error"}, "pydrex.exceptions.ConfigError.__init__": {"fullname": "pydrex.exceptions.ConfigError.__init__", "modulename": "pydrex.exceptions", "qualname": "ConfigError.__init__", "kind": "function", "doc": "

    \n", "signature": "(message)"}, "pydrex.exceptions.ConfigError.message": {"fullname": "pydrex.exceptions.ConfigError.message", "modulename": "pydrex.exceptions", "qualname": "ConfigError.message", "kind": "variable", "doc": "

    \n"}, "pydrex.exceptions.MeshError": {"fullname": "pydrex.exceptions.MeshError", "modulename": "pydrex.exceptions", "qualname": "MeshError", "kind": "class", "doc": "

    Exception raised for errors in the input mesh.

    \n\n

    Attributes:\n message \u2014 explanation of the error

    \n", "bases": "Error"}, "pydrex.exceptions.MeshError.__init__": {"fullname": "pydrex.exceptions.MeshError.__init__", "modulename": "pydrex.exceptions", "qualname": "MeshError.__init__", "kind": "function", "doc": "

    \n", "signature": "(message)"}, "pydrex.exceptions.MeshError.message": {"fullname": "pydrex.exceptions.MeshError.message", "modulename": "pydrex.exceptions", "qualname": "MeshError.message", "kind": "variable", "doc": "

    \n"}, "pydrex.exceptions.IterationError": {"fullname": "pydrex.exceptions.IterationError", "modulename": "pydrex.exceptions", "qualname": "IterationError", "kind": "class", "doc": "

    Exception raised for errors in numerical iteration schemes.

    \n\n

    Attributes:\n message \u2014 explanation of the error

    \n", "bases": "Error"}, "pydrex.exceptions.IterationError.__init__": {"fullname": "pydrex.exceptions.IterationError.__init__", "modulename": "pydrex.exceptions", "qualname": "IterationError.__init__", "kind": "function", "doc": "

    \n", "signature": "(message)"}, "pydrex.exceptions.IterationError.message": {"fullname": "pydrex.exceptions.IterationError.message", "modulename": "pydrex.exceptions", "qualname": "IterationError.message", "kind": "variable", "doc": "

    \n"}, "pydrex.exceptions.SCSVError": {"fullname": "pydrex.exceptions.SCSVError", "modulename": "pydrex.exceptions", "qualname": "SCSVError", "kind": "class", "doc": "

    Exception raised for errors in SCSV file I/O.

    \n\n

    Attributes:

    \n\n\n", "bases": "Error"}, "pydrex.exceptions.SCSVError.__init__": {"fullname": "pydrex.exceptions.SCSVError.__init__", "modulename": "pydrex.exceptions", "qualname": "SCSVError.__init__", "kind": "function", "doc": "

    \n", "signature": "(message)"}, "pydrex.exceptions.SCSVError.message": {"fullname": "pydrex.exceptions.SCSVError.message", "modulename": "pydrex.exceptions", "qualname": "SCSVError.message", "kind": "variable", "doc": "

    \n"}, "pydrex.geometry": {"fullname": "pydrex.geometry", "modulename": "pydrex.geometry", "kind": "module", "doc": "
    \n

    PyDRex: Functions for geometric coordinate conversions and projections.

    \n
    \n"}, "pydrex.geometry.to_cartesian": {"fullname": "pydrex.geometry.to_cartesian", "modulename": "pydrex.geometry", "qualname": "to_cartesian", "kind": "function", "doc": "

    Convert spherical to cartesian coordinates in \u211d\u00b3.

    \n\n

    Spherical coordinate convention:

    \n\n\n\n

    By default, a radius of r = 1 is used for the sphere.\nReturns a tuple containing arrays of x, y, and z values.

    \n", "signature": "(\u03c6, \u03b8, r=1):", "funcdef": "def"}, "pydrex.geometry.to_spherical": {"fullname": "pydrex.geometry.to_spherical", "modulename": "pydrex.geometry", "qualname": "to_spherical", "kind": "function", "doc": "

    Convert cartesian coordinates in \u211d\u00b3 to spherical coordinates.

    \n\n

    Spherical coordinate convention:

    \n\n\n\n

    Returns a tuple containing arrays of r, \u03d5 and \u03b8 values.

    \n", "signature": "(x, y, z):", "funcdef": "def"}, "pydrex.geometry.poles": {"fullname": "pydrex.geometry.poles", "modulename": "pydrex.geometry", "qualname": "poles", "kind": "function", "doc": "

    Extract 3D vectors of crystallographic directions from orientation matrices.

    \n\n

    Expects orientations to be an array with shape (N, 3, 3).\nThe optional arguments ref_axes and hkl can be used to change\nthe global reference axes and the crystallographic direction respectively.\nThe reference axes should be given as a string of two letters,\ne.g. \"xz\" (default), which specify the second and third axes\nof the global right-handed reference frame. The third letter in the set \"xyz\"\ndetermines the first axis. The ref_axes will therefore become the\nhorizontal and vertical axes of pole figures used to plot the directions.

    \n", "signature": "(orientations, ref_axes='xz', hkl=[1, 0, 0]):", "funcdef": "def"}, "pydrex.geometry.lambert_equal_area": {"fullname": "pydrex.geometry.lambert_equal_area", "modulename": "pydrex.geometry", "qualname": "lambert_equal_area", "kind": "function", "doc": "

    Project axial data from a 3D sphere onto a 2D disk.

    \n\n

    Project points from a 3D sphere of radius 1, given in Cartesian coordinates,\nto points on a 2D disk using a Lambert equal area azimuthal projection.\nReturns arrays of the X and Y coordinates in the unit disk.

    \n\n

    This implementation first maps all points onto the same hemisphere,\nand then projects that hemisphere onto the disk.

    \n", "signature": "(xvals, yvals, zvals):", "funcdef": "def"}, "pydrex.geometry.shirley_concentric_squaredisk": {"fullname": "pydrex.geometry.shirley_concentric_squaredisk", "modulename": "pydrex.geometry", "qualname": "shirley_concentric_squaredisk", "kind": "function", "doc": "

    Project points from a square onto a disk using the concentric Shirley method.

    \n\n

    The concentric method of Shirley & Chiu 1997 is optimised to preserve area.\nSee also: http://marc-b-reynolds.github.io/math/2017/01/08/SquareDisc.html.

    \n\n

    This can be used to set up uniform grids on a disk, e.g.

    \n\n
    \n
    >>> a = [x / 5.0 for x in range(-5, 6)]\n>>> x = [[x] * len(a) for x in a]\n>>> y = [a for _ in a]\n>>> x_flat = [j for i in x for j in i]\n>>> y_flat = [j for i in y for j in i]\n>>> x_disk, y_disk = shirley_concentric_squaredisk(x_flat, y_flat)\n>>> r = x_disk**2 + y_disk**2\n>>> r\narray([1.  , 1.  , 1.  , 1.  , 1.  , 1.  , 1.  , 1.  , 1.  , 1.  , 1.  ,\n       1.  , 0.64, 0.64, 0.64, 0.64, 0.64, 0.64, 0.64, 0.64, 0.64, 1.  ,\n       1.  , 0.64, 0.36, 0.36, 0.36, 0.36, 0.36, 0.36, 0.36, 0.64, 1.  ,\n       1.  , 0.64, 0.36, 0.16, 0.16, 0.16, 0.16, 0.16, 0.36, 0.64, 1.  ,\n       1.  , 0.64, 0.36, 0.16, 0.04, 0.04, 0.04, 0.16, 0.36, 0.64, 1.  ,\n       1.  , 0.64, 0.36, 0.16, 0.04, 0.  , 0.04, 0.16, 0.36, 0.64, 1.  ,\n       1.  , 0.64, 0.36, 0.16, 0.04, 0.04, 0.04, 0.16, 0.36, 0.64, 1.  ,\n       1.  , 0.64, 0.36, 0.16, 0.16, 0.16, 0.16, 0.16, 0.36, 0.64, 1.  ,\n       1.  , 0.64, 0.36, 0.36, 0.36, 0.36, 0.36, 0.36, 0.36, 0.64, 1.  ,\n       1.  , 0.64, 0.64, 0.64, 0.64, 0.64, 0.64, 0.64, 0.64, 0.64, 1.  ,\n       1.  , 1.  , 1.  , 1.  , 1.  , 1.  , 1.  , 1.  , 1.  , 1.  , 1.  ])\n>>> from math import atan2\n>>> \u03b8 = [atan2(y, x) for y, x in zip(y_disk, x_disk)]\n>>> max(\u03b8)\n3.141592653589793\n>>> min(\u03b8)\n-2.9845130209101467\n
    \n
    \n", "signature": "(xvals, yvals):", "funcdef": "def"}, "pydrex.interpolations": {"fullname": "pydrex.interpolations", "modulename": "pydrex.interpolations", "kind": "module", "doc": "
    \n

    PyDRex: Interpolation callbacks and helpers.

    \n
    \n"}, "pydrex.interpolations.default_interpolators": {"fullname": "pydrex.interpolations.default_interpolators", "modulename": "pydrex.interpolations", "qualname": "default_interpolators", "kind": "function", "doc": "

    Create a dictionary of default interpolator callbacks for PyDRex input.

    \n\n

    Args:

    \n\n\n\n

    Optionaly pass a string to mpl_interp to use\nmatplotlib.tri.CubicTriInterpolator with the chosen smoothing algorithm.\nOnly valid for 2D data with pre-existing triangulations.

    \n\n

    See also create_interpolators.

    \n", "signature": "(config, coords, vtk_output, mpl_interp=None):", "funcdef": "def"}, "pydrex.interpolations.create_interpolators": {"fullname": "pydrex.interpolations.create_interpolators", "modulename": "pydrex.interpolations", "qualname": "create_interpolators", "kind": "function", "doc": "

    Create interpolator callbacks for data arrays.

    \n\n

    Args:

    \n\n\n\n

    Optional kwargs will be passed to the interpolation constructor.

    \n\n

    Returns a list of interpolator callbacks, one for each data vector component.

    \n\n

    The triangles arg is required only for matplotlib.tri.CubicTriInterpolator.\nSee the documentation of that constructor for details.

    \n", "signature": "(interpolator, coords, data, triangles=None, **kwargs):", "funcdef": "def"}, "pydrex.interpolations.get_velocity": {"fullname": "pydrex.interpolations.get_velocity", "modulename": "pydrex.interpolations", "qualname": "get_velocity", "kind": "function", "doc": "

    Interpolates the velocity at a given point.

    \n", "signature": "(point, interpolators):", "funcdef": "def"}, "pydrex.interpolations.get_velocity_gradient": {"fullname": "pydrex.interpolations.get_velocity_gradient", "modulename": "pydrex.interpolations", "qualname": "get_velocity_gradient", "kind": "function", "doc": "

    Return the interpolated velocity gradient tensor at a given point.

    \n", "signature": "(point, interpolators):", "funcdef": "def"}, "pydrex.interpolations.get_deformation_mechanism": {"fullname": "pydrex.interpolations.get_deformation_mechanism", "modulename": "pydrex.interpolations", "qualname": "get_deformation_mechanism", "kind": "function", "doc": "

    Return the interpolated deformation mechanism ID at the given point.

    \n", "signature": "(point, interpolators):", "funcdef": "def"}, "pydrex.io": {"fullname": "pydrex.io", "modulename": "pydrex.io", "kind": "module", "doc": "
    \n

    PyDRex: Mesh, configuration and supporting data Input/Output functions.

    \n
    \n\n

    PyDRex can read/write three kinds of plain text files:

    \n\n\n\n

    SCSV files are our custom CSV files with a YAML header. The header is used for data\nattribution and metadata, as well as a column type spec. There is no official spec for\nSCSV files at the moment but they should follow the format of existing SCSV files in\nthe data/ folder of the source repository. For supported cell types, see\nSCSV_TYPEMAP.

    \n"}, "pydrex.io.DEFAULT_PARAMS": {"fullname": "pydrex.io.DEFAULT_PARAMS", "modulename": "pydrex.io", "qualname": "DEFAULT_PARAMS", "kind": "variable", "doc": "

    Default simulation parameters.

    \n", "default_value": "{'olivine_fraction': 1.0, 'enstatite_fraction': 0.0, 'stress_exponent': 1.5, 'deformation_exponent': 3.5, 'gbm_mobility': 125, 'gbs_threshold': 0.3, 'nucleation_efficiency': 5.0, 'number_of_grains': 2500, 'initial_olivine_fabric': 'A'}"}, "pydrex.io.SCSV_TYPEMAP": {"fullname": "pydrex.io.SCSV_TYPEMAP", "modulename": "pydrex.io", "qualname": "SCSV_TYPEMAP", "kind": "variable", "doc": "

    Mapping of supported SCSV field types to corresponding Python types.

    \n", "default_value": "{'string': <class 'str'>, 'integer': <class 'int'>, 'float': <class 'float'>, 'boolean': <class 'bool'>, 'complex': <class 'complex'>}"}, "pydrex.io.read_scsv": {"fullname": "pydrex.io.read_scsv", "modulename": "pydrex.io", "qualname": "read_scsv", "kind": "function", "doc": "

    Read data from an SCSV file.

    \n\n

    See also save_scsv, read_scsv_header.

    \n", "signature": "(file):", "funcdef": "def"}, "pydrex.io.write_scsv_header": {"fullname": "pydrex.io.write_scsv_header", "modulename": "pydrex.io", "qualname": "write_scsv_header", "kind": "function", "doc": "

    Write YAML header to an SCSV stream.

    \n\n

    Args:

    \n\n\n\n

    See also read_scsv, save_scsv.

    \n", "signature": "(stream, schema, comments=None):", "funcdef": "def"}, "pydrex.io.save_scsv": {"fullname": "pydrex.io.save_scsv", "modulename": "pydrex.io", "qualname": "save_scsv", "kind": "function", "doc": "

    Save data to SCSV file.

    \n\n

    Args:

    \n\n\n\n

    Optional keyword arguments are passed to write_scsv_header. See also read_scsv.

    \n", "signature": "(file, schema, data, **kwargs):", "funcdef": "def"}, "pydrex.io.parse_config": {"fullname": "pydrex.io.parse_config", "modulename": "pydrex.io", "qualname": "parse_config", "kind": "function", "doc": "

    Parse a TOML file containing PyDRex configuration.

    \n", "signature": "(path):", "funcdef": "def"}, "pydrex.io.read_mesh": {"fullname": "pydrex.io.read_mesh", "modulename": "pydrex.io", "qualname": "read_mesh", "kind": "function", "doc": "

    Wrapper of meshio.read, see https://github.com/nschloe/meshio.

    \n", "signature": "(meshfile, *args, **kwargs):", "funcdef": "def"}, "pydrex.io.resolve_path": {"fullname": "pydrex.io.resolve_path", "modulename": "pydrex.io", "qualname": "resolve_path", "kind": "function", "doc": "

    Resolve relative paths and create parent directories if necessary.

    \n\n

    Relative paths are interpreted with respect to the current working directory,\ni.e. the directory from whith the current Python process was executed,\nunless a specific reference directory is provided with refdir.

    \n", "signature": "(path, refdir=None):", "funcdef": "def"}, "pydrex.io.stringify": {"fullname": "pydrex.io.stringify", "modulename": "pydrex.io", "qualname": "stringify", "kind": "function", "doc": "

    Return a cleaned version of a string for use in filenames, etc.

    \n", "signature": "(s):", "funcdef": "def"}, "pydrex.io.data": {"fullname": "pydrex.io.data", "modulename": "pydrex.io", "qualname": "data", "kind": "function", "doc": "

    Get resolved path to a pydrex data folder.

    \n", "signature": "(folder):", "funcdef": "def"}, "pydrex.logger": {"fullname": "pydrex.logger", "modulename": "pydrex.logger", "kind": "module", "doc": "
    \n

    PyDRex: logger settings and boilerplate.

    \n
    \n\n

    Python's logging module is weird and its methods don't allow us to specify\nwhich logger to use, so just using logging.debug for example always uses\nthe \"root\" logger, which spams a bunch of messages from other imports/modules.\nInstead, the methods in this module are thin wrappers that use custom\nlogging objects (pydrex.logger.LOGGER and pydrex.logger.CONSOLE_LOGGER).\nThe method quiet_aliens can be invoked to suppress most messages\nfrom third-party modules, except critical errors and warnings from Numba.

    \n\n

    By default, PyDRex emits INFO level messages to the console.\nThis can be changed globally by setting the new level with CONSOLE_LOGGER.setLevel:

    \n\n
    \n
    from pydrex import logger as _log\n_log.info("this message will be printed to the console")\n\n_log.CONSOLE_LOGGER.setLevel("ERROR")\n_log.info("this message will NOT be printed to the console")\n_log.error("this message will be printed to the console")\n
    \n
    \n\n

    To change the console logging level for a particular local context,\nuse the handler_level context manager:

    \n\n
    \n
    _log.CONSOLE_LOGGER.setLevel("INFO")\n_log.info("this message will be printed to the console")\n\nwith handler_level("ERROR"):\n    _log.info("this message will NOT be printed to the console")\n\n_log.info("this message will be printed to the console")\n
    \n
    \n\n

    To save debug logs to a file, the logfile_enable context manager is recommended.\nAlways use the old printf style formatting for log messages, not fstrings,\notherwise compute time will be wasted on string conversions when logging is disabled:

    \n\n
    \n
    _log.quiet_aliens()  # Suppress third-party log messages except CRITICAL from Numba.\nwith _log.logfile_enable("my_log_file.log"):  # Overwrite existing file unless mode="a".\n    value = 42\n    _log.critical("critical error with value: %s", value)\n    _log.error("runtime error with value: %s", value)\n    _log.warning("warning with value: %s", value)\n    _log.info("information message with value: %s", value)\n    _log.debug("verbose debugging message with value: %s", value)\n    ... # Construct Minerals, update orientations, etc.\n
    \n
    \n"}, "pydrex.logger.ConsoleFormatter": {"fullname": "pydrex.logger.ConsoleFormatter", "modulename": "pydrex.logger", "qualname": "ConsoleFormatter", "kind": "class", "doc": "

    Log formatter that uses terminal color codes.

    \n", "bases": "logging.Formatter"}, "pydrex.logger.ConsoleFormatter.colorfmt": {"fullname": "pydrex.logger.ConsoleFormatter.colorfmt", "modulename": "pydrex.logger", "qualname": "ConsoleFormatter.colorfmt", "kind": "function", "doc": "

    \n", "signature": "(self, code):", "funcdef": "def"}, "pydrex.logger.ConsoleFormatter.format": {"fullname": "pydrex.logger.ConsoleFormatter.format", "modulename": "pydrex.logger", "qualname": "ConsoleFormatter.format", "kind": "function", "doc": "

    Format the specified record as text.

    \n\n

    The record's attribute dictionary is used as the operand to a\nstring formatting operation which yields the returned string.\nBefore formatting the dictionary, a couple of preparatory steps\nare carried out. The message attribute of the record is computed\nusing LogRecord.getMessage(). If the formatting string uses the\ntime (as determined by a call to usesTime(), formatTime() is\ncalled to format the event time. If there is exception information,\nit is formatted using formatException() and appended to the message.

    \n", "signature": "(self, record):", "funcdef": "def"}, "pydrex.logger.LOGGER": {"fullname": "pydrex.logger.LOGGER", "modulename": "pydrex.logger", "qualname": "LOGGER", "kind": "variable", "doc": "

    \n", "default_value": "<Logger pydrex (DEBUG)>"}, "pydrex.logger.LOGGER_CONSOLE": {"fullname": "pydrex.logger.LOGGER_CONSOLE", "modulename": "pydrex.logger", "qualname": "LOGGER_CONSOLE", "kind": "variable", "doc": "

    \n", "default_value": "<StreamHandler (INFO)>"}, "pydrex.logger.handler_level": {"fullname": "pydrex.logger.handler_level", "modulename": "pydrex.logger", "qualname": "handler_level", "kind": "function", "doc": "

    Set logging handler level for current context.

    \n\n

    Args:

    \n\n\n", "signature": "(level, handler=<StreamHandler (INFO)>):", "funcdef": "def"}, "pydrex.logger.logfile_enable": {"fullname": "pydrex.logger.logfile_enable", "modulename": "pydrex.logger", "qualname": "logfile_enable", "kind": "function", "doc": "

    Enable logging to a file at path with given level.

    \n", "signature": "(path, level=10, mode='w'):", "funcdef": "def"}, "pydrex.logger.critical": {"fullname": "pydrex.logger.critical", "modulename": "pydrex.logger", "qualname": "critical", "kind": "function", "doc": "

    Log a CRITICAL message in PyDRex.

    \n", "signature": "(msg, *args, **kwargs):", "funcdef": "def"}, "pydrex.logger.error": {"fullname": "pydrex.logger.error", "modulename": "pydrex.logger", "qualname": "error", "kind": "function", "doc": "

    Log an ERROR message in PyDRex.

    \n", "signature": "(msg, *args, **kwargs):", "funcdef": "def"}, "pydrex.logger.warning": {"fullname": "pydrex.logger.warning", "modulename": "pydrex.logger", "qualname": "warning", "kind": "function", "doc": "

    Log a WARNING message in PyDRex.

    \n", "signature": "(msg, *args, **kwargs):", "funcdef": "def"}, "pydrex.logger.info": {"fullname": "pydrex.logger.info", "modulename": "pydrex.logger", "qualname": "info", "kind": "function", "doc": "

    Log an INFO message in PyDRex.

    \n", "signature": "(msg, *args, **kwargs):", "funcdef": "def"}, "pydrex.logger.debug": {"fullname": "pydrex.logger.debug", "modulename": "pydrex.logger", "qualname": "debug", "kind": "function", "doc": "

    Log a DEBUG message in PyDRex.

    \n", "signature": "(msg, *args, **kwargs):", "funcdef": "def"}, "pydrex.logger.exception": {"fullname": "pydrex.logger.exception", "modulename": "pydrex.logger", "qualname": "exception", "kind": "function", "doc": "

    Log a message with level ERROR but retain exception information.

    \n\n

    This function should only be called from an exception handler.

    \n", "signature": "(msg, *args, **kwargs):", "funcdef": "def"}, "pydrex.logger.quiet_aliens": {"fullname": "pydrex.logger.quiet_aliens", "modulename": "pydrex.logger", "qualname": "quiet_aliens", "kind": "function", "doc": "

    Restrict alien loggers \ud83d\udc7d because I'm trying to find MY bugs, thanks.

    \n", "signature": "():", "funcdef": "def"}, "pydrex.minerals": {"fullname": "pydrex.minerals", "modulename": "pydrex.minerals", "kind": "module", "doc": "
    \n

    PyDRex: Computations of mineral texture and elasticity.

    \n
    \n"}, "pydrex.minerals.OLIVINE_STIFFNESS": {"fullname": "pydrex.minerals.OLIVINE_STIFFNESS", "modulename": "pydrex.minerals", "qualname": "OLIVINE_STIFFNESS", "kind": "variable", "doc": "

    Stiffness tensor for olivine (Voigt representation), with units of GPa.

    \n\n

    The source of the values used here is unknown, but they are copied\nfrom the original DRex code: http://www.ipgp.fr/~kaminski/web_doudoud/DRex.tar.gz [88K download]

    \n", "default_value": "array([[3.2071e+02, 6.984e+01, 7.122e+01, 0.e+00, 0.e+00, 0.e+00],\n [6.984e+01, 1.9725e+02, 7.48e+01, 0.e+00, 0.e+00, 0.e+00],\n [7.122e+01, 7.48e+01, 2.3432e+02, 0.e+00, 0.e+00, 0.e+00],\n [0.e+00, 0.e+00, 0.e+00, 6.377e+01, 0.e+00, 0.e+00],\n [0.e+00, 0.e+00, 0.e+00, 0.e+00, 7.767e+01, 0.e+00],\n [0.e+00, 0.e+00, 0.e+00, 0.e+00, 0.e+00, 7.836e+01]])"}, "pydrex.minerals.ENSTATITE_STIFFNESS": {"fullname": "pydrex.minerals.ENSTATITE_STIFFNESS", "modulename": "pydrex.minerals", "qualname": "ENSTATITE_STIFFNESS", "kind": "variable", "doc": "

    Stiffness tensor for enstatite (Voigt representation), with units of GPa.

    \n\n

    The source of the values used here is unknown, but they are copied\nfrom the original DRex code: http://www.ipgp.fr/~kaminski/web_doudoud/DRex.tar.gz [88K download]

    \n", "default_value": "array([[2.369e+02, 7.96e+01, 6.32e+01, 0.e+00, 0.e+00, 0.e+00],\n [7.96e+01, 1.805e+02, 5.68e+01, 0.e+00, 0.e+00, 0.e+00],\n [6.32e+01, 5.68e+01, 2.304e+02, 0.e+00, 0.e+00, 0.e+00],\n [0.e+00, 0.e+00, 0.e+00, 8.43e+01, 0.e+00, 0.e+00],\n [0.e+00, 0.e+00, 0.e+00, 0.e+00, 7.94e+01, 0.e+00],\n [0.e+00, 0.e+00, 0.e+00, 0.e+00, 0.e+00, 8.01e+01]])"}, "pydrex.minerals.OLIVINE_PRIMARY_AXIS": {"fullname": "pydrex.minerals.OLIVINE_PRIMARY_AXIS", "modulename": "pydrex.minerals", "qualname": "OLIVINE_PRIMARY_AXIS", "kind": "variable", "doc": "

    Primary slip axis name for for the given olivine fabric.

    \n", "default_value": "{<MineralFabric.olivine_A: 0>: 'a', <MineralFabric.olivine_B: 1>: 'c', <MineralFabric.olivine_C: 2>: 'c', <MineralFabric.olivine_D: 3>: 'a', <MineralFabric.olivine_E: 4>: 'a'}"}, "pydrex.minerals.OLIVINE_SLIP_SYSTEMS": {"fullname": "pydrex.minerals.OLIVINE_SLIP_SYSTEMS", "modulename": "pydrex.minerals", "qualname": "OLIVINE_SLIP_SYSTEMS", "kind": "variable", "doc": "

    Slip systems for olivine in conventional order.

    \n\n

    Tuples contain the slip plane normal and slip direction vectors.\nThe order of slip systems returned matches the order of critical shear stresses\nreturned by pydrex.core.get_crss.

    \n", "default_value": "(([0, 1, 0], [1, 0, 0]), ([0, 0, 1], [1, 0, 0]), ([0, 1, 0], [0, 0, 1]), ([1, 0, 0], [0, 0, 1]))"}, "pydrex.minerals.voigt_averages": {"fullname": "pydrex.minerals.voigt_averages", "modulename": "pydrex.minerals", "qualname": "voigt_averages", "kind": "function", "doc": "

    Calculate elastic tensors as the Voigt averages of a collection of minerals.

    \n\n

    Args:

    \n\n\n\n

    Raises a ValueError if the minerals contain an unequal number of grains or stored\ntexture results.

    \n", "signature": "(minerals, weights):", "funcdef": "def"}, "pydrex.minerals.Mineral": {"fullname": "pydrex.minerals.Mineral", "modulename": "pydrex.minerals", "qualname": "Mineral", "kind": "class", "doc": "

    Class for storing polycrystal texture for a single mineral phase.

    \n\n

    A Mineral stores texture data for an aggregate of grains*.\nAdditionally, mineral fabric type and deformation regime are also tracked.\nTo provide an initial texture for the mineral, use the constructor arguments\nfractions_init and orientations_init. By default,\na uniform volume distribution of random orientations is generated.

    \n\n

    The update_orientations method computes new orientations and grain volumes\nfor a given velocity gradient. These results are stored in the .orientations and\n.fractions attributes of the Mineral instance. The method also returns the\nupdated macroscopic deformation gradient based on the provided initial deformation\ngradient.

    \n\n

    *Note that the \"number of grains\" is a static integer value that\ndoes not track the actual number of physical grains in the deforming polycrystal.\nInstead, this number acts as a \"number of bins\" for the statistical resolution of\nthe crystallographic orientation distribution. The value is roughly equivalent to\n(a multiple of) the number of initial, un-recrystallised grains in the polycrystal.\nIt is assumed that recrystallised grains do not grow large enough to require\nrotation tracking.

    \n\n

    Examples:

    \n\n

    Mineral with isotropic initial texture:

    \n\n
    \n
    >>> import pydrex\n>>> pydrex.Mineral(\n>>>     phase=pydrex.MineralPhase.olivine,\n>>>     fabric=pydrex.MineralFabric.olivine_A,\n>>>     regime=pydrex.DeformationRegime.dislocation,\n>>>     n_grains=2000,\n>>> )\nMineral(phase=0, fabric=0, regime=1, n_grains=2000, fractions=<list of ndarray (2000,)>, orientations=<list of ndarray (2000, 3, 3)>)\n
    \n
    \n\n

    Mineral with specified initial texture and default phase, fabric and regime settings\nwhich are for an olivine A-type mineral in the dislocation creep regime.\nThe initial grain volume fractions should be normalised.

    \n\n
    \n
    >>> import numpy as np\n>>> from scipy.spatial.transform import Rotation\n>>> import pydrex\n>>> rng = np.random.default_rng()\n>>> n_grains = 2000\n>>> pydrex.Mineral(\n>>>     n_grains=n_grains,\n>>>     fractions_init=np.full(n_grains, 1 / n_grains),\n>>>     orientations_init=Rotation.from_euler(\n>>>         "zxz", [[x * np.pi / 2, np.pi / /2, np.pi / 2] for x in rng.random(n_grains)]\n>>>     ).inv().as_matrix(),\n>>> )\nMineral(phase=0, fabric=0, regime=1, n_grains=2000, fractions=<list of ndarray (2000,)>, orientations=<list of ndarray (2000, 3, 3)>)\n
    \n
    \n\n

    Attributes:

    \n\n\n"}, "pydrex.minerals.Mineral.__init__": {"fullname": "pydrex.minerals.Mineral.__init__", "modulename": "pydrex.minerals", "qualname": "Mineral.__init__", "kind": "function", "doc": "

    \n", "signature": "(\tphase: int = <MineralPhase.olivine: 0>,\tfabric: int = <MineralFabric.olivine_A: 0>,\tregime: int = <DeformationRegime.dislocation: 1>,\tn_grains: int = 1000,\tfractions_init: numpy.ndarray = None,\torientations_init: numpy.ndarray = None,\tfractions: list = <factory>,\torientations: list = <factory>,\tseed: int = None,\tlband: int = None,\tuband: int = None)"}, "pydrex.minerals.Mineral.phase": {"fullname": "pydrex.minerals.Mineral.phase", "modulename": "pydrex.minerals", "qualname": "Mineral.phase", "kind": "variable", "doc": "

    \n", "annotation": ": int", "default_value": "<MineralPhase.olivine: 0>"}, "pydrex.minerals.Mineral.fabric": {"fullname": "pydrex.minerals.Mineral.fabric", "modulename": "pydrex.minerals", "qualname": "Mineral.fabric", "kind": "variable", "doc": "

    \n", "annotation": ": int", "default_value": "<MineralFabric.olivine_A: 0>"}, "pydrex.minerals.Mineral.regime": {"fullname": "pydrex.minerals.Mineral.regime", "modulename": "pydrex.minerals", "qualname": "Mineral.regime", "kind": "variable", "doc": "

    \n", "annotation": ": int", "default_value": "<DeformationRegime.dislocation: 1>"}, "pydrex.minerals.Mineral.n_grains": {"fullname": "pydrex.minerals.Mineral.n_grains", "modulename": "pydrex.minerals", "qualname": "Mineral.n_grains", "kind": "variable", "doc": "

    \n", "annotation": ": int", "default_value": "1000"}, "pydrex.minerals.Mineral.fractions_init": {"fullname": "pydrex.minerals.Mineral.fractions_init", "modulename": "pydrex.minerals", "qualname": "Mineral.fractions_init", "kind": "variable", "doc": "

    \n", "annotation": ": numpy.ndarray", "default_value": "None"}, "pydrex.minerals.Mineral.orientations_init": {"fullname": "pydrex.minerals.Mineral.orientations_init", "modulename": "pydrex.minerals", "qualname": "Mineral.orientations_init", "kind": "variable", "doc": "

    \n", "annotation": ": numpy.ndarray", "default_value": "None"}, "pydrex.minerals.Mineral.fractions": {"fullname": "pydrex.minerals.Mineral.fractions", "modulename": "pydrex.minerals", "qualname": "Mineral.fractions", "kind": "variable", "doc": "

    \n", "annotation": ": list"}, "pydrex.minerals.Mineral.orientations": {"fullname": "pydrex.minerals.Mineral.orientations", "modulename": "pydrex.minerals", "qualname": "Mineral.orientations", "kind": "variable", "doc": "

    \n", "annotation": ": list"}, "pydrex.minerals.Mineral.seed": {"fullname": "pydrex.minerals.Mineral.seed", "modulename": "pydrex.minerals", "qualname": "Mineral.seed", "kind": "variable", "doc": "

    \n", "annotation": ": int", "default_value": "None"}, "pydrex.minerals.Mineral.lband": {"fullname": "pydrex.minerals.Mineral.lband", "modulename": "pydrex.minerals", "qualname": "Mineral.lband", "kind": "variable", "doc": "

    \n", "annotation": ": int", "default_value": "None"}, "pydrex.minerals.Mineral.uband": {"fullname": "pydrex.minerals.Mineral.uband", "modulename": "pydrex.minerals", "qualname": "Mineral.uband", "kind": "variable", "doc": "

    \n", "annotation": ": int", "default_value": "None"}, "pydrex.minerals.Mineral.update_orientations": {"fullname": "pydrex.minerals.Mineral.update_orientations", "modulename": "pydrex.minerals", "qualname": "Mineral.update_orientations", "kind": "function", "doc": "

    Update orientations and volume distribution for the Mineral.

