From c68e8c96beedc77b67022e4454d21cd95cd06904 Mon Sep 17 00:00:00 2001 From: hkwang <98353449+hkwang@users.noreply.github.com> Date: Mon, 22 Jul 2024 11:45:31 -0400 Subject: [PATCH] Delete 5_Bivariate_priors.ipynb --- 5_Bivariate_priors.ipynb | 962 --------------------------------------- 1 file changed, 962 deletions(-) delete mode 100644 5_Bivariate_priors.ipynb diff --git a/5_Bivariate_priors.ipynb b/5_Bivariate_priors.ipynb deleted file mode 100644 index 19dd873..0000000 --- a/5_Bivariate_priors.ipynb +++ /dev/null @@ -1,962 +0,0 @@ -{ - "cells": [ - { - "cell_type": "code", - "execution_count": 1, - "metadata": {}, - "outputs": [], - "source": [ - "import numpy as np\n", - "from matplotlib import pyplot as plt\n", - "from numpy.random import default_rng\n", - "from tqdm import tqdm\n", - "from time import perf_counter \n", - "from scipy.stats import pearsonr, poisson, wishart, multivariate_normal, norm, vonmises, multivariate_t, laplace\n", - "from scipy.special import gamma, factorial, gammaln\n", - "from scipy.special import i0 as I0\n", - "from dw_tools import bivariate_tools\n", - "\n", - "new_rc_params = {\n", - " 'text.usetex': False,\n", - " \"svg.fonttype\": 'none',\n", - " \"font.size\" : 12,\n", - "}\n", - "plt.rcParams.update(new_rc_params)\n", - "fig_dir = \"results_figs/\"" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": {}, - "outputs": [], - "source": [ - "# %autosave 300\n", - "# %load_ext autoreload\n", - "# %autoreload 2" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# A model for bivariate priors" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Introduction\n", - "In this notebook, we examine the joint distribution of pairs of structure factor amplitudes conditional on a third reference set of amplitudes. We will assume that the two datasets have joint correlation parameter $r_x$ as specified below, and both of their correlations with the reference dataset are described by a correlation parameter $r$. These parameters play the same role as $r$ or $r_{DW}$ in the preceding notebooks.\n", - "\n", - "Under the multivariate Wilson model, we examine:\n", - "1. **Joint probability distributions of $(E_1,E_2,E_3)$**. We compute the joint probability distribution of $(E_1, E_2)$, both unconditional and conditional on $E_3$.\n", - "2. **The Bivariate Rice Distribution**. We present a formalism for bivariate Rice distributions introduced by Abu-Dayya & Beaulieu (1994). To do so, we first review the derivation of the Rice distribution to establish notation. We find that the joint distribution of $(E_1, E_2)$ conditional on $E_3$ can be parametrized in the formalism of Abu-Dayya & Beaulieu and yields results consistent with numerical simulations up to numerical and sampling errors.\n", - "3. **Normal approximations to the distribution of $\\Delta|E|$.** We fit the distribution of $\\Delta|E| = |E_2| - |E_1|$ to a normal PDF and examine the variance of the centric and acentric $\\Delta|E|$. " - ] - }, - { - "cell_type": "markdown", - "metadata": { - "tags": [] - }, - "source": [ - "# Joint probability distributions of $(E_1,E_2,E_3)$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Consider three normalized structure factors for related structures, $\\left(E_1, E_2, E_3=E_{ref}\\right)$ with joint probability density. In the multivariate Wilson model,\n", - "\n", - "$$\n", - "P\\left(E_1,E_2,E_3\\right) = P\\left(E_{1x},E_{2x},E_{3x},E_{1y},E_{2y},E_{3y}\\right)=N\\left(0,C\\right)\n", - "$$\n", - "\n", - "(note the rearrangement of rows), with \n", - "\n", - "$$\n", - "C = \\frac{1}{2}\n", - "\\begin{bmatrix}\n", - "1 & r_x & r & 0 & 0 & 0 \\\\\n", - "r_x & 1 & r & 0 & 0 & 0 \\\\\n", - "r & r & 1 & 0 & 0 & 0 \\\\\n", - "0 & 0 & 0 & 1 & r_x & r \\\\\n", - "0 & 0 & 0 & r_x & 1 & r \\\\\n", - "0 & 0 & 0 & r & r & 1 \n", - "\\end{bmatrix}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Conditional joint probability distribution of $(E_1, E_2)$ given $E_3$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### General considerations\n", - "Following https://en.wikipedia.org/wiki/Multivariate_normal_distribution#Conditional_distributions, \n", - "\n", - "$$\n", - "P\\left(E_1,E_2 | E_3\\right) = P\\left(E_{1x},E_{2x},E_{1y},E_{2x}|E_{3x}, E_{3y}\\right)=\\mathcal{N}\\left(r E_3,C_{1,2|3}\\right)\n", - "$$\n", - "\n", - "(note the rearrangement of rows), with conditional covariance matrix\n", - "\n", - "$$\n", - "C_{1,2|3} = \\frac{1}{2}\n", - "\\begin{bmatrix}\n", - "1 -r^2 & r_x -r^2 & 0 & 0 \\\\\n", - "r_x -r^2 & 1 -r^2 & 0 & 0 \\\\\n", - "0 & 0 & 1 -r^2 & r_x -r^2 \\\\\n", - "0 & 0 & r_x-r^2 & 1 -r^2 \n", - "\\end{bmatrix}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Note that $r$ and $r_x$ cannot adopt arbitrary combinations of values. Specifically, the conditional covariance matrix is only positive definite if $1+r_x \\geq 2r^2$. $E_1$ and $E_2$ are conditionally independent (and uncorrelated) when $r_x = r^2$. In that case, $1+r_x = 1+r^2 \\geq 2r^2 $." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "For use of the bivariate Rice distribution below, we will also want to know the Pearson correlation coefficient for complex structure factors,\n", - "\n", - "$$\n", - "\\begin{align}\n", - "\\rho\\left(E_1,E_2|E_3\\right) & = \\frac{\\mathbb{E}(E_1 E_2^*)-\\mathbb{E}(E_1)\\mathbb{E}(E_2^*)}\n", - " {\\sqrt{Var(E_1)Var(E_2)}} \\\\\n", - " & = \\frac{\\mathbb{E}\\left((E_1-\\mu_{1|3}+\\mu_{1|3}) (E_2-\\mu_{2|3}+\\mu_{2|3})^*\\right)\n", - " -\\mathbb{E}(E_1)\\mathbb{E}(E_2^*)}\n", - " {\\sqrt{Var(E_1)Var(E_2)}} \\\\\n", - " & = \\frac{Cov(E_1, E_2^*)+\\mu\\mu^*-\\mu\\mu^*}\n", - " {\\sqrt{Var(E_1)Var(E_2)}} \\\\\n", - " & = \\frac{Cov(E_{1x}, E_{2x}) + Cov(E_{1y}, E_{2y})+0}{\\sqrt{Var(E_1)Var(E_2)}} \\\\\n", - " & = \\frac{r_x-r^2}{1-r^2}\n", - "\\end{align}\n", - "$$\n", - "\n", - "with the variances analogously defined as $Var(E_1)=\\mathbb{E}(E_1 E_1^*)-\\mathbb{E}(E_1)\\mathbb{E}(E_1^*)$, etc." - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": {}, - "outputs": [], - "source": [ - "def rho_xy(r,rx):\n", - " return (rx-r**2)/(1-r**2)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Numerical check:" - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "expected rho(x, y): 0.7222\n", - "observed rho(x, y): 0.7222\n", - "Expected errors : ~0.0003\n" - ] - } - ], - "source": [ - "rng = default_rng()\n", - "r = 0.8\n", - "rx = 