    \n\n

    Update crystalline orientations and grain volume distribution\nfor minerals undergoing plastic deformation.

    \n\n

    Args:

    \n\n\n\n

    Any additional (optional) keyword arguments are passed to\nscipy.integrate.LSODA.

    \n\n

    Array values must provide a NumPy-compatible interface:\nhttps://numpy.org/doc/stable/user/whatisnumpy.html

    \n", "signature": "(\tself,\tconfig,\tdeformation_gradient,\tget_velocity_gradient,\tpathline,\t**kwargs):", "funcdef": "def"}, "pydrex.minerals.Mineral.save": {"fullname": "pydrex.minerals.Mineral.save", "modulename": "pydrex.minerals", "qualname": "Mineral.save", "kind": "function", "doc": "

    Save CPO data for all stored timesteps to a numpy NPZ file.

    \n\n

    If postfix is not None, the data is appended to the NPZ file\nin fields ending with \"_postfix\".

    \n\n

    Raises a ValueError if the data shapes are not compatible.

    \n\n

    See also: numpy.savez, Mineral.load, Mineral.from_file.

    \n", "signature": "(self, filename, postfix=None):", "funcdef": "def"}, "pydrex.minerals.Mineral.load": {"fullname": "pydrex.minerals.Mineral.load", "modulename": "pydrex.minerals", "qualname": "Mineral.load", "kind": "function", "doc": "

    Load CPO data from a numpy NPZ file.

    \n\n

    If postfix is not None, data is read from fields ending with \"_postfix\".

    \n\n

    See also: Mineral.save, Mineral.from_file.

    \n", "signature": "(self, filename, postfix=None):", "funcdef": "def"}, "pydrex.minerals.Mineral.from_file": {"fullname": "pydrex.minerals.Mineral.from_file", "modulename": "pydrex.minerals", "qualname": "Mineral.from_file", "kind": "function", "doc": "

    Construct a Mineral instance using data from a numpy NPZ file.

    \n\n

    If postfix is not None, data is read from fields ending with \u201c_postfix\u201d.

    \n\n

    See also: Mineral.save, Mineral.load.

    \n", "signature": "(cls, filename, postfix=None):", "funcdef": "def"}, "pydrex.mock": {"fullname": "pydrex.mock", "modulename": "pydrex.mock", "kind": "module", "doc": "
    \n

    PyDRex: Mock objects for testing and reproducibility.

    \n
    \n"}, "pydrex.mock.PARAMS_FRATERS2021": {"fullname": "pydrex.mock.PARAMS_FRATERS2021", "modulename": "pydrex.mock", "qualname": "PARAMS_FRATERS2021", "kind": "variable", "doc": "

    Values used for tests 1, 2 and 4 in https://doi.org/10.1029/2021gc009846.

    \n", "default_value": "{'olivine_fraction': 0.7, 'enstatite_fraction': 0.3, 'initial_olivine_fabric': <MineralFabric.olivine_A: 0>, 'stress_exponent': 1.5, 'deformation_exponent': 3.5, 'gbm_mobility': 125, 'gbs_threshold': 0.3, 'nucleation_efficiency': 5, 'number_of_grains': 500}"}, "pydrex.mock.PARAMS_KAMINSKI2001_FIG5_SOLID": {"fullname": "pydrex.mock.PARAMS_KAMINSKI2001_FIG5_SOLID", "modulename": "pydrex.mock", "qualname": "PARAMS_KAMINSKI2001_FIG5_SOLID", "kind": "variable", "doc": "

    Values used for the M*=0 test in https://doi.org/10.1016/s0012-821x(01)00356-9.

    \n", "default_value": "{'olivine_fraction': 1, 'enstatite_fraction': 0, 'initial_olivine_fabric': <MineralFabric.olivine_A: 0>, 'stress_exponent': 1.5, 'deformation_exponent': 3.5, 'gbm_mobility': 0, 'gbs_threshold': 0, 'nucleation_efficiency': 5, 'number_of_grains': 3375}"}, "pydrex.mock.PARAMS_KAMINSKI2001_FIG5_SHORTDASH": {"fullname": "pydrex.mock.PARAMS_KAMINSKI2001_FIG5_SHORTDASH", "modulename": "pydrex.mock", "qualname": "PARAMS_KAMINSKI2001_FIG5_SHORTDASH", "kind": "variable", "doc": "

    Values used for the M*=50 test in https://doi.org/10.1016/s0012-821x(01)00356-9.

    \n", "default_value": "{'olivine_fraction': 1, 'enstatite_fraction': 0, 'initial_olivine_fabric': <MineralFabric.olivine_A: 0>, 'stress_exponent': 1.5, 'deformation_exponent': 3.5, 'gbm_mobility': 50, 'gbs_threshold': 0, 'nucleation_efficiency': 5, 'number_of_grains': 3375}"}, "pydrex.mock.PARAMS_KAMINSKI2001_FIG5_LONGDASH": {"fullname": "pydrex.mock.PARAMS_KAMINSKI2001_FIG5_LONGDASH", "modulename": "pydrex.mock", "qualname": "PARAMS_KAMINSKI2001_FIG5_LONGDASH", "kind": "variable", "doc": "

    Values used for the M*=200 test in https://doi.org/10.1016/s0012-821x(01)00356-9.

    \n", "default_value": "{'olivine_fraction': 1, 'enstatite_fraction': 0, 'initial_olivine_fabric': <MineralFabric.olivine_A: 0>, 'stress_exponent': 1.5, 'deformation_exponent': 3.5, 'gbm_mobility': 200, 'gbs_threshold': 0, 'nucleation_efficiency': 5, 'number_of_grains': 3375}"}, "pydrex.mock.PARAMS_KAMINSKI2004_FIG4_TRIANGLES": {"fullname": "pydrex.mock.PARAMS_KAMINSKI2004_FIG4_TRIANGLES", "modulename": "pydrex.mock", "qualname": "PARAMS_KAMINSKI2004_FIG4_TRIANGLES", "kind": "variable", "doc": "

    Values used for the \u03c7=0.4 test in https://doi.org/10.1111/j.1365-246x.2004.02308.x.

    \n", "default_value": "{'olivine_fraction': 1, 'enstatite_fraction': 0, 'initial_olivine_fabric': <MineralFabric.olivine_A: 0>, 'stress_exponent': 1.5, 'deformation_exponent': 3.5, 'gbm_mobility': 125, 'gbs_threshold': 0.4, 'nucleation_efficiency': 5, 'number_of_grains': 4394}"}, "pydrex.mock.PARAMS_KAMINSKI2004_FIG4_SQUARES": {"fullname": "pydrex.mock.PARAMS_KAMINSKI2004_FIG4_SQUARES", "modulename": "pydrex.mock", "qualname": "PARAMS_KAMINSKI2004_FIG4_SQUARES", "kind": "variable", "doc": "

    Values used for the \u03c7=0.2 test in https://doi.org/10.1111/j.1365-246x.2004.02308.x.

    \n", "default_value": "{'olivine_fraction': 1, 'enstatite_fraction': 0, 'initial_olivine_fabric': <MineralFabric.olivine_A: 0>, 'stress_exponent': 1.5, 'deformation_exponent': 3.5, 'gbm_mobility': 125, 'gbs_threshold': 0.2, 'nucleation_efficiency': 5, 'number_of_grains': 4394}"}, "pydrex.mock.PARAMS_KAMINSKI2004_FIG4_CIRCLES": {"fullname": "pydrex.mock.PARAMS_KAMINSKI2004_FIG4_CIRCLES", "modulename": "pydrex.mock", "qualname": "PARAMS_KAMINSKI2004_FIG4_CIRCLES", "kind": "variable", "doc": "

    Values used for the \u03c7=0 test in https://doi.org/10.1111/j.1365-246x.2004.02308.x.

    \n", "default_value": "{'olivine_fraction': 1, 'enstatite_fraction': 0, 'initial_olivine_fabric': <MineralFabric.olivine_A: 0>, 'stress_exponent': 1.5, 'deformation_exponent': 3.5, 'gbm_mobility': 125, 'gbs_threshold': 0, 'nucleation_efficiency': 5, 'number_of_grains': 4394}"}, "pydrex.mock.PARAMS_HEDJAZIAN2017": {"fullname": "pydrex.mock.PARAMS_HEDJAZIAN2017", "modulename": "pydrex.mock", "qualname": "PARAMS_HEDJAZIAN2017", "kind": "variable", "doc": "

    Values used for the MOR model in https://doi.org/10.1016/j.epsl.2016.12.004.

    \n", "default_value": "{'olivine_fraction': 0.7, 'enstatite_fraction': 0.3, 'initial_olivine_fabric': <MineralFabric.olivine_A: 0>, 'stress_exponent': 1.5, 'deformation_exponent': 3.5, 'gbm_mobility': 10, 'gbs_threshold': 0.2, 'nucleation_efficiency': 5, 'number_of_grains': 2197}"}, "pydrex.pathlines": {"fullname": "pydrex.pathlines", "modulename": "pydrex.pathlines", "kind": "module", "doc": "
    \n

    PyDRex: Functions for pathline construction.

    \n
    \n"}, "pydrex.pathlines.get_pathline": {"fullname": "pydrex.pathlines.get_pathline", "modulename": "pydrex.pathlines", "qualname": "get_pathline", "kind": "function", "doc": "

    Determine the pathline for a particle in a steady state flow.

    \n\n

    The pathline will intersect the given point and follow a curve determined by\nthe interpolated velocity gradient.

    \n\n

    Args:\n point (NumPy array) \u2014 coordinates of the point\n interp_velocity (interpolator) \u2014 returns velocity vector at a point\n interp_velocity_gradient (interpolator) \u2014 returns \u2207v (3x3 matrix) at a point\n min_coords (iterable) \u2014 lower bound coordinate of the interpolation grid\n max_coords (iterable) \u2014 upper bound coordinate of the interpolation grid

    \n\n

    Returns a tuple containing the time points and an interpolant that can be used\nto evaluate the pathline position (see scipy.integrate.OdeSolution).

    \n", "signature": "(\tpoint,\tinterp_velocity,\tinterp_velocity_gradient,\tmin_coords,\tmax_coords):", "funcdef": "def"}, "pydrex.stats": {"fullname": "pydrex.stats", "modulename": "pydrex.stats", "kind": "module", "doc": "
    \n

    PyDRex: Statistical methods for orientation and elasticity data.

    \n
    \n"}, "pydrex.stats.resample_orientations": {"fullname": "pydrex.stats.resample_orientations", "modulename": "pydrex.stats", "qualname": "resample_orientations", "kind": "function", "doc": "

    Generate new samples from orientations weighed by the volume distribution.

    \n\n

    If the optional number of samples n_samples is not specified,\nit will be set to the number of original \"grains\" (length of fractions).\nThe argument seed can be used to seed the random number generator.

    \n", "signature": "(orientations, fractions, n_samples=None, seed=None):", "funcdef": "def"}, "pydrex.stats.misorientations_random": {"fullname": "pydrex.stats.misorientations_random", "modulename": "pydrex.stats", "qualname": "misorientations_random", "kind": "function", "doc": "

    Get expected count of misorientation angles for an isotropic aggregate.

    \n\n

    Estimate the expected number of misorientation angles between grains\nthat would fall within $($low, high$)$ in degrees for an aggregate\nwith randomly oriented grains, where low $\u2208 [0, $high$)$,\nand high is bounded by the maximum theoretical misorientation angle\nfor the given symmetry system.

    \n\n

    The optional argument system accepts a tuple of integers (a, b)\nthat specifies the crystal symmetry system according to:

    \n\n
    system  triclinic  monoclinic  orthorhombic  rhombohedral tetragonal hexagonal\n------------------------------------------------------------------------------\na       1          2           2             3            4          6\nb       1          2           4             6            8          12\n\u03b8max    180\u00b0       180\u00b0        120\u00b0          120\u00b0         90\u00b0        90\u00b0\n
    \n\n

    This is identically Table 1 in Grimmer 1979.\nThe orthorhombic system (olivine) is selected by default.

    \n", "signature": "(low, high, system=(2, 4)):", "funcdef": "def"}, "pydrex.stats.point_density": {"fullname": "pydrex.stats.point_density", "modulename": "pydrex.stats", "qualname": "point_density", "kind": "function", "doc": "

    Estimate point density of orientation data on the unit sphere.

    \n\n

    Estimates the density of orientations on the unit sphere by counting the input data\nthat falls within small areas around a uniform grid of spherical counting locations.\nThe input data is expected in cartesian coordinates, and the contouring is performed\nusing kernel functions defined in Vollmer 1995.\nThe following optional parameters control the contouring method:

    \n\n\n\n

    Any other keyword arguments are passed to the kernel function calls.\nMost kernels accept a parameter \u03c3 to control the degree of smoothing.

    \n", "signature": "(\tx_data,\ty_data,\tz_data,\tgridsteps=101,\tweights=1,\tkernel='linear_inverse_kamb',\taxial=True,\t**kwargs):", "funcdef": "def"}, "pydrex.stats.exponential_kamb": {"fullname": "pydrex.stats.exponential_kamb", "modulename": "pydrex.stats", "qualname": "exponential_kamb", "kind": "function", "doc": "

    Kernel function from Vollmer 1995 for exponential smoothing.

    \n", "signature": "(cos_dist, \u03c3=10, axial=True):", "funcdef": "def"}, "pydrex.stats.linear_inverse_kamb": {"fullname": "pydrex.stats.linear_inverse_kamb", "modulename": "pydrex.stats", "qualname": "linear_inverse_kamb", "kind": "function", "doc": "

    Kernel function from Vollmer 1995 for linear smoothing.

    \n", "signature": "(cos_dist, \u03c3=10, axial=True):", "funcdef": "def"}, "pydrex.stats.square_inverse_kamb": {"fullname": "pydrex.stats.square_inverse_kamb", "modulename": "pydrex.stats", "qualname": "square_inverse_kamb", "kind": "function", "doc": "

    Kernel function from Vollmer 1995 for inverse square smoothing.

    \n", "signature": "(cos_dist, \u03c3=10, axial=True):", "funcdef": "def"}, "pydrex.stats.kamb_count": {"fullname": "pydrex.stats.kamb_count", "modulename": "pydrex.stats", "qualname": "kamb_count", "kind": "function", "doc": "

    Original Kamb 1959 kernel function (raw count within radius).

    \n", "signature": "(cos_dist, \u03c3=10, axial=True):", "funcdef": "def"}, "pydrex.stats.schmidt_count": {"fullname": "pydrex.stats.schmidt_count", "modulename": "pydrex.stats", "qualname": "schmidt_count", "kind": "function", "doc": "

    Schmidt (a.k.a. 1%) counting kernel function.

    \n", "signature": "(cos_dist, axial=None):", "funcdef": "def"}, "pydrex.stats.SPHERICAL_COUNTING_KERNELS": {"fullname": "pydrex.stats.SPHERICAL_COUNTING_KERNELS", "modulename": "pydrex.stats", "qualname": "SPHERICAL_COUNTING_KERNELS", "kind": "variable", "doc": "

    Kernel functions that return an un-summed distribution and a normalization factor.

    \n\n

    Supported kernel functions are based on the discussion in\nVollmer 1995.\nKamb methods accept the parameter \u03c3 (default: 10) to control the degree of smoothing.\nValues lower than 3 and higher than 20 are not recommended.

    \n", "default_value": "{'kamb_count': <function kamb_count>, 'schmidt_count': <function schmidt_count>, 'exponential_kamb': <function exponential_kamb>, 'linear_inverse_kamb': <function linear_inverse_kamb>, 'square_inverse_kamb': <function square_inverse_kamb>}"}, "pydrex.tensors": {"fullname": "pydrex.tensors", "modulename": "pydrex.tensors", "kind": "module", "doc": "
    \n

    PyDRex: Tensor operation functions and helpers.

    \n
    \n\n

    For Voigt notation, the symmetric 6x6 matrix representation is used,\nwhich assumes that the fourth order tensor being represented as such is also symmetric.\nThe vectorial notation uses 21 components which are the independent components of the\nsymmetric 6x6 matrix.

    \n"}, "pydrex.tensors.PERMUTATION_SYMBOL": {"fullname": "pydrex.tensors.PERMUTATION_SYMBOL", "modulename": "pydrex.tensors", "qualname": "PERMUTATION_SYMBOL", "kind": "variable", "doc": "

    \n", "default_value": "array([[[0.e+00, 0.e+00, 0.e+00],\n [0.e+00, 0.e+00, 1.e+00],\n [0.e+00, -1.e+00, 0.e+00]],\n\n [[0.e+00, 0.e+00, -1.e+00],\n [0.e+00, 0.e+00, 0.e+00],\n [1.e+00, 0.e+00, 0.e+00]],\n\n [[0.e+00, 1.e+00, 0.e+00],\n [-1.e+00, 0.e+00, 0.e+00],\n [0.e+00, 0.e+00, 0.e+00]]])"}, "pydrex.tensors.voigt_decompose": {"fullname": "pydrex.tensors.voigt_decompose", "modulename": "pydrex.tensors", "qualname": "voigt_decompose", "kind": "function", "doc": "

    Decompose elastic tensor (as 6x6 Voigt matrix) into distinct contractions.

    \n\n

    Return the only two independent contractions of the elastic tensor, given as a 6x6\nVoigt matrix. For the equivalent 4-th order elastic tensor, the contractions are:

    \n\n\n\n

    See Equations 3.4 & 3.5 in Browaeys & Chevrot.

    \n", "signature": "(matrix):", "funcdef": "def"}, "pydrex.tensors.hex_projector": {"fullname": "pydrex.tensors.hex_projector", "modulename": "pydrex.tensors", "qualname": "hex_projector", "kind": "function", "doc": "

    Projector p\u2084 onto hexagonal (a.k.a. transverse isotropy) symmetry.

    \n\n

    See Browaeys & Chevrot.

    \n", "signature": "(x):", "funcdef": "def"}, "pydrex.tensors.upper_tri_to_symmetric": {"fullname": "pydrex.tensors.upper_tri_to_symmetric", "modulename": "pydrex.tensors", "qualname": "upper_tri_to_symmetric", "kind": "function", "doc": "

    Create symmetric array using upper triangle of input array.

    \n\n
    \n
    >>> import numpy as np\n>>> upper_tri_to_symmetric(np.array([\n>>>         [ 1.,  2.,  3.,  4.],\n>>>         [ 0.,  5.,  6.,  7.],\n>>>         [ 0.,  0.,  8.,  9.],\n>>>         [ 9.,  0.,  0., 10.]\n>>> ]))\narray([[ 1.,  2.,  3.,  4.],\n       [ 2.,  5.,  6.,  7.],\n       [ 3.,  6.,  8.,  9.],\n       [ 4.,  7.,  9., 10.]])\n
    \n
    \n", "signature": "(arr):", "funcdef": "def"}, "pydrex.tensors.voigt_to_elastic_tensor": {"fullname": "pydrex.tensors.voigt_to_elastic_tensor", "modulename": "pydrex.tensors", "qualname": "voigt_to_elastic_tensor", "kind": "function", "doc": "

    Create 4-th order elastic tensor from an equivalent Voigt matrix.

    \n\n

    See also: elastic_tensor_to_voigt.

    \n", "signature": "(matrix):", "funcdef": "def"}, "pydrex.tensors.elastic_tensor_to_voigt": {"fullname": "pydrex.tensors.elastic_tensor_to_voigt", "modulename": "pydrex.tensors", "qualname": "elastic_tensor_to_voigt", "kind": "function", "doc": "

    Create a 6x6 Voigt matrix from an equivalent 4-th order elastic tensor.

    \n", "signature": "(tensor):", "funcdef": "def"}, "pydrex.tensors.voigt_matrix_to_vector": {"fullname": "pydrex.tensors.voigt_matrix_to_vector", "modulename": "pydrex.tensors", "qualname": "voigt_matrix_to_vector", "kind": "function", "doc": "

    Create the 21-component Voigt vector equivalent to the 6x6 Voigt matrix.

    \n", "signature": "(matrix):", "funcdef": "def"}, "pydrex.tensors.voigt_vector_to_matrix": {"fullname": "pydrex.tensors.voigt_vector_to_matrix", "modulename": "pydrex.tensors", "qualname": "voigt_vector_to_matrix", "kind": "function", "doc": "

    Create the 6x6 matrix representation of the 21-component Voigt vector.

    \n\n

    See also: voigt_matrix_to_vector.

    \n", "signature": "(vector):", "funcdef": "def"}, "pydrex.tensors.rotate": {"fullname": "pydrex.tensors.rotate", "modulename": "pydrex.tensors", "qualname": "rotate", "kind": "function", "doc": "

    Rotate 4-th order tensor using a 3x3 rotation matrix.

    \n", "signature": "(tensor, rotation):", "funcdef": "def"}, "pydrex.utils": {"fullname": "pydrex.utils", "modulename": "pydrex.utils", "kind": "module", "doc": "
    \n

    PyDRex: Miscellaneous utility methods.

    \n
    \n"}, "pydrex.utils.remove_nans": {"fullname": "pydrex.utils.remove_nans", "modulename": "pydrex.utils", "qualname": "remove_nans", "kind": "function", "doc": "

    Remove NaN values from array.

    \n", "signature": "(a):", "funcdef": "def"}, "pydrex.utils.readable_timestamp": {"fullname": "pydrex.utils.readable_timestamp", "modulename": "pydrex.utils", "qualname": "readable_timestamp", "kind": "function", "doc": "

    Convert timestamp in fractional seconds to human readable format.

    \n", "signature": "(timestamp, tformat='%H:%M:%S'):", "funcdef": "def"}, "pydrex.utils.angle_fse_simpleshear": {"fullname": "pydrex.utils.angle_fse_simpleshear", "modulename": "pydrex.utils", "qualname": "angle_fse_simpleshear", "kind": "function", "doc": "

    Get angle of FSE long axis anticlockwise from the X axis in simple shear.

    \n", "signature": "(strain):", "funcdef": "def"}, "pydrex.velocity_gradients": {"fullname": "pydrex.velocity_gradients", "modulename": "pydrex.velocity_gradients", "kind": "module", "doc": "
    \n

    PyDRex: Steady-state solutions of velocity gradients for various flows.

    \n
    \n"}, "pydrex.velocity_gradients.simple_shear_2d": {"fullname": "pydrex.velocity_gradients.simple_shear_2d", "modulename": "pydrex.velocity_gradients", "qualname": "simple_shear_2d", "kind": "function", "doc": "

    Return simple shear velocity gradient callable f(x) for the given parameters.

    \n", "signature": "(direction, deformation_plane, strain_rate):", "funcdef": "def"}, "pydrex.visualisation": {"fullname": "pydrex.visualisation", "modulename": "pydrex.visualisation", "kind": "module", "doc": "
    \n

    PyDRex: Visualisation functions for test outputs and examples.

    \n
    \n"}, "pydrex.visualisation.polefigures": {"fullname": "pydrex.visualisation.polefigures", "modulename": "pydrex.visualisation", "qualname": "polefigures", "kind": "function", "doc": "

    Plot pole figures of a series of (Nx3x3) orientation matrix stacks.

    \n\n

    Produces [100], [010] and [001] pole figures for (resampled) orientations.\nFor the argument specification, check the output of pydrex-polefigures --help\non the command line.

    \n", "signature": "(\torientations,\tref_axes,\ti_range,\tdensity=False,\tsavefile='polefigures.png',\tstrains=None,\t**kwargs):", "funcdef": "def"}, "pydrex.visualisation.simple_shear_stationary_2d": {"fullname": "pydrex.visualisation.simple_shear_stationary_2d", "modulename": "pydrex.visualisation", "qualname": "simple_shear_stationary_2d", "kind": "function", "doc": "

    Plot diagnostics for stationary A-type olivine 2D simple shear box tests.

    \n", "signature": "(\tstrains,\tangles,\tpoint100_symmetry,\ttarget_angles=None,\tangles_err=None,\tsavefile='pydrex_simple_shear_stationary_2d.png',\tmarkers='.',\t\u03b8_fse=None,\tlabels=None,\ta_type=True):", "funcdef": "def"}, "pydrex.visualisation.corner_flow_2d": {"fullname": "pydrex.visualisation.corner_flow_2d", "modulename": "pydrex.visualisation", "qualname": "corner_flow_2d", "kind": "function", "doc": "

    Plot diagnostics for prescribed path 2D corner flow tests.

    \n", "signature": "(\tx_paths,\tz_paths,\tangles,\tindices,\tdirections,\ttimestamps,\txlabel,\tsavefile='pydrex_corner_2d.png',\tmarkers='.',\tlabels=None,\txlims=None,\tzlims=None,\tcpo_threshold=0.33,\t\u03a0_levels=(0.1, 0.5, 1, 2, 3),\ttick_formatter=<function <lambda>>):", "funcdef": "def"}, "pydrex.visualisation.single_olivineA_simple_shear": {"fullname": "pydrex.visualisation.single_olivineA_simple_shear", "modulename": "pydrex.visualisation", "qualname": "single_olivineA_simple_shear", "kind": "function", "doc": "

    \n", "signature": "(\tinitial_angles,\trotation_rates,\ttarget_rotation_rates,\tsavefile='single_olivineA_simple_shear.png'):", "funcdef": "def"}, "pydrex.vtk_helpers": {"fullname": "pydrex.vtk_helpers", "modulename": "pydrex.vtk_helpers", "kind": "module", "doc": "
    \n

    PyDRex: VTK wrappers and helper functions.

    \n
    \n"}, "pydrex.vtk_helpers.get_output": {"fullname": "pydrex.vtk_helpers.get_output", "modulename": "pydrex.vtk_helpers", "qualname": "get_output", "kind": "function", "doc": "

    Get a reference to an unstructured (XML) VTK grid stored in filename.

    \n\n

    Only supports modern vtk formats, i.e. .vtu and .pvtu files.

    \n", "signature": "(filename):", "funcdef": "def"}, "pydrex.vtk_helpers.read_tuple_array": {"fullname": "pydrex.vtk_helpers.read_tuple_array", "modulename": "pydrex.vtk_helpers", "qualname": "read_tuple_array", "kind": "function", "doc": "

    Read tuples from VTK points into a numpy array.

    \n\n

    Create a numpy array from tuples extracted from a vtkPointData object.\nThe returned array has a shape of either (N, d) for vector data,\nor (N, d, d) for matrix data, where N is the number of VTK nodes\nand d is the dimension (3 by default, or 2 if skip3 is True).

    \n\n

    If skip3 is True, the domain is assumed to be two-dimensional,\nand any values corresponding to a third dimension are skipped.

    \n\n

    Throws a LookupError if the fieldname string does not match any data.

    \n", "signature": "(points, fieldname, skip3=False):", "funcdef": "def"}, "pydrex.vtk_helpers.read_coord_array": {"fullname": "pydrex.vtk_helpers.read_coord_array", "modulename": "pydrex.vtk_helpers", "qualname": "read_coord_array", "kind": "function", "doc": "

    Read coordinates from vtkgrid into a numpy array.

    \n\n

    Create a numpy array with coordinates extracted from a vtk{Uns,S}tructuredGrid\nobject.

    \n\n

    If skip_empty is True (default), columns full of zeros are skipped.\nThese are often present in VTK output files from 2D simulations.

    \n\n

    If depth_conversion is True (default), the last nonzero column is assumed\nto contain height values which are converted to depth values by subtraction\nfrom the maximum value.

    \n", "signature": "(vtkgrid, skip_empty=True, convert_depth=True):", "funcdef": "def"}, "pydrex.vtk_helpers.get_steps": {"fullname": "pydrex.vtk_helpers.get_steps", "modulename": "pydrex.vtk_helpers", "qualname": "get_steps", "kind": "function", "doc": "

    Get forward difference of 2D array a, with repeated last elements.

    \n\n

    The repeated last elements ensure that output and input arrays have equal shape.

    \n\n

    Examples:

    \n\n
    \n
    >>> _get_steps(np.array([1, 2, 3, 4, 5]))\narray([[1, 1, 1, 1, 1]])\n
    \n
    \n\n
    \n
    >>> _get_steps(np.array([[1, 2, 3, 4, 5], [1, 3, 6, 9, 10]]))\narray([[1, 1, 1, 1, 1],\n       [2, 3, 3, 1, 1]])\n
    \n
    \n\n
    \n
    >>> _get_steps(np.array([[1, 2, 3, 4, 5], [1, 3, 6, 9, 10], [1, 0, 0, 0, np.inf]]))\narray([[ 1.,  1.,  1.,  1.,  1.],\n       [ 2.,  3.,  3.,  1.,  1.],\n       [-1.,  0.,  0., inf, nan]])\n
    \n
    \n", "signature": "(a):", "funcdef": "def"}, "tests": {"fullname": "tests", "modulename": "tests", "kind": "module", "doc": "

    PyDRex tests

    \n\n

    Running the tests requires pytest.\nFrom the root of the source tree, run pytest.\nTo print more verbose information (including INFO level logging),\nuse the flag pytest -v.\nThe custom optional flag --outdir=\"OUT\" can be used\nto produce output figures, data dumps and logs and save them in the directory \"OUT\".\nThe value \".\" can be used to save these in the current directory.\nLong tests/examples are disabled by default to prevent clogging up the CI,\nthey can be enabled with --runslow.\nTo mark a test as slow,\nadd the @pytest.mark.slow decorator above its method definition.

    \n\n

    Tests should not produce persistent output by default.\nIf a test method can produce such output for debugging, it should accept the outdir\npositional argument, and check if its value is not None.\nIf outdir is None then no persistent output should be produced.\nIf outdir is a directory path (string):

    \n\n\n"}, "tests.conftest": {"fullname": "tests.conftest", "modulename": "tests.conftest", "kind": "module", "doc": "
    \n

    Configuration and fixtures for PyDRex tests.

    \n
    \n"}, "tests.conftest.pytest_addoption": {"fullname": "tests.conftest.pytest_addoption", "modulename": "tests.conftest", "qualname": "pytest_addoption", "kind": "function", "doc": "

    \n", "signature": "(parser):", "funcdef": "def"}, "tests.conftest.PytestConsoleLogger": {"fullname": "tests.conftest.PytestConsoleLogger", "modulename": "tests.conftest", "qualname": "PytestConsoleLogger", "kind": "class", "doc": "

    Pytest plugin that allows linking up a custom console logger.

    \n", "bases": "_pytest.logging.LoggingPlugin"}, "tests.conftest.PytestConsoleLogger.__init__": {"fullname": "tests.conftest.PytestConsoleLogger.__init__", "modulename": "tests.conftest", "qualname": "PytestConsoleLogger.__init__", "kind": "function", "doc": "

    Create a new plugin to capture log messages.

    \n\n

    The formatter can be safely shared across all handlers so\ncreate a single one for the entire test session here.

    \n", "signature": "(config, *args, **kwargs)"}, "tests.conftest.PytestConsoleLogger.name": {"fullname": "tests.conftest.PytestConsoleLogger.name", "modulename": "tests.conftest", "qualname": "PytestConsoleLogger.name", "kind": "variable", "doc": "

    \n", "default_value": "'pytest-console-logger'"}, "tests.conftest.PytestConsoleLogger.log_cli_handler": {"fullname": "tests.conftest.PytestConsoleLogger.log_cli_handler", "modulename": "tests.conftest", "qualname": "PytestConsoleLogger.log_cli_handler", "kind": "variable", "doc": "

    \n"}, "tests.conftest.PytestConsoleLogger.pytest_runtest_teardown": {"fullname": "tests.conftest.PytestConsoleLogger.pytest_runtest_teardown", "modulename": "tests.conftest", "qualname": "PytestConsoleLogger.pytest_runtest_teardown", "kind": "function", "doc": "

    \n", "signature": "(self, item):", "funcdef": "def"}, "tests.conftest.pytest_configure": {"fullname": "tests.conftest.pytest_configure", "modulename": "tests.conftest", "qualname": "pytest_configure", "kind": "function", "doc": "

    \n", "signature": "(config):", "funcdef": "def"}, "tests.conftest.pytest_collection_modifyitems": {"fullname": "tests.conftest.pytest_collection_modifyitems", "modulename": "tests.conftest", "qualname": "pytest_collection_modifyitems", "kind": "function", "doc": "

    \n", "signature": "(config, items):", "funcdef": "def"}, "tests.conftest.outdir": {"fullname": "tests.conftest.outdir", "modulename": "tests.conftest", "qualname": "outdir", "kind": "function", "doc": "

    \n", "signature": "(request):", "funcdef": "def"}, "tests.conftest.ncpus": {"fullname": "tests.conftest.ncpus", "modulename": "tests.conftest", "qualname": "ncpus", "kind": "function", "doc": "

    \n", "signature": "(request):", "funcdef": "def"}, "tests.conftest.console_handler": {"fullname": "tests.conftest.console_handler", "modulename": "tests.conftest", "qualname": "console_handler", "kind": "function", "doc": "

    \n", "signature": "(request):", "funcdef": "def"}, "tests.conftest.params_Fraters2021": {"fullname": "tests.conftest.params_Fraters2021", "modulename": "tests.conftest", "qualname": "params_Fraters2021", "kind": "function", "doc": "

    \n", "signature": "():", "funcdef": "def"}, "tests.conftest.params_Kaminski2001_fig5_solid": {"fullname": "tests.conftest.params_Kaminski2001_fig5_solid", "modulename": "tests.conftest", "qualname": "params_Kaminski2001_fig5_solid", "kind": "function", "doc": "

    \n", "signature": "():", "funcdef": "def"}, "tests.conftest.params_Kaminski2001_fig5_shortdash": {"fullname": "tests.conftest.params_Kaminski2001_fig5_shortdash", "modulename": "tests.conftest", "qualname": "params_Kaminski2001_fig5_shortdash", "kind": "function", "doc": "

    \n", "signature": "():", "funcdef": "def"}, "tests.conftest.params_Kaminski2001_fig5_longdash": {"fullname": "tests.conftest.params_Kaminski2001_fig5_longdash", "modulename": "tests.conftest", "qualname": "params_Kaminski2001_fig5_longdash", "kind": "function", "doc": "

    \n", "signature": "():", "funcdef": "def"}, "tests.conftest.params_Kaminski2004_fig4_triangles": {"fullname": "tests.conftest.params_Kaminski2004_fig4_triangles", "modulename": "tests.conftest", "qualname": "params_Kaminski2004_fig4_triangles", "kind": "function", "doc": "

    \n", "signature": "():", "funcdef": "def"}, "tests.conftest.params_Kaminski2004_fig4_squares": {"fullname": "tests.conftest.params_Kaminski2004_fig4_squares", "modulename": "tests.conftest", "qualname": "params_Kaminski2004_fig4_squares", "kind": "function", "doc": "

    \n", "signature": "():", "funcdef": "def"}, "tests.conftest.params_Kaminski2004_fig4_circles": {"fullname": "tests.conftest.params_Kaminski2004_fig4_circles", "modulename": "tests.conftest", "qualname": "params_Kaminski2004_fig4_circles", "kind": "function", "doc": "

    \n", "signature": "():", "funcdef": "def"}, "tests.conftest.params_Hedjazian2017": {"fullname": "tests.conftest.params_Hedjazian2017", "modulename": "tests.conftest", "qualname": "params_Hedjazian2017", "kind": "function", "doc": "

    \n", "signature": "():", "funcdef": "def"}, "tests.conftest.hkl": {"fullname": "tests.conftest.hkl", "modulename": "tests.conftest", "qualname": "hkl", "kind": "function", "doc": "

    \n", "signature": "(request):", "funcdef": "def"}, "tests.conftest.ref_axes": {"fullname": "tests.conftest.ref_axes", "modulename": "tests.conftest", "qualname": "ref_axes", "kind": "function", "doc": "

    \n", "signature": "(request):", "funcdef": "def"}, "tests.conftest.seeds": {"fullname": "tests.conftest.seeds", "modulename": "tests.conftest", "qualname": "seeds", "kind": "function", "doc": "

    1000 unique seeds for ensemble runs that need an RNG seed.

    \n", "signature": "():", "funcdef": "def"}, "tests.conftest.seed": {"fullname": "tests.conftest.seed", "modulename": "tests.conftest", "qualname": "seed", "kind": "function", "doc": "

    Default seed for test RNG.

    \n", "signature": "():", "funcdef": "def"}, "tests.conftest.seeds_nearX45": {"fullname": "tests.conftest.seeds_nearX45", "modulename": "tests.conftest", "qualname": "seeds_nearX45", "kind": "function", "doc": "

    41 seeds which have the initial hexagonal symmetry axis near 45\u00b0 from X.

    \n", "signature": "():", "funcdef": "def"}, "tests.test_config": {"fullname": "tests.test_config", "modulename": "tests.test_config", "kind": "module", "doc": "
    \n

    PyDRex: tests for configuration file format.

    \n
    \n"}, "tests.test_config.test_specfile": {"fullname": "tests.test_config.test_specfile", "modulename": "tests.test_config", "qualname": "test_specfile", "kind": "function", "doc": "

    Test TOML spec file parsing.

    \n", "signature": "():", "funcdef": "def"}, "tests.test_core": {"fullname": "tests.test_core", "modulename": "tests.test_core", "kind": "module", "doc": "
    \n

    PyDRex: tests for core D-Rex routines.

    \n
    \n"}, "tests.test_core.SUBDIR": {"fullname": "tests.test_core.SUBDIR", "modulename": "tests.test_core", "qualname": "SUBDIR", "kind": "variable", "doc": "

    \n", "default_value": "'core'"}, "tests.test_core.TestSimpleShearOPX": {"fullname": "tests.test_core.TestSimpleShearOPX", "modulename": "tests.test_core", "qualname": "TestSimpleShearOPX", "kind": "class", "doc": "

    Single-grain orthopyroxene crystallographic rotation rate tests.

    \n"}, "tests.test_core.TestSimpleShearOPX.class_id": {"fullname": "tests.test_core.TestSimpleShearOPX.class_id", "modulename": "tests.test_core", "qualname": "TestSimpleShearOPX.class_id", "kind": "variable", "doc": "

    \n", "default_value": "'simple_shear_OPX'"}, "tests.test_core.TestSimpleShearOPX.test_shear_dudz": {"fullname": "tests.test_core.TestSimpleShearOPX.test_shear_dudz", "modulename": "tests.test_core", "qualname": "TestSimpleShearOPX.test_shear_dudz", "kind": "function", "doc": "

    \n", "signature": "(self, outdir):", "funcdef": "def"}, "tests.test_core.TestSimpleShearOPX.test_shear_dvdx": {"fullname": "tests.test_core.TestSimpleShearOPX.test_shear_dvdx", "modulename": "tests.test_core", "qualname": "TestSimpleShearOPX.test_shear_dvdx", "kind": "function", "doc": "

    \n", "signature": "(self, outdir):", "funcdef": "def"}, "tests.test_core.TestSimpleShearOlivineA": {"fullname": "tests.test_core.TestSimpleShearOlivineA", "modulename": "tests.test_core", "qualname": "TestSimpleShearOlivineA", "kind": "class", "doc": "

    Single-grain A-type olivine analytical rotation rate tests.

    \n"}, "tests.test_core.TestSimpleShearOlivineA.class_id": {"fullname": "tests.test_core.TestSimpleShearOlivineA.class_id", "modulename": "tests.test_core", "qualname": "TestSimpleShearOlivineA.class_id", "kind": "variable", "doc": "

    \n", "default_value": "'simple_shear_Ol'"}, "tests.test_core.TestSimpleShearOlivineA.test_shear_dvdx_slip_010_100": {"fullname": "tests.test_core.TestSimpleShearOlivineA.test_shear_dvdx_slip_010_100", "modulename": "tests.test_core", "qualname": "TestSimpleShearOlivineA.test_shear_dvdx_slip_010_100", "kind": "function", "doc": "

    Single grain of olivine A-type, simple shear on (010)[100].

    \n\n

    Velocity gradient:\n$$\\bm{L} = \\begin{bmatrix} 0 & 0 & 0 \\cr 2 & 0 & 0 \\cr 0 & 0 & 0 \\end{bmatrix}$$

    \n", "signature": "(self, outdir):", "funcdef": "def"}, "tests.test_core.TestSimpleShearOlivineA.test_shear_dudz_slip_001_100": {"fullname": "tests.test_core.TestSimpleShearOlivineA.test_shear_dudz_slip_001_100", "modulename": "tests.test_core", "qualname": "TestSimpleShearOlivineA.test_shear_dudz_slip_001_100", "kind": "function", "doc": "

    Single grain of olivine A-type, simple shear on (001)[100].

    \n\n

    Velocity gradient:\n$$\\bm{L} = \\begin{bmatrix} 0 & 0 & 2 \\cr 0 & 0 & 0 \\cr 0 & 0 & 0 \\end{bmatrix}$$

    \n", "signature": "(self, outdir):", "funcdef": "def"}, "tests.test_core.TestSimpleShearOlivineA.test_shear_dwdx_slip_001_100": {"fullname": "tests.test_core.TestSimpleShearOlivineA.test_shear_dwdx_slip_001_100", "modulename": "tests.test_core", "qualname": "TestSimpleShearOlivineA.test_shear_dwdx_slip_001_100", "kind": "function", "doc": "

    Single grain of olivine A-type, simple shear on (001)[100].

    \n\n

    Velocity gradient:\n$$\\bm{L} = \\begin{bmatrix} 0 & 0 & 0 \\cr 0 & 0 & 0 \\cr 2 & 0 & 0 \\end{bmatrix}$$

    \n", "signature": "(self, outdir):", "funcdef": "def"}, "tests.test_core.TestSimpleShearOlivineA.test_shear_dvdz_slip_010_001": {"fullname": "tests.test_core.TestSimpleShearOlivineA.test_shear_dvdz_slip_010_001", "modulename": "tests.test_core", "qualname": "TestSimpleShearOlivineA.test_shear_dvdz_slip_010_001", "kind": "function", "doc": "

    Single grain of olivine A-type, simple shear on (010)[001].

    \n\n

    Velocity gradient:\n$$\\bm{L} = \\begin{bmatrix} 0 & 0 & 0 \\cr 0 & 0 & 2 \\cr 0 & 0 & 0 \\end{bmatrix}$$

    \n", "signature": "(self, outdir):", "funcdef": "def"}, "tests.test_corner_flow_2d": {"fullname": "tests.test_corner_flow_2d", "modulename": "tests.test_corner_flow_2d", "kind": "module", "doc": "
    \n

    PyDRex: 2D corner flow tests

    \n
    \n\n

    The flow field is defined by:\n$$\n\\bm{u} = \\frac{dr}{dt} \\bm{\\hat{r}} + r \\frac{d\u03b8}{dt} \\bm{\\hat{\u03b8}}\n= \\frac{2 U}{\u03c0}(\u03b8\\sin\u03b8 - \\cos\u03b8) \u22c5 \\bm{\\hat{r}} + \\frac{2 U}{\u03c0}\u03b8\\cos\u03b8 \u22c5 \\bm{\\hat{\u03b8}}\n$$\nwhere $\u03b8 = 0$ points vertically downwards along the ridge axis\nand $\u03b8 = \u03c0/2$ points along the surface. $U$ is the half spreading velocity.\nStreamlines for the flow obey:\n$$\n\u03c8 = \\frac{2 U r}{\u03c0}\u03b8\\cos\u03b8\n$$\nand are related to the velocity through:\n$$\n\\bm{u} = -\\frac{1}{r} \u22c5 \\frac{d\u03c8}{d\u03b8} \u22c5 \\bm{\\hat{r}} + \\frac{d\u03c8}{dr}\\bm{\\hat{\u03b8}}\n$$\nConversion to Cartesian ($x,y,z$) coordinates yields:\n$$\n\\bm{u} = \\frac{2U}{\u03c0} \\left[\n\\tan^{-1}\\left(\\frac{x}{-z}\\right) + \\frac{xz}{x^{2} + z^{2}} \\right] \\bm{\\hat{x}} +\n\\frac{2U}{\u03c0} \\frac{z^{2}}{x^{2} + z^{2}} \\bm{\\hat{z}}\n$$\nwhere\n\\begin{align*}\nx &= r \\sin\u03b8 \\cr\nz &= -r \\cos\u03b8\n\\end{align*}\nand the velocity gradient is:\n$$\nL = \\frac{4 U}{\u03c0{(x^{2}+z^{2})}^{2}} \u22c5\n\\begin{bmatrix}\n -x^{2}z & 0 & x^{3} \\cr\n 0 & 0 & 0 \\cr\n -xz^{2} & 0 & x^{2}z\n\\end{bmatrix}\n$$

    \n\n

    See also Fig. 5 in Kaminski & Ribe, 2002.

    \n"}, "tests.test_corner_flow_2d.get_velocity": {"fullname": "tests.test_corner_flow_2d.get_velocity", "modulename": "tests.test_corner_flow_2d", "qualname": "get_velocity", "kind": "function", "doc": "

    Return velocity in a corner flow (Cartesian coordinate basis).

    \n", "signature": "(x, z, plate_velocity):", "funcdef": "def"}, "tests.test_corner_flow_2d.get_velocity_gradient": {"fullname": "tests.test_corner_flow_2d.get_velocity_gradient", "modulename": "tests.test_corner_flow_2d", "qualname": "get_velocity_gradient", "kind": "function", "doc": "

    Return velocity gradient in a corner flow (Cartesian coordinate basis).

    \n", "signature": "(x, z, plate_velocity):", "funcdef": "def"}, "tests.test_corner_flow_2d.TestOlivineA": {"fullname": "tests.test_corner_flow_2d.TestOlivineA", "modulename": "tests.test_corner_flow_2d", "qualname": "TestOlivineA", "kind": "class", "doc": "

    Tests for pure A-type olivine polycrystals in 2D corner flows.

    \n"}, "tests.test_corner_flow_2d.TestOlivineA.test_corner_prescribed_init_isotropic": {"fullname": "tests.test_corner_flow_2d.TestOlivineA.test_corner_prescribed_init_isotropic", "modulename": "tests.test_corner_flow_2d", "qualname": "TestOlivineA.test_corner_prescribed_init_isotropic", "kind": "function", "doc": "

    Test CPO evolution in prescribed 2D corner flow.

    \n\n

    Initial condition: random orientations and uniform volumes in all Minerals.

    \n\n

    Plate velocity: 2 cm/yr

    \n", "signature": "(self, params_Kaminski2001_fig5_shortdash, seed, outdir):", "funcdef": "def"}, "tests.test_diagnostics": {"fullname": "tests.test_diagnostics", "modulename": "tests.test_diagnostics", "kind": "module", "doc": "
    \n

    PyDRex: tests for texture diagnostics.

    \n
    \n"}, "tests.test_diagnostics.TestSymmetryPGR": {"fullname": "tests.test_diagnostics.TestSymmetryPGR", "modulename": "tests.test_diagnostics", "qualname": "TestSymmetryPGR", "kind": "class", "doc": "

    Test Point-Girdle-Random (eigenvalue) symmetry diagnostics.

    \n"}, "tests.test_diagnostics.TestSymmetryPGR.test_pointX": {"fullname": "tests.test_diagnostics.TestSymmetryPGR.test_pointX", "modulename": "tests.test_diagnostics", "qualname": "TestSymmetryPGR.test_pointX", "kind": "function", "doc": "

    Test diagnostics of point symmetry aligned to the X axis.

    \n", "signature": "(self):", "funcdef": "def"}, "tests.test_diagnostics.TestSymmetryPGR.test_random": {"fullname": "tests.test_diagnostics.TestSymmetryPGR.test_random", "modulename": "tests.test_diagnostics", "qualname": "TestSymmetryPGR.test_random", "kind": "function", "doc": "

    Test diagnostics of random grain orientations.

    \n", "signature": "(self):", "funcdef": "def"}, "tests.test_diagnostics.TestSymmetryPGR.test_girdle": {"fullname": "tests.test_diagnostics.TestSymmetryPGR.test_girdle", "modulename": "tests.test_diagnostics", "qualname": "TestSymmetryPGR.test_girdle", "kind": "function", "doc": "

    Test diagnostics of girdled orientations.

    \n", "signature": "(self):", "funcdef": "def"}, "tests.test_diagnostics.TestVolumeWeighting": {"fullname": "tests.test_diagnostics.TestVolumeWeighting", "modulename": "tests.test_diagnostics", "qualname": "TestVolumeWeighting", "kind": "class", "doc": "

    Tests for volumetric resampling of orientation data.

    \n"}, "tests.test_diagnostics.TestVolumeWeighting.test_upsample": {"fullname": "tests.test_diagnostics.TestVolumeWeighting.test_upsample", "modulename": "tests.test_diagnostics", "qualname": "TestVolumeWeighting.test_upsample", "kind": "function", "doc": "

    Test upsampling of the raw orientation data.

    \n", "signature": "(self):", "funcdef": "def"}, "tests.test_diagnostics.TestVolumeWeighting.test_downsample": {"fullname": "tests.test_diagnostics.TestVolumeWeighting.test_downsample", "modulename": "tests.test_diagnostics", "qualname": "TestVolumeWeighting.test_downsample", "kind": "function", "doc": "

    Test downsampling of orientation data.

    \n", "signature": "(self):", "funcdef": "def"}, "tests.test_diagnostics.TestBinghamStats": {"fullname": "tests.test_diagnostics.TestBinghamStats", "modulename": "tests.test_diagnostics", "qualname": "TestBinghamStats", "kind": "class", "doc": "

    Tests for antipodally symmetric (bingham) statistics.

    \n"}, "tests.test_diagnostics.TestBinghamStats.test_average_0": {"fullname": "tests.test_diagnostics.TestBinghamStats.test_average_0", "modulename": "tests.test_diagnostics", "qualname": "TestBinghamStats.test_average_0", "kind": "function", "doc": "

    Test bingham average of vectors aligned to the reference frame.

    \n", "signature": "(self):", "funcdef": "def"}, "tests.test_diagnostics.TestBinghamStats.test_average_twopoles90Z": {"fullname": "tests.test_diagnostics.TestBinghamStats.test_average_twopoles90Z", "modulename": "tests.test_diagnostics", "qualname": "TestBinghamStats.test_average_twopoles90Z", "kind": "function", "doc": "

    Test bingham average of vectors rotated by \u00b190\u00b0 around Z.

    \n", "signature": "(self):", "funcdef": "def"}, "tests.test_diagnostics.TestBinghamStats.test_average_spread10X": {"fullname": "tests.test_diagnostics.TestBinghamStats.test_average_spread10X", "modulename": "tests.test_diagnostics", "qualname": "TestBinghamStats.test_average_spread10X", "kind": "function", "doc": "

    Test bingham average of vectors spread within 10\u00b0 of the \u00b1X-axis.

    \n", "signature": "(self):", "funcdef": "def"}, "tests.test_diagnostics.TestMIndex": {"fullname": "tests.test_diagnostics.TestMIndex", "modulename": "tests.test_diagnostics", "qualname": "TestMIndex", "kind": "class", "doc": "

    Tests for the M-index texture strength diagnostic.

    \n"}, "tests.test_diagnostics.TestMIndex.test_texture_uniform": {"fullname": "tests.test_diagnostics.TestMIndex.test_texture_uniform", "modulename": "tests.test_diagnostics", "qualname": "TestMIndex.test_texture_uniform", "kind": "function", "doc": "

    Test M-index for random (uniform distribution) grain orientations.

    \n", "signature": "(self):", "funcdef": "def"}, "tests.test_diagnostics.TestMIndex.test_texture_spread10X": {"fullname": "tests.test_diagnostics.TestMIndex.test_texture_spread10X", "modulename": "tests.test_diagnostics", "qualname": "TestMIndex.test_texture_spread10X", "kind": "function", "doc": "

    Test M-index for grains spread within 10\u00b0 of the \u00b1X axis.

    \n", "signature": "(self):", "funcdef": "def"}, "tests.test_diagnostics.TestMIndex.test_texture_spread30X": {"fullname": "tests.test_diagnostics.TestMIndex.test_texture_spread30X", "modulename": "tests.test_diagnostics", "qualname": "TestMIndex.test_texture_spread30X", "kind": "function", "doc": "

    Test M-index for grains spread within 45\u00b0 of the \u00b1X axis.

    \n", "signature": "(self):", "funcdef": "def"}, "tests.test_diagnostics.TestMIndex.test_textures_increasing": {"fullname": "tests.test_diagnostics.TestMIndex.test_textures_increasing", "modulename": "tests.test_diagnostics", "qualname": "TestMIndex.test_textures_increasing", "kind": "function", "doc": "

    Test M-index for textures of increasing strength.

    \n", "signature": "(self):", "funcdef": "def"}, "tests.test_diagnostics.TestMIndex.test_texture_girdle": {"fullname": "tests.test_diagnostics.TestMIndex.test_texture_girdle", "modulename": "tests.test_diagnostics", "qualname": "TestMIndex.test_texture_girdle", "kind": "function", "doc": "

    Test M-index for girdled texture.

    \n", "signature": "(self):", "funcdef": "def"}, "tests.test_doctests": {"fullname": "tests.test_doctests", "modulename": "tests.test_doctests", "kind": "module", "doc": "
    \n

    PyDRex: Run doctests for applicable modules.

    \n
    \n"}, "tests.test_doctests.test_doctests": {"fullname": "tests.test_doctests.test_doctests", "modulename": "tests.test_doctests", "qualname": "test_doctests", "kind": "function", "doc": "

    Run doctests as well.

    \n", "signature": "():", "funcdef": "def"}, "tests.test_geometry": {"fullname": "tests.test_geometry", "modulename": "tests.test_geometry", "kind": "module", "doc": "
    \n

    PyDRex: Tests for geometric conversions and projections.

    \n
    \n"}, "tests.test_geometry.test_poles_example": {"fullname": "tests.test_geometry.test_poles_example", "modulename": "tests.test_geometry", "qualname": "test_poles_example", "kind": "function", "doc": "

    Test poles (directions of crystallographic axes) of example data.

    \n", "signature": "(hkl, ref_axes):", "funcdef": "def"}, "tests.test_geometry.test_lambert_equal_area": {"fullname": "tests.test_geometry.test_lambert_equal_area", "modulename": "tests.test_geometry", "qualname": "test_lambert_equal_area", "kind": "function", "doc": "

    Test Lambert equal area projection.

    \n", "signature": "(seed):", "funcdef": "def"}, "tests.test_scsv": {"fullname": "tests.test_scsv", "modulename": "tests.test_scsv", "kind": "module", "doc": "
    \n

    PyDRex: tests for the SCSV plain text file format.

    \n
    \n"}, "tests.test_scsv.test_validate_schema": {"fullname": "tests.test_scsv.test_validate_schema", "modulename": "tests.test_scsv", "qualname": "test_validate_schema", "kind": "function", "doc": "

    Test SCSV schema validation.

    \n", "signature": "(console_handler):", "funcdef": "def"}, "tests.test_scsv.test_read_specfile": {"fullname": "tests.test_scsv.test_read_specfile", "modulename": "tests.test_scsv", "qualname": "test_read_specfile", "kind": "function", "doc": "

    Test SCSV spec file parsing.

    \n", "signature": "():", "funcdef": "def"}, "tests.test_scsv.test_save_specfile": {"fullname": "tests.test_scsv.test_save_specfile", "modulename": "tests.test_scsv", "qualname": "test_save_specfile", "kind": "function", "doc": "

    Test SCSV spec file reproduction.

    \n", "signature": "(outdir):", "funcdef": "def"}, "tests.test_scsv.test_read_Kaminski2002": {"fullname": "tests.test_scsv.test_read_Kaminski2002", "modulename": "tests.test_scsv", "qualname": "test_read_Kaminski2002", "kind": "function", "doc": "

    \n", "signature": "():", "funcdef": "def"}, "tests.test_scsv.test_read_Kaminski2004": {"fullname": "tests.test_scsv.test_read_Kaminski2004", "modulename": "tests.test_scsv", "qualname": "test_read_Kaminski2004", "kind": "function", "doc": "

    \n", "signature": "():", "funcdef": "def"}, "tests.test_scsv.test_read_Skemer2016": {"fullname": "tests.test_scsv.test_read_Skemer2016", "modulename": "tests.test_scsv", "qualname": "test_read_Skemer2016", "kind": "function", "doc": "

    \n", "signature": "():", "funcdef": "def"}, "tests.test_simple_shear_2d": {"fullname": "tests.test_simple_shear_2d", "modulename": "tests.test_simple_shear_2d", "kind": "module", "doc": "
    \n

    PyDRex: 2D simple shear tests.

    \n
    \n"}, "tests.test_simple_shear_2d.SUBDIR": {"fullname": "tests.test_simple_shear_2d.SUBDIR", "modulename": "tests.test_simple_shear_2d", "qualname": "SUBDIR", "kind": "variable", "doc": "

    \n", "default_value": "'2d_simple_shear'"}, "tests.test_simple_shear_2d.TestOlivineA": {"fullname": "tests.test_simple_shear_2d.TestOlivineA", "modulename": "tests.test_simple_shear_2d", "qualname": "TestOlivineA", "kind": "class", "doc": "

    Tests for A-type olivine polycrystals in 2D simple shear.

    \n"}, "tests.test_simple_shear_2d.TestOlivineA.class_id": {"fullname": "tests.test_simple_shear_2d.TestOlivineA.class_id", "modulename": "tests.test_simple_shear_2d", "qualname": "TestOlivineA.class_id", "kind": "variable", "doc": "

    \n", "default_value": "'olivineA'"}, "tests.test_simple_shear_2d.TestOlivineA.get_position": {"fullname": "tests.test_simple_shear_2d.TestOlivineA.get_position", "modulename": "tests.test_simple_shear_2d", "qualname": "TestOlivineA.get_position", "kind": "function", "doc": "

    \n", "signature": "(cls, t):", "funcdef": "def"}, "tests.test_simple_shear_2d.TestOlivineA.run": {"fullname": "tests.test_simple_shear_2d.TestOlivineA.run", "modulename": "tests.test_simple_shear_2d", "qualname": "TestOlivineA.run", "kind": "function", "doc": "

    Reusable logic for 2D olivine simple shear tests.

    \n\n

    Always returns a tuple with 4 elements\n(mineral, mean_angles, texture_symmetry, \u03b8_fse),\nbut if return_fse is None then the last tuple element is also None.

    \n", "signature": "(\tcls,\tparams,\ttimestamps,\tstrain_rate,\tget_velocity_gradient,\tshear_direction,\tseed=None,\tlog_param=None,\tuse_bingham_average=False,\treturn_fse=True):", "funcdef": "def"}, "tests.test_simple_shear_2d.TestOlivineA.postprocess": {"fullname": "tests.test_simple_shear_2d.TestOlivineA.postprocess", "modulename": "tests.test_simple_shear_2d", "qualname": "TestOlivineA.postprocess", "kind": "function", "doc": "

    Reusable postprocessing routine for olivine 2D simple shear simulations.

    \n", "signature": "(\tcls,\tstrains,\tangles,\tpoint100_symmetry,\t\u03b8_fse,\tlabels,\tmarkers,\toutdir,\tout_basepath,\ttarget_interpolator=None):", "funcdef": "def"}, "tests.test_simple_shear_2d.TestOlivineA.interp_GBM_Kaminski2001": {"fullname": "tests.test_simple_shear_2d.TestOlivineA.interp_GBM_Kaminski2001", "modulename": "tests.test_simple_shear_2d", "qualname": "TestOlivineA.interp_GBM_Kaminski2001", "kind": "function", "doc": "

    Interpolate Kaminski & Ribe, 2001 data to get target angles at strains.

    \n", "signature": "(cls, strains):", "funcdef": "def"}, "tests.test_simple_shear_2d.TestOlivineA.interp_GBS_Kaminski2004": {"fullname": "tests.test_simple_shear_2d.TestOlivineA.interp_GBS_Kaminski2004", "modulename": "tests.test_simple_shear_2d", "qualname": "TestOlivineA.interp_GBS_Kaminski2004", "kind": "function", "doc": "

    Interpolate Kaminski & Ribe, 2001 data to get target angles at strains.

    \n", "signature": "(cls, strains):", "funcdef": "def"}, "tests.test_simple_shear_2d.TestOlivineA.test_dvdx_GBM_ensemble": {"fullname": "tests.test_simple_shear_2d.TestOlivineA.test_dvdx_GBM_ensemble", "modulename": "tests.test_simple_shear_2d", "qualname": "TestOlivineA.test_dvdx_GBM_ensemble", "kind": "function", "doc": "

    Test a-axis alignment to shear in Y direction (init. SCCS near 45\u00b0 from X).

    \n\n

    Velocity gradient:\n$$\\bm{L} = \\begin{bmatrix} 0 & 0 & 0 \\cr 2 & 0 & 0 \\cr 0 & 0 & 0 \\end{bmatrix}$$

    \n\n

    Tests the effect of grain boundary migration, similar to Fig. 5 in\nKaminski 2001.

    \n", "signature": "(\tself,\tparams_Kaminski2001_fig5_solid,\tparams_Kaminski2001_fig5_shortdash,\tparams_Kaminski2001_fig5_longdash,\tseeds_nearX45,\toutdir,\tncpus):", "funcdef": "def"}, "tests.test_simple_shear_2d.TestOlivineA.test_dudz_GBS_ensemble": {"fullname": "tests.test_simple_shear_2d.TestOlivineA.test_dudz_GBS_ensemble", "modulename": "tests.test_simple_shear_2d", "qualname": "TestOlivineA.test_dudz_GBS_ensemble", "kind": "function", "doc": "

    Test a-axis alignment to shear in X direction (init. SCCS near 45\u00b0 from X).

    \n\n

    Velocity gradient:\n$$\\bm{L} = \\begin{bmatrix} 0 & 0 & 2 \\cr 0 & 0 & 0 \\cr 0 & 0 & 0 \\end{bmatrix}$$

    \n", "signature": "(\tself,\tparams_Kaminski2004_fig4_circles,\tparams_Kaminski2004_fig4_squares,\tparams_Kaminski2004_fig4_triangles,\tseeds_nearX45,\toutdir,\tncpus):", "funcdef": "def"}, "tests.test_simple_shear_2d.TestOlivineA.test_boundary_mobility": {"fullname": "tests.test_simple_shear_2d.TestOlivineA.test_boundary_mobility", "modulename": "tests.test_simple_shear_2d", "qualname": "TestOlivineA.test_boundary_mobility", "kind": "function", "doc": "

    Test that the grain boundary mobility parameter has an effect.