0.9\n", - "mean= np.asarray([1.5,1.5,0,0])\n", - "n_samples = int(1e7)\n", - "cov = 0.5*\\\n", - " np.asarray([[ 1-r**2, rx-r**2,0, 0 ],\\\n", - " [rx-r**2, 1-r**2,0, 0 ],\\\n", - " [0, 0, 1-r**2, rx-r**2],\\\n", - " [0, 0, rx-r**2, 1-r**2]])\n", - "vals = rng.multivariate_normal(mean,cov,n_samples)\n", - "\n", - "cov_1_2 = np.cov(vals[:,0],vals[:,1]) + np.cov(vals[:,2],vals[:,3])\n", - "var_1_1 = np.var(vals[:,0]) + np.var(vals[:,2])\n", - "var_2_2 = np.var(vals[:,1]) + np.var(vals[:,3])\n", - "print(f\"expected rho(x, y): {rho_xy(r,rx):.4f}\")\n", - "print(f\"observed rho(x, y): {cov_1_2[0,1]/np.sqrt(var_1_1*var_2_2):.4f}\") #I should improve the variable names\n", - "print(f\"Expected errors : ~{1/np.sqrt(n_samples):.4f}\")" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "tags": [] - }, - "source": [ - "# The Bivariate Rice Distribution \n", - "### (Abu-Dayya & Beaulieu; Beaulieu & Hemachandra)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "**First, we'll consider briefly the derivation of the univariate Rice distribution**.\n", - "\n", - "Consider, again, a pair of variables $\\left(E_1, E_{3}\\right)$, with $E_1=(E_{1x}, E_{1y})$, and $E_{3}=(E_{3x}, E_{3y})$ jointly normal, $\\sim N\\left((0,0,0,0),C\\right)$, with \n", - "\n", - "$$\n", - "C = \n", - "\\frac{\\Sigma}{2}\n", - "\\begin{bmatrix}\n", - "1 & 0 & r & 0 \\\\\n", - "0 & 1 & 0 & r \\\\\n", - "r & 0 & 1 & 0 \\\\\n", - "0 & r & 0 & 1 \n", - "\\end{bmatrix}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The notation is such that $\\left<|E_1|^2\\right>=\\left=\\Sigma$. For already normalized structure factors, rather than $F$'s, $\\Sigma=1$." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now, when we have a known value for $E_3=(E_{3,x}, E_{3,y})$, the conditional distribution of (complex) $E$ becomes a bivariate normal with mean $\\mu = r E_{3}$, with $r$ playing the role of $r_{DW}$ in the double-Wilson model, and covariance matrix \n", - "\n", - "$$C_{1|3} = \\frac{\\Sigma}{2}\n", - "\\begin{bmatrix}\n", - "1-r^2 & 0 \\\\\n", - "0 & 1-r^2\n", - "\\end{bmatrix}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "It is helpful to write this in polar coordinates using $E_1 = R_1 \\left(\\cos(\\phi_1),\\sin(\\phi_1)\\right)$ and $\\mu = r E_3 = R_3 \\left(\\cos(\\phi_3),\\sin(\\phi_3)\\right)$, such that\n", - "\n", - "$$\n", - "\\begin{align}\n", - "P\\left(R_1,\\phi_1 | R_3, \\phi_3\\right) & = R_1 \\frac{1}{2 \\pi \\sqrt{\\det(C_{1|3})}} * \n", - " \\exp\\left(\n", - " -\\frac{1}{2}\n", - " \\left(R_1\\cos(\\phi_1)-R_3\\cos(\\phi_3), \n", - " R_1\\sin(\\phi_1)-R_3\\sin(\\phi_3)\n", - " \\right)\n", - " C_{1|3}^{-1}\n", - " \\left(R_1\\cos(\\phi_1)-R_3\\cos(\\phi_3), \n", - " R_1\\sin(\\phi_1)-R_3\\sin(\\phi_3)\n", - " \\right)^T\n", - " \\right)\\\\\n", - " & = \n", - " R_1 \\frac{1}{2 \\pi \\sqrt{\\det(C_{1|3})}} * \n", - " \\exp\\left(\n", - " -\\frac{R_1^2 + R_3^2}{\\Sigma(1-r^2)}\n", - " +\\frac{R_1 R_3 (\\cos(\\phi_1)\\cos(\\phi_3)-\n", - " \\sin(\\phi_1)\\sin(\\phi_3))}\n", - " {\\Sigma(1-r^2)} \n", - " \\right) \\\\\n", - " & = \n", - " \\frac{R_1}{\\pi \\Sigma (1-r^2)} \n", - " \\exp\\left(\n", - " -\\frac{R_1^2 + R_3^2}{\\Sigma(1-r^2)}\n", - " +\\frac{R_1 R_3 \\cos(\\phi_1-\\phi_3)}{\\Sigma(1-r^2)} \n", - " \\right)\n", - "\\end{align} \n", - "$$\n", - "\n", - "where we use that $C_{1|3}^{-1} = \\frac{2}{\\Sigma} \\frac{1}{1-r^2}$ and $\\det(C_{1|3}) = \\left(\\frac{\\Sigma}{2}(1-r^2)\\right)^2$." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We can marginalize over $\\Delta\\phi = \\phi_1-\\phi_3$,\n", - "\n", - "$$\n", - "\\begin{align}\n", - "P\\left(R_1 | R_3\\right) & = \\int_{0}^{2\\pi} d\\Delta\\phi\n", - " \\frac{R_1}{\\pi \\Sigma (1-r^2)} * \n", - " \\exp\\left(\n", - " -\\frac{R_1^2 + R_3^2}{\\Sigma(1-r^2)}\n", - " +\\frac{R_1 R_3 \\cos(\\Delta\\phi)}{\\Sigma(1-r^2)} \n", - " \\right) \\\\\n", - " & = \\frac{2 R_1}{\\Sigma (1-r^2)} \n", - " \\exp\\left(\n", - " -\\frac{R_1^2 + R_3^2}{\\Sigma(1-r^2)}\n", - " \\right)\n", - " I_0\\left(\n", - " \\frac{2 R_1 R_3}{\\Sigma(1-r^2)} \n", - " \\right)\n", - "\\end{align} \n", - "$$\n", - "\n", - "which is the Rice distribution. For comparison to Bricogne (1999), his $R_B$ is our $R_1$, his $r_B$ is our $R_3=r|E_3|$, and his $\\Sigma_B$ is $\\frac{\\Sigma}{2}(1-r^2)$, our per-term conditional variance (we added the $B$ subscripts to indicate \"Bricogne\")." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Abu-Dayya & Beaulieu, \"Switched Diversity in Microcellular Ricean Channels\"" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The Rice distribution is of interest in the wireless communication literature. The equation above maps to the \"Ricean PDF\" in eq. 1 of Abu-Dayya and Beaulieu (1994), with $K = R_3^2/\\Sigma(1-r^2)$ in our terms, or $R^2/\\Sigma$ in Bricogne (1999), eq. 1.6's, and $\\frac{1+K}{\\beta}=2/\\Sigma(1-r^2)$ in our terms, or $1/\\Sigma_B$ in Bricogne's. Recall that $R_3=r|E_3|$. In this formalism,\n", - "\n", - "$$P\\left(R_1\\right|E_3) = \\frac{R_1(1+K)}{\\beta}\\exp\\left(-K-\\frac{(1+K)R_1^2}{2\\beta}\\right)\\times \n", - " I_0\\left(2R_1\\sqrt{\\frac{K(1+K)}{2\\beta}}\\right)\n", - "$$ " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "**This formalism is worth studying, because Abu-Dayya and Beaulieu derive a bivariate Rice distribution, with**\n", - "\n", - "$$\n", - "\\begin{align}\n", - "P\\left(R_1,R_2 | R_3\\right) = & \\frac{(1+K)^2 R_1 R_2}{2\\pi \\beta^2(1-v^2)}\n", - " \\exp\\left(\n", - " \\frac{-2K}{1+v} - \\frac{(1+K)(R_1^2+R_2^2)}{2(1-v^2)\\beta}\n", - " \\right) \\\\ \n", - " & \\times\n", - " \\int_{0}^{2\\pi} \\exp\\left(\n", - " \\frac{v(1+K)R_1 R_2 \\cos \\theta}{(1-v^2)\\beta}\n", - " \\right) \\\\\n", - " & \\times I_0\\left(\n", - " \\sqrt{\\frac{2K(1+K)(R_1^2 + R_2^2+2R_1R_2\\cos\\theta}{\\beta(1+v)^2}}\n", - " \\right) d\\theta\n", - "\\end{align}\n", - "$$\n", - "\n", - "with \n", - "\n", - "$$\n", - "v = \\frac{\\left<\\left(E_1^* - \\left\\right)\\left(E_2 - \\left\\right)\\right>}\n", - " {\\sqrt{\n", - " \\left<\\left|E_1 - \\left\\right|^2\\right>\n", - " \\left<\\left|E_2 - \\left\\right|^2\\right> \n", - " }}\n", - "$$\n", - "\n", - "For the case of the pdf of $E_1$ and $E_2$ conditional on $E_3$, we derive and validate an expression for $v$ above, namely\n", - "\n", - "$$\n", - "v=\\frac{r_x-r^2}{1-r^2}\n", - "$$\n", - "\n", - "Note that the expression for $v$ is equivalent to the expression for $\\rho_{k,j}=\\lambda_k \\lambda_j$ in Beaulieu & Hemachandra (2011)." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Acentric structure factors" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We begin by sampling directly from the conditional distribution of $E_1$ and $E_2$ given $E_3$. We treat centric structure factors below in the section **Normal approximations to the distribution of $\\Delta|E|$**. " - ] - }, - { - "cell_type": "code", - "execution_count": 65, - "metadata": {}, - "outputs": [], - "source": [ - "rng = default_rng()\n", - "r = 0.5 #0.95 \n", - "rx = 0.8\n", - "Eref = 0.2 #2.0 #\n", - "n_samples=int(2e7)\n", - "mean = np.asarray([r*Eref, r*Eref, 0, 0]) # conditional mean, equal to r * E3\n", - "\n", - "cov = 0.5*\\\n", - " np.asarray([[ 1-r**2, rx-r**2,0, 0 ],\\\n", - " [rx-r**2, 1-r**2,0, 0 ],\\\n", - " [0, 0, 1-r**2, rx-r**2],\\\n", - " [0, 0, rx-r**2, 1-r**2]])\n", - "vals = rng.multivariate_normal(mean,cov,n_samples)\n", - "R1_sq=vals[:,0]**2 + vals[:,2]**2\n", - "R2_sq=vals[:,1]**2 + vals[:,3]**2\n", - "R1_abs=np.sqrt(R1_sq)\n", - "R2_abs=np.sqrt(R2_sq)\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Implementing eq. 15 of Abu-Dayya and Beaulieu--see ```bivariate_tools.Bivariate_Rice```" - ] - }, - { - "cell_type": "code", - "execution_count": 66, - "metadata": {}, - "outputs": [], - "source": [ - "# R3 = np.sqrt(float(mean[0]**2 + mean[2]**2)) # r*E3\n", - "E3 = Eref\n", - "R3 = r*E3\n", - "K = R3**2 /(1-r**2)\n", - "p1 = 2 /(1-r**2)\n", - "v = (rx-r**2)/(1-r**2)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "**We implemented this as follows**" - ] - }, - { - "cell_type": "code", - "execution_count": 67, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "0.23884417406312358\n", - "0.23884417406312358\n" - ] - } - ], - "source": [ - "R1=0.5\n", - "R2=1.2\n", - "print(bivariate_tools.Bivariate_Rice(R1,R2,K,p1,v))\n", - "print(bivariate_tools.Bivariate_Rice_wrapper(E1=R1, E2=R2, rx=rx, Sigma=1.0, E3=E3, r=r))" - ] - }, - { - "cell_type": "code", - "execution_count": 68, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "(160000, 2)\n", - "Elapsed time: 4.8 s\n", - "Integrated probability density: 0.9954\n" - ] - } - ], - "source": [ - "nx, ny = (400,400)\n", - "xy_max = 6\n", - "xbase = np.linspace(0.001, xy_max, nx)\n", - "ybase = np.linspace(0.001, xy_max, ny)\n", - "xx,yy = np.meshgrid(xbase,ybase)\n", - "y_in = np.transpose(np.array([xx.flatten(), yy.flatten()]))\n", - "print(y_in.shape)\n", - "\n", - "t1_start = perf_counter() \n", - "result = np.zeros((nx,ny))\n", - "for i in range(nx):\n", - " for j in range(ny):\n", - " result[i,j] = bivariate_tools.Bivariate_Rice(xbase[i],ybase[j],K,p1,v)\n", - "t1_end = perf_counter() \n", - "\n", - "print(f\"Elapsed time: {t1_end-t1_start:.3} s\")\n", - "print(f\"Integrated probability density: {np.sum(result[:])*((xy_max/nx)*(xy_max/ny)):.4}\")" - ] - }, - { - "cell_type": "code", - "execution_count": 69, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "(xmax,ymax) = (xy_max,xy_max)\n", - "xedges = np.linspace(0,xmax,nx+1)\n", - "yedges = np.linspace(0,ymax,ny+1)\n", - "Hx_emp, xedges, yedges = np.histogram2d(R1_abs, R2_abs, bins=(xedges, yedges),density=True)\n", - "\n", - "plt.figure(figsize=(16,5)) \n", - "plt.subplot(1,3,1) \n", - "plt.imshow(Hx_emp, interpolation='none', extent=[0,xmax,0,ymax],origin='lower')\n", - "plt.xlabel(r\"x=$\\sqrt{E_{1x}^2+E_{1y}^2}$\"); plt.ylabel(r\"y=$\\sqrt{E_{2x}^2+E_{2y}^2}$\")\n", - "plt.text(1.5,6.2,\"Empirical 2D\")\n", - "plt.colorbar(); \n", - "\n", - "plt.subplot(1,3,2) \n", - "plt.imshow(result, interpolation='none', extent=[0,xmax,0,ymax],origin='lower')\n", - "plt.text(1.5,6.2,\"Bivariate Rice\")\n", - "plt.colorbar()\n", - " \n", - "plt.subplot(1,3,3)\n", - "plt.imshow(Hx_emp-result, interpolation='none', extent=[0,xmax,0,ymax],origin='lower',vmin=-0.2,vmax=0.2)\n", - "plt.text(1.5,6.2,\"Difference\")\n", - "plt.colorbar(); plt.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Up to numerical and sampling errors, the empirical 2D looks very similar to the bivariate Rice distribution. " - ] - }, - { - "cell_type": "markdown", - "metadata": { - "tags": [] - }, - "source": [ - "# Normal approximations to the distribution of $\\Delta|E|$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "It is also of interest to determine if we can approximate the distribution of differences in structure factor amplitudes directly. If so, we could approximate $P\\left(|E_1|,|E_2|\\right)\\approx P\\left(|E_2|-|E_1|\\right)\\cdot P\\left(|E_1|\\right)$. \n", - "\n", - "First, we will take a look at the normal approximation of the Rice distribution. " - ] - }, - { - "cell_type": "code", - "execution_count": 70, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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Ti6e7g74d3bsbwy769TPGg9lAoxA/lv6nAy3DAnlswWbeX3tQdzprNuOgnzTzXczNw8PVgd+OBg1g9myjLtDZs0Yxsrw8q4YI9PHg0xFt6dOiFq99v4cJS3fo5HONCpcRBUhISCAqKsqp5ifLysqicePGnDlzxurHduBPmrmysvMc94znUp9/bhQjGzTIeADRirzcXXlrYEse6lSfeX8e41z6RXIddJxXREQEISEhpBfqeP/oo4/o3Lmz/RpVgtdee43777+/oIBYVlYWw4cPx9/fn9DQUN58880SX7tmzRpcXFyoUqVKwTJ37twS9z9y5Ag333wzPj4+NG7cmJ9++qnEfSdNmoS7u3uRYx86dAgAT09Phg8fzuuvv36N/+qSOcknzfaychz8jKew//wHpk+HL76AW2+FJOuWQHVxEcb1bMxL/ZqSmZ3H4cR0cnKte3ZlLTk5Obz11lvlOoZSijwrnz0WlpWVxdy5cxkyZEjBukmTJrF//36OHj3K6tWrmTp1akFFxOLUqlWLtLS0guW+++4rcd/BgwfTqlUrzp49y8svv8xdd91FQkJCifsPHDiwyLHr1atXsO3uu+9m7ty5ZGVZd6IBJ/mk2d7FnDyHmceqVMaMgQUL4I8/oHNnsMHp8JDrw6nq68GF7FwOJaaT7YDJ5+mnn2batGkkJydftu3333+nTZs2BAQE0KZNG37//feCbZ07d2b8+PF06NABHx8fDh06hIjw7rvv0rBhQ/z8/JgwYQIHDx6kffv2+Pv7M2DAAC5evAiUrYzo+vXrCQwMLFKi9NNPP2XChAkEBQXRpEkT/v3vf/PJJ5+U+/3Yt28fmzZtYvLkyXh7e3PnnXfSrFkzvvzyy2s6Xp06dQgKCuLPP/8sd9sK04nHIisnFw83J3s7Bg2Cb781hldk22bslbeHKxHVfLiYk8ehhHQu5uQZie7S5d13jRdkZBS/Pf9DlZhY/PaFC43tZaw1ExsbS+fOnZk2bVqR9efOnaNXr148/vjjnD17ljFjxtCrVy/Onj1bsM///vc/Zs2aRWpqKuHh4QCsWLGCjRs38ueffzJ16lRGjhzJZ599xvHjx9mxYwcLFiwAKCgjevToUY4dO4a3tzePPvposW28tFxqUlISJ0+epEWLFgXrWrRoUWINIIAzZ84QEhJCZGQko0ePLnJ5WdjOnTupV69eQfXA0hx72bJlVK1alZiYGN57773Ltjdp0oStW7eW+Ppr4WSfNNsxznic8O3o1g02b4batSE3F+LjrR7Cz8udyGBfcnLzOJSQRp6DdThPmTKFt99+u8jlxLfffkvDhg259957cXNzY/DgwTRu3Jhly5YV7DNs2DBiYmJwc3PD3fLQ5tixY/H39ycmJoamTZvSvXt36tWrR0BAAD179mTz5s3AP2VEfXx88PPzY/z48SXW8ElOTi6SCPKrEeZXHMz/vrjKhgCNGzdmy5YtnDp1ip9//pmNGzcyZsyYYvdNS0srctyrHXvAgAHs3r2bhIQEPvzwQ6ZMmVKQXPP5+fkVe0ZZHg724Ir