    \n", "signature": "(self, seed, outdir):", "funcdef": "def"}, "tests.test_simple_shear_2d.TestOlivineA.test_boudary_sliding": {"fullname": "tests.test_simple_shear_2d.TestOlivineA.test_boudary_sliding", "modulename": "tests.test_simple_shear_2d", "qualname": "TestOlivineA.test_boudary_sliding", "kind": "function", "doc": "

    Test that the grain boundary sliding parameter has an effect.

    \n", "signature": "(self, seed, outdir):", "funcdef": "def"}, "tests.test_simple_shear_2d.TestOlivineA.test_ngrains": {"fullname": "tests.test_simple_shear_2d.TestOlivineA.test_ngrains", "modulename": "tests.test_simple_shear_2d", "qualname": "TestOlivineA.test_ngrains", "kind": "function", "doc": "

    Test that solvers work up to 10000 grains.

    \n", "signature": "(self, seed, outdir):", "funcdef": "def"}, "tests.test_tensors": {"fullname": "tests.test_tensors", "modulename": "tests.test_tensors", "kind": "module", "doc": "
    \n

    PyDRex: Tests for tensor operations.

    \n
    \n"}, "tests.test_tensors.test_voigt_decompose": {"fullname": "tests.test_tensors.test_voigt_decompose", "modulename": "tests.test_tensors", "qualname": "test_voigt_decompose", "kind": "function", "doc": "

    Test decomposition of Voigt 6x6 matrix into distinct contractions.

    \n", "signature": "():", "funcdef": "def"}, "tests.test_tensors.test_voigt_tensor": {"fullname": "tests.test_tensors.test_voigt_tensor", "modulename": "tests.test_tensors", "qualname": "test_voigt_tensor", "kind": "function", "doc": "

    Test elasticity tensor <-> 6x6 Voigt matrix conversions.

    \n", "signature": "():", "funcdef": "def"}, "tests.test_tensors.test_voigt_to_vector": {"fullname": "tests.test_tensors.test_voigt_to_vector", "modulename": "tests.test_tensors", "qualname": "test_voigt_to_vector", "kind": "function", "doc": "

    Test Voigt vector construction.

    \n", "signature": "():", "funcdef": "def"}, "tests.test_vtk_helpers": {"fullname": "tests.test_vtk_helpers", "modulename": "tests.test_vtk_helpers", "kind": "module", "doc": "
    \n

    PyDRex: Tests for VTK readers and helpers.

    \n
    \n"}, "tests.test_vtk_helpers.test_vtk_2d_array_shapes": {"fullname": "tests.test_vtk_helpers.test_vtk_2d_array_shapes", "modulename": "tests.test_vtk_helpers", "qualname": "test_vtk_2d_array_shapes", "kind": "function", "doc": "

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0, "s": {"docs": {"pydrex.diagnostics.misorientation_angles": {"tf": 1.4142135623730951}}, "df": 1}}}}}}}}}, "i": {"docs": {}, "df": 0, "e": {"docs": {}, "df": 0, "t": {"docs": {"pydrex.logger": {"tf": 1.4142135623730951}}, "df": 1}}}, "o": {"docs": {}, "df": 0, "t": {"docs": {"pydrex.logger": {"tf": 5.656854249492381}, "pydrex.minerals.Mineral": {"tf": 1.4142135623730951}}, "df": 2}}}}}}}, "pipeline": ["trimmer"], "_isPrebuiltIndex": true}; // mirrored in build-search-index.js (part 1) // Also split on html tags. this is a cheap heuristic, but good enough. diff --git a/tests/test_simple_shear_2d.html b/tests/test_simple_shear_2d.html index 8b9a60f6..b12de8d5 100644 --- a/tests/test_simple_shear_2d.html +++ b/tests/test_simple_shear_2d.html @@ -86,6 +86,9 @@

    API Documentation

  • test_boudary_sliding
    • +
  • + test_ngrains +
    • @@ -182,641 +185,672 @@

    66 msg_start = f"X = {params['gbs_threshold']}; " 67 case "gbm_mobility": 68 msg_start = f"M∗ = {params['gbm_mobility']}; " - 69 case _: - 70 msg_start = "" - 71 - 72 if seed is not None: - 73 msg_start += f"# {seed}; " - 74 - 75 _log.info(msg_start + "step %s/%s (t = %s)", t, n_timestamps - 1, time) + 69 case "number_of_grains": + 70 msg_start = f"N = {params['number_of_grains']}; " + 71 case _: + 72 msg_start = "" + 73 + 74 if seed is not None: + 75 msg_start += f"# {seed}; " 76 - 77 deformation_gradient = mineral.update_orientations( - 78 params, - 79 deformation_gradient, - 80 get_velocity_gradient, - 81 pathline=(time, timestamps[t], cls.get_position), - 82 ) - 83 _log.debug( - 84 "› velocity gradient = %s", - 85 get_velocity_gradient(None).flatten(), - 86 ) - 87 _log.debug("› strain D₀t = %.2f", strain_rate * timestamps[t]) - 88 _log.debug( - 89 "› grain fractions: median = %s, max = %s, min = %s", - 90 np.median(mineral.fractions[-1]), - 91 np.max(mineral.fractions[-1]), - 92 np.min(mineral.fractions[-1]), - 93 ) - 94 if return_fse: - 95 _, fse_v = _diagnostics.finite_strain(deformation_gradient) - 96 θ_fse[t] = _diagnostics.smallest_angle(fse_v, shear_direction) - 97 - 98 # Compute texture diagnostics. - 99 texture_symmetry = np.zeros(n_timestamps) -100 if use_bingham_average: -101 mean_angles = np.zeros(n_timestamps) -102 for idx, matrices in enumerate(mineral.orientations): -103 orientations_resampled, _ = _stats.resample_orientations( -104 matrices, mineral.fractions[idx], seed=seed -105 ) -106 if use_bingham_average: -107 direction_mean = _diagnostics.bingham_average( -108 orientations_resampled, -109 axis=_minerals.OLIVINE_PRIMARY_AXIS[mineral.fabric], -110 ) -111 mean_angles[idx] = _diagnostics.smallest_angle( -112 direction_mean, shear_direction -113 ) -114 texture_symmetry[idx] = _diagnostics.symmetry( -115 orientations_resampled, -116 axis=_minerals.OLIVINE_PRIMARY_AXIS[mineral.fabric], -117 )[0] -118 -119 if not use_bingham_average: -120 # Use SCCS axis (hexagonal symmetry) for the angle instead (opt). -121 mean_angles = np.array( -122 [ -123 _diagnostics.smallest_angle( -124 _diagnostics.anisotropy(v)[1][2, :], shear_direction -125 ) -126 for v in _minerals.voigt_averages([mineral], params) -127 ] -128 ) -129 -130 if return_fse: -131 return mineral, mean_angles, texture_symmetry, θ_fse -132 return mineral, mean_angles, texture_symmetry, None -133 -134 @classmethod -135 def postprocess( -136 cls, -137 strains, -138 angles, -139 point100_symmetry, -140 θ_fse, -141 labels, -142 markers, -143 outdir, -144 out_basepath, -145 target_interpolator=None, -146 ): -147 """Reusable postprocessing routine for olivine 2D simple shear simulations.""" -148 _log.info("postprocessing results...") -149 if target_interpolator is not None: -150 result_angles = angles.mean(axis=1) -151 result_angles_err = angles.std(axis=1) -152 result_point100_symmetry = point100_symmetry.mean(axis=1) -153 target_angles = target_interpolator(strains) -154 else: -155 result_angles = angles -156 result_angles_err = None -157 result_point100_symmetry = point100_symmetry -158 target_angles = None -159 -160 if outdir is not None: -161 schema = { -162 "delimiter": ",", -163 "missing": "-", -164 "fields": [ -165 { -166 "name": "strain", -167 "type": "integer", -168 "unit": "percent", -169 "fill": 999999, -170 } -171 ], -172 } -173 _io.save_scsv( -174 f"{out_basepath}_strains.scsv", -175 schema, -176 [[int(D * 200) for D in strains]], # Shear strain % is 200 * D₀. -177 ) -178 _vis.simple_shear_stationary_2d( -179 strains, -180 result_angles, -181 result_point100_symmetry, -182 target_angles=target_angles, -183 angles_err=result_angles_err, -184 savefile=f"{out_basepath}.png", -185 markers=markers, -186 θ_fse=θ_fse, -187 labels=labels, -188 ) -189 return result_angles, result_angles_err, result_point100_symmetry, target_angles -190 -191 @classmethod -192 def interp_GBM_Kaminski2001(cls, strains): -193 """Interpolate Kaminski & Ribe, 2001 data to get target angles at `strains`.""" -194 _log.info("interpolating target CPO angles...") -195 data = _io.read_scsv(_io.data("thirdparty") / "Kaminski2001_GBMshear.scsv") -196 cs_M0 = PchipInterpolator( -197 _utils.remove_nans(data.equivalent_strain_M0) / 200, -198 _utils.remove_nans(data.angle_M0), -199 ) -200 cs_M50 = PchipInterpolator( -201 _utils.remove_nans(data.equivalent_strain_M50) / 200, -202 _utils.remove_nans(data.angle_M50), -203 ) -204 cs_M200 = PchipInterpolator( -205 _utils.remove_nans(data.equivalent_strain_M200) / 200, -206 _utils.remove_nans(data.angle_M200), -207 ) -208 return [cs_M0(strains), cs_M50(strains), cs_M200(strains)] -209 -210 @classmethod -211 def interp_GBS_Kaminski2004(cls, strains): -212 """Interpolate Kaminski & Ribe, 2001 data to get target angles at `strains`.""" -213 _log.info("interpolating target CPO angles...") -214 data = _io.read_scsv(_io.data("thirdparty") / "Kaminski2004_GBSshear.scsv") -215 cs_X0 = PchipInterpolator( -216 _utils.remove_nans(data.dimensionless_time_X0), -217 45 + _utils.remove_nans(data.angle_X0), -218 ) -219 cs_X0d2 = PchipInterpolator( -220 _utils.remove_nans(data.dimensionless_time_X0d2), -221 45 + _utils.remove_nans(data.angle_X0d2), -222 ) -223 cs_X0d4 = PchipInterpolator( -224 _utils.remove_nans(data.dimensionless_time_X0d4), -225 45 + _utils.remove_nans(data.angle_X0d4), -226 ) -227 return [cs_X0(strains), cs_X0d2(strains), cs_X0d4(strains)] -228 -229 @pytest.mark.slow -230 def test_dvdx_GBM_ensemble( -231 self, -232 params_Kaminski2001_fig5_solid, # GBM = 0 -233 params_Kaminski2001_fig5_shortdash, # GBM = 50 -234 params_Kaminski2001_fig5_longdash, # GBM = 200 -235 seeds_nearX45, # Use `seeds` if you have lots of RAM and patience (or cores) -236 outdir, -237 ncpus, -238 ): -239 r"""Test a-axis alignment to shear in Y direction (init. SCCS near 45° from X). -240 -241 Velocity gradient: -242 $$\bm{L} = \begin{bmatrix} 0 & 0 & 0 \cr 2 & 0 & 0 \cr 0 & 0 & 0 \end{bmatrix}$$ -243 -244 Tests the effect of grain boundary migration, similar to Fig. 5 in -245 [Kaminski 2001](https://doi.org/10.1016%2Fs0012-821x%2801%2900356-9). -246 -247 """ -248 strain_rate = 5e-6 # Strain rate from Fraters & Billen, 2021, fig. 3. -249 timestamps = np.linspace(0, 2e5, 201) # Solve until D₀t=1 ('shear' γ=2). -250 n_timestamps = len(timestamps) -251 i_strain_50p = [0, 50, 100, 150, 200] # Indices for += 50% strain. -252 -253 shear_direction = [0, 1, 0] # Used to calculate the angular diagnostics. -254 get_velocity_gradient = _dv.simple_shear_2d("Y", "X", strain_rate) -255 -256 # Output setup with optional logging and data series labels. -257 θ_fse = np.empty(n_timestamps) -258 angles = np.empty((3, len(seeds_nearX45), n_timestamps)) -259 point100_symmetry = np.empty_like(angles) -260 optional_logging = cl.nullcontext() -261 if outdir is not None: -262 out_basepath = f"{outdir}/{SUBDIR}/{self.class_id}_dvdx_GBM_ensemble" -263 optional_logging = _log.logfile_enable(f"{out_basepath}.log") -264 labels = [] -265 -266 with optional_logging: -267 wall_start = perf_counter() -268 clock_start = process_time() -269 for p, params in enumerate( -270 ( -271 params_Kaminski2001_fig5_solid, # GBM = 0 -272 params_Kaminski2001_fig5_shortdash, # GBM = 50 -273 params_Kaminski2001_fig5_longdash, # GBM = 200 -274 ), -275 ): -276 if p == 0: -277 return_fse = True -278 else: -279 return_fse = False -280 -281 _run = ft.partial( -282 self.run, -283 params, -284 timestamps, -285 strain_rate, -286 get_velocity_gradient, -287 shear_direction, -288 log_param="gbm_mobility", -289 use_bingham_average=False, -290 return_fse=return_fse, -291 ) -292 with Pool(processes=ncpus) as pool: -293 for s, out in enumerate(pool.imap_unordered(_run, seeds_nearX45)): -294 mineral, mean_angles, texture_symmetry, fse_angles = out -295 angles[p, s, :] = mean_angles -296 point100_symmetry[p, s, :] = texture_symmetry -297 if return_fse: -298 θ_fse += fse_angles -299 -300 if return_fse: -301 θ_fse /= len(seeds_nearX45) -302 -303 # Update labels and store the last mineral of the ensemble for polefigs. -304 if outdir is not None: -305 labels.append(f"$M^∗$ = {params['gbm_mobility']}") -306 mineral.save( -307 f"{out_basepath}.npz", -308 postfix=f"M{params['gbm_mobility']}", -309 ) -310 -311 _log.info( -312 "elapsed walltime: %s", -313 _utils.readable_timestamp(np.abs(perf_counter() - wall_start)), -314 ) -315 _log.info( -316 "elapsed CPU time: %s", -317 _utils.readable_timestamp(np.abs(process_time() - clock_start)), -318 ) -319 -320 # Take ensemble means and optionally plot figure. -321 strains = timestamps * strain_rate -322 res = self.postprocess( -323 strains, -324 angles, -325 point100_symmetry, -326 θ_fse, -327 labels, -328 ("o", "v", "s"), -329 outdir, -330 out_basepath, -331 target_interpolator=self.interp_GBM_Kaminski2001, -332 ) -333 result_angles, result_angles_err, result_point100_symmetry, target_angles = res -334 -335 # Check that FSE is correct. -336 # First, get theoretical FSE axis for simple shear. -337 # We want the angle from the Y axis (shear direction), so subtract from 90. -338 θ_fse_eq = [90 - _utils.angle_fse_simpleshear(strain) for strain in strains] -339 nt.assert_allclose(θ_fse, θ_fse_eq, rtol=1e-7, atol=0) -340 -341 # Check that M*=0 angles match FSE, ignoring the first portion (<100% strain). -342 # Average orientations of near-isotropic distributions are unstable. -343 nt.assert_allclose( -344 θ_fse[i_strain_50p[2] :], -345 result_angles[0][i_strain_50p[2] :], -346 rtol=0.11, -347 atol=0, -348 ) -349 # Check that M*=0 matches target angles for strain > 100%. -350 nt.assert_allclose( -351 target_angles[0][i_strain_50p[2]], -352 result_angles[0][i_strain_50p[2]], -353 atol=1, -354 rtol=0, -355 ) -356 # Check that standard deviation decreases or stagnates (0.01 tolerance). -357 # Check for smooth decrease or stagnation in ensemble average (0.01 tolerance). -358 for angles, angles_err in zip(result_angles, result_angles_err): -359 assert np.all(np.diff(angles_err) < 0.01) -360 assert np.all(np.diff(angles[i_strain_50p[1] :]) < 0.01) -361 -362 # Check point symmetry of [100] at strains of 0%, 50%, 100%, 150% & 200%. -363 nt.assert_allclose( -364 [0.015, 0.11, 0.19, 0.27, 0.34], -365 result_point100_symmetry[0].take(i_strain_50p), -366 rtol=0, -367 atol=0.015, -368 ) -369 nt.assert_allclose( -370 [0.015, 0.15, 0.33, 0.57, 0.72], -371 result_point100_symmetry[1].take(i_strain_50p), -372 rtol=0, -373 atol=0.015, -374 ) -375 nt.assert_allclose( -376 [0.015, 0.22, 0.64, 0.86, 0.91], -377 result_point100_symmetry[2].take(i_strain_50p), -378 rtol=0, -379 atol=0.015, -380 ) -381 -382 @pytest.mark.slow -383 def test_dudz_GBS_ensemble( -384 self, -385 params_Kaminski2004_fig4_circles, # GBS = 0 -386 params_Kaminski2004_fig4_squares, # GBS = 0.2 -387 params_Kaminski2004_fig4_triangles, # GBS = 0.4 -388 seeds_nearX45, # Use `seeds` if you have lots of RAM and patience (or cores) -389 outdir, -390 ncpus, -391 ): -392 r"""Test a-axis alignment to shear in X direction (init. SCCS near 45° from X). -393 -394 Velocity gradient: -395 $$\bm{L} = \begin{bmatrix} 0 & 0 & 2 \cr 0 & 0 & 0 \cr 0 & 0 & 0 \end{bmatrix}$$ -396 -397 """ -398 strain_rate = 5e-6 # Strain rate from Fraters & Billen, 2021, fig. 3. -399 timestamps = np.linspace(0, 5e5, 251) # Solve until D₀t=2.5 ('shear' γ=5). -400 n_timestamps = len(timestamps) -401 i_strain_100p = [0, 50, 100, 150, 200] # Indices for += 100% strain. -402 -403 shear_direction = [1, 0, 0] # Used to calculate the angular diagnostics. -404 get_velocity_gradient = _dv.simple_shear_2d("X", "Z", strain_rate) -405 -406 # Output setup with optional logging and data series labels. -407 θ_fse = np.empty(n_timestamps) -408 angles = np.empty((3, len(seeds_nearX45), n_timestamps)) -409 point100_symmetry = np.empty_like(angles) -410 optional_logging = cl.nullcontext() -411 if outdir is not None: -412 out_basepath = f"{outdir}/{SUBDIR}/{self.class_id}_dudz_GBS_ensemble" -413 optional_logging = _log.logfile_enable(f"{out_basepath}.log") -414 labels = [] -415 -416 with optional_logging: -417 wall_start = perf_counter() -418 clock_start = process_time() -419 for p, params in enumerate( -420 ( -421 params_Kaminski2004_fig4_circles, # GBS = 0 -422 params_Kaminski2004_fig4_squares, # GBS = 0.2 -423 params_Kaminski2004_fig4_triangles, # GBS = 0.4 -424 ), -425 ): -426 if p == 0: -427 return_fse = True -428 else: -429 return_fse = False -430 -431 _run = ft.partial( -432 self.run, -433 params, -434 timestamps, -435 strain_rate, -436 get_velocity_gradient, -437 shear_direction, -438 log_param="gbs_threshold", -439 use_bingham_average=False, -440 return_fse=return_fse, -441 ) -442 with Pool(processes=ncpus) as pool: -443 for s, out in enumerate(pool.imap_unordered(_run, seeds_nearX45)): -444 mineral, mean_angles, texture_symmetry, fse_angles = out -445 angles[p, s, :] = mean_angles -446 point100_symmetry[p, s, :] = texture_symmetry -447 if return_fse: -448 θ_fse += fse_angles -449 -450 if return_fse: -451 θ_fse /= len(seeds_nearX45) -452 -453 # Update labels and store the last mineral of the ensemble for polefigs. -454 if outdir is not None: -455 labels.append(f"$f_{{gbs}}$ = {params['gbs_threshold']}") -456 mineral.save( -457 f"{out_basepath}.npz", -458 postfix=f"X{params['gbs_threshold']}", -459 ) -460 -461 _log.info( -462 "elapsed walltime: %s", -463 _utils.readable_timestamp(np.abs(perf_counter() - wall_start)), -464 ) -465 _log.info( -466 "elapsed CPU time: %s", -467 _utils.readable_timestamp(np.abs(process_time() - clock_start)), -468 ) -469 -470 # Take ensemble means and optionally plot figure. -471 strains = timestamps * strain_rate -472 res = self.postprocess_ensemble( -473 strains, -474 angles, -475 point100_symmetry, -476 θ_fse, -477 labels, -478 ("o", "v", "s"), -479 outdir, -480 out_basepath, -481 target_interpolator=self.interp_GBS_Kaminski2004, -482 ) -483 result_angles, result_angles_err, result_point100_symmetry, target_angles = res -484 -485 # Check that FSE is correct. -486 # First, get theoretical FSE axis for simple shear. -487 # We want the angle from the Y axis (shear direction), so subtract from 90. -488 θ_fse_eq = [90 - _utils.angle_fse_simpleshear(strain) for strain in strains] -489 nt.assert_allclose(θ_fse, θ_fse_eq, rtol=1e-7, atol=0) -490 -491 # Check point symmetry of [100] at strains of 0%, 100%, 200%, 300% & 400%. -492 nt.assert_allclose( -493 [0.015, 0.52, 0.86, 0.93, 0.94], -494 point100_symmetry[0].take(i_strain_100p), -495 rtol=0, -496 atol=0.015, -497 ) -498 nt.assert_allclose( -499 [0.015, 0.42, 0.71, 0.77, 0.79], -500 point100_symmetry[1].take(i_strain_100p), -501 rtol=0, -502 atol=0.015, -503 ) -504 nt.assert_allclose( -505 [0.015, 0.36, 0.57, 0.6, 0.62], -506 point100_symmetry[2].take(i_strain_100p), -507 rtol=0, -508 atol=0.015, -509 ) -510 -511 # Check that standard deviation decreases or stagnates (0.01 tolerance). -512 # Check for smooth decrease or stagnation in ensemble average (0.01 tolerance). -513 for angles, angles_err in zip(result_angles, result_angles_err): -514 assert np.all(np.diff(angles_err) < 0.01) -515 assert np.all(np.diff(angles[i_strain_100p[1] :]) < 0.01) -516 -517 def test_boundary_mobility(self, seed, outdir): -518 """Test that the grain boundary mobility parameter has an effect.""" -519 shear_direction = [0, 1, 0] # Used to calculate the angular diagnostics. -520 strain_rate = 1.0 -521 get_velocity_gradient = _dv.simple_shear_2d("Y", "X", strain_rate) -522 timestamps = np.linspace(0, 1, 201) # Solve until D₀t=1 ('shear' γ=2). -523 i_strain_50p = 50 # Index of 50% strain. -524 params = _io.DEFAULT_PARAMS -525 gbm_mobilities = (0, 10, 50, 125, 200) # Must be in ascending order. -526 markers = ("x", ".", "*", "d", "s") -527 angles = np.empty((len(gbm_mobilities), len(timestamps))) -528 point100_symmetry = np.empty_like(angles) -529 θ_fse = np.empty_like(angles) -530 minerals = [] -531 -532 optional_logging = cl.nullcontext() -533 if outdir is not None: -534 out_basepath = f"{outdir}/{SUBDIR}/{self.class_id}_mobility" -535 optional_logging = _log.logfile_enable(f"{out_basepath}.log") -536 labels = [] -537 -538 with optional_logging: -539 for i, M in enumerate(gbm_mobilities): -540 params["gbm_mobility"] = M -541 out = self.run( -542 params, -543 timestamps, -544 strain_rate, -545 get_velocity_gradient, -546 shear_direction, -547 seed=seed, -548 log_param="gbm_mobility", -549 return_fse=True, -550 ) -551 minerals.append(out[0]) -552 angles[i] = out[1] -553 point100_symmetry[i] = out[2] -554 θ_fse[i] = out[3] -555 if outdir is not None: -556 labels.append(f"$M^∗$ = {params['gbm_mobility']}") -557 -558 if outdir is not None: -559 strains = timestamps * strain_rate -560 self.postprocess( -561 strains, -562 angles, -563 point100_symmetry, -564 np.mean(θ_fse, axis=0), -565 labels, -566 markers, -567 outdir, -568 out_basepath, -569 ) -570 -571 # Check that GBM speeds up the alignment. -572 _log.info("checking grain orientations...") -573 halfway = int(len(timestamps) / 2) -574 assert np.all( -575 np.array( -576 [ -577 θ[halfway] - angles[i][halfway] -578 for i, θ in enumerate(angles[:-1], start=1) -579 ] -580 ) -581 > 0 -582 ) -583 assert np.all( -584 np.array( -585 [θ[-1] - angles[i][-1] for i, θ in enumerate(angles[:-1], start=1)] -586 ) -587 > 0 -588 ) -589 # Check that M*=0 doesn't affect grain sizes. -590 _log.info("checking grain sizes...") -591 for i, time in enumerate(timestamps): -592 nt.assert_allclose( -593 minerals[0].fractions[i], -594 np.full(params["number_of_grains"], 1 / params["number_of_grains"]), -595 ) -596 # Check that M*=0 matches FSE past 100% strain. -597 nt.assert_allclose( -598 angles[0][i_strain_50p:], -599 np.mean(θ_fse, axis=0)[i_strain_50p:], -600 atol=1, -601 rtol=0, -602 ) -603 # Check that GBM causes decreasing grain size median. -604 assert np.all( -605 np.array( -606 [ -607 np.median(m.fractions[halfway]) -608 - np.median(minerals[i].fractions[halfway]) -609 for i, m in enumerate(minerals[:-1], start=1) -610 ] -611 ) -612 > 0 -613 ) -614 -615 def test_boudary_sliding(self, seed, outdir): -616 """Test that the grain boundary sliding parameter has an effect.""" -617 strain_rate = 1.0 -618 shear_direction = [1, 0, 0] # Used to calculate the angular diagnostics. -619 get_velocity_gradient = _dv.simple_shear_2d("X", "Z", strain_rate) -620 timestamps = np.linspace(0, 2.5, 251) # Solve until D₀t=2.5 ('shear' γ=5). -621 i_strain_200p = 100 # Index of 50% strain. -622 params = _io.DEFAULT_PARAMS -623 gbs_thresholds = (0, 0.2, 0.4, 0.6) # Must be in ascending order. -624 markers = (".", "*", "d", "s") -625 angles = np.empty((len(gbs_thresholds), len(timestamps))) -626 point100_symmetry = np.empty_like(angles) -627 θ_fse = np.empty_like(angles) -628 minerals = [] -629 -630 optional_logging = cl.nullcontext() -631 if outdir is not None: -632 out_basepath = f"{outdir}/{SUBDIR}/{self.class_id}_sliding" -633 optional_logging = _log.logfile_enable(f"{out_basepath}.log") -634 labels = [] -635 -636 with optional_logging: -637 for i, f in enumerate(gbs_thresholds): -638 params["gbs_threshold"] = f -639 out = self.run( -640 params, -641 timestamps, -642 strain_rate, -643 get_velocity_gradient, -644 shear_direction, -645 seed=seed, -646 log_param="gbs_threshold", -647 return_fse=True, -648 ) -649 minerals.append(out[0]) -650 angles[i] = out[1] -651 point100_symmetry[i] = out[2] -652 θ_fse[i] = out[3] -653 if outdir is not None: -654 labels.append(f"$M^∗$ = {params['gbs_threshold']}") -655 -656 if outdir is not None: -657 strains = timestamps * strain_rate -658 self.postprocess( -659 strains, -660 angles, -661 point100_symmetry, -662 np.mean(θ_fse, axis=0), -663 labels, -664 markers, -665 outdir, -666 out_basepath, -667 ) -668 -669 # Check that GBS sets an upper bound on P_[100]. -670 _log.info("checking degree of [100] point symmetry...") -671 nt.assert_allclose( -672 np.full(len(point100_symmetry[0][i_strain_200p:]), 0.0), -673 point100_symmetry[0][i_strain_200p:] - 0.95, -674 atol=0.05, -675 rtol=0, -676 ) -677 nt.assert_allclose( -678 np.full(len(point100_symmetry[1][i_strain_200p:]), 0.0), -679 point100_symmetry[1][i_strain_200p:] - 0.78, -680 atol=0.05, -681 rtol=0, -682 ) -683 nt.assert_allclose( -684 np.full(len(point100_symmetry[2][i_strain_200p:]), 0.0), -685 point100_symmetry[2][i_strain_200p:] - 0.61, -686 atol=0.05, -687 rtol=0, -688 ) -689 nt.assert_allclose( -690 np.full(len(point100_symmetry[3][i_strain_200p:]), 0.0), -691 point100_symmetry[3][i_strain_200p:] - 0.44, -692 atol=0.055, -693 rtol=0, -694 ) -695 # Check that angles always reach within 5° of the shear direction. -696 _log.info("checking grain orientations...") -697 for θ in angles: -698 nt.assert_allclose( -699 np.full(len(θ[i_strain_200p:]), 0.0), -700 2.5 - θ[i_strain_200p:], -701 atol=2.5, -702 rtol=0, -703 ) + 77 _log.info(msg_start + "step %s/%s (t = %s)", t, n_timestamps - 1, time) + 78 + 79 deformation_gradient = mineral.update_orientations( + 80 params, + 81 deformation_gradient, + 82 get_velocity_gradient, + 83 pathline=(time, timestamps[t], cls.get_position), + 84 ) + 85 _log.debug( + 86 "› velocity gradient = %s", + 87 get_velocity_gradient(None).flatten(), + 88 ) + 89 _log.debug("› strain D₀t = %.2f", strain_rate * timestamps[t]) + 90 _log.debug( + 91 "› grain fractions: median = %s, max = %s, min = %s", + 92 np.median(mineral.fractions[-1]), + 93 np.max(mineral.fractions[-1]), + 94 np.min(mineral.fractions[-1]), + 95 ) + 96 if return_fse: + 97 _, fse_v = _diagnostics.finite_strain(deformation_gradient) + 98 θ_fse[t] = _diagnostics.smallest_angle(fse_v, shear_direction) + 99 +100 # Compute texture diagnostics. +101 texture_symmetry = np.zeros(n_timestamps) +102 if use_bingham_average: +103 mean_angles = np.zeros(n_timestamps) +104 for idx, matrices in enumerate(mineral.orientations): +105 orientations_resampled, _ = _stats.resample_orientations( +106 matrices, mineral.fractions[idx], seed=seed +107 ) +108 if use_bingham_average: +109 direction_mean = _diagnostics.bingham_average( +110 orientations_resampled, +111 axis=_minerals.OLIVINE_PRIMARY_AXIS[mineral.fabric], +112 ) +113 mean_angles[idx] = _diagnostics.smallest_angle( +114 direction_mean, shear_direction +115 ) +116 texture_symmetry[idx] = _diagnostics.symmetry( +117 orientations_resampled, +118 axis=_minerals.OLIVINE_PRIMARY_AXIS[mineral.fabric], +119 )[0] +120 +121 if not use_bingham_average: +122 # Use SCCS axis (hexagonal symmetry) for the angle instead (opt). +123 mean_angles = np.array( +124 [ +125 _diagnostics.smallest_angle( +126 _diagnostics.anisotropy(v)[1][2, :], shear_direction +127 ) +128 for v in _minerals.voigt_averages([mineral], params) +129 ] +130 ) +131 +132 if return_fse: +133 return mineral, mean_angles, texture_symmetry, θ_fse +134 return mineral, mean_angles, texture_symmetry, None +135 +136 @classmethod +137 def postprocess( +138 cls, +139 strains, +140 angles, +141 point100_symmetry, +142 θ_fse, +143 labels, +144 markers, +145 outdir, +146 out_basepath, +147 target_interpolator=None, +148 ): +149 """Reusable postprocessing routine for olivine 2D simple shear simulations.""" +150 _log.info("postprocessing results...") +151 if target_interpolator is not None: +152 result_angles = angles.mean(axis=1) +153 result_angles_err = angles.std(axis=1) +154 result_point100_symmetry = point100_symmetry.mean(axis=1) +155 target_angles = target_interpolator(strains) +156 else: +157 result_angles = angles +158 result_angles_err = None +159 result_point100_symmetry = point100_symmetry +160 target_angles = None +161 +162 if outdir is not None: +163 schema = { +164 "delimiter": ",", +165 "missing": "-", +166 "fields": [ +167 { +168 "name": "strain", +169 "type": "integer", +170 "unit": "percent", +171 "fill": 999999, +172 } +173 ], +174 } +175 _io.save_scsv( +176 f"{out_basepath}_strains.scsv", +177 schema, +178 [[int(D * 200) for D in strains]], # Shear strain % is 200 * D₀. +179 ) +180 _vis.simple_shear_stationary_2d( +181 strains, +182 result_angles, +183 result_point100_symmetry, +184 target_angles=target_angles, +185 angles_err=result_angles_err, +186 savefile=f"{out_basepath}.png", +187 markers=markers, +188 θ_fse=θ_fse, +189 labels=labels, +190 ) +191 return result_angles, result_angles_err, result_point100_symmetry, target_angles +192 +193 @classmethod +194 def interp_GBM_Kaminski2001(cls, strains): +195 """Interpolate Kaminski & Ribe, 2001 data to get target angles at `strains`.""" +196 _log.info("interpolating target CPO angles...") +197 data = _io.read_scsv(_io.data("thirdparty") / "Kaminski2001_GBMshear.scsv") +198 cs_M0 = PchipInterpolator( +199 _utils.remove_nans(data.equivalent_strain_M0) / 200, +200 _utils.remove_nans(data.angle_M0), +201 ) +202 cs_M50 = PchipInterpolator( +203 _utils.remove_nans(data.equivalent_strain_M50) / 200, +204 _utils.remove_nans(data.angle_M50), +205 ) +206 cs_M200 = PchipInterpolator( +207 _utils.remove_nans(data.equivalent_strain_M200) / 200, +208 _utils.remove_nans(data.angle_M200), +209 ) +210 return [cs_M0(strains), cs_M50(strains), cs_M200(strains)] +211 +212 @classmethod +213 def interp_GBS_Kaminski2004(cls, strains): +214 """Interpolate Kaminski & Ribe, 2001 data to get target angles at `strains`.""" +215 _log.info("interpolating target CPO angles...") +216 data = _io.read_scsv(_io.data("thirdparty") / "Kaminski2004_GBSshear.scsv") +217 cs_X0 = PchipInterpolator( +218 _utils.remove_nans(data.dimensionless_time_X0), +219 45 + _utils.remove_nans(data.angle_X0), +220 ) +221 cs_X0d2 = PchipInterpolator( +222 _utils.remove_nans(data.dimensionless_time_X0d2), +223 45 + _utils.remove_nans(data.angle_X0d2), +224 ) +225 cs_X0d4 = PchipInterpolator( +226 _utils.remove_nans(data.dimensionless_time_X0d4), +227 45 + _utils.remove_nans(data.angle_X0d4), +228 ) +229 return [cs_X0(strains), cs_X0d2(strains), cs_X0d4(strains)] +230 +231 @pytest.mark.slow +232 def test_dvdx_GBM_ensemble( +233 self, +234 params_Kaminski2001_fig5_solid, # GBM = 0 +235 params_Kaminski2001_fig5_shortdash, # GBM = 50 +236 params_Kaminski2001_fig5_longdash, # GBM = 200 +237 seeds_nearX45, # Use `seeds` if you have lots of RAM and patience (or cores) +238 outdir, +239 ncpus, +240 ): +241 r"""Test a-axis alignment to shear in Y direction (init. SCCS near 45° from X). +242 +243 Velocity gradient: +244 $$\bm{L} = \begin{bmatrix} 0 & 0 & 0 \cr 2 & 0 & 0 \cr 0 & 0 & 0 \end{bmatrix}$$ +245 +246 Tests the effect of grain boundary migration, similar to Fig. 5 in +247 [Kaminski 2001](https://doi.org/10.1016%2Fs0012-821x%2801%2900356-9). +248 +249 """ +250 strain_rate = 5e-6 # Strain rate from Fraters & Billen, 2021, fig. 3. +251 timestamps = np.linspace(0, 2e5, 201) # Solve until D₀t=1 ('shear' γ=2). +252 n_timestamps = len(timestamps) +253 i_strain_50p = [0, 50, 100, 150, 200] # Indices for += 50% strain. +254 +255 shear_direction = [0, 1, 0] # Used to calculate the angular diagnostics. +256 get_velocity_gradient = _dv.simple_shear_2d("Y", "X", strain_rate) +257 +258 # Output setup with optional logging and data series labels. +259 θ_fse = np.empty(n_timestamps) +260 angles = np.empty((3, len(seeds_nearX45), n_timestamps)) +261 point100_symmetry = np.empty_like(angles) +262 optional_logging = cl.nullcontext() +263 if outdir is not None: +264 out_basepath = f"{outdir}/{SUBDIR}/{self.class_id}_dvdx_GBM_ensemble" +265 optional_logging = _log.logfile_enable(f"{out_basepath}.log") +266 labels = [] +267 +268 with optional_logging: +269 wall_start = perf_counter() +270 clock_start = process_time() +271 for p, params in enumerate( +272 ( +273 params_Kaminski2001_fig5_solid, # GBM = 0 +274 params_Kaminski2001_fig5_shortdash, # GBM = 50 +275 params_Kaminski2001_fig5_longdash, # GBM = 200 +276 ), +277 ): +278 if p == 0: +279 return_fse = True +280 else: +281 return_fse = False +282 +283 _run = ft.partial( +284 self.run, +285 params, +286 timestamps, +287 strain_rate, +288 get_velocity_gradient, +289 shear_direction, +290 log_param="gbm_mobility", +291 use_bingham_average=False, +292 return_fse=return_fse, +293 ) +294 with Pool(processes=ncpus) as pool: +295 for s, out in enumerate(pool.imap_unordered(_run, seeds_nearX45)): +296 mineral, mean_angles, texture_symmetry, fse_angles = out +297 angles[p, s, :] = mean_angles +298 point100_symmetry[p, s, :] = texture_symmetry +299 if return_fse: +300 θ_fse += fse_angles +301 +302 if return_fse: +303 θ_fse /= len(seeds_nearX45) +304 +305 # Update labels and store the last mineral of the ensemble for polefigs. +306 if outdir is not None: +307 labels.append(f"$M^∗$ = {params['gbm_mobility']}") +308 mineral.save( +309 f"{out_basepath}.npz", +310 postfix=f"M{params['gbm_mobility']}", +311 ) +312 +313 _log.info( +314 "elapsed walltime: %s", +315 _utils.readable_timestamp(np.abs(perf_counter() - wall_start)), +316 ) +317 _log.info( +318 "elapsed CPU time: %s", +319 _utils.readable_timestamp(np.abs(process_time() - clock_start)), +320 ) +321 +322 # Take ensemble means and optionally plot figure. +323 strains = timestamps * strain_rate +324 res = self.postprocess( +325 strains, +326 angles, +327 point100_symmetry, +328 θ_fse, +329 labels, +330 ("o", "v", "s"), +331 outdir, +332 out_basepath, +333 target_interpolator=self.interp_GBM_Kaminski2001, +334 ) +335 result_angles, result_angles_err, result_point100_symmetry, target_angles = res +336 +337 # Check that FSE is correct. +338 # First, get theoretical FSE axis for simple shear. +339 # We want the angle from the Y axis (shear direction), so subtract from 90. +340 θ_fse_eq = [90 - _utils.angle_fse_simpleshear(strain) for strain in strains] +341 nt.assert_allclose(θ_fse, θ_fse_eq, rtol=1e-7, atol=0) +342 +343 # Check that M*=0 angles match FSE, ignoring the first portion (<100% strain). +344 # Average orientations of near-isotropic distributions are unstable. +345 nt.assert_allclose( +346 θ_fse[i_strain_50p[2] :], +347 result_angles[0][i_strain_50p[2] :], +348 rtol=0.11, +349 atol=0, +350 ) +351 # Check that M*=0 matches target angles for strain > 100%. +352 nt.assert_allclose( +353 target_angles[0][i_strain_50p[2]], +354 result_angles[0][i_strain_50p[2]], +355 atol=1, +356 rtol=0, +357 ) +358 # Check that standard deviation decreases or stagnates (0.01 tolerance). +359 # Check for smooth decrease or stagnation in ensemble average (0.01 tolerance). +360 for angles, angles_err in zip(result_angles, result_angles_err): +361 assert np.all(np.diff(angles_err) < 0.01) +362 assert np.all(np.diff(angles[i_strain_50p[1] :]) < 0.01) +363 +364 # Check point symmetry of [100] at strains of 0%, 50%, 100%, 150% & 200%. +365 nt.assert_allclose( +366 [0.015, 0.11, 0.19, 0.27, 0.34], +367 result_point100_symmetry[0].take(i_strain_50p), +368 rtol=0, +369 atol=0.015, +370 ) +371 nt.assert_allclose( +372 [0.015, 0.15, 0.33, 0.57, 0.72], +373 result_point100_symmetry[1].take(i_strain_50p), +374 rtol=0, +375 atol=0.015, +376 ) +377 nt.assert_allclose( +378 [0.015, 0.22, 0.64, 0.86, 0.91], +379 result_point100_symmetry[2].take(i_strain_50p), +380 rtol=0, +381 atol=0.015, +382 ) +383 +384 @pytest.mark.slow +385 def test_dudz_GBS_ensemble( +386 self, +387 params_Kaminski2004_fig4_circles, # GBS = 0 +388 params_Kaminski2004_fig4_squares, # GBS = 0.2 +389 params_Kaminski2004_fig4_triangles, # GBS = 0.4 +390 seeds_nearX45, # Use `seeds` if you have lots of RAM and patience (or cores) +391 outdir, +392 ncpus, +393 ): +394 r"""Test a-axis alignment to shear in X direction (init. SCCS near 45° from X). +395 +396 Velocity gradient: +397 $$\bm{L} = \begin{bmatrix} 0 & 0 & 2 \cr 0 & 0 & 0 \cr 0 & 0 & 0 \end{bmatrix}$$ +398 +399 """ +400 strain_rate = 5e-6 # Strain rate from Fraters & Billen, 2021, fig. 3. +401 timestamps = np.linspace(0, 5e5, 251) # Solve until D₀t=2.5 ('shear' γ=5). +402 n_timestamps = len(timestamps) +403 i_strain_100p = [0, 50, 100, 150, 200] # Indices for += 100% strain. +404 +405 shear_direction = [1, 0, 0] # Used to calculate the angular diagnostics. +406 get_velocity_gradient = _dv.simple_shear_2d("X", "Z", strain_rate) +407 +408 # Output setup with optional logging and data series labels. +409 θ_fse = np.empty(n_timestamps) +410 angles = np.empty((3, len(seeds_nearX45), n_timestamps)) +411 point100_symmetry = np.empty_like(angles) +412 optional_logging = cl.nullcontext() +413 if outdir is not None: +414 out_basepath = f"{outdir}/{SUBDIR}/{self.class_id}_dudz_GBS_ensemble" +415 optional_logging = _log.logfile_enable(f"{out_basepath}.log") +416 labels = [] +417 +418 with optional_logging: +419 wall_start = perf_counter() +420 clock_start = process_time() +421 for p, params in enumerate( +422 ( +423 params_Kaminski2004_fig4_circles, # GBS = 0 +424 params_Kaminski2004_fig4_squares, # GBS = 0.2 +425 params_Kaminski2004_fig4_triangles, # GBS = 0.4 +426 ), +427 ): +428 if p == 0: +429 return_fse = True +430 else: +431 return_fse = False +432 +433 _run = ft.partial( +434 self.run, +435 params, +436 timestamps, +437 strain_rate, +438 get_velocity_gradient, +439 shear_direction, +440 log_param="gbs_threshold", +441 use_bingham_average=False, +442 return_fse=return_fse, +443 ) +444 with Pool(processes=ncpus) as pool: +445 for s, out in enumerate(pool.imap_unordered(_run, seeds_nearX45)): +446 mineral, mean_angles, texture_symmetry, fse_angles = out +447 angles[p, s, :] = mean_angles +448 point100_symmetry[p, s, :] = texture_symmetry +449 if return_fse: +450 θ_fse += fse_angles +451 +452 if return_fse: +453 θ_fse /= len(seeds_nearX45) +454 +455 # Update labels and store the last mineral of the ensemble for polefigs. +456 if outdir is not None: +457 labels.append(f"$f_{{gbs}}$ = {params['gbs_threshold']}") +458 mineral.save( +459 f"{out_basepath}.npz", +460 postfix=f"X{params['gbs_threshold']}", +461 ) +462 +463 _log.info( +464 "elapsed walltime: %s", +465 _utils.readable_timestamp(np.abs(perf_counter() - wall_start)), +466 ) +467 _log.info( +468 "elapsed CPU time: %s", +469 _utils.readable_timestamp(np.abs(process_time() - clock_start)), +470 ) +471 +472 # Take ensemble means and optionally plot figure. +473 strains = timestamps * strain_rate +474 res = self.postprocess_ensemble( +475 strains, +476 angles, +477 point100_symmetry, +478 θ_fse, +479 labels, +480 ("o", "v", "s"), +481 outdir, +482 out_basepath, +483 target_interpolator=self.interp_GBS_Kaminski2004, +484 ) +485 result_angles, result_angles_err, result_point100_symmetry, target_angles = res +486 +487 # Check that FSE is correct. +488 # First, get theoretical FSE axis for simple shear. +489 # We want the angle from the Y axis (shear direction), so subtract from 90. +490 θ_fse_eq = [90 - _utils.angle_fse_simpleshear(strain) for strain in strains] +491 nt.assert_allclose(θ_fse, θ_fse_eq, rtol=1e-7, atol=0) +492 +493 # Check point symmetry of [100] at strains of 0%, 100%, 200%, 300% & 400%. +494 nt.assert_allclose( +495 [0.015, 0.52, 0.86, 0.93, 0.94], +496 point100_symmetry[0].take(i_strain_100p), +497 rtol=0, +498 atol=0.015, +499 ) +500 nt.assert_allclose( +501 [0.015, 0.42, 0.71, 0.77, 0.79], +502 point100_symmetry[1].take(i_strain_100p), +503 rtol=0, +504 atol=0.015, +505 ) +506 nt.assert_allclose( +507 [0.015, 0.36, 0.57, 0.6, 0.62], +508 point100_symmetry[2].take(i_strain_100p), +509 rtol=0, +510 atol=0.015, +511 ) +512 +513 # Check that standard deviation decreases or stagnates (0.01 tolerance). +514 # Check for smooth decrease or stagnation in ensemble average (0.01 tolerance). +515 for angles, angles_err in zip(result_angles, result_angles_err): +516 assert np.all(np.diff(angles_err) < 0.01) +517 assert np.all(np.diff(angles[i_strain_100p[1] :]) < 0.01) +518 +519 def test_boundary_mobility(self, seed, outdir): +520 """Test that the grain boundary mobility parameter has an effect.""" +521 shear_direction = [0, 1, 0] # Used to calculate the angular diagnostics. +522 strain_rate = 1.0 +523 get_velocity_gradient = _dv.simple_shear_2d("Y", "X", strain_rate) +524 timestamps = np.linspace(0, 1, 201) # Solve until D₀t=1 ('shear' γ=2). +525 i_strain_50p = 50 # Index of 50% strain. +526 params = _io.DEFAULT_PARAMS +527 gbm_mobilities = (0, 10, 50, 125, 200) # Must be in ascending order. +528 markers = ("x", ".", "*", "d", "s") +529 angles = np.empty((len(gbm_mobilities), len(timestamps))) +530 point100_symmetry = np.empty_like(angles) +531 θ_fse = np.empty_like(angles) +532 minerals = [] +533 +534 optional_logging = cl.nullcontext() +535 if outdir is not None: +536 out_basepath = f"{outdir}/{SUBDIR}/{self.class_id}_mobility" +537 optional_logging = _log.logfile_enable(f"{out_basepath}.log") +538 labels = [] +539 +540 with optional_logging: +541 for i, M in enumerate(gbm_mobilities): +542 params["gbm_mobility"] = M +543 out = self.run( +544 params, +545 timestamps, +546 strain_rate, +547 get_velocity_gradient, +548 shear_direction, +549 seed=seed, +550 log_param="gbm_mobility", +551 return_fse=True, +552 ) +553 minerals.append(out[0]) +554 angles[i] = out[1] +555 point100_symmetry[i] = out[2] +556 θ_fse[i] = out[3] +557 if outdir is not None: +558 labels.append(f"$M^∗$ = {params['gbm_mobility']}") +559 +560 if outdir is not None: +561 strains = timestamps * strain_rate +562 self.postprocess( +563 strains, +564 angles, +565 point100_symmetry, +566 np.mean(θ_fse, axis=0), +567 labels, +568 markers, +569 outdir, +570 out_basepath, +571 ) +572 +573 # Check that GBM speeds up the alignment. +574 _log.info("checking grain orientations...") +575 halfway = int(len(timestamps) / 2) +576 assert np.all( +577 np.array( +578 [ +579 θ[halfway] - angles[i][halfway] +580 for i, θ in enumerate(angles[:-1], start=1) +581 ] +582 ) +583 > 0 +584 ) +585 assert np.all( +586 np.array( +587 [θ[-1] - angles[i][-1] for i, θ in enumerate(angles[:-1], start=1)] +588 ) +589 > 0 +590 ) +591 # Check that M*=0 doesn't affect grain sizes. +592 _log.info("checking grain sizes...") +593 for i, time in enumerate(timestamps): +594 nt.assert_allclose( +595 minerals[0].fractions[i], +596 np.full(params["number_of_grains"], 1 / params["number_of_grains"]), +597 ) +598 # Check that M*=0 matches FSE past 100% strain. +599 nt.assert_allclose( +600 angles[0][i_strain_50p:], +601 np.mean(θ_fse, axis=0)[i_strain_50p:], +602 atol=1, +603 rtol=0, +604 ) +605 # Check that GBM causes decreasing grain size median. +606 assert np.all( +607 np.array( +608 [ +609 np.median(m.fractions[halfway]) +610 - np.median(minerals[i].fractions[halfway]) +611 for i, m in enumerate(minerals[:-1], start=1) +612 ] +613 ) +614 > 0 +615 ) +616 +617 def test_boudary_sliding(self, seed, outdir): +618 """Test that the grain boundary sliding parameter has an effect.""" +619 strain_rate = 1.0 +620 shear_direction = [1, 0, 0] # Used to calculate the angular diagnostics. +621 get_velocity_gradient = _dv.simple_shear_2d("X", "Z", strain_rate) +622 timestamps = np.linspace(0, 2.5, 251) # Solve until D₀t=2.5 ('shear' γ=5). +623 i_strain_200p = 100 # Index of 50% strain. +624 params = _io.DEFAULT_PARAMS +625 gbs_thresholds = (0, 0.2, 0.4, 0.6) # Must be in ascending order. +626 markers = (".", "*", "d", "s") +627 angles = np.empty((len(gbs_thresholds), len(timestamps))) +628 point100_symmetry = np.empty_like(angles) +629 θ_fse = np.empty_like(angles) +630 minerals = [] +631 +632 optional_logging = cl.nullcontext() +633 if outdir is not None: +634 out_basepath = f"{outdir}/{SUBDIR}/{self.class_id}_sliding" +635 optional_logging = _log.logfile_enable(f"{out_basepath}.log") +636 labels = [] +637 +638 with optional_logging: +639 for i, f in enumerate(gbs_thresholds): +640 params["gbs_threshold"] = f +641 out = self.run( +642 params, +643 timestamps, +644 strain_rate, +645 get_velocity_gradient, +646 shear_direction, +647 seed=seed, +648 log_param="gbs_threshold", +649 return_fse=True, +650 ) +651 minerals.append(out[0]) +652 angles[i] = out[1] +653 point100_symmetry[i] = out[2] +654 θ_fse[i] = out[3] +655 if outdir is not None: +656 labels.append(f"$M^∗$ = {params['gbs_threshold']}") +657 +658 if outdir is not None: +659 strains = timestamps * strain_rate +660 self.postprocess( +661 strains, +662 angles, +663 point100_symmetry, +664 np.mean(θ_fse, axis=0), +665 labels, +666 markers, +667 outdir, +668 out_basepath, +669 ) +670 +671 # Check that GBS sets an upper bound on P_[100]. +672 _log.info("checking degree of [100] point symmetry...") +673 nt.assert_allclose( +674 np.full(len(point100_symmetry[0][i_strain_200p:]), 0.0), +675 point100_symmetry[0][i_strain_200p:] - 0.95, +676 atol=0.05, +677 rtol=0, +678 ) +679 nt.assert_allclose( +680 np.full(len(point100_symmetry[1][i_strain_200p:]), 0.0), +681 point100_symmetry[1][i_strain_200p:] - 0.78, +682 atol=0.05, +683 rtol=0, +684 ) +685 nt.assert_allclose( +686 np.full(len(point100_symmetry[2][i_strain_200p:]), 0.0), +687 point100_symmetry[2][i_strain_200p:] - 0.61, +688 atol=0.05, +689 rtol=0, +690 ) +691 nt.assert_allclose( +692 np.full(len(point100_symmetry[3][i_strain_200p:]), 0.0), +693 point100_symmetry[3][i_strain_200p:] - 0.44, +694 atol=0.055, +695 rtol=0, +696 ) +697 # Check that angles always reach within 5° of the shear direction. +698 _log.info("checking grain orientations...") +699 for θ in angles: +700 nt.assert_allclose( +701 np.full(len(θ[i_strain_200p:]), 0.0), +702 2.5 - θ[i_strain_200p:], +703 atol=2.5, +704 rtol=0, +705 ) +706 +707 @pytest.mark.slow +708 def test_ngrains(self, seed, outdir): +709 """Test that solvers work up to 10000 grains.""" +710 shear_direction = [0, 1, 0] +711 strain_rate = 1.0 +712 get_velocity_gradient = _dv.simple_shear_2d("Y", "X", strain_rate) +713 timestamps = np.linspace(0, 1, 201) # Solve until D₀t=1 ('shear' γ=2). +714 params = _io.DEFAULT_PARAMS +715 grain_counts = (100, 1000, 2000, 5000, 10000) +716 +717 optional_logging = cl.nullcontext() +718 if outdir is not None: +719 out_basepath = f"{outdir}/{SUBDIR}/{self.class_id}_ngrains" +720 optional_logging = _log.logfile_enable(f"{out_basepath}.log") +721 +722 with optional_logging: +723 for i, N in enumerate(grain_counts): +724 params["number_of_grains"] = N +725 self.run( +726 params, +727 timestamps, +728 strain_rate, +729 get_velocity_gradient, +730 shear_direction, +731 seed=seed, +732 log_param="number_of_grains", +733 return_fse=True, +734 ) @@ -888,641 +922,672 @@

    67 msg_start = f"X = {params['gbs_threshold']}; " 68 case "gbm_mobility": 69 msg_start = f"M∗ = {params['gbm_mobility']}; " - 70 case _: - 71 msg_start = "" - 72 - 73 if seed is not None: - 74 msg_start += f"# {seed}; " - 75 - 76 _log.info(msg_start + "step %s/%s (t = %s)", t, n_timestamps - 1, time) + 70 case "number_of_grains": + 71 msg_start = f"N = {params['number_of_grains']}; " + 72 case _: + 73 msg_start = "" + 74 + 75 if seed is not None: + 76 msg_start += f"# {seed}; " 77 - 78 deformation_gradient = mineral.update_orientations( - 79 params, - 80 deformation_gradient, - 81 get_velocity_gradient, - 82 pathline=(time, timestamps[t], cls.get_position), - 83 ) - 84 _log.debug( - 85 "› velocity gradient = %s", - 86 get_velocity_gradient(None).flatten(), - 87 ) - 88 _log.debug("› strain D₀t = %.2f", strain_rate * timestamps[t]) - 89 _log.debug( - 90 "› grain fractions: median = %s, max = %s, min = %s", - 91 np.median(mineral.fractions[-1]), - 92 np.max(mineral.fractions[-1]), - 93 np.min(mineral.fractions[-1]), - 94 ) - 95 if return_fse: - 96 _, fse_v = _diagnostics.finite_strain(deformation_gradient) - 97 θ_fse[t] = _diagnostics.smallest_angle(fse_v, shear_direction) - 98 - 99 # Compute texture diagnostics. -100 texture_symmetry = np.zeros(n_timestamps) -101 if use_bingham_average: -102 mean_angles = np.zeros(n_timestamps) -103 for idx, matrices in enumerate(mineral.orientations): -104 orientations_resampled, _ = _stats.resample_orientations( -105 matrices, mineral.fractions[idx], seed=seed -106 ) -107 if use_bingham_average: -108 direction_mean = _diagnostics.bingham_average( -109 orientations_resampled, -110 axis=_minerals.OLIVINE_PRIMARY_AXIS[mineral.fabric], -111 ) -112 mean_angles[idx] = _diagnostics.smallest_angle( -113 direction_mean, shear_direction -114 ) -115 texture_symmetry[idx] = _diagnostics.symmetry( -116 orientations_resampled, -117 axis=_minerals.OLIVINE_PRIMARY_AXIS[mineral.fabric], -118 )[0] -119 -120 if not use_bingham_average: -121 # Use SCCS axis (hexagonal symmetry) for the angle instead (opt). -122 mean_angles = np.array( -123 [ -124 _diagnostics.smallest_angle( -125 _diagnostics.anisotropy(v)[1][2, :], shear_direction -126 ) -127 for v in _minerals.voigt_averages([mineral], params) -128 ] -129 ) -130 -131 if return_fse: -132 return mineral, mean_angles, texture_symmetry, θ_fse -133 return mineral, mean_angles, texture_symmetry, None -134 -135 @classmethod -136 def postprocess( -137 cls, -138 strains, -139 angles, -140 point100_symmetry, -141 θ_fse, -142 labels, -143 markers, -144 outdir, -145 out_basepath, -146 target_interpolator=None, -147 ): -148 """Reusable postprocessing routine for olivine 2D simple shear simulations.""" -149 _log.info("postprocessing results...") -150 if target_interpolator is not None: -151 result_angles = angles.mean(axis=1) -152 result_angles_err = angles.std(axis=1) -153 result_point100_symmetry = point100_symmetry.mean(axis=1) -154 target_angles = target_interpolator(strains) -155 else: -156 result_angles = angles -157 result_angles_err = None -158 result_point100_symmetry = point100_symmetry -159 target_angles = None -160 -161 if outdir is not None: -162 schema = { -163 "delimiter": ",", -164 "missing": "-", -165 "fields": [ -166 { -167 "name": "strain", -168 "type": "integer", -169 "unit": "percent", -170 "fill": 999999, -171 } -172 ], -173 } -174 _io.save_scsv( -175 f"{out_basepath}_strains.scsv", -176 schema, -177 [[int(D * 200) for D in strains]], # Shear strain % is 200 * D₀. -178 ) -179 _vis.simple_shear_stationary_2d( -180 strains, -181 result_angles, -182 result_point100_symmetry, -183 target_angles=target_angles, -184 angles_err=result_angles_err, -185 savefile=f"{out_basepath}.png", -186 markers=markers, -187 θ_fse=θ_fse, -188 labels=labels, -189 ) -190 return result_angles, result_angles_err, result_point100_symmetry, target_angles -191 -192 @classmethod -193 def interp_GBM_Kaminski2001(cls, strains): -194 """Interpolate Kaminski & Ribe, 2001 data to get target angles at `strains`.""" -195 _log.info("interpolating target CPO angles...") -196 data = _io.read_scsv(_io.data("thirdparty") / "Kaminski2001_GBMshear.scsv") -197 cs_M0 = PchipInterpolator( -198 _utils.remove_nans(data.equivalent_strain_M0) / 200, -199 _utils.remove_nans(data.angle_M0), -200 ) -201 cs_M50 = PchipInterpolator( -202 _utils.remove_nans(data.equivalent_strain_M50) / 200, -203 _utils.remove_nans(data.angle_M50), -204 ) -205 cs_M200 = PchipInterpolator( -206 _utils.remove_nans(data.equivalent_strain_M200) / 200, -207 _utils.remove_nans(data.angle_M200), -208 ) -209 return [cs_M0(strains), cs_M50(strains), cs_M200(strains)] -210 -211 @classmethod -212 def interp_GBS_Kaminski2004(cls, strains): -213 """Interpolate Kaminski & Ribe, 2001 data to get target angles at `strains`.""" -214 _log.info("interpolating target CPO angles...") -215 data = _io.read_scsv(_io.data("thirdparty") / "Kaminski2004_GBSshear.scsv") -216 cs_X0 = PchipInterpolator( -217 _utils.remove_nans(data.dimensionless_time_X0), -218 45 + _utils.remove_nans(data.angle_X0), -219 ) -220 cs_X0d2 = PchipInterpolator( -221 _utils.remove_nans(data.dimensionless_time_X0d2), -222 45 + _utils.remove_nans(data.angle_X0d2), -223 ) -224 cs_X0d4 = PchipInterpolator( -225 _utils.remove_nans(data.dimensionless_time_X0d4), -226 45 + _utils.remove_nans(data.angle_X0d4), -227 ) -228 return [cs_X0(strains), cs_X0d2(strains), cs_X0d4(strains)] -229 -230 @pytest.mark.slow -231 def test_dvdx_GBM_ensemble( -232 self, -233 params_Kaminski2001_fig5_solid, # GBM = 0 -234 params_Kaminski2001_fig5_shortdash, # GBM = 50 -235 params_Kaminski2001_fig5_longdash, # GBM = 200 -236 seeds_nearX45, # Use `seeds` if you have lots of RAM and patience (or cores) -237 outdir, -238 ncpus, -239 ): -240 r"""Test a-axis alignment to shear in Y direction (init. SCCS near 45° from X). -241 -242 Velocity gradient: -243 $$\bm{L} = \begin{bmatrix} 0 & 0 & 0 \cr 2 & 0 & 0 \cr 0 & 0 & 0 \end{bmatrix}$$ -244 -245 Tests the effect of grain boundary migration, similar to Fig. 5 in -246 [Kaminski 2001](https://doi.org/10.1016%2Fs0012-821x%2801%2900356-9). -247 -248 """ -249 strain_rate = 5e-6 # Strain rate from Fraters & Billen, 2021, fig. 3. -250 timestamps = np.linspace(0, 2e5, 201) # Solve until D₀t=1 ('shear' γ=2). -251 n_timestamps = len(timestamps) -252 i_strain_50p = [0, 50, 100, 150, 200] # Indices for += 50% strain. -253 -254 shear_direction = [0, 1, 0] # Used to calculate the angular diagnostics. -255 get_velocity_gradient = _dv.simple_shear_2d("Y", "X", strain_rate) -256 -257 # Output setup with optional logging and data series labels. -258 θ_fse = np.empty(n_timestamps) -259 angles = np.empty((3, len(seeds_nearX45), n_timestamps)) -260 point100_symmetry = np.empty_like(angles) -261 optional_logging = cl.nullcontext() -262 if outdir is not None: -263 out_basepath = f"{outdir}/{SUBDIR}/{self.class_id}_dvdx_GBM_ensemble" -264 optional_logging = _log.logfile_enable(f"{out_basepath}.log") -265 labels = [] -266 -267 with optional_logging: -268 wall_start = perf_counter() -269 clock_start = process_time() -270 for p, params in enumerate( -271 ( -272 params_Kaminski2001_fig5_solid, # GBM = 0 -273 params_Kaminski2001_fig5_shortdash, # GBM = 50 -274 params_Kaminski2001_fig5_longdash, # GBM = 200 -275 ), -276 ): -277 if p == 0: -278 return_fse = True -279 else: -280 return_fse = False -281 -282 _run = ft.partial( -283 self.run, -284 params, -285 timestamps, -286 strain_rate, -287 get_velocity_gradient, -288 shear_direction, -289 log_param="gbm_mobility", -290 use_bingham_average=False, -291 return_fse=return_fse, -292 ) -293 with Pool(processes=ncpus) as pool: -294 for s, out in enumerate(pool.imap_unordered(_run, seeds_nearX45)): -295 mineral, mean_angles, texture_symmetry, fse_angles = out -296 angles[p, s, :] = mean_angles -297 point100_symmetry[p, s, :] = texture_symmetry -298 if return_fse: -299 θ_fse += fse_angles -300 -301 if return_fse: -302 θ_fse /= len(seeds_nearX45) -303 -304 # Update labels and store the last mineral of the ensemble for polefigs. -305 if outdir is not None: -306 labels.append(f"$M^∗$ = {params['gbm_mobility']}") -307 mineral.save( -308 f"{out_basepath}.npz", -309 postfix=f"M{params['gbm_mobility']}", -310 ) -311 -312 _log.info( -313 "elapsed walltime: %s", -314 _utils.readable_timestamp(np.abs(perf_counter() - wall_start)), -315 ) -316 _log.info( -317 "elapsed CPU time: %s", -318 _utils.readable_timestamp(np.abs(process_time() - clock_start)), -319 ) -320 -321 # Take ensemble means and optionally plot figure. -322 strains = timestamps * strain_rate -323 res = self.postprocess( -324 strains, -325 angles, -326 point100_symmetry, -327 θ_fse, -328 labels, -329 ("o", "v", "s"), -330 outdir, -331 out_basepath, -332 target_interpolator=self.interp_GBM_Kaminski2001, -333 ) -334 result_angles, result_angles_err, result_point100_symmetry, target_angles = res -335 -336 # Check that FSE is correct. -337 # First, get theoretical FSE axis for simple shear. -338 # We want the angle from the Y axis (shear direction), so subtract from 90. -339 θ_fse_eq = [90 - _utils.angle_fse_simpleshear(strain) for strain in strains] -340 nt.assert_allclose(θ_fse, θ_fse_eq, rtol=1e-7, atol=0) -341 -342 # Check that M*=0 angles match FSE, ignoring the first portion (<100% strain). -343 # Average orientations of near-isotropic distributions are unstable. -344 nt.assert_allclose( -345 θ_fse[i_strain_50p[2] :], -346 result_angles[0][i_strain_50p[2] :], -347 rtol=0.11, -348 atol=0, -349 ) -350 # Check that M*=0 matches target angles for strain > 100%. -351 nt.assert_allclose( -352 target_angles[0][i_strain_50p[2]], -353 result_angles[0][i_strain_50p[2]], -354 atol=1, -355 rtol=0, -356 ) -357 # Check that standard deviation decreases or stagnates (0.01 tolerance). -358 # Check for smooth decrease or stagnation in ensemble average (0.01 tolerance). -359 for angles, angles_err in zip(result_angles, result_angles_err): -360 assert np.all(np.diff(angles_err) < 0.01) -361 assert np.all(np.diff(angles[i_strain_50p[1] :]) < 0.01) -362 -363 # Check point symmetry of [100] at strains of 0%, 50%, 100%, 150% & 200%. -364 nt.assert_allclose( -365 [0.015, 0.11, 0.19, 0.27, 0.34], -366 result_point100_symmetry[0].take(i_strain_50p), -367 rtol=0, -368 atol=0.015, -369 ) -370 nt.assert_allclose( -371 [0.015, 0.15, 0.33, 0.57, 0.72], -372 result_point100_symmetry[1].take(i_strain_50p), -373 rtol=0, -374 atol=0.015, -375 ) -376 nt.assert_allclose( -377 [0.015, 0.22, 0.64, 0.86, 0.91], -378 result_point100_symmetry[2].take(i_strain_50p), -379 rtol=0, -380 atol=0.015, -381 ) -382 -383 @pytest.mark.slow -384 def test_dudz_GBS_ensemble( -385 self, -386 params_Kaminski2004_fig4_circles, # GBS = 0 -387 params_Kaminski2004_fig4_squares, # GBS = 0.2 -388 params_Kaminski2004_fig4_triangles, # GBS = 0.4 -389 seeds_nearX45, # Use `seeds` if you have lots of RAM and patience (or cores) -390 outdir, -391 ncpus, -392 ): -393 r"""Test a-axis alignment to shear in X direction (init. SCCS near 45° from X). -394 -395 Velocity gradient: -396 $$\bm{L} = \begin{bmatrix} 0 & 0 & 2 \cr 0 & 0 & 0 \cr 0 & 0 & 0 \end{bmatrix}$$ -397 -398 """ -399 strain_rate = 5e-6 # Strain rate from Fraters & Billen, 2021, fig. 3. -400 timestamps = np.linspace(0, 5e5, 251) # Solve until D₀t=2.5 ('shear' γ=5). -401 n_timestamps = len(timestamps) -402 i_strain_100p = [0, 50, 100, 150, 200] # Indices for += 100% strain. -403 -404 shear_direction = [1, 0, 0] # Used to calculate the angular diagnostics. -405 get_velocity_gradient = _dv.simple_shear_2d("X", "Z", strain_rate) -406 -407 # Output setup with optional logging and data series labels. -408 θ_fse = np.empty(n_timestamps) -409 angles = np.empty((3, len(seeds_nearX45), n_timestamps)) -410 point100_symmetry = np.empty_like(angles) -411 optional_logging = cl.nullcontext() -412 if outdir is not None: -413 out_basepath = f"{outdir}/{SUBDIR}/{self.class_id}_dudz_GBS_ensemble" -414 optional_logging = _log.logfile_enable(f"{out_basepath}.log") -415 labels = [] -416 -417 with optional_logging: -418 wall_start = perf_counter() -419 clock_start = process_time() -420 for p, params in enumerate( -421 ( -422 params_Kaminski2004_fig4_circles, # GBS = 0 -423 params_Kaminski2004_fig4_squares, # GBS = 0.2 -424 params_Kaminski2004_fig4_triangles, # GBS = 0.4 -425 ), -426 ): -427 if p == 0: -428 return_fse = True -429 else: -430 return_fse = False -431 -432 _run = ft.partial( -433 self.run, -434 params, -435 timestamps, -436 strain_rate, -437 get_velocity_gradient, -438 shear_direction, -439 log_param="gbs_threshold", -440 use_bingham_average=False, -441 return_fse=return_fse, -442 ) -443 with Pool(processes=ncpus) as pool: -444 for s, out in enumerate(pool.imap_unordered(_run, seeds_nearX45)): -445 mineral, mean_angles, texture_symmetry, fse_angles = out -446 angles[p, s, :] = mean_angles -447 point100_symmetry[p, s, :] = texture_symmetry -448 if return_fse: -449 θ_fse += fse_angles -450 -451 if return_fse: -452 θ_fse /= len(seeds_nearX45) -453 -454 # Update labels and store the last mineral of the ensemble for polefigs. -455 if outdir is not None: -456 labels.append(f"$f_{{gbs}}$ = {params['gbs_threshold']}") -457 mineral.save( -458 f"{out_basepath}.npz", -459 postfix=f"X{params['gbs_threshold']}", -460 ) -461 -462 _log.info( -463 "elapsed walltime: %s", -464 _utils.readable_timestamp(np.abs(perf_counter() - wall_start)), -465 ) -466 _log.info( -467 "elapsed CPU time: %s", -468 _utils.readable_timestamp(np.abs(process_time() - clock_start)), -469 ) -470 -471 # Take ensemble means and optionally plot figure. -472 strains = timestamps * strain_rate -473 res = self.postprocess_ensemble( -474 strains, -475 angles, -476 point100_symmetry, -477 θ_fse, -478 labels, -479 ("o", "v", "s"), -480 outdir, -481 out_basepath, -482 target_interpolator=self.interp_GBS_Kaminski2004, -483 ) -484 result_angles, result_angles_err, result_point100_symmetry, target_angles = res -485 -486 # Check that FSE is correct. -487 # First, get theoretical FSE axis for simple shear. -488 # We want the angle from the Y axis (shear direction), so subtract from 90. -489 θ_fse_eq = [90 - _utils.angle_fse_simpleshear(strain) for strain in strains] -490 nt.assert_allclose(θ_fse, θ_fse_eq, rtol=1e-7, atol=0) -491 -492 # Check point symmetry of [100] at strains of 0%, 100%, 200%, 300% & 400%. -493 nt.assert_allclose( -494 [0.015, 0.52, 0.86, 0.93, 0.94], -495 point100_symmetry[0].take(i_strain_100p), -496 rtol=0, -497 atol=0.015, -498 ) -499 nt.assert_allclose( -500 [0.015, 0.42, 0.71, 0.77, 0.79], -501 point100_symmetry[1].take(i_strain_100p), -502 rtol=0, -503 atol=0.015, -504 ) -505 nt.assert_allclose( -506 [0.015, 0.36, 0.57, 0.6, 0.62], -507 point100_symmetry[2].take(i_strain_100p), -508 rtol=0, -509 atol=0.015, -510 ) -511 -512 # Check that standard deviation decreases or stagnates (0.01 tolerance). -513 # Check for smooth decrease or stagnation in ensemble average (0.01 tolerance). -514 for angles, angles_err in zip(result_angles, result_angles_err): -515 assert np.all(np.diff(angles_err) < 0.01) -516 assert np.all(np.diff(angles[i_strain_100p[1] :]) < 0.01) -517 -518 def test_boundary_mobility(self, seed, outdir): -519 """Test that the grain boundary mobility parameter has an effect.""" -520 shear_direction = [0, 1, 0] # Used to calculate the angular diagnostics. -521 strain_rate = 1.0 -522 get_velocity_gradient = _dv.simple_shear_2d("Y", "X", strain_rate) -523 timestamps = np.linspace(0, 1, 201) # Solve until D₀t=1 ('shear' γ=2). -524 i_strain_50p = 50 # Index of 50% strain. -525 params = _io.DEFAULT_PARAMS -526 gbm_mobilities = (0, 10, 50, 125, 200) # Must be in ascending order. -527 markers = ("x", ".", "*", "d", "s") -528 angles = np.empty((len(gbm_mobilities), len(timestamps))) -529 point100_symmetry = np.empty_like(angles) -530 θ_fse = np.empty_like(angles) -531 minerals = [] -532 -533 optional_logging = cl.nullcontext() -534 if outdir is not None: -535 out_basepath = f"{outdir}/{SUBDIR}/{self.class_id}_mobility" -536 optional_logging = _log.logfile_enable(f"{out_basepath}.log") -537 labels = [] -538 -539 with optional_logging: -540 for i, M in enumerate(gbm_mobilities): -541 params["gbm_mobility"] = M -542 out = self.run( -543 params, -544 timestamps, -545 strain_rate, -546 get_velocity_gradient, -547 shear_direction, -548 seed=seed, -549 log_param="gbm_mobility", -550 return_fse=True, -551 ) -552 minerals.append(out[0]) -553 angles[i] = out[1] -554 point100_symmetry[i] = out[2] -555 θ_fse[i] = out[3] -556 if outdir is not None: -557 labels.append(f"$M^∗$ = {params['gbm_mobility']}") -558 -559 if outdir is not None: -560 strains = timestamps * strain_rate -561 self.postprocess( -562 strains, -563 angles, -564 point100_symmetry, -565 np.mean(θ_fse, axis=0), -566 labels, -567 markers, -568 outdir, -569 out_basepath, -570 ) -571 -572 # Check that GBM speeds up the alignment. -573 _log.info("checking grain orientations...") -574 halfway = int(len(timestamps) / 2) -575 assert np.all( -576 np.array( -577 [ -578 θ[halfway] - angles[i][halfway] -579 for i, θ in enumerate(angles[:-1], start=1) -580 ] -581 ) -582 > 0 -583 ) -584 assert np.all( -585 np.array( -586 [θ[-1] - angles[i][-1] for i, θ in enumerate(angles[:-1], start=1)] -587 ) -588 > 0 -589 ) -590 # Check that M*=0 doesn't affect grain sizes. -591 _log.info("checking grain sizes...") -592 for i, time in enumerate(timestamps): -593 nt.assert_allclose( -594 minerals[0].fractions[i], -595 np.full(params["number_of_grains"], 1 / params["number_of_grains"]), -596 ) -597 # Check that M*=0 matches FSE past 100% strain. -598 nt.assert_allclose( -599 angles[0][i_strain_50p:], -600 np.mean(θ_fse, axis=0)[i_strain_50p:], -601 atol=1, -602 rtol=0, -603 ) -604 # Check that GBM causes decreasing grain size median. -605 assert np.all( -606 np.array( -607 [ -608 np.median(m.fractions[halfway]) -609 - np.median(minerals[i].fractions[halfway]) -610 for i, m in enumerate(minerals[:-1], start=1) -611 ] -612 ) -613 > 0 -614 ) -615 -616 def test_boudary_sliding(self, seed, outdir): -617 """Test that the grain boundary sliding parameter has an effect.""" -618 strain_rate = 1.0 -619 shear_direction = [1, 0, 0] # Used to calculate the angular diagnostics. -620 get_velocity_gradient = _dv.simple_shear_2d("X", "Z", strain_rate) -621 timestamps = np.linspace(0, 2.5, 251) # Solve until D₀t=2.5 ('shear' γ=5). -622 i_strain_200p = 100 # Index of 50% strain. -623 params = _io.DEFAULT_PARAMS -624 gbs_thresholds = (0, 0.2, 0.4, 0.6) # Must be in ascending order. -625 markers = (".", "*", "d", "s") -626 angles = np.empty((len(gbs_thresholds), len(timestamps))) -627 point100_symmetry = np.empty_like(angles) -628 θ_fse = np.empty_like(angles) -629 minerals = [] -630 -631 optional_logging = cl.nullcontext() -632 if outdir is not None: -633 out_basepath = f"{outdir}/{SUBDIR}/{self.class_id}_sliding" -634 optional_logging = _log.logfile_enable(f"{out_basepath}.log") -635 labels = [] -636 -637 with optional_logging: -638 for i, f in enumerate(gbs_thresholds): -639 params["gbs_threshold"] = f -640 out = self.run( -641 params, -642 timestamps, -643 strain_rate, -644 get_velocity_gradient, -645 shear_direction, -646 seed=seed, -647 log_param="gbs_threshold", -648 return_fse=True, -649 ) -650 minerals.append(out[0]) -651 angles[i] = out[1] -652 point100_symmetry[i] = out[2] -653 θ_fse[i] = out[3] -654 if outdir is not None: -655 labels.append(f"$M^∗$ = {params['gbs_threshold']}") -656 -657 if outdir is not None: -658 strains = timestamps * strain_rate -659 self.postprocess( -660 strains, -661 angles, -662 point100_symmetry, -663 np.mean(θ_fse, axis=0), -664 labels, -665 markers, -666 outdir, -667 out_basepath, -668 ) -669 -670 # Check that GBS sets an upper bound on P_[100]. -671 _log.info("checking degree of [100] point symmetry...") -672 nt.assert_allclose( -673 np.full(len(point100_symmetry[0][i_strain_200p:]), 0.0), -674 point100_symmetry[0][i_strain_200p:] - 0.95, -675 atol=0.05, -676 rtol=0, -677 ) -678 nt.assert_allclose( -679 np.full(len(point100_symmetry[1][i_strain_200p:]), 0.0), -680 point100_symmetry[1][i_strain_200p:] - 0.78, -681 atol=0.05, -682 rtol=0, -683 ) -684 nt.assert_allclose( -685 np.full(len(point100_symmetry[2][i_strain_200p:]), 0.0), -686 point100_symmetry[2][i_strain_200p:] - 0.61, -687 atol=0.05, -688 rtol=0, -689 ) -690 nt.assert_allclose( -691 np.full(len(point100_symmetry[3][i_strain_200p:]), 0.0), -692 point100_symmetry[3][i_strain_200p:] - 0.44, -693 atol=0.055, -694 rtol=0, -695 ) -696 # Check that angles always reach within 5° of the shear direction. -697 _log.info("checking grain orientations...") -698 for θ in angles: -699 nt.assert_allclose( -700 np.full(len(θ[i_strain_200p:]), 0.0), -701 2.5 - θ[i_strain_200p:], -702 atol=2.5, -703 rtol=0, -704 ) + 78 _log.info(msg_start + "step %s/%s (t = %s)", t, n_timestamps - 1, time) + 79 + 80 deformation_gradient = mineral.update_orientations( + 81 params, + 82 deformation_gradient, + 83 get_velocity_gradient, + 84 pathline=(time, timestamps[t], cls.get_position), + 85 ) + 86 _log.debug( + 87 "› velocity gradient = %s", + 88 get_velocity_gradient(None).flatten(), + 89 ) + 90 _log.debug("› strain D₀t = %.2f", strain_rate * timestamps[t]) + 91 _log.debug( + 92 "› grain fractions: median = %s, max = %s, min = %s", + 93 np.median(mineral.fractions[-1]), + 94 np.max(mineral.fractions[-1]), + 95 np.min(mineral.fractions[-1]), + 96 ) + 97 if return_fse: + 98 _, fse_v = _diagnostics.finite_strain(deformation_gradient) + 99 θ_fse[t] = _diagnostics.smallest_angle(fse_v, shear_direction) +100 +101 # Compute texture diagnostics. +102 texture_symmetry = np.zeros(n_timestamps) +103 if use_bingham_average: +104 mean_angles = np.zeros(n_timestamps) +105 for idx, matrices in enumerate(mineral.orientations): +106 orientations_resampled, _ = _stats.resample_orientations( +107 matrices, mineral.fractions[idx], seed=seed +108 ) +109 if use_bingham_average: +110 direction_mean = _diagnostics.bingham_average( +111 orientations_resampled, +112 axis=_minerals.OLIVINE_PRIMARY_AXIS[mineral.fabric], +113 ) +114 mean_angles[idx] = _diagnostics.smallest_angle( +115 direction_mean, shear_direction +116 ) +117 texture_symmetry[idx] = _diagnostics.symmetry( +118 orientations_resampled, +119 axis=_minerals.OLIVINE_PRIMARY_AXIS[mineral.fabric], +120 )[0] +121 +122 if not use_bingham_average: +123 # Use SCCS axis (hexagonal symmetry) for the angle instead (opt). +124 mean_angles = np.array( +125 [ +126 _diagnostics.smallest_angle( +127 _diagnostics.anisotropy(v)[1][2, :], shear_direction +128 ) +129 for v in _minerals.voigt_averages([mineral], params) +130 ] +131 ) +132 +133 if return_fse: +134 return mineral, mean_angles, texture_symmetry, θ_fse +135 return mineral, mean_angles, texture_symmetry, None +136 +137 @classmethod +138 def postprocess( +139 cls, +140 strains, +141 angles, +142 point100_symmetry, +143 θ_fse, +144 labels, +145 markers, +146 outdir, +147 out_basepath, +148 target_interpolator=None, +149 ): +150 """Reusable postprocessing routine for olivine 2D simple shear simulations.""" +151 _log.info("postprocessing results...") +152 if target_interpolator is not None: +153 result_angles = angles.mean(axis=1) +154 result_angles_err = angles.std(axis=1) +155 result_point100_symmetry = point100_symmetry.mean(axis=1) +156 target_angles = target_interpolator(strains) +157 else: +158 result_angles = angles +159 result_angles_err = None +160 result_point100_symmetry = point100_symmetry +161 target_angles = None +162 +163 if outdir is not None: +164 schema = { +165 "delimiter": ",", +166 "missing": "-", +167 "fields": [ +168 { +169 "name": "strain", +170 "type": "integer", +171 "unit": "percent", +172 "fill": 999999, +173 } +174 ], +175 } +176 _io.save_scsv( +177 f"{out_basepath}_strains.scsv", +178 schema, +179 [[int(D * 200) for D in strains]], # Shear strain % is 200 * D₀. +180 ) +181 _vis.simple_shear_stationary_2d( +182 strains, +183 result_angles, +184 result_point100_symmetry, +185 target_angles=target_angles, +186 angles_err=result_angles_err, +187 savefile=f"{out_basepath}.png", +188 markers=markers, +189 θ_fse=θ_fse, +190 labels=labels, +191 ) +192 return result_angles, result_angles_err, result_point100_symmetry, target_angles +193 +194 @classmethod +195 def interp_GBM_Kaminski2001(cls, strains): +196 """Interpolate Kaminski & Ribe, 2001 data to get target angles at `strains`.""" +197 _log.info("interpolating target CPO angles...") +198 data = _io.read_scsv(_io.data("thirdparty") / "Kaminski2001_GBMshear.scsv") +199 cs_M0 = PchipInterpolator( +200 _utils.remove_nans(data.equivalent_strain_M0) / 200, +201 _utils.remove_nans(data.angle_M0), +202 ) +203 cs_M50 = PchipInterpolator( +204 _utils.remove_nans(data.equivalent_strain_M50) / 200, +205 _utils.remove_nans(data.angle_M50), +206 ) +207 cs_M200 = PchipInterpolator( +208 _utils.remove_nans(data.equivalent_strain_M200) / 200, +209 _utils.remove_nans(data.angle_M200), +210 ) +211 return [cs_M0(strains), cs_M50(strains), cs_M200(strains)] +212 +213 @classmethod +214 def interp_GBS_Kaminski2004(cls, strains): +215 """Interpolate Kaminski & Ribe, 2001 data to get target angles at `strains`.""" +216 _log.info("interpolating target CPO angles...") +217 data = _io.read_scsv(_io.data("thirdparty") / "Kaminski2004_GBSshear.scsv") +218 cs_X0 = PchipInterpolator( +219 _utils.remove_nans(data.dimensionless_time_X0), +220 45 + _utils.remove_nans(data.angle_X0), +221 ) +222 cs_X0d2 = PchipInterpolator( +223 _utils.remove_nans(data.dimensionless_time_X0d2), +224 45 + _utils.remove_nans(data.angle_X0d2), +225 ) +226 cs_X0d4 = PchipInterpolator( +227 _utils.remove_nans(data.dimensionless_time_X0d4), +228 45 + _utils.remove_nans(data.angle_X0d4), +229 ) +230 return [cs_X0(strains), cs_X0d2(strains), cs_X0d4(strains)] +231 +232 @pytest.mark.slow +233 def test_dvdx_GBM_ensemble( +234 self, +235 params_Kaminski2001_fig5_solid, # GBM = 0 +236 params_Kaminski2001_fig5_shortdash, # GBM = 50 +237 params_Kaminski2001_fig5_longdash, # GBM = 200 +238 seeds_nearX45, # Use `seeds` if you have lots of RAM and patience (or cores) +239 outdir, +240 ncpus, +241 ): +242 r"""Test a-axis alignment to shear in Y direction (init. SCCS near 45° from X). +243 +244 Velocity gradient: +245 $$\bm{L} = \begin{bmatrix} 0 & 0 & 0 \cr 2 & 0 & 0 \cr 0 & 0 & 0 \end{bmatrix}$$ +246 +247 Tests the effect of grain boundary migration, similar to Fig. 5 in +248 [Kaminski 2001](https://doi.org/10.1016%2Fs0012-821x%2801%2900356-9). +249 +250 """ +251 strain_rate = 5e-6 # Strain rate from Fraters & Billen, 2021, fig. 3. +252 timestamps = np.linspace(0, 2e5, 201) # Solve until D₀t=1 ('shear' γ=2). +253 n_timestamps = len(timestamps) +254 i_strain_50p = [0, 50, 100, 150, 200] # Indices for += 50% strain. +255 +256 shear_direction = [0, 1, 0] # Used to calculate the angular diagnostics. +257 get_velocity_gradient = _dv.simple_shear_2d("Y", "X", strain_rate) +258 +259 # Output setup with optional logging and data series labels. +260 θ_fse = np.empty(n_timestamps) +261 angles = np.empty((3, len(seeds_nearX45), n_timestamps)) +262 point100_symmetry = np.empty_like(angles) +263 optional_logging = cl.nullcontext() +264 if outdir is not None: +265 out_basepath = f"{outdir}/{SUBDIR}/{self.class_id}_dvdx_GBM_ensemble" +266 optional_logging = _log.logfile_enable(f"{out_basepath}.log") +267 labels = [] +268 +269 with optional_logging: +270 wall_start = perf_counter() +271 clock_start = process_time() +272 for p, params in enumerate( +273 ( +274 params_Kaminski2001_fig5_solid, # GBM = 0 +275 params_Kaminski2001_fig5_shortdash, # GBM = 50 +276 params_Kaminski2001_fig5_longdash, # GBM = 200 +277 ), +278 ): +279 if p == 0: +280 return_fse = True +281 else: +282 return_fse = False +283 +284 _run = ft.partial( +285 self.run, +286 params, +287 timestamps, +288 strain_rate, +289 get_velocity_gradient, +290 shear_direction, +291 log_param="gbm_mobility", +292 use_bingham_average=False, +293 return_fse=return_fse, +294 ) +295 with Pool(processes=ncpus) as pool: +296 for s, out in enumerate(pool.imap_unordered(_run, seeds_nearX45)): +297 mineral, mean_angles, texture_symmetry, fse_angles = out +298 angles[p, s, :] = mean_angles +299 point100_symmetry[p, s, :] = texture_symmetry +300 if return_fse: +301 θ_fse += fse_angles +302 +303 if return_fse: +304 θ_fse /= len(seeds_nearX45) +305 +306 # Update labels and store the last mineral of the ensemble for polefigs. +307 if outdir is not None: +308 labels.append(f"$M^∗$ = {params['gbm_mobility']}") +309 mineral.save( +310 f"{out_basepath}.npz", +311 postfix=f"M{params['gbm_mobility']}", +312 ) +313 +314 _log.info( +315 "elapsed walltime: %s", +316 _utils.readable_timestamp(np.abs(perf_counter() - wall_start)), +317 ) +318 _log.info( +319 "elapsed CPU time: %s", +320 _utils.readable_timestamp(np.abs(process_time() - clock_start)), +321 ) +322 +323 # Take ensemble means and optionally plot figure. +324 strains = timestamps * strain_rate +325 res = self.postprocess( +326 strains, +327 angles, +328 point100_symmetry, +329 θ_fse, +330 labels, +331 ("o", "v", "s"), +332 outdir, +333 out_basepath, +334 target_interpolator=self.interp_GBM_Kaminski2001, +335 ) +336 result_angles, result_angles_err, result_point100_symmetry, target_angles = res +337 +338 # Check that FSE is correct. +339 # First, get theoretical FSE axis for simple shear. +340 # We want the angle from the Y axis (shear direction), so subtract from 90. +341 θ_fse_eq = [90 - _utils.angle_fse_simpleshear(strain) for strain in strains] +342 nt.assert_allclose(θ_fse, θ_fse_eq, rtol=1e-7, atol=0) +343 +344 # Check that M*=0 angles match FSE, ignoring the first portion (<100% strain). +345 # Average orientations of near-isotropic distributions are unstable. +346 nt.assert_allclose( +347 θ_fse[i_strain_50p[2] :], +348 result_angles[0][i_strain_50p[2] :], +349 rtol=0.11, +350 atol=0, +351 ) +352 # Check that M*=0 matches target angles for strain > 100%. +353 nt.assert_allclose( +354 target_angles[0][i_strain_50p[2]], +355 result_angles[0][i_strain_50p[2]], +356 atol=1, +357 rtol=0, +358 ) +359 # Check that standard deviation decreases or stagnates (0.01 tolerance). +360 # Check for smooth decrease or stagnation in ensemble average (0.01 tolerance). +361 for angles, angles_err in zip(result_angles, result_angles_err): +362 assert np.all(np.diff(angles_err) < 0.01) +363 assert np.all(np.diff(angles[i_strain_50p[1] :]) < 0.01) +364 +365 # Check point symmetry of [100] at strains of 0%, 50%, 100%, 150% & 200%. +366 nt.assert_allclose( +367 [0.015, 0.11, 0.19, 0.27, 0.34], +368 result_point100_symmetry[0].take(i_strain_50p), +369 rtol=0, +370 atol=0.015, +371 ) +372 nt.assert_allclose( +373 [0.015, 0.15, 0.33, 0.57, 0.72], +374 result_point100_symmetry[1].take(i_strain_50p), +375 rtol=0, +376 atol=0.015, +377 ) +378 nt.assert_allclose( +379 [0.015, 0.22, 0.64, 0.86, 0.91], +380 result_point100_symmetry[2].take(i_strain_50p), +381 rtol=0, +382 atol=0.015, +383 ) +384 +385 @pytest.mark.slow +386 def test_dudz_GBS_ensemble( +387 self, +388 params_Kaminski2004_fig4_circles, # GBS = 0 +389 params_Kaminski2004_fig4_squares, # GBS = 0.2 +390 params_Kaminski2004_fig4_triangles, # GBS = 0.4 +391 seeds_nearX45, # Use `seeds` if you have lots of RAM and patience (or cores) +392 outdir, +393 ncpus, +394 ): +395 r"""Test a-axis alignment to shear in X direction (init. SCCS near 45° from X). +396 +397 Velocity gradient: +398 $$\bm{L} = \begin{bmatrix} 0 & 0 & 2 \cr 0 & 0 & 0 \cr 0 & 0 & 0 \end{bmatrix}$$ +399 +400 """ +401 strain_rate = 5e-6 # Strain rate from Fraters & Billen, 2021, fig. 3. +402 timestamps = np.linspace(0, 5e5, 251) # Solve until D₀t=2.5 ('shear' γ=5). +403 n_timestamps = len(timestamps) +404 i_strain_100p = [0, 50, 100, 150, 200] # Indices for += 100% strain. +405 +406 shear_direction = [1, 0, 0] # Used to calculate the angular diagnostics. +407 get_velocity_gradient = _dv.simple_shear_2d("X", "Z", strain_rate) +408 +409 # Output setup with optional logging and data series labels. +410 θ_fse = np.empty(n_timestamps) +411 angles = np.empty((3, len(seeds_nearX45), n_timestamps)) +412 point100_symmetry = np.empty_like(angles) +413 optional_logging = cl.nullcontext() +414 if outdir is not None: +415 out_basepath = f"{outdir}/{SUBDIR}/{self.class_id}_dudz_GBS_ensemble" +416 optional_logging = _log.logfile_enable(f"{out_basepath}.log") +417 labels = [] +418 +419 with optional_logging: +420 wall_start = perf_counter() +421 clock_start = process_time() +422 for p, params in enumerate( +423 ( +424 params_Kaminski2004_fig4_circles, # GBS = 0 +425 params_Kaminski2004_fig4_squares, # GBS = 0.2 +426 params_Kaminski2004_fig4_triangles, # GBS = 0.4 +427 ), +428 ): +429 if p == 0: +430 return_fse = True +431 else: +432 return_fse = False +433 +434 _run = ft.partial( +435 self.run, +436 params, +437 timestamps, +438 strain_rate, +439 get_velocity_gradient, +440 shear_direction, +441 log_param="gbs_threshold", +442 use_bingham_average=False, +443 return_fse=return_fse, +444 ) +445 with Pool(processes=ncpus) as pool: +446 for s, out in enumerate(pool.imap_unordered(_run, seeds_nearX45)): +447 mineral, mean_angles, texture_symmetry, fse_angles = out +448 angles[p, s, :] = mean_angles +449 point100_symmetry[p, s, :] = texture_symmetry +450 if return_fse: +451 θ_fse += fse_angles +452 +453 if return_fse: +454 θ_fse /= len(seeds_nearX45) +455 +456 # Update labels and store the last mineral of the ensemble for polefigs. +457 if outdir is not None: +458 labels.append(f"$f_{{gbs}}$ = {params['gbs_threshold']}") +459 mineral.save( +460 f"{out_basepath}.npz", +461 postfix=f"X{params['gbs_threshold']}", +462 ) +463 +464 _log.info( +465 "elapsed walltime: %s", +466 _utils.readable_timestamp(np.abs(perf_counter() - wall_start)), +467 ) +468 _log.info( +469 "elapsed CPU time: %s", +470 _utils.readable_timestamp(np.abs(process_time() - clock_start)), +471 ) +472 +473 # Take ensemble means and optionally plot figure. +474 strains = timestamps * strain_rate +475 res = self.postprocess_ensemble( +476 strains, +477 angles, +478 point100_symmetry, +479 θ_fse, +480 labels, +481 ("o", "v", "s"), +482 outdir, +483 out_basepath, +484 target_interpolator=self.interp_GBS_Kaminski2004, +485 ) +486 result_angles, result_angles_err, result_point100_symmetry, target_angles = res +487 +488 # Check that FSE is correct. +489 # First, get theoretical FSE axis for simple shear. +490 # We want the angle from the Y axis (shear direction), so subtract from 90. +491 θ_fse_eq = [90 - _utils.angle_fse_simpleshear(strain) for strain in strains] +492 nt.assert_allclose(θ_fse, θ_fse_eq, rtol=1e-7, atol=0) +493 +494 # Check point symmetry of [100] at strains of 0%, 100%, 200%, 300% & 400%. +495 nt.assert_allclose( +496 [0.015, 0.52, 0.86, 0.93, 0.94], +497 point100_symmetry[0].take(i_strain_100p), +498 rtol=0, +499 atol=0.015, +500 ) +501 nt.assert_allclose( +502 [0.015, 0.42, 0.71, 0.77, 0.79], +503 point100_symmetry[1].take(i_strain_100p), +504 rtol=0, +505 atol=0.015, +506 ) +507 nt.assert_allclose( +508 [0.015, 0.36, 0.57, 0.6, 0.62], +509 point100_symmetry[2].take(i_strain_100p), +510 rtol=0, +511 atol=0.015, +512 ) +513 +514 # Check that standard deviation decreases or stagnates (0.01 tolerance). +515 # Check for smooth decrease or stagnation in ensemble average (0.01 tolerance). +516 for angles, angles_err in zip(result_angles, result_angles_err): +517 assert np.all(np.diff(angles_err) < 0.01) +518 assert np.all(np.diff(angles[i_strain_100p[1] :]) < 0.01) +519 +520 def test_boundary_mobility(self, seed, outdir): +521 """Test that the grain boundary mobility parameter has an effect.""" +522 shear_direction = [0, 1, 0] # Used to calculate the angular diagnostics. +523 strain_rate = 1.0 +524 get_velocity_gradient = _dv.simple_shear_2d("Y", "X", strain_rate) +525 timestamps = np.linspace(0, 1, 201) # Solve until D₀t=1 ('shear' γ=2). +526 i_strain_50p = 50 # Index of 50% strain. +527 params = _io.DEFAULT_PARAMS +528 gbm_mobilities = (0, 10, 50, 125, 200) # Must be in ascending order. +529 markers = ("x", ".", "*", "d", "s") +530 angles = np.empty((len(gbm_mobilities), len(timestamps))) +531 point100_symmetry = np.empty_like(angles) +532 θ_fse = np.empty_like(angles) +533 minerals = [] +534 +535 optional_logging = cl.nullcontext() +536 if outdir is not None: +537 out_basepath = f"{outdir}/{SUBDIR}/{self.class_id}_mobility" +538 optional_logging = _log.logfile_enable(f"{out_basepath}.log") +539 labels = [] +540 +541 with optional_logging: +542 for i, M in enumerate(gbm_mobilities): +543 params["gbm_mobility"] = M +544 out = self.run( +545 params, +546 timestamps, +547 strain_rate, +548 get_velocity_gradient, +549 shear_direction, +550 seed=seed, +551 log_param="gbm_mobility", +552 return_fse=True, +553 ) +554 minerals.append(out[0]) +555 angles[i] = out[1] +556 point100_symmetry[i] = out[2] +557 θ_fse[i] = out[3] +558 if outdir is not None: +559 labels.append(f"$M^∗$ = {params['gbm_mobility']}") +560 +561 if outdir is not None: +562 strains = timestamps * strain_rate +563 self.postprocess( +564 strains, +565 angles, +566 point100_symmetry, +567 np.mean(θ_fse, axis=0), +568 labels, +569 markers, +570 outdir, +571 out_basepath, +572 ) +573 +574 # Check that GBM speeds up the alignment. +575 _log.info("checking grain orientations...") +576 halfway = int(len(timestamps) / 2) +577 assert np.all( +578 np.array( +579 [ +580 θ[halfway] - angles[i][halfway] +581 for i, θ in enumerate(angles[:-1], start=1) +582 ] +583 ) +584 > 0 +585 ) +586 assert np.all( +587 np.array( +588 [θ[-1] - angles[i][-1] for i, θ in enumerate(angles[:-1], start=1)] +589 ) +590 > 0 +591 ) +592 # Check that M*=0 doesn't affect grain sizes. +593 _log.info("checking grain sizes...") +594 for i, time in enumerate(timestamps): +595 nt.assert_allclose( +596 minerals[0].fractions[i], +597 np.full(params["number_of_grains"], 1 / params["number_of_grains"]), +598 ) +599 # Check that M*=0 matches FSE past 100% strain. +600 nt.assert_allclose( +601 angles[0][i_strain_50p:], +602 np.mean(θ_fse, axis=0)[i_strain_50p:], +603 atol=1, +604 rtol=0, +605 ) +606 # Check that GBM causes decreasing grain size median. +607 assert np.all( +608 np.array( +609 [ +610 np.median(m.fractions[halfway]) +611 - np.median(minerals[i].fractions[halfway]) +612 for i, m in enumerate(minerals[:-1], start=1) +613 ] +614 ) +615 > 0 +616 ) +617 +618 def test_boudary_sliding(self, seed, outdir): +619 """Test that the grain boundary sliding parameter has an effect.""" +620 strain_rate = 1.0 +621 shear_direction = [1, 0, 0] # Used to calculate the angular diagnostics. +622 get_velocity_gradient = _dv.simple_shear_2d("X", "Z", strain_rate) +623 timestamps = np.linspace(0, 2.5, 251) # Solve until D₀t=2.5 ('shear' γ=5). +624 i_strain_200p = 100 # Index of 50% strain. +625 params = _io.DEFAULT_PARAMS +626 gbs_thresholds = (0, 0.2, 0.4, 0.6) # Must be in ascending order. +627 markers = (".", "*", "d", "s") +628 angles = np.empty((len(gbs_thresholds), len(timestamps))) +629 point100_symmetry = np.empty_like(angles) +630 θ_fse = np.empty_like(angles) +631 minerals = [] +632 +633 optional_logging = cl.nullcontext() +634 if outdir is not None: +635 out_basepath = f"{outdir}/{SUBDIR}/{self.class_id}_sliding" +636 optional_logging = _log.logfile_enable(f"{out_basepath}.log") +637 labels = [] +638 +639 with optional_logging: +640 for i, f in enumerate(gbs_thresholds): +641 params["gbs_threshold"] = f +642 out = self.run( +643 params, +644 timestamps, +645 strain_rate, +646 get_velocity_gradient, +647 shear_direction, +648 seed=seed, +649 log_param="gbs_threshold", +650 return_fse=True, +651 ) +652 minerals.append(out[0]) +653 angles[i] = out[1] +654 point100_symmetry[i] = out[2] +655 θ_fse[i] = out[3] +656 if outdir is not None: +657 labels.append(f"$M^∗$ = {params['gbs_threshold']}") +658 +659 if outdir is not None: +660 strains = timestamps * strain_rate +661 self.postprocess( +662 strains, +663 angles, +664 point100_symmetry, +665 np.mean(θ_fse, axis=0), +666 labels, +667 markers, +668 outdir, +669 out_basepath, +670 ) +671 +672 # Check that GBS sets an upper bound on P_[100]. +673 _log.info("checking degree of [100] point symmetry...") +674 nt.assert_allclose( +675 np.full(len(point100_symmetry[0][i_strain_200p:]), 0.0), +676 point100_symmetry[0][i_strain_200p:] - 0.95, +677 atol=0.05, +678 rtol=0, +679 ) +680 nt.assert_allclose( +681 np.full(len(point100_symmetry[1][i_strain_200p:]), 0.0), +682 point100_symmetry[1][i_strain_200p:] - 0.78, +683 atol=0.05, +684 rtol=0, +685 ) +686 nt.assert_allclose( +687 np.full(len(point100_symmetry[2][i_strain_200p:]), 0.0), +688 point100_symmetry[2][i_strain_200p:] - 0.61, +689 atol=0.05, +690 rtol=0, +691 ) +692 nt.assert_allclose( +693 np.full(len(point100_symmetry[3][i_strain_200p:]), 0.0), +694 point100_symmetry[3][i_strain_200p:] - 0.44, +695 atol=0.055, +696 rtol=0, +697 ) +698 # Check that angles always reach within 5° of the shear direction. +699 _log.info("checking grain orientations...") +700 for θ in angles: +701 nt.assert_allclose( +702 np.full(len(θ[i_strain_200p:]), 0.0), +703 2.5 - θ[i_strain_200p:], +704 atol=2.5, +705 rtol=0, +706 ) +707 +708 @pytest.mark.slow +709 def test_ngrains(self, seed, outdir): +710 """Test that solvers work up to 10000 grains.""" +711 shear_direction = [0, 1, 0] +712 strain_rate = 1.0 +713 get_velocity_gradient = _dv.simple_shear_2d("Y", "X", strain_rate) +714 timestamps = np.linspace(0, 1, 201) # Solve until D₀t=1 ('shear' γ=2). +715 params = _io.DEFAULT_PARAMS +716 grain_counts = (100, 1000, 2000, 5000, 10000) +717 +718 optional_logging = cl.nullcontext() +719 if outdir is not None: +720 out_basepath = f"{outdir}/{SUBDIR}/{self.class_id}_ngrains" +721 optional_logging = _log.logfile_enable(f"{out_basepath}.log") +722 +723 with optional_logging: +724 for i, N in enumerate(grain_counts): +725 params["number_of_grains"] = N +726 self.run( +727 params, +728 timestamps, +729 strain_rate, +730 get_velocity_gradient, +731 shear_direction, +732 seed=seed, +733 log_param="number_of_grains", +734 return_fse=True, +735 ) @@ -1610,70 +1675,72 @@