9ZOU4UefypfLLVo4aBcuWwdq1xgwYVuTr6Ua96r4cTsxgz+fLqBfsi5d7MZemPj6wZk3JBwoOvvL2q5T1LE7Tpk3p3bs3r732Gk2aNAGMkqHhl7wH4eHhnDhxolCoy2NdrYTp6dOngbKVEb20XGr+vF8pKSkFnc0pKSlFklNhoaGhBeVMIyMjmTp1Kr169eKD/KE1hVSpUoWUlKLF+K907OhCExLccMMNPPHEEyxevJjBgwcXrE9NTbV6+VMn/aRZn9G57ER9PMW5/344fx5uuQVKKGRVHt4eRvJBweHEdLIcaHzX5MmT+fDDDwsSS61atQoKfeU7duxYQZF3KN+c8GUpI3ppudSgoCBq1qxZ5PJl69atxMSUrp61iJT4mENMTAyHDh0qkujKe+zdu3cXuSy0Bp14LC468xlPvuuuM55yjo+Hrl3hCncyrpWXuyv1qvuiFBxyoOTToEEDBg4cyIwZMwC47bbb2LdvH/PnzycnJ4eFCxeya9cuevfubZV4ZSkj2rZtW5KTk4ucbQ0dOpSXXnqJpKQk9uzZw4cffsiwYcOKff2aNWs4duwYSimOHz/OuHHj6Nu3b8H2SZMmFTxC0KhRI1q2bMnkyZPJzMzkq6++Ytu2bUVmlyhs6dKlJCUloZTir7/+YsaMGUWOfeLECc6dO3fVSoll5TSfNBFZIyKZIpJmWaw2b2tennL8BwhLq107Y4qdQ4eM+b1s0B/j5e5KZHVflFJG8slxjOQzceLEgk7XatWqsXz5cqZPn061atWYOnUqy5cvJzg42CqxylJG1MPDg2HDhjFv3ryCdZMnT6Z+/fqEh4fTqVMnnn766SLHqFKlCuvWrQNg06ZNtG/fHl9fX2644QaaNm1akGDBKP6ePx0OwOeff86GDRsICgpi3LhxLF68mPwZddetW1dwqZe/b4MGDfDz82Po0KGMHTu2yK36+fPnc999911TqdUrKq4soSMuwBrggbK+rjSlTy9czFHhY5erd1bvv+q+TmPFCqXWrCn3Ya5U+jQjK0ftOJGsdp88r7KyrV+2tSI5c+aMioqKUhkZGVY/dosWLVRiYqLVj5uZmamioqJUfHz8Vfcta+lT3bmM0b8DVIwznny33vrP9ytXGjNduFn3v9vbw5V6wb4cSkznUGI69atXwb0ivYdWVL16dfbs2WOTYxc3q4Y1eHp62qzNzvZb8qqIJIrIbyLS2VoHzb9U8CzuLo2z27zZGGT6yCM2uezy9nAjspovObnKeMLZhk8AaxWHMyWesUA9oDYwC1gmIvWL21FERorIBhHZcKVHxfNdtJzxOOVzPFfTqhU8+yx8+KFRy9kGfDzdCK/mQ1ZOHkcTMyrFHF5a+TjEJ83ScaxKWH4FUEqtV0qlKqWylFJzgd+Ay+ekNfadpZSKVUrF5neqXUlWRU48AC+/DPfcY0wo+L//2SSEn5c7YUHepF/M4di5DId7yFBzLA7Rx6OU6nwtLwOsUi6wmq8HL/SJppnZM0yYRQTmzDGe7Rkxwqhm2KBBqV+ulCrVMy+BPh7k5ilOJF/gRNIF6gR5mzYFjGY/6hr+yJQq8YhICNAdaAEEAsnAVmClUup0maOWkYgEAu2AtUAOMBC4CRhljeMH+nhwf4dIaxzKcXl4wJIl8MMPZUo6rq6uZGdn4+HhUar9q1XxJCdPEZ+SiZurUDPAjsXzNVNcuHChYMhJaV3x2kJEmojIYmAXcC/gDpy2fL0X2Ckii0Uk+gqHsQZ34CUgAUgEHgP6KaWs9ixPpRAQYMzZDrBlizGN8lUEBgYSHx9fprIRNfw8qerrQUJqFmfTrFtOQXMcSikyMjI4ceIENWrUKNNrr3bG8wkwDbhHKXXZb5CIeAB9gdlA+zJFLgOlVALQxlbHr3QSE+HGG40BposXg0vJf3+Cg4OJi4tj796y5XilFOfTL3LmWB7VqngUP65Lc3ru7u6EhITg7+9fptddMfEopdpdZftF4AvLojmL4GB48UUYPdooJj9pUom7uri4ULdu3WsKk5aVQ//3/+D4uQQWPdie6Fpl++XUKq6r3sYRkf5mNEQz2RNPwLBhMHkyfPWVTUJU8XTj42FtqOLpxvBP/tbzdmkFSnP/eHbhH0TE+qXuNPOJGPN2tWljJKAjR2wSJjTAiznD2pCamc3wT/4m42KOTeJozqU0iefS+6Fl677WHJenp1G3+fHHjUJiNhJdy5+Z91zH7tMpPP3FNj1zhVaqxHPpb4n+ralIwsON/h5391Ld5bpWN0fVYFyPxny7/RQzfz5gsziacyjNczyeIjKl0M/el/yMUmqidZulme7QIbjpJmO+rnvvtUmIkTfVY8/pVKav3EdUqB/dY0JtEkdzfKU545kPhBVaPr/k5zolv1RzGnXrGg8WPvQQXKEweHmICK/e0YzmdQIYvXALe08XXwdYq/ikol9vx8bGqg0bNti7Gc7h1Clo2RJq1IC//wZLPWBrO30+kz4zf8XL3YVv/tORIN/SPRWtOR8R2aiUir10falHRYpItIg8KCLPWr7a+mllzWw1axrT0OzYAWPH2ixMaIAXH9zbmvjzWTyxcIvDzlSq2U5pnuMREZkDbAeeA24HxgPbRORj0aMAK5aePY27XPv2QY7tbn1fVzeIF26P5pd9Cbz9836bxdEcU2k6l0cCnYHrlVJ/568UkTbAAuBB4H2btE6zjzfeMKoVXmEohTXc3bYuG48m8daq/bQMC6RzVNnG+2jOqzS/WfcCjxdOOgCWn0dZtmsViYeHkXSOHzdq+NioH1BEeLlfM6JC/Bi1cAtxSRk2iaM5ntIknmiMchTFWWvZrlVEy5YZRcTypye2AW8PV94b0prcXMV/PtvkMDNWaLZVmsTjqpQq9r6nZX0FLdun8fDD0KMHPPMMHDxoszCRwb680b8FW+PO8+LyXTaLozmO0vTxuIvIzZRc7c8hqhhqNiBi1Gpu2tSYpXTNGpv1+/RoGsqDN9Xjg18OERtelX6tbDeEQ7O/0iSNM8Ccq2zXKqo6deCtt4yBpLNmGQ8Y2sjTt0ax6VgS47/aTsuwQCKCfW0WS7Ovq/75UkpFKKUir7SY0VDNjoYOhRkzYPBgm4Zxc3Xh/wa1ws3Vhcc/31ww+4dW8ZT2OZ6RIjJDRIaZ0CbN0YjAY48ZpVMvXoRc23UA1w705vU7m7Mt7jxv/GCbyeQ0+yvNBfs0YDIQijGhXsmz02sVW1ISxMbCf/9r0zA9moYy5Pq6fLjuMGv26iv5iqg0iWcA0EkpNQC4Bbjbtk3SHFZgINSrBxMnGqPZbej5XtE0DvXjqS+2ciZVVy6saEqTeAKUUvsAlFK7gKq2bZLmsERg5kxwdTVutdtwgLGXuytvD25FWlYOYxZu1bOTVjClqkAoIpEiUk9E6gGuhX+2rCs3EXnUMu1wloh8Usz2W0Rkj4hkiMhqEQm3RlytjOrUMWr2/PgjLFhg01ANQ/yY2DuGXw8kMmudbc+wNHOVJvH4AgcKLf7AwUI/W2uE30mMubMuu3UvIsHAEmACxhnXBmChleJqZfXww9CunTE7qY0NbhtGj5hQpv+4l10nU2weTzNHaW6nuyilXC1fi1usMmGSUmqJUupr4Gwxm+8AdiqlvlBKZQKTgBYi0tgasbUycnU1Zqb4/nubhxIRXrmjGQHeHoxZtEUPqaggnGW4QwzGlMkAKKXSMc66YuzWosquZk2jTnNyss0qFuar6uvB1Luased0Km/+uM+msTRzXG0K4yWW8hdX2qeNiCyxbrMuUwU4f8m684BfCW0aaekv2pCQkGDjplVyt98O/fpBpm3vPHVpHMLgtmHMWneI9YeKOynWnMnVznjeB94Vkb0iMktEnrR8qJ8UkQ9EZC8wE3jvSgcRkTUiokpYfi1FO9Mw+pYK8wdKGrw6SykVq5SKrV69eikOr12zF16AAweMGj429nyvaMKCfHjyi62kZmbbPJ5mO1dMPEqpH5VSbYB7gONAO+AuoC1wDBiklGqnlFp5leN0VkpJCUvHUrRzJ9Ai/wcR8QXqW9Zr9nTLLTBgALzyis0mBczn6+nGmwNacDL5gh7F7uRK1cejlNqglHpRKTVAKdVdKTVQKfWyUmqztRoiIm4i4gW4Ytyy9xKR/EGsXwFNReROyz4TgW1KKf1MvSOYNs0YtT5mjM1DxUZU5cFO9Vm0IY4fd562eTzNNspS7L1eCUttEbFGJ/XzwAVgHDDE8v3zAEqpBOBO4GUgCePMa5AVYmrWEBZmVCrMyrJ5Xw/A6K6NaFLTn+e+2kFyxkWbx9Osr9TT24hIHsYsovl1eQq/MA/4BnhEKRVv1RaWk57exiR5eTav0VzYjhPn6ffOb9zeshZvDmhpWlytbMo9vQ3wb+AzoCHgBUQB84BHgGYYtX3eKX9TNaeUn3QOHYIltr7JCU1rB/Bw5/os2XSC1Xv0QFJnU5YznjiggeUBvvx1PsA+pVQdEQkC9iulgm3T1Gujz3hMNnAgLF8Oe/cawytsKCsnl94zfiUtK4cfRt+Ev5e7TeNpZWeNMx4XIOKSdXUxOoPBuOWty6BWdq+9Zlx2PfWUzUN5urnyRv8WxKdk8up3+j6DMylL4vk/4GcReVlEHhKRl4BVlvUAvYA/rNs8zelERhrF4RcuhD9s/+vQMiyQf99YjwV/HeO3A4k2j6dZR5nmTheRHkB/oBZwCliklFpho7ZZhb7UsoO0NGjUCOrWNZKPjSebzczOpedb68jOzeOHUTfh66lPvB2FNS61UEqtUEqNUEr1VEoNd/Sko9lJlSrGJVebNqbcXvdyd2XqXc05kXyBN37Ya/N4WvmV5TkedxGZLCKHRCTT8nWyiHjYsoGakxo6FN5+G7y9TQnXJqIqQ68PZ+4fR9hyPNmUmNq1K8sZz1SgK/AQxvCFh4AuwOs2aJdWUaxbB/PmmRLqqVujCPHz4tkl28nJ1TNUOLKyJJ7+wO2W8Vt7lVI/Av/CqMmsacWbNg0eeQTibf9cqZ+XO5Nuj2H3qRTm/HbY5vG0a1eWxFNSD6Ftew415zZ1Kly4YIxiN8GtMSF0bRLCf1fu5/i5DFNiamVXlsTzBbBMRG4VkSaWO1xfW9ZrWvGioowzng8/tHnBMDAqFk7uG4MITFy6g7LctdXMU5bE8wzwE8awiI3A28Bq4GkbtEurSCZOBD8/ePZZU8LVDvRmTLdGrN6bwHfb9Qh2R3TFBx5EpMslq9ZYFuGfQaIdgZ+t3TCtAqlWDV56ybi1rpTNn+sBGHZDBF9vOcGkZTvp2DCYAG89nMKRXPEBQhEpqYcu/0UCKKWUVaa4sQX9AGHltT3uPH3f+ZW729XlpX7N7N2cSqmkBwiveMajlIq0XZO0Sic3Fz77zBg82uXSk2nra1YngKHtI5j7xxEGxIbRvE6gzWNqpeMss0xoFUFeHkyZAqNHG9+bYEz3RlTz9WTi0p16NlIHohOPZh53d6OvZ9s2m89Cms/fy51nezZmy/FkFm+MMyWmdnU68WjmGjAAWrWCCRPgojllS//Vqjatw4N4bcUezmfo2SkcgU48mrlcXIy51w8fhlmzTAopTOkbQ3LGRaav1INIHYFOPJr5uneHESOM2j0miakVwJDrw5n351F2nrx0bkjNbDrxaOYTgY8+gl69TA37ZLcognw8eGHpTv1Es505TOIRkUct0w5nicgnl2yLsMw6mlZomWCnpmrWkpICr79uFA4zQYCPO2N7NGbD0SSWbDphSkyteA6TeICTwEvAnCvsE6iUqmJZXjSpXZqt7NoF48bBO+ZNTnJX6zq0DAvk1e/3kKKnQbYbh0k8SqklSqmvgbP2botmkuuvh549jRHsqammhHRxEV7s25Sz6VnM+Gm/KTG1yzlM4imloyISJyIfi4hDTaOjXaNJk+DcOaNaoUma1QlgQOsw5v5xhMOJ6abF1f7hLIknEWgDhAOtAT+MyQWLJSIjLf1FGxISEkxqonZN2raF3r2NgmHnzbvb9OStjfBwdeGV73abFlP7hymJR0TWWDqHi1t+vdrrlVJpSqkNSqkcyxTJjwLdRcS/hP1nKaVilVKx1atXt/Y/R7O2yZOhdWvjzMckNfy8eOTmBqzcFc/veloc05mSeJRSnZVSUsLS8VoOafmqqx9WBNddBytXmvpcD8CIjpHUDvRmyvJd5OpxXKZymEstEXETES+MmUldRcRLRNws29qJSJSIuIhINWAGsEYppZ8Eq0iOHoXvvzctnJe7K8/d1oQ9p1NZtOG4aXE1B0o8wPPABWAcMMTy/fOWbfWAFUAqsAPIAgbboY2aLY0eDffcY9odLoDbmoXSJiKIaT/s1bfXTeQwiUcpNamYy7BJlm0LlFKRSilfpVRNpdRQpZSuaVnRjBsHSUnw/vumhRQRJvSO5mz6Rd5ZfcC0uJWdwyQeTaNtW+jaFaZPN2amMEnzOoHceV0dPv71CMfO6pkpzKATj+ZYxo835uCac6UH2K3vmR5RuLqIvr1uEp14NMfSqZOxnDxpatgQfy8e7lyfFTtPs+GIebf1KyudeDTHIgKrVsHLL5se+oEbI6nh58kr3+3Wo9dtTCcezfG4uhpfN282CsSbxMfDjdHdGrHpWDI/7LT9lMuVmU48mmP65RfjwcIvzJ2otn/rOtSv7svUFXvIzjWnIH1lpBOP5pg6doQmTeCVV0ybkQLAzdWFsT0acygxnYV/64cKbUUnHs0xubgYUx5v3w7Ll5sault0CG0igvi/n/aTnpVjauzKQicezXENHgwREUaVQhOJCON6NiExLYuP1pU0ma5WHjrxaI7LzQ3GjIEdO+C4uZc9rcOD6BETyqxfDpKQmmVq7MpAJx7NsT3wABw7BmFhpod+ukcUmTl5zFilKxVam048mmPz9oaAAFAK0s2tFli/ehUGtw1jwV/HdKVCK9OJR3N8ubnQrh08+aTpoZ+4pREebi5M+0FPBGhNOvFojs/VFVq2hE8+gTNnTA1d3c+TER0j+Xb7KXac0OWfrEUnHs05PPmkMdf6zJmmh37gxnr4e7nx5sp9pseuqHTi0ZxDVBTcfrsxB5fJfT0B3u481Lk+P+85w8ajegCpNejEozmPp582CsJ/VuIEIzYz7IYIgqt48sYPe/UAUivQiUdzHh06wDffwLBhpof28XDjPzfX589D5/jtgJ5zsrx04tGcS58+4OFhl9B3t6tLrQAv3vhRn/WUl048mvOZOxf69zc9rKebK090bcjW48n8tNvcu2sVjU48mvNJTYXFi+HPP00Pfed1dYgM9mX6j3vJ03NxXTOHSDwi4ikis0XkqIikishmEel5yT63iMgeEckQkdUiEm6v9mp2dt994O8Pb71lemg3VxdGdW3IntOpLNtmbnnWisQhEg/gBhwHOgEBwARgkYhEAIhIMLDEsr4qsAFYaJeWavbn5wcjRhhnPSdOmB6+T/NaNA714/9+2k+OLhZ2TRwi8Sil0i3zah1RSuUppZYDh4HWll3uAHYqpb5QSmUCk4AWItLYTk3W7O2xx4wCYe++a3poFxdhTLdGHE5MZ8lm8xNfReAQiedSIhICNAJ2WlbFAFvztyul0oGDlvVaZRQZCZMnQ5cudgnfLTqEZrUDmPnzAV0i9Rq42bsBlxIRd+AzYK5Sao9ldRUg4ZJdzwN+JRxjJDDS8mOaiJR2hF8wkFi2FldY+r0oqsT3w2OsyS1xDKX9/Si2L9aUxCMiazD6b4rzm1Kqo2U/F+B/wEXg0UL7pAH+l7zOH2Mu9csopWYBs66hnRuUUrFlfV1FpN+LovT7UVR53w9TEo9SqvPV9hERAWYDIcBtSqnsQpt3AvcV2tcXqM8/l2KapjkRR+rjeQ9oAvRRSl06cfZXQFMRuVNEvICJwLZCl2KapjkRh0g8lmdyHgRaAqdFJM2y3AOglEoA7gReBpKAdsAgGzSlzJdnFZh+L4rS70dR5Xo/RI850TTNbA5xxqNpWuWiE4+maaar9IlHRKqKyFcikm4ZK3a3vdtkL6UZM1dZiUhDEckUkXn2bou9icggEdlt+cwcFJEby3oMh3uA0A7ewXhuKASjc/tbEdmqlKqMt+oLj5k7BtyGMWaumVLqiD0b5gDeAf62dyPsTUS6Aa8DA4G/gJrXdJzK3LlseR4oCWiqlNpnWfc/4IRSapxdG+cgRGQbMFkp9aW922IvIjIIY7zgLqCBUmqInZtkNyLyOzBbKTW7PMep7JdajYDc/KRjsRU9BgwodsxcpSMi/sAUwPxJvRyMiLgCsUB1ETkgInEiMlNEvMt6rMqeeKpgjPkqrMQxYJVJCWPmKqMXMf7Cmzt5u2MKAdyBu4AbMbomWgHPl/VAlT3xlGkMWGVxhTFzlYqItAS6Av+1c1McRf6IgreVUqeUUonAmxh9gWVS2TuX9wFuItJQKbXfsq4FlfvS4kpj5iqbzkAEcMx4W6gCuIpItFLqOju2yy6UUkkiEgeUu2O4UncuA4jI5xhv5AMYp47fATdU0rtaiMj7GO9DV6VUmp2bY1ci4kPRM+KnMBLRw5ZhPJWOiEwBegK9gGzgG2CNUmpCWY5T2c94AB4B5gBngLMYv1SVNenkj5nLwhgzl7/pQaWU+bPo2ZlSKgPIyP9ZRNKAzMqadCxexKjFsw/IBBZhjKEsk0p/xqNpmvkqe+eypml2oBOPpmmm04lH0zTT6cSjaZrpdOLRNM10OvFommY6nXg0TTOdTjyaaURkkohMsuHxh4nIJ7Y6vmY9OvFodiEiR0TkQqEZRdJEZOZVXlNTRL4RkZMiokQkwqTmalamE49mT32UUlUKLVcbCZ8HrMCY6khzYnqsluY0lFLxwLsion9vnZw+49E0zXQ68Wj29LWIJBda/m3vBmnm0Kesmj31U0r9ZO9GaObTZzyapplOJx7NqYiIF+Bp+dHT8rPmZHTi0exp2SXP8XxVitdcwCjSD7CHfwqQa05E9/FodqGUirjG18nV99IcnT7j0TTNdPqMRzPTmqvtYJnlorgpgucppR66ysu3AMllbpVmOl3sXdM00+lLLU3TTKcTj6ZpptOJR9M00+nEo2ma6XTi0TTNdP8PDmTkXs/g63cAAAAASUVORK5CYII=\n", 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" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "plt.figure(figsize=(4,2.5))\n", - "\n", - "plt.plot(xbase,np.log((6/200)*np.sum(result,axis=0)),label=\"Rice (marginal)\")\n", - "loc=np.sqrt(np.sum(mean[[0,2]]**2))\n", - "\n", - "plt.plot(xbase,np.log(norm.pdf(xbase,loc=loc, scale=0.5)),'r--',label=\"Normal(0.5,0.5)\")\n", - "plt.ylabel(\"log(PDF)\")\n", - "plt.xlabel(\"|E_1|\")\n", - "plt.ylim([-20,2])\n", - "plt.legend()\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Pretty bad!" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Acentric $\\Delta|E|$\n", - "In contrast, we find that the differences in structure factor amplitudes between related datasets can often be captured quite accurately using normal distributions." - ] - }, - { - "cell_type": "code", - "execution_count": 71, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "[]" - ] - }, - "execution_count": 71, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "plt.figure(figsize=(5,3))\n", - "plt.hist(R1_abs-R2_abs,100, density=True)\n", - "plt.yscale(\"log\")\n", - "xl=plt.xlim()\n", - "yl=plt.ylim()\n", - "\n", - "x=np.linspace(0.85*xl[0],0.85*xl[1],100)\n", - "y1= norm.pdf(x,0,np.std(R1_abs-R2_abs))\n", - "# y2=laplace.pdf(x,0,np.std(R1_abs-R2_abs)/np.sqrt(2))\n", - "\n", - "plt.plot(x,y1,'r-')\n", - "# plt.plot(x,y2,'m-')\n", - "plt.ylim(yl)\n", - "ref=\"{ref}\"\n", - "plt.title(f\"$r$={r}, $r_x$={rx}, $E_{ref}$ = {Eref}, std($\\Delta F$)={np.std(R1_abs-R2_abs):.3}\")\n", - "plt.xlabel(r\"$\\Delta |F|$\")\n", - "plt.ylabel(\"Density\")\n", - "plt.ylim([1e-6,5])\n", - "plt.grid(linestyle=\"--\")\n", - "plt.savefig(fig_dir+f\"acentric_differences_r{r}_Eref{Eref}.svg\")\n", - "plt.plot()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Centric $\\Delta|E|$\n", - "\n", - "To compute $\\Delta|E|$, we first compute the conditional distribution of $|E_{1c}|,|E_{2c}|$ given $|E_{3c}|$, analogous to the above two sections.\n", - "\n", - "Following https://en.wikipedia.org/wiki/Multivariate_normal_distribution#Conditional_distributions, \n", - "\n", - "$$\n", - "P\\left(E_{1c},E_{2c} | E_{3c}\\right) = N\\left(r E_{3c},C_{1c|3c}\\right)\n", - "$$\n", - "\n", - "with \n", - "\n", - "$$\n", - "C_{1c|3c} = \n", - "\\begin{bmatrix}\n", - "1 -r^2 & r_x -r^2 \\\\\n", - "r_x -r^2 & 1 -r^2 \n", - "\\end{bmatrix}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We then have that \n", - "\n", - "$$\n", - "P\\Bigl(|E_{1c}|,|E_{2c}| \\Big| |E_{3c}|\\Bigr) = P\\Bigl(E_{1c},E_{2c} \\Big| E_{3c}\\Bigr) + \n", - " P\\Bigl(-E_{1c},E_{2c} \\Big| E_{3c}\\Bigr) +\n", - " P\\Bigl(E_{1c},-E_{2c} \\Big| E_{3c}\\Bigr) +\n", - " P\\Bigl(-E_{1c},-E_{2c} \\Big| E_{3c}\\Bigr)\n", - "$$\n", - "\n", - "There should not be any need to further simplify this." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We implemented two ways to calculate the folded normal--in terms of $r$, $r_x$, $\\Sigma$, $E_3$ or in terms of the conditional mean and variance" - ] - }, - { - "cell_type": "code", - "execution_count": 72, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "0.0018564955499625726\n", - "0.0018564955499625726\n" - ] - } - ], - "source": [ - "r = 0.5 #0.95 #\n", - "rx = 0.8\n", - "E3 = 0.2/r #2.0/r #\n", - "mean= r*np.asarray([E3,E3])\n", - "cov = np.asarray([[ 1-r**2, rx-r**2],\\\n", - " [rx-r**2, 1-r**2]])\n", - "\n", - "print(bivariate_tools.FoldedNorm2D_wrapper(3, 2, rx=rx, Sigma=1.0, E3=E3, r=r))\n", - "print(bivariate_tools.FoldedNorm2D(3,2, mean, cov))" - ] - }, - { - "cell_type": "code", - "execution_count": 73, - "metadata": {}, - "outputs": [], - "source": [ - "rng = default_rng()\n", - "n_samples=int(1e7)\n", - "\n", - "# print(cov)\n", - "vals = rng.multivariate_normal(mean,cov,n_samples)\n", - "R1_abs=np.abs(vals[:,0])\n", - "R2_abs=np.abs(vals[:,1])" - ] - }, - { - "cell_type": "code", - "execution_count": 74, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "(40000, 2)\n", - "(200, 200)\n", - "Elapsed time: 0.0063 s\n", - "Integrated probability density: 1.01\n" - ] - } - ], - "source": [ - "nx, ny = (200,200)\n", - "xy_max = 4\n", - "xbase = np.linspace(0.001, xy_max, nx)\n", - "ybase = np.linspace(0.001, xy_max, ny)\n", - "xx,yy = np.meshgrid(xbase,ybase)\n", - "y_in = np.transpose(np.array([xx.flatten(), yy.flatten()]))\n", - "print(y_in.shape)\n", - "\n", - "t1_start = perf_counter() \n", - "result = bivariate_tools.FoldedNorm2D_all(y_in[:,0].reshape(-1,1), y_in[:,1].reshape(-1,1), mean, cov)\n", - "result = result.reshape(nx,ny)\n", - "print(result.shape)\n", - "t1_end = perf_counter() \n", - "\n", - "print(f\"Elapsed time: {t1_end-t1_start:.3} s\")\n", - "print(f\"Integrated probability density: {np.sum(result[:])*((xy_max/nx)*(xy_max/ny)):.3}\")" - ] - }, - { - "cell_type": "code", - "execution_count": 75, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", 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" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "xedges = np.linspace(0,4,201)\n", - "yedges = np.linspace(0,4,201)\n", - "Hx_emp, xedges, yedges = np.histogram2d(R1_abs, R2_abs, bins=(xedges, yedges),density=True)\n", - "\n", - "plt.figure(figsize=(16,5)) \n", - "plt.subplot(1,3,1) \n", - "plt.text(1,4.2,\"Empirical 2D\")\n", - "plt.imshow(Hx_emp, interpolation='none', extent=[0,4,0,4],origin='lower')\n", - "plt.xlabel(r\"x=$|E_1|$\"); plt.ylabel(r\"y=$|E_2|$\")\n", - "plt.colorbar(); \n", - "\n", - "plt.subplot(1,3,2) \n", - "plt.imshow(result, interpolation='none', extent=[0,4,0,4],origin='lower')\n", - "plt.text(0.2,4.2,\"Bivariate Folded Normal\")\n", - "plt.colorbar()\n", - " \n", - "plt.subplot(1,3,3)\n", - "plt.imshow(Hx_emp-result, interpolation='none', extent=[0,4,0,4],origin='lower',vmin=-0.05,vmax=0.05)\n", - "plt.text(1,4.2,\"Difference\")\n", - "plt.colorbar(); plt.show()" - ] - }, - { - "cell_type": "code", - "execution_count": 76, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "[]" - ] - }, - "execution_count": 76, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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kZVQl09R0TpwwAu2bb8KXX0JRERkNW/Blz+EsbNuTlS07kRsZupFts6JjWZnYiZWJnXir50UAtDyyl/7bVvF41Hb473/hP/+BFi1g7Fi49lro1Clk+9dUH8Ii8CqlpmIEWV+fHQRGWO3QsmVLq3cRMtzkChb47tgB06YZgW7/fnbVa8qcPlcwr9NANjZpU6VH/lUHAqthuat+M97rfi7vATHtrmZIxnKmFa2FZ5+FJ5+EIUPg5puNu+EQ3wW7KR9o19K4vpOcQCmvk5ycnBzX9KDkJlcIoe/atfD44/DOO1BUxBftT+ft0y5gSVIPlISmSnqD2orDeVUvq2187DArWu6AF1+E336D9u3hjjvgmmsgOrrqorgrH9QE1xrTSU4o0Z14WEeVfX/9Fa680qhRMHs23HILZGRw42X3sbhtz5AFXYAJyaF5sXKgbgOSDnel3ajnmDTiHmjUCCZPhlNOMYJxXl6V9+GmfKBdS6MDryZ8ycyEiRMhJQXmz4d776XHhFdIijqbpOlrnLbzi6IID58nn0nSkAcY86dHoE0bIwCfeirMmgU17IlTY6ADr0lsbKzTCn7jJlcIwjc3F/75T6Pe7IwZvHbaRfS87mWSCvpxOKZste7Qsv+ERVXCRFia1IOk/vcwfuRDrM9WMGoUDBgAq1YFlaSb8oF2LY0u49WEF99+CzfdBBs28EWHvvxz8LVsa+SeFzP+ElFUSEbHvXDvvbB/v1F88vDDUL9+5RtrwhJdxhsEejA+6/DL9/BhmDABzjrLaOzw6afceNl9tgfdSZ3sqehfFOEhaXNzuo1+zih6eP55o0jlk0/8TsNN+UC7lkYHXpOgOrpwCDe5gh++n39uvDibMYNpfa8gecSTJC0sskeuDHUj7X0CzIqOJSn2fIZf/TS/5kbCRRfBuHHGD1EluCkfaNfS6MCrcY6cHJgyBc4/nw25Hi6+6mmeGHQNubWinDaznV+ad2T4+H/B/ffDzJnQvTuYva9pqh+6jNekoKCAyMiwaE9SKW5yhXJ816+HkSONurm33kpy5KCQtjILltoRirwiZzu/6bF7A3OXToOMDCMQP/CAz8YXbsoHNcFVl/EGwcaNGytfKUxwkyv48H37bUhNZf/WnYwb+RBJ0eeERdAFGJboTBGHNz+3SKbz8Mf4IGWo8cLt3HNhz56T1nNTPtCupdGB16S4k2k34CZX8PLNzzfe3l99NfTqxQXXPMeidr2clStDcv3weAI8XjuGOy68jTvPvxW+/x569oQyFfvdlA+0a2l04NXYw969RveJL7zAy70vpX3fO9hbr7HTVmHPrG7ncN7oJ9l+rBAGDoTXXnNaSRMC3FHoYgNdunRxWsFv3OQK0N3jgdNPNx6X336bf6xu4LRSuczdZn13joHya7O2DB//LD+ve82ocrd2LTzxhKvygXYtjb7jNdHVXSziyy+pf+GF7DlwlItH/ZOkMA66AHG1w6OooSyHY+Jof9oUZvS8CJ55Bi6/nDxz7DM34KY8q6uT2UjxAI9uwDWur78OF1zA8aZNGXH106xu3sFpo0oZ2sL5l2vlURjhYeo5k3jw7Bvh44+JHT4c9u1zWssvXJNnscdVB15N6FEKHnsMrruOxYldefvuR/g9rqnTVtWGN3pdzIRL76XOlgwyknuAi4ZO1xjowGvSqlUrpxX8JqxdlTL6nb3nHhg9mutGPsjSY+7pIOWnfe64JL45pQ//nPQwjXKy4IwzjIE8w5iwzrNlsMPVHbnMBuLj451W8JuwdS0shBtvhGee4fVeF9O21WjyPbVYf9jZBgmB4CbXeY1SGDnmcfZk53Go9xmwYoXTSuUStnnWB3a46sBr4qYey8LStaDAGF3hlVf4T79RPHTWxJIOysd1cM8Is25z3dS0DSPHPM6x2jEwdKgxqnIYEpZ5thzscNWBV1N1Cgpg/Hh4+22eGDiOpwaOs32o85rM9obNuWLsExAfb7RyC9Pgq/kDHXhN4uKs7WA7lISVa3HQnTmTxweNZ1q/USet8vtx9wRht7pmxjXh9HPuI6NWHNlDzjZau4URYZVnK8EOV91JjiZ4ior4oPswrljzDY8PGs/0viOdNqrxNDt6gHffuYd2BUeNTuVT/eqzRRMCdCc5QbBkyRKnFfwmLFyVgilTuGLNNzzTf2yFQXdKSoGNYlXD7a576zVmzJX/YEdEHQ4NGAqrVztgdjJhkWf9xA5XHXhNCgrcc8GFg+v0fqNg2jRePP0ynjvjygrXre2iXFYdXDPjmjDmykfJjawF55wDmzfbK+aDcMiz/mKHq4uymSZseOYZJqd9wNs9zuexwdfqF2lhyI4GCYy98lEOZuWwPbU/vW95y2kljRe6jNekqKiIiAh3/A456vrWWzBuHJ8kn8mU4X+jKKLyTmUiUBThjuBc3Vy7797AzHfv5beGzem8cZVjg2nWhOtLl/EGwdq1a51W8BunXK/+0/+Rf821fN+mG7dddIdfQRfgkjbh2/9BWaqba3qLZCZd+ndO2b8DLr0U8vJsMDsZfX2VRgdekwMHDjit4DeOuKanM23uP9ncuBU3XnofeZG1/N60XZx7nqqqo+vitj352wW3wnffMbvnecaLUZvR11dpdODVVEqfm9/g9/5nkV27DtdeMZXsqDpOK2kCZG7KEJ4ccDWXrf3OGMNN4yi6I3ST7t27O63gN7a6HjvGqx/+H7F5xxk59gky45oEnMSsreHXuXh5VGfXF/qNotWRPVz5yCPctuo4c7oMZdtjF1pkVxp9fZVG3/GaHD161GkFv7HNtagIxo2j096tTBl+F782axtUMvEx7nl8r9auItw37CaWte7KY58/R8+d660R84G+vkqjA69JRkaG0wp+Y4dr0t2f8Hz/MTB7No8OmcCC9sG3gBqY4J4XVtXdtcATyeQR97A7rikvz3kEfvvNArOT0ddXaXTg1fjkwvWLmbLsPd7pNozXUoc7raMJIYdj4rj+8geoXVjA2tOHcurtHzqtVOPQgdckKSnJaQW/sdz1l1948rN/sbxlJx48Z3KVG0gs3eOebFZTXLc0bsWfL76DTnu38vhnz1te00FfX6VxTy6zmEaNGjmt4DdWuSbd/Qndb32X7QOHkRVVl8kj7gmo2lh5bMt2R4MEqFmuC9r35qmBV3PJ+oXw9NMhsvKNvr5K4/rAKyL9RGSZiCwUkXdEJKhIsXLlylCrWYZVrqKK+Nf8p4jPPsDkEX9nX2xoMuCY9u7pXLymuU7rO5JPks+k8G93ceWYf5J09ychMDsZfX2VxvWBF/gNGKqUGgRkAJc47ONabln6HkMyVvDwWRNZ1fJUp3U0diDCXeffyraGLXh+3hM0O+qehg5uxvWBVym1WymVY84WAEG9lm7YsGHopCwm1K5Jd3/C1X/6P25bMpPZKUP4X4/zQ5r+dhc9vtdE1+yoOkwacQ9183J44aPHIT8/JOl6U5OvL1/4HXhFZLaIjAj2Ud5M4xYRWS4iuSIyo8xnjURkjogcE5HfRGRMgGm3Bc4H5gfjVpMreDc7eoB/ffwUG5u05t5hN4e8t7Hq3CjBSULpuqlpG+4+78/03rWOFweMDnmRQ02+vnwRyB3v98ADQKaITBeRM4LY327gEeA1H5+9AOQB8cBYYLqIpACISIKILPExJZifxwFvAFcrpYLqBWThwoXBbOYIIXUtKOC5j58kuiCPm0fcTU7t6NClbXJbF/f0xVqTXed1HsTM7ucxKe1DBm/5KaRp19jrqxz8bjKslHoaeNoMhlcB74hIPvAm8D+l1BY/0pgNICKpQGLxchGpC1wOdFFKZQNLRGQecDVwt1IqE+jvK00RiQTeAaYqpTb4ezw+3ILd1HZC4Vp8R3Pb4re5dccabrvwr2xp3KrK6foiwj1P7zXe9aGzbuC03b/yzCfPws7rITGx8o38oKZdX5URcF8NSqm1wD0i8inwH+BB4HYR+Qm4XSmVHoRHR6BQKbXRa1k6MMiPbUcDfYAHROQBYLpS6j3vFURkIjARoEWLFixYsACAdu3aUa