    67 msg_start = f"X = {params['gbs_threshold']}; " 68 case "gbm_mobility": 69 msg_start = f"M∗ = {params['gbm_mobility']}; " - 70 case _: - 71 msg_start = "" - 72 - 73 if seed is not None: - 74 msg_start += f"# {seed}; " - 75 - 76 _log.info(msg_start + "step %s/%s (t = %s)", t, n_timestamps - 1, time) + 70 case "number_of_grains": + 71 msg_start = f"N = {params['number_of_grains']}; " + 72 case _: + 73 msg_start = "" + 74 + 75 if seed is not None: + 76 msg_start += f"# {seed}; " 77 - 78 deformation_gradient = mineral.update_orientations( - 79 params, - 80 deformation_gradient, - 81 get_velocity_gradient, - 82 pathline=(time, timestamps[t], cls.get_position), - 83 ) - 84 _log.debug( - 85 "› velocity gradient = %s", - 86 get_velocity_gradient(None).flatten(), - 87 ) - 88 _log.debug("› strain D₀t = %.2f", strain_rate * timestamps[t]) - 89 _log.debug( - 90 "› grain fractions: median = %s, max = %s, min = %s", - 91 np.median(mineral.fractions[-1]), - 92 np.max(mineral.fractions[-1]), - 93 np.min(mineral.fractions[-1]), - 94 ) - 95 if return_fse: - 96 _, fse_v = _diagnostics.finite_strain(deformation_gradient) - 97 θ_fse[t] = _diagnostics.smallest_angle(fse_v, shear_direction) - 98 - 99 # Compute texture diagnostics. -100 texture_symmetry = np.zeros(n_timestamps) -101 if use_bingham_average: -102 mean_angles = np.zeros(n_timestamps) -103 for idx, matrices in enumerate(mineral.orientations): -104 orientations_resampled, _ = _stats.resample_orientations( -105 matrices, mineral.fractions[idx], seed=seed -106 ) -107 if use_bingham_average: -108 direction_mean = _diagnostics.bingham_average( -109 orientations_resampled, -110 axis=_minerals.OLIVINE_PRIMARY_AXIS[mineral.fabric], -111 ) -112 mean_angles[idx] = _diagnostics.smallest_angle( -113 direction_mean, shear_direction -114 ) -115 texture_symmetry[idx] = _diagnostics.symmetry( -116 orientations_resampled, -117 axis=_minerals.OLIVINE_PRIMARY_AXIS[mineral.fabric], -118 )[0] -119 -120 if not use_bingham_average: -121 # Use SCCS axis (hexagonal symmetry) for the angle instead (opt). -122 mean_angles = np.array( -123 [ -124 _diagnostics.smallest_angle( -125 _diagnostics.anisotropy(v)[1][2, :], shear_direction -126 ) -127 for v in _minerals.voigt_averages([mineral], params) -128 ] -129 ) -130 -131 if return_fse: -132 return mineral, mean_angles, texture_symmetry, θ_fse -133 return mineral, mean_angles, texture_symmetry, None + 78 _log.info(msg_start + "step %s/%s (t = %s)", t, n_timestamps - 1, time) + 79 + 80 deformation_gradient = mineral.update_orientations( + 81 params, + 82 deformation_gradient, + 83 get_velocity_gradient, + 84 pathline=(time, timestamps[t], cls.get_position), + 85 ) + 86 _log.debug( + 87 "› velocity gradient = %s", + 88 get_velocity_gradient(None).flatten(), + 89 ) + 90 _log.debug("› strain D₀t = %.2f", strain_rate * timestamps[t]) + 91 _log.debug( + 92 "› grain fractions: median = %s, max = %s, min = %s", + 93 np.median(mineral.fractions[-1]), + 94 np.max(mineral.fractions[-1]), + 95 np.min(mineral.fractions[-1]), + 96 ) + 97 if return_fse: + 98 _, fse_v = _diagnostics.finite_strain(deformation_gradient) + 99 θ_fse[t] = _diagnostics.smallest_angle(fse_v, shear_direction) +100 +101 # Compute texture diagnostics. +102 texture_symmetry = np.zeros(n_timestamps) +103 if use_bingham_average: +104 mean_angles = np.zeros(n_timestamps) +105 for idx, matrices in enumerate(mineral.orientations): +106 orientations_resampled, _ = _stats.resample_orientations( +107 matrices, mineral.fractions[idx], seed=seed +108 ) +109 if use_bingham_average: +110 direction_mean = _diagnostics.bingham_average( +111 orientations_resampled, +112 axis=_minerals.OLIVINE_PRIMARY_AXIS[mineral.fabric], +113 ) +114 mean_angles[idx] = _diagnostics.smallest_angle( +115 direction_mean, shear_direction +116 ) +117 texture_symmetry[idx] = _diagnostics.symmetry( +118 orientations_resampled, +119 axis=_minerals.OLIVINE_PRIMARY_AXIS[mineral.fabric], +120 )[0] +121 +122 if not use_bingham_average: +123 # Use SCCS axis (hexagonal symmetry) for the angle instead (opt). +124 mean_angles = np.array( +125 [ +126 _diagnostics.smallest_angle( +127 _diagnostics.anisotropy(v)[1][2, :], shear_direction +128 ) +129 for v in _minerals.voigt_averages([mineral], params) +130 ] +131 ) +132 +133 if return_fse: +134 return mineral, mean_angles, texture_symmetry, θ_fse +135 return mineral, mean_angles, texture_symmetry, None @@ -1698,62 +1765,62 @@

    - 
    135    @classmethod
-136    def postprocess(
-137        cls,
-138        strains,
-139        angles,
-140        point100_symmetry,
-141        θ_fse,
-142        labels,
-143        markers,
-144        outdir,
-145        out_basepath,
-146        target_interpolator=None,
-147    ):
-148        """Reusable postprocessing routine for olivine 2D simple shear simulations."""
-149        _log.info("postprocessing results...")
-150        if target_interpolator is not None:
-151            result_angles = angles.mean(axis=1)
-152            result_angles_err = angles.std(axis=1)
-153            result_point100_symmetry = point100_symmetry.mean(axis=1)
-154            target_angles = target_interpolator(strains)
-155        else:
-156            result_angles = angles
-157            result_angles_err = None
-158            result_point100_symmetry = point100_symmetry
-159            target_angles = None
-160
-161        if outdir is not None:
-162            schema = {
-163                "delimiter": ",",
-164                "missing": "-",
-165                "fields": [
-166                    {
-167                        "name": "strain",
-168                        "type": "integer",
-169                        "unit": "percent",
-170                        "fill": 999999,
-171                    }
-172                ],
-173            }
-174            _io.save_scsv(
-175                f"{out_basepath}_strains.scsv",
-176                schema,
-177                [[int(D * 200) for D in strains]],  # Shear strain % is 200 * D₀.
-178            )
-179            _vis.simple_shear_stationary_2d(
-180                strains,
-181                result_angles,
-182                result_point100_symmetry,
-183                target_angles=target_angles,
-184                angles_err=result_angles_err,
-185                savefile=f"{out_basepath}.png",
-186                markers=markers,
-187                θ_fse=θ_fse,
-188                labels=labels,
-189            )
-190        return result_angles, result_angles_err, result_point100_symmetry, target_angles
+            
    137    @classmethod
+138    def postprocess(
+139        cls,
+140        strains,
+141        angles,
+142        point100_symmetry,
+143        θ_fse,
+144        labels,
+145        markers,
+146        outdir,
+147        out_basepath,
+148        target_interpolator=None,
+149    ):
+150        """Reusable postprocessing routine for olivine 2D simple shear simulations."""
+151        _log.info("postprocessing results...")
+152        if target_interpolator is not None:
+153            result_angles = angles.mean(axis=1)
+154            result_angles_err = angles.std(axis=1)
+155            result_point100_symmetry = point100_symmetry.mean(axis=1)
+156            target_angles = target_interpolator(strains)
+157        else:
+158            result_angles = angles
+159            result_angles_err = None
+160            result_point100_symmetry = point100_symmetry
+161            target_angles = None
+162
+163        if outdir is not None:
+164            schema = {
+165                "delimiter": ",",
+166                "missing": "-",
+167                "fields": [
+168                    {
+169                        "name": "strain",
+170                        "type": "integer",
+171                        "unit": "percent",
+172                        "fill": 999999,
+173                    }
+174                ],
+175            }
+176            _io.save_scsv(
+177                f"{out_basepath}_strains.scsv",
+178                schema,
+179                [[int(D * 200) for D in strains]],  # Shear strain % is 200 * D₀.
+180            )
+181            _vis.simple_shear_stationary_2d(
+182                strains,
+183                result_angles,
+184                result_point100_symmetry,
+185                target_angles=target_angles,
+186                angles_err=result_angles_err,
+187                savefile=f"{out_basepath}.png",
+188                markers=markers,
+189                θ_fse=θ_fse,
+190                labels=labels,
+191            )
+192        return result_angles, result_angles_err, result_point100_symmetry, target_angles
 
    
 
 
@@ -1774,24 +1841,24 @@
    - 
    192    @classmethod
-193    def interp_GBM_Kaminski2001(cls, strains):
-194        """Interpolate Kaminski & Ribe, 2001 data to get target angles at `strains`."""
-195        _log.info("interpolating target CPO angles...")
-196        data = _io.read_scsv(_io.data("thirdparty") / "Kaminski2001_GBMshear.scsv")
-197        cs_M0 = PchipInterpolator(
-198            _utils.remove_nans(data.equivalent_strain_M0) / 200,
-199            _utils.remove_nans(data.angle_M0),
-200        )
-201        cs_M50 = PchipInterpolator(
-202            _utils.remove_nans(data.equivalent_strain_M50) / 200,
-203            _utils.remove_nans(data.angle_M50),
-204        )
-205        cs_M200 = PchipInterpolator(
-206            _utils.remove_nans(data.equivalent_strain_M200) / 200,
-207            _utils.remove_nans(data.angle_M200),
-208        )
-209        return [cs_M0(strains), cs_M50(strains), cs_M200(strains)]
+            
    194    @classmethod
+195    def interp_GBM_Kaminski2001(cls, strains):
+196        """Interpolate Kaminski & Ribe, 2001 data to get target angles at `strains`."""
+197        _log.info("interpolating target CPO angles...")
+198        data = _io.read_scsv(_io.data("thirdparty") / "Kaminski2001_GBMshear.scsv")
+199        cs_M0 = PchipInterpolator(
+200            _utils.remove_nans(data.equivalent_strain_M0) / 200,
+201            _utils.remove_nans(data.angle_M0),
+202        )
+203        cs_M50 = PchipInterpolator(
+204            _utils.remove_nans(data.equivalent_strain_M50) / 200,
+205            _utils.remove_nans(data.angle_M50),
+206        )
+207        cs_M200 = PchipInterpolator(
+208            _utils.remove_nans(data.equivalent_strain_M200) / 200,
+209            _utils.remove_nans(data.angle_M200),
+210        )
+211        return [cs_M0(strains), cs_M50(strains), cs_M200(strains)]
 
    
 
 
@@ -1812,24 +1879,24 @@
    - 
    211    @classmethod
-212    def interp_GBS_Kaminski2004(cls, strains):
-213        """Interpolate Kaminski & Ribe, 2001 data to get target angles at `strains`."""
-214        _log.info("interpolating target CPO angles...")
-215        data = _io.read_scsv(_io.data("thirdparty") / "Kaminski2004_GBSshear.scsv")
-216        cs_X0 = PchipInterpolator(
-217            _utils.remove_nans(data.dimensionless_time_X0),
-218            45 + _utils.remove_nans(data.angle_X0),
-219        )
-220        cs_X0d2 = PchipInterpolator(
-221            _utils.remove_nans(data.dimensionless_time_X0d2),
-222            45 + _utils.remove_nans(data.angle_X0d2),
-223        )
-224        cs_X0d4 = PchipInterpolator(
-225            _utils.remove_nans(data.dimensionless_time_X0d4),
-226            45 + _utils.remove_nans(data.angle_X0d4),
-227        )
-228        return [cs_X0(strains), cs_X0d2(strains), cs_X0d4(strains)]
+            
    213    @classmethod
+214    def interp_GBS_Kaminski2004(cls, strains):
+215        """Interpolate Kaminski & Ribe, 2001 data to get target angles at `strains`."""
+216        _log.info("interpolating target CPO angles...")
+217        data = _io.read_scsv(_io.data("thirdparty") / "Kaminski2004_GBSshear.scsv")
+218        cs_X0 = PchipInterpolator(
+219            _utils.remove_nans(data.dimensionless_time_X0),
+220            45 + _utils.remove_nans(data.angle_X0),
+221        )
+222        cs_X0d2 = PchipInterpolator(
+223            _utils.remove_nans(data.dimensionless_time_X0d2),
+224            45 + _utils.remove_nans(data.angle_X0d2),
+225        )
+226        cs_X0d4 = PchipInterpolator(
+227            _utils.remove_nans(data.dimensionless_time_X0d4),
+228            45 + _utils.remove_nans(data.angle_X0d4),
+229        )
+230        return [cs_X0(strains), cs_X0d2(strains), cs_X0d4(strains)]
 
    
 
 
@@ -1850,158 +1917,158 @@
    - 
    230    @pytest.mark.slow
-231    def test_dvdx_GBM_ensemble(
-232        self,
-233        params_Kaminski2001_fig5_solid,  # GBM = 0
-234        params_Kaminski2001_fig5_shortdash,  # GBM = 50
-235        params_Kaminski2001_fig5_longdash,  # GBM = 200
-236        seeds_nearX45,  # Use `seeds` if you have lots of RAM and patience (or cores)
-237        outdir,
-238        ncpus,
-239    ):
-240        r"""Test a-axis alignment to shear in Y direction (init. SCCS near 45° from X).
-241
-242        Velocity gradient:
-243        $$\bm{L} = \begin{bmatrix} 0 & 0 & 0 \cr 2 & 0 & 0 \cr 0 & 0 & 0 \end{bmatrix}$$
-244
-245        Tests the effect of grain boundary migration, similar to Fig. 5 in
-246        [Kaminski 2001](https://doi.org/10.1016%2Fs0012-821x%2801%2900356-9).
-247
-248        """
-249        strain_rate = 5e-6  # Strain rate from Fraters & Billen, 2021, fig. 3.
-250        timestamps = np.linspace(0, 2e5, 201)  # Solve until D₀t=1 ('shear' γ=2).
-251        n_timestamps = len(timestamps)
-252        i_strain_50p = [0, 50, 100, 150, 200]  # Indices for += 50% strain.
-253
-254        shear_direction = [0, 1, 0]  # Used to calculate the angular diagnostics.
-255        get_velocity_gradient = _dv.simple_shear_2d("Y", "X", strain_rate)
-256
-257        # Output setup with optional logging and data series labels.
-258        θ_fse = np.empty(n_timestamps)
-259        angles = np.empty((3, len(seeds_nearX45), n_timestamps))
-260        point100_symmetry = np.empty_like(angles)
-261        optional_logging = cl.nullcontext()
-262        if outdir is not None:
-263            out_basepath = f"{outdir}/{SUBDIR}/{self.class_id}_dvdx_GBM_ensemble"
-264            optional_logging = _log.logfile_enable(f"{out_basepath}.log")
-265            labels = []
-266
-267        with optional_logging:
-268            wall_start = perf_counter()
-269            clock_start = process_time()
-270            for p, params in enumerate(
-271                (
-272                    params_Kaminski2001_fig5_solid,  # GBM = 0
-273                    params_Kaminski2001_fig5_shortdash,  # GBM = 50
-274                    params_Kaminski2001_fig5_longdash,  # GBM = 200
-275                ),
-276            ):
-277                if p == 0:
-278                    return_fse = True
-279                else:
-280                    return_fse = False
-281
-282                _run = ft.partial(
-283                    self.run,
-284                    params,
-285                    timestamps,
-286                    strain_rate,
-287                    get_velocity_gradient,
-288                    shear_direction,
-289                    log_param="gbm_mobility",
-290                    use_bingham_average=False,
-291                    return_fse=return_fse,
-292                )
-293                with Pool(processes=ncpus) as pool:
-294                    for s, out in enumerate(pool.imap_unordered(_run, seeds_nearX45)):
-295                        mineral, mean_angles, texture_symmetry, fse_angles = out
-296                        angles[p, s, :] = mean_angles
-297                        point100_symmetry[p, s, :] = texture_symmetry
-298                        if return_fse:
-299                            θ_fse += fse_angles
-300
-301                if return_fse:
-302                    θ_fse /= len(seeds_nearX45)
-303
-304                # Update labels and store the last mineral of the ensemble for polefigs.
-305                if outdir is not None:
-306                    labels.append(f"$M^∗$ = {params['gbm_mobility']}")
-307                    mineral.save(
-308                        f"{out_basepath}.npz",
-309                        postfix=f"M{params['gbm_mobility']}",
-310                    )
-311
-312            _log.info(
-313                "elapsed walltime: %s",
-314                _utils.readable_timestamp(np.abs(perf_counter() - wall_start)),
-315            )
-316            _log.info(
-317                "elapsed CPU time: %s",
-318                _utils.readable_timestamp(np.abs(process_time() - clock_start)),
-319            )
-320
-321        # Take ensemble means and optionally plot figure.
-322        strains = timestamps * strain_rate
-323        res = self.postprocess(
-324            strains,
-325            angles,
-326            point100_symmetry,
-327            θ_fse,
-328            labels,
-329            ("o", "v", "s"),
-330            outdir,
-331            out_basepath,
-332            target_interpolator=self.interp_GBM_Kaminski2001,
-333        )
-334        result_angles, result_angles_err, result_point100_symmetry, target_angles = res
-335
-336        # Check that FSE is correct.
-337        # First, get theoretical FSE axis for simple shear.
-338        # We want the angle from the Y axis (shear direction), so subtract from 90.
-339        θ_fse_eq = [90 - _utils.angle_fse_simpleshear(strain) for strain in strains]
-340        nt.assert_allclose(θ_fse, θ_fse_eq, rtol=1e-7, atol=0)
-341
-342        # Check that M*=0 angles match FSE, ignoring the first portion (<100% strain).
-343        # Average orientations of near-isotropic distributions are unstable.
-344        nt.assert_allclose(
-345            θ_fse[i_strain_50p[2] :],
-346            result_angles[0][i_strain_50p[2] :],
-347            rtol=0.11,
-348            atol=0,
-349        )
-350        # Check that M*=0 matches target angles for strain > 100%.
-351        nt.assert_allclose(
-352            target_angles[0][i_strain_50p[2]],
-353            result_angles[0][i_strain_50p[2]],
-354            atol=1,
-355            rtol=0,
-356        )
-357        # Check that standard deviation decreases or stagnates (0.01 tolerance).
-358        # Check for smooth decrease or stagnation in ensemble average (0.01 tolerance).
-359        for angles, angles_err in zip(result_angles, result_angles_err):
-360            assert np.all(np.diff(angles_err) < 0.01)
-361            assert np.all(np.diff(angles[i_strain_50p[1] :]) < 0.01)
-362
-363        # Check point symmetry of [100] at strains of 0%, 50%, 100%, 150% & 200%.
-364        nt.assert_allclose(
-365            [0.015, 0.11, 0.19, 0.27, 0.34],
-366            result_point100_symmetry[0].take(i_strain_50p),
-367            rtol=0,
-368            atol=0.015,
-369        )
-370        nt.assert_allclose(
-371            [0.015, 0.15, 0.33, 0.57, 0.72],
-372            result_point100_symmetry[1].take(i_strain_50p),
-373            rtol=0,
-374            atol=0.015,
-375        )
-376        nt.assert_allclose(
-377            [0.015, 0.22, 0.64, 0.86, 0.91],
-378            result_point100_symmetry[2].take(i_strain_50p),
-379            rtol=0,
-380            atol=0.015,
-381        )
+            
    232    @pytest.mark.slow
+233    def test_dvdx_GBM_ensemble(
+234        self,
+235        params_Kaminski2001_fig5_solid,  # GBM = 0
+236        params_Kaminski2001_fig5_shortdash,  # GBM = 50
+237        params_Kaminski2001_fig5_longdash,  # GBM = 200
+238        seeds_nearX45,  # Use `seeds` if you have lots of RAM and patience (or cores)
+239        outdir,
+240        ncpus,
+241    ):
+242        r"""Test a-axis alignment to shear in Y direction (init. SCCS near 45° from X).
+243
+244        Velocity gradient:
+245        $$\bm{L} = \begin{bmatrix} 0 & 0 & 0 \cr 2 & 0 & 0 \cr 0 & 0 & 0 \end{bmatrix}$$
+246
+247        Tests the effect of grain boundary migration, similar to Fig. 5 in
+248        [Kaminski 2001](https://doi.org/10.1016%2Fs0012-821x%2801%2900356-9).
+249
+250        """
+251        strain_rate = 5e-6  # Strain rate from Fraters & Billen, 2021, fig. 3.
+252        timestamps = np.linspace(0, 2e5, 201)  # Solve until D₀t=1 ('shear' γ=2).
+253        n_timestamps = len(timestamps)
+254        i_strain_50p = [0, 50, 100, 150, 200]  # Indices for += 50% strain.
+255
+256        shear_direction = [0, 1, 0]  # Used to calculate the angular diagnostics.
+257        get_velocity_gradient = _dv.simple_shear_2d("Y", "X", strain_rate)
+258
+259        # Output setup with optional logging and data series labels.
+260        θ_fse = np.empty(n_timestamps)
+261        angles = np.empty((3, len(seeds_nearX45), n_timestamps))
+262        point100_symmetry = np.empty_like(angles)
+263        optional_logging = cl.nullcontext()
+264        if outdir is not None:
+265            out_basepath = f"{outdir}/{SUBDIR}/{self.class_id}_dvdx_GBM_ensemble"
+266            optional_logging = _log.logfile_enable(f"{out_basepath}.log")
+267            labels = []
+268
+269        with optional_logging:
+270            wall_start = perf_counter()
+271            clock_start = process_time()
+272            for p, params in enumerate(
+273                (
+274                    params_Kaminski2001_fig5_solid,  # GBM = 0
+275                    params_Kaminski2001_fig5_shortdash,  # GBM = 50
+276                    params_Kaminski2001_fig5_longdash,  # GBM = 200
+277                ),
+278            ):
+279                if p == 0:
+280                    return_fse = True
+281                else:
+282                    return_fse = False
+283
+284                _run = ft.partial(
+285                    self.run,
+286                    params,
+287                    timestamps,
+288                    strain_rate,
+289                    get_velocity_gradient,
+290                    shear_direction,
+291                    log_param="gbm_mobility",
+292                    use_bingham_average=False,
+293                    return_fse=return_fse,
+294                )
+295                with Pool(processes=ncpus) as pool:
+296                    for s, out in enumerate(pool.imap_unordered(_run, seeds_nearX45)):
+297                        mineral, mean_angles, texture_symmetry, fse_angles = out
+298                        angles[p, s, :] = mean_angles
+299                        point100_symmetry[p, s, :] = texture_symmetry
+300                        if return_fse:
+301                            θ_fse += fse_angles
+302
+303                if return_fse:
+304                    θ_fse /= len(seeds_nearX45)
+305
+306                # Update labels and store the last mineral of the ensemble for polefigs.
+307                if outdir is not None:
+308                    labels.append(f"$M^∗$ = {params['gbm_mobility']}")
+309                    mineral.save(
+310                        f"{out_basepath}.npz",
+311                        postfix=f"M{params['gbm_mobility']}",
+312                    )
+313
+314            _log.info(
+315                "elapsed walltime: %s",
+316                _utils.readable_timestamp(np.abs(perf_counter() - wall_start)),
+317            )
+318            _log.info(
+319                "elapsed CPU time: %s",
+320                _utils.readable_timestamp(np.abs(process_time() - clock_start)),
+321            )
+322
+323        # Take ensemble means and optionally plot figure.
+324        strains = timestamps * strain_rate
+325        res = self.postprocess(
+326            strains,
+327            angles,
+328            point100_symmetry,
+329            θ_fse,
+330            labels,
+331            ("o", "v", "s"),
+332            outdir,
+333            out_basepath,
+334            target_interpolator=self.interp_GBM_Kaminski2001,
+335        )
+336        result_angles, result_angles_err, result_point100_symmetry, target_angles = res
+337
+338        # Check that FSE is correct.
+339        # First, get theoretical FSE axis for simple shear.
+340        # We want the angle from the Y axis (shear direction), so subtract from 90.
+341        θ_fse_eq = [90 - _utils.angle_fse_simpleshear(strain) for strain in strains]
+342        nt.assert_allclose(θ_fse, θ_fse_eq, rtol=1e-7, atol=0)
+343
+344        # Check that M*=0 angles match FSE, ignoring the first portion (<100% strain).
+345        # Average orientations of near-isotropic distributions are unstable.
+346        nt.assert_allclose(
+347            θ_fse[i_strain_50p[2] :],
+348            result_angles[0][i_strain_50p[2] :],
+349            rtol=0.11,
+350            atol=0,
+351        )
+352        # Check that M*=0 matches target angles for strain > 100%.
+353        nt.assert_allclose(
+354            target_angles[0][i_strain_50p[2]],
+355            result_angles[0][i_strain_50p[2]],
+356            atol=1,
+357            rtol=0,
+358        )
+359        # Check that standard deviation decreases or stagnates (0.01 tolerance).
+360        # Check for smooth decrease or stagnation in ensemble average (0.01 tolerance).
+361        for angles, angles_err in zip(result_angles, result_angles_err):
+362            assert np.all(np.diff(angles_err) < 0.01)
+363            assert np.all(np.diff(angles[i_strain_50p[1] :]) < 0.01)
+364
+365        # Check point symmetry of [100] at strains of 0%, 50%, 100%, 150% & 200%.
+366        nt.assert_allclose(
+367            [0.015, 0.11, 0.19, 0.27, 0.34],
+368            result_point100_symmetry[0].take(i_strain_50p),
+369            rtol=0,
+370            atol=0.015,
+371        )
+372        nt.assert_allclose(
+373            [0.015, 0.15, 0.33, 0.57, 0.72],
+374            result_point100_symmetry[1].take(i_strain_50p),
+375            rtol=0,
+376            atol=0.015,
+377        )
+378        nt.assert_allclose(
+379            [0.015, 0.22, 0.64, 0.86, 0.91],
+380            result_point100_symmetry[2].take(i_strain_50p),
+381            rtol=0,
+382            atol=0.015,
+383        )
 