9ePdLT08nOzmb16tWkpKSwaNEiACIjI+nfvz8rV64kKysLgNTUVPbs2cOOHTsA6NChA1FRUaxZswaAZs2a0bFjx5LhQ6KioujXrx/Lly8nOzsbgD59+rBz50527doFQHJyMh6Ph3Xr1gGQkJBA27ZtWbZsGQAxMTH06dOHtLQ0cnJyyM7OJjc3l61bt5KZmQlA586dKSwsZMMG47enZcuWJCYmkpaWBkBsbCypqaksW7aM3Nxcbu9aQNqn65iy7D3WDRhKu9EDab9NEVdbMbSFUUz+074I1h+WkiHPfz8uzNziYUpKQcnoB8+u9nBJm6KSnrJmbfUQH6NKWlUt3ROBR+D2rsbd2fZsYdZWD7d1KSBCoEjBs2siGdm2kNaxRhozt3hIilWcEW+ksSgzgj05wsi2hkdGlvDRbxHc1tWYzyuC59dGMqZ9Ic3rGGm8uclDpwaK3k2NNL7dHUFWnjAiydhmwxHhy50RTEkx5o8VCC+u99A46g/XVzd46NlEcVpjI40vdkaQXwQXtTbm1x6KYHGmMKmTkcbhPOHVDR4mJBfSoLbh8eJ6DwMSFCkNjW3mb4+gVgScm2jMrzoQwcr9woRkI439J4Q3NnmY1KmQupFGGs+v9TAssYjk+sb83G0e4mor4mMM11Cdp23Zwpj2HpYn3Mmo+2/nhzPO58dHHkI8HrolNmDQoEGkp6dz6NAhAHr27MnBgwfZtm0bUPp6AmjcuHHJ9ZSdnc2SJUvC8noC6NevX8n1lJ2dzd69ewO6ngIloI7QRSQZ4253DEaxwFvmtA+4CZiilKq0Qb+IPAIkKqWuMecHALOUUgle69wAjFVKDfZb0A/0YJcG3W99l89fu4XjtaO5aPy/LSli0LiXK1Z/zVOf/osnBo5jWr9RtnWm42Ys6QhdRJZjlPM2AsYopToppf6hlNqhlDqhlHomSF+AbKDsmMpxgG09axT/SruBqrgm3f0JSXfN57HPn6fx8SP8+eI7LQ+6xXeqbkC7GnzQ5SzmdRrIXxe/TY/dQZfglVBTri9/CaSo4TFgXkUvr/y52y2HjUCkiHRQSm0yl3UHbOu2vvjxyQ1U1fXK9C84f+NSHhlyHWsTTgmRVfkUFyG4Ae1qYvZk1nPXr/z74ydJua0Vx6LqBH3nW5OuL38IpFbDvb6Crnkn7BciEiki0YAH8IhItIhEKqWOAbOBh0WkroicidEQQo/QF2LaHNrN/d/+l8VtevBq7xFO62jCmKzoWP5y8e20OryH+779r9M61YpA7njbl10gIgK0CyCN+zBexhVzFfAQMBWjjPg1YC9wAJhsvsizhZ49e9q1qyoTqGtxDQZPUSHvz3+GgggPd17wF5TY035m5hb31I3VrqVZnpjCi30v56YfPuCbU/oAwd3xVufrKxgqDbwi8qb5b5TX/8UkEUBxgFJqKkaQ9fXZQWCEv2mFmoMHDxIXV7aYOTwJ1vXGtA/ptftX/nzxnUGNJBEsSbGK34+7o56Wdj2ZZ/uPZXDGCh77/Dl6TUnmQN0GAAEVO9SE6ysQ/Lnl2WJO3v9vATYD/6Oa9I1QXCXGDQTj2nlPBrct+R8fnzqAeZ39qaUXOoqrhbkB7Xoy+Z5a3HrRHdTLPcb/fTktqC4kq/v1FSiV3vEqpR4CEJEflFJfWG6kCRnFRQy1CvN56tNnORxTj/uHTXbYSuNGNjVtwzMDruKeBTMYvn6R7T/e1Y0KA6+IDFRKLTJn80VkqK/1lFLfhtzMZtq1C6So2lkCdb1l6ft03ruVGy67j8Mx9j/uLcp0T19M2rV8Xul9KeduXMbDX01nWeuuJT/s/hQ5VOfrKxgqO3PTvP5/tZypWrzurFevntMKfhOIa8qeLdy87D0+TBnCVx36WmhVPnty3FFmCtq1IooiPNxxwW1EF+Txjy9eCKjIobpeX8FSYeBVSnXx+r9tOZN7fsoqoDpW8I4sLOCJT//NwTr1eejsGy22Kh/dKMEanHDNaJzI0/2v4pzNaVz062K/t6uO11dVCLivhmJEZAhQoJTy/9vXWI53d343/TiblL0ZTLz0XrKiYx200lQnXut9CRduWMzUr1/i+zbdS+U53bTYPwJpMrzQbNiAiNwFvAu8KyJ/t0rOTho3buy0gt/449r+wA5u/X4m85P782XHfjZYlU9Glnse37Vr5RRGeLjr/FuJO3GMB755xa9tqtv1VVUCKZ3vAvxg/n8DMBjoC0wKsZMjpKSkOK3gN5W5iirisc+eJ6dWNFPPca6IoZiPfnPPCyvt6h8bmiYxrd9ILl23gMFbKm+8Wp2ur1AQyJmLAJSItMfo1Wy9UmoH4J4xPSqguCtIN+DLNenuT0oe+Uanf0HvXet4dMgE9td1/vQUd9/oBrSr/0zrO4rNjRJ55MtpxOSdqHBdt19foSaQwLsEo//dp4A5AGYQ3m+BlyZImmYf5O4FM1jauhuzup7ttI6mGpMXWYt7zruFxKy9/OX7mcAfNwBWjVZcXQgk8F4DHAZ+4Y9mv6cC/w6pkUNERgb9ntF2KnJ98JtXiCrI495zQz92WrDkuacxmHYNkJ9adWFm9/OY8NNcUvaUPwhNdbm+QkVAHaFXB6pTR+hl7yoGZazgjVkP8nT/sTx/5miHrDQ1jbgT2Xzz30nsimvGZVc9SVGE0XlPTavhYFVH6LVFZKKITBORN72n4FXDh5UrVzqt4De+XKPyc3n4q+lsaZTIS32ucMCqfMa0d0+5qXYNnKzoWB4ZMoEev29kdLrvXgXcfn2FmkCKGt4A/oIxKsSWMpPrKR4Dyg34cr3phw9ocziT+4ZNJi+ylgNW5VM8Dpob0K7B8VHnwXzfpht/W/gGTY4ZHYl7l/W6/foKNYEUZpwHtFVKHbbIRRMkSQd3MSltFnM7D2JZm+5O62hqIiI8cM5kPnttCvd89xq3X3S700ZhTSB3vNuBKKtEnCY11a+imbDgzgXZf5TvKsVDX79Erqc2jw6Z4KxYOby5yT2di2vX4NnSuBUv97mMy9d+R+8da0p95qbryw7XQALvm8BHIjJaRIZ6T1bJ2cmePXucVvCbTg3+eMQ8Z3Mag7au5F/9x7IvtpGDVuXj7RvuaNeq8ULfUeyq15SHv3oRT9EfZdBuur7scA0k8N4CxAP/oBr2TrZjxw6nFfymd1OjHlFUfi4PfPMKG5q05s2e4fsGudjXDWjXqpFTO5pHhk6g075tjPn5M8Ao6/30hzWuqdtrRyzwu4y3CiMIa0KAd6a9vavxd1Lah7Q6sofRV/6DAo976klqqjefJZ/JkjbduWPRW3xy6gAO1qnvtFLYEVBjbxGpJSIDRORP5nxdEalrjZq9dOjQwWkFv/l2dwQtj+xlctoHzD91AMvadHNaqUK+3e2e/g+0awgQ4cGzJ1En/wS3LzYGCg9bVx/YEQsCqcfbFdgIvIJRxAAwCGNkYNcTFeWe94ZZecI9C15HIfxjyLVO61RKVl54tKDzB+0aGrY0acWbPS9i9M9f0HlPRomrG5oT2xELAvkZmg48oJQ6Fcg3ly0E+ofcygHWrFlT+Uphwk0nfuGiXxfzUp/L2B3XzGmdShmRFB4V/f1Bu4aOf585mkMx9Xjgm5cZ0abAaR2/sSMWBBJ4U4C3zf8VgFLqGBATailN+UQUFTLgrVfZXa8JL/a53GkdjaZcsqJjeWbAVfTdsYZTflzqtE5YEUjg3Qb08l4gIqdjDPPuepo1C887x7KPZpev+YZmv2Xw2OBrOVEr2kEz/9lwJHwficuiXUPLO93PZX3TJHrPfIOogjyndfzCjlgQSOC9H/hERB4CokTkHuAD4D5LzGymY8eOTitUSp28HO5c9BarWiQzr9NAp3X85sud7nmxol1DS1GEh0eGXk+TA3u5ZsW8kuXh3H2kHbHA7zOnlJqP0Wy4KbAAaA1cqpT60ho1e1myZInTCpVyY9qHNDt2iE0TrwubLh/9YUpKeJdFeqNdQ8/3ST3YeloqNy99n0bHjzitUyl2xIIKA6+IPOw9AZdidHy+AtgHXGIu11hMQtZ+Jv44h3mdBrLnlGSndTSagPh+9DXUyT/BX5bMdFolLKjsjreV19QBuBs4CzgFGGrOu6cCbAWEe3WyOxa/RYQq4olB4zlW4J67XcBVvtrVGnY2a8X/TjufMT9/Rvv94d1K1I5Y4HdH6CLyLjBLKfWh17LLgJFKKdf0uu2GjtDLlnt12pvBJ6/fysunX8pjQ65zyEqjqRqNjh9h4UvXs6xNdyZedvKrIbd3nG5JR+jA+cDcMss+Ai4III2wJZyD8d0LZnAkOpZp/UYBML6DO8r2inGTr3a1hvEdCjlYpz7T+45k2KYfTuq9LJywIxYEEng3AzeXWXYT1aQj9OzsbKcVfNJ/6yoGbV3Jf874E1nRsQA0iQ6/Xqkqwk2+2tUail1fSx1OZmwj/v7d6xCmw47ZEQsCCbzXA38VkZ0ikiYiO4HbzeUaCxBVxD0LXmdH/XjeOs3dj2EaDcCJWtE8PeAqTvt9A+dv+N5pHccIaLBLEakF9AVaAL8Dy5RS+RVvFV6UV8abk5NDTIxzjfB81Wccvm4Bz338FH+++A7mdR5csrxBbcXhMG6nXxY3+WpXa/B2jSgq5LPXpxBZVMiwCdMojDi5Q3cny3uDjQVWlfGilMpXSi1WSr2nlFrktqBbETt37nRaoRS1CvO5ffHbrGvWlo/LNJbo2SQ8H9HKw02+2tUavF2LIjw8OXA87Q/uYuQvXzlo5Rs7YkH4N32xiV27djmtUIo/pX9Jm8OZPDFwPEpKn6bTGodfB9gV4SZf7WoNZV2/PuV0lrfsxF++n0l0/gmHrHxjRyzQgTcMick7wa1L3yGtVRcWtOtV+QYajdsQ4fFB40nIPsj4lfNP+jhcmxOHimoReM1x4PZVJY3kZGdag/nKYNeumEfTY4d5fOB4n02Dv3BBG31v3OSrXa3Bl+tPrbrwbbtUblo2i7gT4VOryI5Y4J4zVw4iEgFcAVSpOYzHEx4jtsadyObGtA/5un1vViZ28rlOvnueMAF3+WpXayjP9amB46ife4zrf5xjr1AF2BELXB94gTEYvaRVKRuuW7cuNDZ+UFHPTNf/OIf6ucd4ZsDV5W5/UWsXXXG4y1e7WkN5ruvi2zE/uT/XrZgXNh3o2BELbAu8InKLiCwXkVwRmVHms0YiMkdEjonIbyIyxs80PcAo4D0LlG2n0fEjXLdiHvNPHcC6+HZO62g0tvBs/7HE5Ocy6YcPnFaxDTuHpt0NPAKcy8mjVrwA5GEMH98Do9/fdKXUWhFJwLijLcsVZlrvK6WKpIrdJCYkJFRp+1Aw+YdZxOTn8mz/in931h5y14OKm3y1qzVU5LqlSSvmpgxm3KpPeLX3Jeyp16TkM++nQrvq9toRC2w7c0qp2UqpucAB7+XmKMWXA/crpbKVUkuAecDV5naZSqn+PqZMoDMwTkQ+BzqIyHPB+rVt6+zo9U2zD3L1qk+ZmzKYLY1bVbju4kx3VJovxk2+2tUaKnP915lj8BQVMjkM7nrtiAV23vGWR0egUCm10WtZOsYIxhWilLqr+H8RWa6U+rOv9URkIjARoEWLFixYsACAdu3aUa9ePdLT08nOzqZNmzakpKSwaNEiACIjI+nfvz8rV64kKysLgNTUVPbs2cOOHca7vA4dOhAVFVUyQF6zZs3o2LFjSWfKUVFR9OvXj+XLl5e0AW9QW9GziSqp2/jFzggmLJpF7aICsq8dyXm1i1icKUzqZHSCcjhPeHWDhwnJhTSorYiPgYdWehiQoEhpaKQxf3sEtSLg3ERjftWBCFbuFyYkG2nsPyG8scnDpE6F1I00KrM/v9bDsMQikusb83O3eYirrRjawkjjp30RrD8sjDM7Y/n9uDBzi4cpKQXUNn+yn13t4ZI2RbSLM9KYtdVDfIxiYIKRxtI9EQxqXlTycmV7tjBrq4fbuhQQIVCk4Nk1kYxsW0jrWCONmVs8JMUqzog3NlqUGcGeHGFkW8MjI0v46LcIbutqzOcVwfNrIxnTvpDmdYw03tzkoVMDRe+mRhrf7o4gK09KBojccET4cmdESWfixwqEF9d7uLdHIQdyDddXN3hOOk/5RX+UV649FFHheQJ4cb1152l0+yL25ITuPG3LFsa0L7TkPMXHwI5jFZynrk3YuGEoYxd/zudDL+PMHo1OOk8LFizweT316dOHnTt3ltS/TU5OxuPxlJTVJiQk0LZtW5YtWwZATEwMffr0IS0tjZycHAD69evH1q1byczMJDs7m9NPP53CwkI2bNgAQMuWLUlMTCQtLQ2A2NhYUlNTWbZsGbm5ZoYJgICaDIcCEXkESFRKXWPOD8DobjLBa50bgLFKqcGh3n95TYYXLFjA4MEh351Pyr5Uiz+6n0Uv3cDczoO564JbK93