    
 
 
@@ -2028,140 +2095,140 @@
    - 
    383    @pytest.mark.slow
-384    def test_dudz_GBS_ensemble(
-385        self,
-386        params_Kaminski2004_fig4_circles,  # GBS = 0
-387        params_Kaminski2004_fig4_squares,  # GBS = 0.2
-388        params_Kaminski2004_fig4_triangles,  # GBS = 0.4
-389        seeds_nearX45,  # Use `seeds` if you have lots of RAM and patience (or cores)
-390        outdir,
-391        ncpus,
-392    ):
-393        r"""Test a-axis alignment to shear in X direction (init. SCCS near 45° from X).
-394
-395        Velocity gradient:
-396        $$\bm{L} = \begin{bmatrix} 0 & 0 & 2 \cr 0 & 0 & 0 \cr 0 & 0 & 0 \end{bmatrix}$$
-397
-398        """
-399        strain_rate = 5e-6  # Strain rate from Fraters & Billen, 2021, fig. 3.
-400        timestamps = np.linspace(0, 5e5, 251)  # Solve until D₀t=2.5 ('shear' γ=5).
-401        n_timestamps = len(timestamps)
-402        i_strain_100p = [0, 50, 100, 150, 200]  # Indices for += 100% strain.
-403
-404        shear_direction = [1, 0, 0]  # Used to calculate the angular diagnostics.
-405        get_velocity_gradient = _dv.simple_shear_2d("X", "Z", strain_rate)
-406
-407        # Output setup with optional logging and data series labels.
-408        θ_fse = np.empty(n_timestamps)
-409        angles = np.empty((3, len(seeds_nearX45), n_timestamps))
-410        point100_symmetry = np.empty_like(angles)
-411        optional_logging = cl.nullcontext()
-412        if outdir is not None:
-413            out_basepath = f"{outdir}/{SUBDIR}/{self.class_id}_dudz_GBS_ensemble"
-414            optional_logging = _log.logfile_enable(f"{out_basepath}.log")
-415            labels = []
-416
-417        with optional_logging:
-418            wall_start = perf_counter()
-419            clock_start = process_time()
-420            for p, params in enumerate(
-421                (
-422                    params_Kaminski2004_fig4_circles,  # GBS = 0
-423                    params_Kaminski2004_fig4_squares,  # GBS = 0.2
-424                    params_Kaminski2004_fig4_triangles,  # GBS = 0.4
-425                ),
-426            ):
-427                if p == 0:
-428                    return_fse = True
-429                else:
-430                    return_fse = False
-431
-432                _run = ft.partial(
-433                    self.run,
-434                    params,
-435                    timestamps,
-436                    strain_rate,
-437                    get_velocity_gradient,
-438                    shear_direction,
-439                    log_param="gbs_threshold",
-440                    use_bingham_average=False,
-441                    return_fse=return_fse,
-442                )
-443                with Pool(processes=ncpus) as pool:
-444                    for s, out in enumerate(pool.imap_unordered(_run, seeds_nearX45)):
-445                        mineral, mean_angles, texture_symmetry, fse_angles = out
-446                        angles[p, s, :] = mean_angles
-447                        point100_symmetry[p, s, :] = texture_symmetry
-448                        if return_fse:
-449                            θ_fse += fse_angles
-450
-451                if return_fse:
-452                    θ_fse /= len(seeds_nearX45)
-453
-454                # Update labels and store the last mineral of the ensemble for polefigs.
-455                if outdir is not None:
-456                    labels.append(f"$f_{{gbs}}$ = {params['gbs_threshold']}")
-457                    mineral.save(
-458                        f"{out_basepath}.npz",
-459                        postfix=f"X{params['gbs_threshold']}",
-460                    )
-461
-462            _log.info(
-463                "elapsed walltime: %s",
-464                _utils.readable_timestamp(np.abs(perf_counter() - wall_start)),
-465            )
-466            _log.info(
-467                "elapsed CPU time: %s",
-468                _utils.readable_timestamp(np.abs(process_time() - clock_start)),
-469            )
-470
-471        # Take ensemble means and optionally plot figure.
-472        strains = timestamps * strain_rate
-473        res = self.postprocess_ensemble(
-474            strains,
-475            angles,
-476            point100_symmetry,
-477            θ_fse,
-478            labels,
-479            ("o", "v", "s"),
-480            outdir,
-481            out_basepath,
-482            target_interpolator=self.interp_GBS_Kaminski2004,
-483        )
-484        result_angles, result_angles_err, result_point100_symmetry, target_angles = res
-485
-486        # Check that FSE is correct.
-487        # First, get theoretical FSE axis for simple shear.
-488        # We want the angle from the Y axis (shear direction), so subtract from 90.
-489        θ_fse_eq = [90 - _utils.angle_fse_simpleshear(strain) for strain in strains]
-490        nt.assert_allclose(θ_fse, θ_fse_eq, rtol=1e-7, atol=0)
-491
-492        # Check point symmetry of [100] at strains of 0%, 100%, 200%, 300% & 400%.
-493        nt.assert_allclose(
-494            [0.015, 0.52, 0.86, 0.93, 0.94],
-495            point100_symmetry[0].take(i_strain_100p),
-496            rtol=0,
-497            atol=0.015,
-498        )
-499        nt.assert_allclose(
-500            [0.015, 0.42, 0.71, 0.77, 0.79],
-501            point100_symmetry[1].take(i_strain_100p),
-502            rtol=0,
-503            atol=0.015,
-504        )
-505        nt.assert_allclose(
-506            [0.015, 0.36, 0.57, 0.6, 0.62],
-507            point100_symmetry[2].take(i_strain_100p),
-508            rtol=0,
-509            atol=0.015,
-510        )
-511
-512        # Check that standard deviation decreases or stagnates (0.01 tolerance).
-513        # Check for smooth decrease or stagnation in ensemble average (0.01 tolerance).
-514        for angles, angles_err in zip(result_angles, result_angles_err):
-515            assert np.all(np.diff(angles_err) < 0.01)
-516            assert np.all(np.diff(angles[i_strain_100p[1] :]) < 0.01)
+            
    385    @pytest.mark.slow
+386    def test_dudz_GBS_ensemble(
+387        self,
+388        params_Kaminski2004_fig4_circles,  # GBS = 0
+389        params_Kaminski2004_fig4_squares,  # GBS = 0.2
+390        params_Kaminski2004_fig4_triangles,  # GBS = 0.4
+391        seeds_nearX45,  # Use `seeds` if you have lots of RAM and patience (or cores)
+392        outdir,
+393        ncpus,
+394    ):
+395        r"""Test a-axis alignment to shear in X direction (init. SCCS near 45° from X).
+396
+397        Velocity gradient:
+398        $$\bm{L} = \begin{bmatrix} 0 & 0 & 2 \cr 0 & 0 & 0 \cr 0 & 0 & 0 \end{bmatrix}$$
+399
+400        """
+401        strain_rate = 5e-6  # Strain rate from Fraters & Billen, 2021, fig. 3.
+402        timestamps = np.linspace(0, 5e5, 251)  # Solve until D₀t=2.5 ('shear' γ=5).
+403        n_timestamps = len(timestamps)
+404        i_strain_100p = [0, 50, 100, 150, 200]  # Indices for += 100% strain.
+405
+406        shear_direction = [1, 0, 0]  # Used to calculate the angular diagnostics.
+407        get_velocity_gradient = _dv.simple_shear_2d("X", "Z", strain_rate)
+408
+409        # Output setup with optional logging and data series labels.
+410        θ_fse = np.empty(n_timestamps)
+411        angles = np.empty((3, len(seeds_nearX45), n_timestamps))
+412        point100_symmetry = np.empty_like(angles)
+413        optional_logging = cl.nullcontext()
+414        if outdir is not None:
+415            out_basepath = f"{outdir}/{SUBDIR}/{self.class_id}_dudz_GBS_ensemble"
+416            optional_logging = _log.logfile_enable(f"{out_basepath}.log")
+417            labels = []
+418
+419        with optional_logging:
+420            wall_start = perf_counter()
+421            clock_start = process_time()
+422            for p, params in enumerate(
+423                (
+424                    params_Kaminski2004_fig4_circles,  # GBS = 0
+425                    params_Kaminski2004_fig4_squares,  # GBS = 0.2
+426                    params_Kaminski2004_fig4_triangles,  # GBS = 0.4
+427                ),
+428            ):
+429                if p == 0:
+430                    return_fse = True
+431                else:
+432                    return_fse = False
+433
+434                _run = ft.partial(
+435                    self.run,
+436                    params,
+437                    timestamps,
+438                    strain_rate,
+439                    get_velocity_gradient,
+440                    shear_direction,
+441                    log_param="gbs_threshold",
+442                    use_bingham_average=False,
+443                    return_fse=return_fse,
+444                )
+445                with Pool(processes=ncpus) as pool:
+446                    for s, out in enumerate(pool.imap_unordered(_run, seeds_nearX45)):
+447                        mineral, mean_angles, texture_symmetry, fse_angles = out
+448                        angles[p, s, :] = mean_angles
+449                        point100_symmetry[p, s, :] = texture_symmetry
+450                        if return_fse:
+451                            θ_fse += fse_angles
+452
+453                if return_fse:
+454                    θ_fse /= len(seeds_nearX45)
+455
+456                # Update labels and store the last mineral of the ensemble for polefigs.
+457                if outdir is not None:
+458                    labels.append(f"$f_{{gbs}}$ = {params['gbs_threshold']}")
+459                    mineral.save(
+460                        f"{out_basepath}.npz",
+461                        postfix=f"X{params['gbs_threshold']}",
+462                    )
+463
+464            _log.info(
+465                "elapsed walltime: %s",
+466                _utils.readable_timestamp(np.abs(perf_counter() - wall_start)),
+467            )
+468            _log.info(
+469                "elapsed CPU time: %s",
+470                _utils.readable_timestamp(np.abs(process_time() - clock_start)),
+471            )
+472
+473        # Take ensemble means and optionally plot figure.
+474        strains = timestamps * strain_rate
+475        res = self.postprocess_ensemble(
+476            strains,
+477            angles,
+478            point100_symmetry,
+479            θ_fse,
+480            labels,
+481            ("o", "v", "s"),
+482            outdir,
+483            out_basepath,
+484            target_interpolator=self.interp_GBS_Kaminski2004,
+485        )
+486        result_angles, result_angles_err, result_point100_symmetry, target_angles = res
+487
+488        # Check that FSE is correct.
+489        # First, get theoretical FSE axis for simple shear.
+490        # We want the angle from the Y axis (shear direction), so subtract from 90.
+491        θ_fse_eq = [90 - _utils.angle_fse_simpleshear(strain) for strain in strains]
+492        nt.assert_allclose(θ_fse, θ_fse_eq, rtol=1e-7, atol=0)
+493
+494        # Check point symmetry of [100] at strains of 0%, 100%, 200%, 300% & 400%.
+495        nt.assert_allclose(
+496            [0.015, 0.52, 0.86, 0.93, 0.94],
+497            point100_symmetry[0].take(i_strain_100p),
+498            rtol=0,
+499            atol=0.015,
+500        )
+501        nt.assert_allclose(
+502            [0.015, 0.42, 0.71, 0.77, 0.79],
+503            point100_symmetry[1].take(i_strain_100p),
+504            rtol=0,
+505            atol=0.015,
+506        )
+507        nt.assert_allclose(
+508            [0.015, 0.36, 0.57, 0.6, 0.62],
+509            point100_symmetry[2].take(i_strain_100p),
+510            rtol=0,
+511            atol=0.015,
+512        )
+513
+514        # Check that standard deviation decreases or stagnates (0.01 tolerance).
+515        # Check for smooth decrease or stagnation in ensemble average (0.01 tolerance).
+516        for angles, angles_err in zip(result_angles, result_angles_err):
+517            assert np.all(np.diff(angles_err) < 0.01)
+518            assert np.all(np.diff(angles[i_strain_100p[1] :]) < 0.01)
 
    
 
 
@@ -2184,103 +2251,103 @@
    - 
    518    def test_boundary_mobility(self, seed, outdir):
-519        """Test that the grain boundary mobility parameter has an effect."""
-520        shear_direction = [0, 1, 0]  # Used to calculate the angular diagnostics.
-521        strain_rate = 1.0
-522        get_velocity_gradient = _dv.simple_shear_2d("Y", "X", strain_rate)
-523        timestamps = np.linspace(0, 1, 201)  # Solve until D₀t=1 ('shear' γ=2).
-524        i_strain_50p = 50  # Index of 50% strain.
-525        params = _io.DEFAULT_PARAMS
-526        gbm_mobilities = (0, 10, 50, 125, 200)  # Must be in ascending order.
-527        markers = ("x", ".", "*", "d", "s")
-528        angles = np.empty((len(gbm_mobilities), len(timestamps)))
-529        point100_symmetry = np.empty_like(angles)
-530        θ_fse = np.empty_like(angles)
-531        minerals = []
-532
-533        optional_logging = cl.nullcontext()
-534        if outdir is not None:
-535            out_basepath = f"{outdir}/{SUBDIR}/{self.class_id}_mobility"
-536            optional_logging = _log.logfile_enable(f"{out_basepath}.log")
-537            labels = []
-538
-539        with optional_logging:
-540            for i, M in enumerate(gbm_mobilities):
-541                params["gbm_mobility"] = M
-542                out = self.run(
-543                    params,
-544                    timestamps,
-545                    strain_rate,
-546                    get_velocity_gradient,
-547                    shear_direction,
-548                    seed=seed,
-549                    log_param="gbm_mobility",
-550                    return_fse=True,
-551                )
-552                minerals.append(out[0])
-553                angles[i] = out[1]
-554                point100_symmetry[i] = out[2]
-555                θ_fse[i] = out[3]
-556                if outdir is not None:
-557                    labels.append(f"$M^∗$ = {params['gbm_mobility']}")
-558
-559        if outdir is not None:
-560            strains = timestamps * strain_rate
-561            self.postprocess(
-562                strains,
-563                angles,
-564                point100_symmetry,
-565                np.mean(θ_fse, axis=0),
-566                labels,
-567                markers,
-568                outdir,
-569                out_basepath,
-570            )
-571
-572        # Check that GBM speeds up the alignment.
-573        _log.info("checking grain orientations...")
-574        halfway = int(len(timestamps) / 2)
-575        assert np.all(
-576            np.array(
-577                [
-578                    θ[halfway] - angles[i][halfway]
-579                    for i, θ in enumerate(angles[:-1], start=1)
-580                ]
-581            )
-582            > 0
-583        )
-584        assert np.all(
-585            np.array(
-586                [θ[-1] - angles[i][-1] for i, θ in enumerate(angles[:-1], start=1)]
-587            )
-588            > 0
-589        )
-590        # Check that M*=0 doesn't affect grain sizes.
-591        _log.info("checking grain sizes...")
-592        for i, time in enumerate(timestamps):
-593            nt.assert_allclose(
-594                minerals[0].fractions[i],
-595                np.full(params["number_of_grains"], 1 / params["number_of_grains"]),
-596            )
-597        # Check that M*=0 matches FSE past 100% strain.
-598        nt.assert_allclose(
-599            angles[0][i_strain_50p:],
-600            np.mean(θ_fse, axis=0)[i_strain_50p:],
-601            atol=1,
-602            rtol=0,
-603        )
-604        # Check that GBM causes decreasing grain size median.
-605        assert np.all(
-606            np.array(
-607                [
-608                    np.median(m.fractions[halfway])
-609                    - np.median(minerals[i].fractions[halfway])
-610                    for i, m in enumerate(minerals[:-1], start=1)
-611                ]
-612            )
-613            > 0
-614        )
+            
    520    def test_boundary_mobility(self, seed, outdir):
+521        """Test that the grain boundary mobility parameter has an effect."""
+522        shear_direction = [0, 1, 0]  # Used to calculate the angular diagnostics.
+523        strain_rate = 1.0
+524        get_velocity_gradient = _dv.simple_shear_2d("Y", "X", strain_rate)
+525        timestamps = np.linspace(0, 1, 201)  # Solve until D₀t=1 ('shear' γ=2).
+526        i_strain_50p = 50  # Index of 50% strain.
+527        params = _io.DEFAULT_PARAMS
+528        gbm_mobilities = (0, 10, 50, 125, 200)  # Must be in ascending order.
+529        markers = ("x", ".", "*", "d", "s")
+530        angles = np.empty((len(gbm_mobilities), len(timestamps)))
+531        point100_symmetry = np.empty_like(angles)
+532        θ_fse = np.empty_like(angles)
+533        minerals = []
+534
+535        optional_logging = cl.nullcontext()
+536        if outdir is not None:
+537            out_basepath = f"{outdir}/{SUBDIR}/{self.class_id}_mobility"
+538            optional_logging = _log.logfile_enable(f"{out_basepath}.log")
+539            labels = []
+540
+541        with optional_logging:
+542            for i, M in enumerate(gbm_mobilities):
+543                params["gbm_mobility"] = M
+544                out = self.run(
+545                    params,
+546                    timestamps,
+547                    strain_rate,
+548                    get_velocity_gradient,
+549                    shear_direction,
+550                    seed=seed,
+551                    log_param="gbm_mobility",
+552                    return_fse=True,
+553                )
+554                minerals.append(out[0])
+555                angles[i] = out[1]
+556                point100_symmetry[i] = out[2]
+557                θ_fse[i] = out[3]
+558                if outdir is not None:
+559                    labels.append(f"$M^∗$ = {params['gbm_mobility']}")
+560
+561        if outdir is not None:
+562            strains = timestamps * strain_rate
+563            self.postprocess(
+564                strains,
+565                angles,
+566                point100_symmetry,
+567                np.mean(θ_fse, axis=0),
+568                labels,
+569                markers,
+570                outdir,
+571                out_basepath,
+572            )
+573
+574        # Check that GBM speeds up the alignment.
+575        _log.info("checking grain orientations...")
+576        halfway = int(len(timestamps) / 2)
+577        assert np.all(
+578            np.array(
+579                [
+580                    θ[halfway] - angles[i][halfway]
+581                    for i, θ in enumerate(angles[:-1], start=1)
+582                ]
+583            )
+584            > 0
+585        )
+586        assert np.all(
+587            np.array(
+588                [θ[-1] - angles[i][-1] for i, θ in enumerate(angles[:-1], start=1)]
+589            )
+590            > 0
+591        )
+592        # Check that M*=0 doesn't affect grain sizes.
+593        _log.info("checking grain sizes...")
+594        for i, time in enumerate(timestamps):
+595            nt.assert_allclose(
+596                minerals[0].fractions[i],
+597                np.full(params["number_of_grains"], 1 / params["number_of_grains"]),
+598            )
+599        # Check that M*=0 matches FSE past 100% strain.
+600        nt.assert_allclose(
+601            angles[0][i_strain_50p:],
+602            np.mean(θ_fse, axis=0)[i_strain_50p:],
+603            atol=1,
+604            rtol=0,
+605        )
+606        # Check that GBM causes decreasing grain size median.
+607        assert np.all(
+608            np.array(
+609                [
+610                    np.median(m.fractions[halfway])
+611                    - np.median(minerals[i].fractions[halfway])
+612                    for i, m in enumerate(minerals[:-1], start=1)
+613                ]
+614            )
+615            > 0
+616        )
 
    
 
 
@@ -2300,95 +2367,95 @@
    - 
    616    def test_boudary_sliding(self, seed, outdir):
-617        """Test that the grain boundary sliding parameter has an effect."""
-618        strain_rate = 1.0
-619        shear_direction = [1, 0, 0]  # Used to calculate the angular diagnostics.
-620        get_velocity_gradient = _dv.simple_shear_2d("X", "Z", strain_rate)
-621        timestamps = np.linspace(0, 2.5, 251)  # Solve until D₀t=2.5 ('shear' γ=5).
-622        i_strain_200p = 100  # Index of 50% strain.
-623        params = _io.DEFAULT_PARAMS
-624        gbs_thresholds = (0, 0.2, 0.4, 0.6)  # Must be in ascending order.
-625        markers = (".", "*", "d", "s")
-626        angles = np.empty((len(gbs_thresholds), len(timestamps)))
-627        point100_symmetry = np.empty_like(angles)
-628        θ_fse = np.empty_like(angles)
-629        minerals = []
-630
-631        optional_logging = cl.nullcontext()
-632        if outdir is not None:
-633            out_basepath = f"{outdir}/{SUBDIR}/{self.class_id}_sliding"
-634            optional_logging = _log.logfile_enable(f"{out_basepath}.log")
-635            labels = []
-636
-637        with optional_logging:
-638            for i, f in enumerate(gbs_thresholds):
-639                params["gbs_threshold"] = f
-640                out = self.run(
-641                    params,
-642                    timestamps,
-643                    strain_rate,
-644                    get_velocity_gradient,
-645                    shear_direction,
-646                    seed=seed,
-647                    log_param="gbs_threshold",
-648                    return_fse=True,
-649                )
-650                minerals.append(out[0])
-651                angles[i] = out[1]
-652                point100_symmetry[i] = out[2]
-653                θ_fse[i] = out[3]
-654                if outdir is not None:
-655                    labels.append(f"$M^∗$ = {params['gbs_threshold']}")
-656
-657        if outdir is not None:
-658            strains = timestamps * strain_rate
-659            self.postprocess(
-660                strains,
-661                angles,
-662                point100_symmetry,
-663                np.mean(θ_fse, axis=0),
-664                labels,
-665                markers,
-666                outdir,
-667                out_basepath,
-668            )
-669
-670        # Check that GBS sets an upper bound on P_[100].
-671        _log.info("checking degree of [100] point symmetry...")
-672        nt.assert_allclose(
-673            np.full(len(point100_symmetry[0][i_strain_200p:]), 0.0),
-674            point100_symmetry[0][i_strain_200p:] - 0.95,
-675            atol=0.05,
-676            rtol=0,
-677        )
-678        nt.assert_allclose(
-679            np.full(len(point100_symmetry[1][i_strain_200p:]), 0.0),
-680            point100_symmetry[1][i_strain_200p:] - 0.78,
-681            atol=0.05,
-682            rtol=0,
-683        )
-684        nt.assert_allclose(
-685            np.full(len(point100_symmetry[2][i_strain_200p:]), 0.0),
-686            point100_symmetry[2][i_strain_200p:] - 0.61,
-687            atol=0.05,
-688            rtol=0,
-689        )
-690        nt.assert_allclose(
-691            np.full(len(point100_symmetry[3][i_strain_200p:]), 0.0),
-692            point100_symmetry[3][i_strain_200p:] - 0.44,
-693            atol=0.055,
-694            rtol=0,
-695        )
-696        # Check that angles always reach within 5° of the shear direction.
-697        _log.info("checking grain orientations...")
-698        for θ in angles:
-699            nt.assert_allclose(
-700                np.full(len(θ[i_strain_200p:]), 0.0),
-701                2.5 - θ[i_strain_200p:],
-702                atol=2.5,
-703                rtol=0,
-704            )
+            
    618    def test_boudary_sliding(self, seed, outdir):
+619        """Test that the grain boundary sliding parameter has an effect."""
+620        strain_rate = 1.0
+621        shear_direction = [1, 0, 0]  # Used to calculate the angular diagnostics.
+622        get_velocity_gradient = _dv.simple_shear_2d("X", "Z", strain_rate)
+623        timestamps = np.linspace(0, 2.5, 251)  # Solve until D₀t=2.5 ('shear' γ=5).
+624        i_strain_200p = 100  # Index of 50% strain.
+625        params = _io.DEFAULT_PARAMS
+626        gbs_thresholds = (0, 0.2, 0.4, 0.6)  # Must be in ascending order.
+627        markers = (".", "*", "d", "s")
+628        angles = np.empty((len(gbs_thresholds), len(timestamps)))
+629        point100_symmetry = np.empty_like(angles)
+630        θ_fse = np.empty_like(angles)
+631        minerals = []
+632
+633        optional_logging = cl.nullcontext()
+634        if outdir is not None:
+635            out_basepath = f"{outdir}/{SUBDIR}/{self.class_id}_sliding"
+636            optional_logging = _log.logfile_enable(f"{out_basepath}.log")
+637            labels = []
+638
+639        with optional_logging:
+640            for i, f in enumerate(gbs_thresholds):
+641                params["gbs_threshold"] = f
+642                out = self.run(
+643                    params,
+644                    timestamps,
+645                    strain_rate,
+646                    get_velocity_gradient,
+647                    shear_direction,
+648                    seed=seed,
+649                    log_param="gbs_threshold",
+650                    return_fse=True,
+651                )
+652                minerals.append(out[0])
+653                angles[i] = out[1]
+654                point100_symmetry[i] = out[2]
+655                θ_fse[i] = out[3]
+656                if outdir is not None:
+657                    labels.append(f"$M^∗$ = {params['gbs_threshold']}")
+658
+659        if outdir is not None:
+660            strains = timestamps * strain_rate
+661            self.postprocess(
+662                strains,
+663                angles,
+664                point100_symmetry,
+665                np.mean(θ_fse, axis=0),
+666                labels,
+667                markers,
+668                outdir,
+669                out_basepath,
+670            )
+671
+672        # Check that GBS sets an upper bound on P_[100].
+673        _log.info("checking degree of [100] point symmetry...")
+674        nt.assert_allclose(
+675            np.full(len(point100_symmetry[0][i_strain_200p:]), 0.0),
+676            point100_symmetry[0][i_strain_200p:] - 0.95,
+677            atol=0.05,
+678            rtol=0,
+679        )
+680        nt.assert_allclose(
+681            np.full(len(point100_symmetry[1][i_strain_200p:]), 0.0),
+682            point100_symmetry[1][i_strain_200p:] - 0.78,
+683            atol=0.05,
+684            rtol=0,
+685        )
+686        nt.assert_allclose(
+687            np.full(len(point100_symmetry[2][i_strain_200p:]), 0.0),
+688            point100_symmetry[2][i_strain_200p:] - 0.61,
+689            atol=0.05,
+690            rtol=0,
+691        )
+692        nt.assert_allclose(
+693            np.full(len(point100_symmetry[3][i_strain_200p:]), 0.0),
+694            point100_symmetry[3][i_strain_200p:] - 0.44,
+695            atol=0.055,
+696            rtol=0,
+697        )
+698        # Check that angles always reach within 5° of the shear direction.
+699        _log.info("checking grain orientations...")
+700        for θ in angles:
+701            nt.assert_allclose(
+702                np.full(len(θ[i_strain_200p:]), 0.0),
+703                2.5 - θ[i_strain_200p:],
+704                atol=2.5,
+705                rtol=0,
+706            )
 
    
 
 
@@ -2396,6 +2463,54 @@
    + +
    + +
    +
    @pytest.mark.slow
    + + def + test_ngrains(self, seed, outdir): + + + +
    + + 
    708    @pytest.mark.slow
+709    def test_ngrains(self, seed, outdir):
+710        """Test that solvers work up to 10000 grains."""
+711        shear_direction = [0, 1, 0]
+712        strain_rate = 1.0
+713        get_velocity_gradient = _dv.simple_shear_2d("Y", "X", strain_rate)
+714        timestamps = np.linspace(0, 1, 201)  # Solve until D₀t=1 ('shear' γ=2).
+715        params = _io.DEFAULT_PARAMS
+716        grain_counts = (100, 1000, 2000, 5000, 10000)
+717
+718        optional_logging = cl.nullcontext()
+719        if outdir is not None:
+720            out_basepath = f"{outdir}/{SUBDIR}/{self.class_id}_ngrains"
+721            optional_logging = _log.logfile_enable(f"{out_basepath}.log")
+722
+723        with optional_logging:
+724            for i, N in enumerate(grain_counts):
+725                params["number_of_grains"] = N
+726                self.run(
+727                    params,
+728                    timestamps,
+729                    strain_rate,
+730                    get_velocity_gradient,
+731                    shear_direction,
+732                    seed=seed,
+733                    log_param="number_of_grains",
+734                    return_fse=True,
+735                )
+
    + + +

    Test that solvers work up to 10000 grains.

    +
    + +