+9q4FPL06HH4z/cNNvtrVGvxxTTyyh29fvpH3u53DfeeW7Y/rD6wucgg2FljWZNgisoG4MsvigKN2SjjZT8NNP8wiQhXx/Bl/8mt9t7TPL8ZNvtrVGvxx3Vk/nve7ncOoX76i5ZG9Nlj5xo5YEA6BdyMQKSLeI1l0B9baKdGnTx87d1dC86x9XJn+BbO6ns3OBv4V6r+6ITzqHPuLm3y1qzX46/pCv1EogZuXOVdRyY5YYGd1skgRiQY8gEdEokUkUil1DJgNPCwidUXkTOAS4C273ICSshsr8VV3d1LaB0QoxQv9/LvbBUrKA92Cm3y1qzX46/p7XFPe63YuV6z+xrG7XjtigZ13vPcBORjjtF1l/l88/sdNGFXM9gLvAJOVUrbe8RYXsttJ/NH9JXe7u+o383u74hc3bsFNvtrVGgJxfbHv5YBRvdIJ7IgFdlYnm6qUkjLTVPOzg0qpEUqpukqp1kqpGjEU6aS0D/EUFTGt70inVTSasGF3XDNmdTubUb98RfOsKnXBErbYXqvBacqr1ZCbm2vJ6KLl9bDUNPsgi1+6nnmdBvK3C/4SUJp1I5WrRph1k692tYZAXROP7OG7lycys8d5PHjO5FKfWV2rIdhY4LZaDWHB1q1bbd3fxB9nE1lYwH8CKNstZkCCu34s3eSrXa0hUNed9eP5oMtZXJn+Jc2OHqh8gxBiRyzQgdckMzPTtn01On6EsT9/xkedB7G9YfOAty+ujO8W3OSrXa0hGNdp/UbhKSrkhp9K91xWUSdTocCOWKADrwNct/wjovPzmNZ3lNMqGk3YsqNBAvM6D2Lsz5/RMEx6LgsVOvCadO7cOaTplfeLHHcim3Er5vNZ8hlsaVJxnwzlMX+7u06bm3y1qzUE6zqt70ii8/O4bvm8EBuVT6hjgS/cc+YsprDQnjqR41bOJy7vONP6BX+3W8tlZ81NvtrVGoJ13dykNZ937Mf4FR/bNkqFHbHARafOWoo7w7CSmLwTXLd8Ht+0783a+PZBp1PcwYpbcJOvdrWGqri+cMafiMs7ztUr7RmDzY5YoAOvjVz5yxc0ysniBV22q9H4zdr49nzXrhfXrpgXdiMSB4sOvCYtW7a0NP1ahfnc8OMc0lp1KXcsNX9ZdcBdp81NvtrVGqrqOr3vSJocP8KoX74qtdyK2g1WxwLQgbeExMRES9MfsXYBLY7uZ3qfK6qc1sr97qg0X4ybfLWrNVTV9cfEFJa37MTEH+cQWVgQIivfWB0LQAfeEqzsGENUEZPSPmRts3YsaNeryum5qXMUcJevdrWGKruKMK3vSBKz9nLx+kUnfRzKur3VrZOcGsuwTT/Q/uBOpve9Aqo4NpxGU1P5tn1vfm3ShklpHyDKPS8WfaEDr0lsbKw1CSvFpB8+5LcGCXyWfGZIktx/wl3B202+2tUaQuIqwot9ryB5/3YGZ6yoenrlYFks8EJ3khMCKnq86b1jDbNm3s1950zm7Z72jJKq0VRXIgsLWPjSDexsEM+fxjzmcx27RiMui+4kJwiKB8ILNTemfciBmDg+6HpWyNIsHlzRLbjJV7taQ6hcCzyRvNp7BH12rOG0Xb+GJM2yWBULvNGB1ySYkUIro8O+3zh7y0+80etiTtSKDlm6xaPPugU3+WpXawil67vdh3E4OpaJP84OWZreWBELyqIDr4VM/HEOx2tF8aYuYtBoQsbx2jG8ddqFnLtxGW0P7nJaJyh0Ga9JQUEBkZHBDZXtq4y32dEDLHlxAu/0OPekjpyrSu0IRV6Re16suMlXu1pDqF2bHDvE99OvY1bXsyscCr6YQMp9g40Fuow3CDZu3BjS9K5Z+TGRRYW8mjoipOkCDHNRG31wl692tYZQu+6v25A5KUO4Ys03NApxl5GhjgW+0IHXZO/e8kc09a6c7U8l7Tp5OYxd9Rmfd+wXVEfnlZFc311PKW7y1a7WYIXrf3uPILogj6tWfRrSdCuKBaFCB14LGLn6a+rnHuO/p1/qtIpGU23Z3KQ137ZLZdzK+UQV5DmtExA68Jp06dIlJOlEFBUy4ae5rGhxKitbVq0znPKYu81jSbpW4SZf7WoNVrm+cvqlNDl+hEvXfBuyNEMVCyoiuLdJ1ZBAq5CUV9wwbNMPtD6yh38MuS4UWj6Jq60Ad7xUAXf5aldrsMp1WeturIlvz4TlH/Fu93MDapLvfQ17v3zT1clsZNOmTSFJZ8JPH7G9fjxfdugbkvR8MbSFe16qgLt8tas1WOYqwqupl9DhwA4GbV0ZkiRDFQsqQgfeENLt94303rWOGb2GUxThnsdAjcbNzO80gD2xjbhu+UdOq/iNLmowadUquIEnvblu+UccrR3D+93OCYFR+fy0z12/l27y1a7WYKVrvqcWb552IXcufotT9m9nc5PWJ61TXrGCL0IRCyrDPWfOYuLj46u2/dH9XPjrEt7rNozsqDohsvLN+sPuKNcrxk2+2tUarHad2eM8TkTWDsldb1VjgT/owGtS1R7Lxq+cT4RSzOh1cYiMymdcB/d0jgLu8tWu1mC166E69ZmdMoTL1n5Hwyo2qAh174W+0IE3BETl5zL65y/4qkMfdjZIcFpHo6mRvN5rONEFeYxO/8JplUrRgdckLi4u6G0vWbeQhieO8nqv4SE0Kp/fj7vnERPc5atdrcEO101N27C4TQ+uWvVplcZlq0os8BcdeE169uwZ3IZKce2Keaxr1pa0VtZXvAaYucVdNSbc5KtdrcEu1xmpF9Pi6H6Gbfoh6DSCjgUBoAOvyZIlS4Laru+O1XTat43Xe11s23hqU1KsHWU11LjJV7tag12u37VL5bcGCVy7fF7QaQQbCwJBB16TgoLgMsY1Kz7mYEwc8zoNCrFR+dR22Vlzk692tQa7XIsiPLzR82J671pHl8zNQaURbCwIBBeduvCjafYhztmUxswe55FbK8ppHY1GA8zqdjbHakUzfsV8p1XKRQdek4EDBwa8zb7Yhlxw7XO2VCHz5tnV7inbA3f5aldrsNP1aFRdZncZyvD1C4OqWhZMLAgUHXhN1q5dG9R2G5omsb9uwxDbVMwlbdzTRh/c5atdrcFu1zd6XkRUYT5X/vJlwNsGGwsCwfWBV0QGi8g3IvKdiATdAe6BAwdCqWUp7eLc0wE2uMtXu1qD3a6bm7Tm+zbdGLvqUzxFlTfe8B7kYMEvGZUOdlBVXB14RSQauB04Xyk1RCk1x2knjUYTHrzZ8yISs/Zx1uYfnVY5CVcHXuAMIAf4WETmiEjQzca6d+8eOiuLmbXVPWV74C5f7WoNTrh+fUofdsY1ZfzKjwPazg5X2wKviNwiIstFJFdEZpT5rJEZOI+JyG8iMsbPZOOBU4CLgVeAqcH6HT16NNhNbSc+xj2PmOAuX+1qDU64FkZ4mNnjfM787Rfa79/h93Z2uNp5x7sbeAR4zcdnLwB5GIF0LDBdRFIARCRBRJb4mBKAw8D3Sqk84Bugc7ByGRkZwW5qOwMT3PNSBdzlq12twSnX97oNIy8ikqt+9n9ATDtcbQu8SqnZSqm5QKm3WCJSF7gcuF8pla2UWgLMA642t8tUSvX3MWUCPwKdRESAHsAWu45Ho9GEPwfqNuDTU8/k8tXfEJN3wmmdEkQpex8BROQRIFEpdY05fxqwVCkV47XOHcAgpVSlFWRF5GbgT0ARcJ1S6qRbVxGZCEw0Z5OBDT6SagLsD+xoHMNNruAuX+1qDTXBtY1Sqqk/K4bDCBSxQNlazkeAev5srJR6AaOooqJ1XgZermgdEVmulEr1Z59O4yZXcJevdrUG7VqacKjVkA2U7YctDnDP2y6NRqMJgHAIvBuBSBHp4LWsO2B98xGNRqNxADurk0WaDR48gEdEokUkUil1DJgNPCwidUXkTOAS4C273EwqLIoIM9zkCu7y1a7WoF29sO3lmohMBR4ss/ghpdRUEWmEUc3sHIxaD3crpWbaIqbRaDQ2Y3utBo1Go6nphEMZr0aj0dQodOD1QkTeFpHfRSRLRDaKyPVOO5WHiESJyKtmE+ujIrJKRM532qs8KmoyHg5Uodm67YT7d1mM2/Io2BcDwqEebzjxT2CCUipXRE4FFojIKqXUCqfFfBAJ7AAGAduBC4D3RaSrUmqbk2LlUNxk/FwgppJ1ncC72XoP4BMRSVdKhWPtmnD/LotxWx4Fm2KAvuP1Qim1VimVWzxrTu0dVCoXpdQxpdRUpdQ2pVSRUmo+sBXo5bSbL8prMh4OVNZsPdwI5+/SG7flUbAvBujAWwYRmSYix4Ffgd8B/3vXcBARiQc6ous/B0NHoFAptdFrWTqQ4pBPtcQtedSOGKADbxmUUjdhNFcegFG/OLfiLZxHRGoB/wPeUEr96rSPC6lSs3VN5bgpj9oRA2pM4BWRBSKiypmWeK+rlCo0HzcTgcnh7CsiERiNTfKAW8LZNYzRzdYtJBzyaKBYHQNqzMs1pdTgIDaLxKEyXn98ze4wX8V4IXSBUirfai9fBPndhhMlzdaVUpvMZbrZeggIlzxaBSyJATXmjrcyRKSZiFwpIrEi4hGRc4HRwLdOu1XAdKA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" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "plt.figure(figsize=(5,3))\n", - "plt.hist(R1_abs-R2_abs,100, density=True)\n", - "plt.yscale(\"log\")\n", - "xl=plt.xlim()\n", - "yl=plt.ylim()\n", - "\n", - "x=np.linspace(0.85*xl[0],0.85*xl[1],100)\n", - "y1= norm.pdf(x,0,np.std(R1_abs-R2_abs))\n", - "# y2=laplace.pdf(x,0,np.std(R1_abs-R2_abs)/np.sqrt(2))\n", - "\n", - "plt.plot(x,y1,'r-')\n", - "# plt.plot(x,y2,'m-')\n", - "plt.ylim(yl)\n", - "ref=\"{ref}\"\n", - "plt.title(f\"$r$={r}, $r_x$={rx}, $E_{ref}$ = {mean[0]}, std($\\Delta F$)={np.std(R1_abs-R2_abs):.3}\")\n", - "plt.xlabel(r\"$\\Delta |F|$\")\n", - "plt.ylabel(\"density\")\n", - "plt.ylim([1e-6,5])\n", - "plt.grid(linestyle=\"--\")\n", - "plt.savefig(fig_dir+f\"centric_differences_r{r}_Eref{mean[0]}.svg\")\n", - "plt.plot()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Magnitude of $\\sigma(\\Delta|E|)$\n", - "We found that $\\sigma(\\Delta |E|)\\approx\\sqrt{1-r}$ for acentric reflections and $\\sigma(\\Delta |E|)\\leq\\sqrt{2(1-r)}$ for centric reflections. Small deviations occur when $E$ is close to zero (towards slightly smaller standard deviation). Histograms look perfectly gaussian in all cases considered.\n", - "\n", - "See **effective_penalty_parameters_DeltaF.xlsx** in the `double-wilson` repository." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "For a single acentric component, we can state that:\n", - "$$\n", - "\\begin{align}\n", - " Var(\\Delta E_x) & = Var\\left(E_{1x} - (r E_{1x} + \\sqrt{1-r^2} \\eta_x)\\right) \\\\\n", - " & = Var\\left((1-r) E_{1x} - \\sqrt{1-r^2} \\eta_x\\right) \\\\\n", - " & = \\frac{1}{2}\\left((1-r)^2 + (1-r^2) - 0\\right) \\\\\n", - " & = (1-r) \n", - "\\end{align}\n", - "$$\n", - "\n", - "where $r E_{1x}$ is the conditional mean of $E_{1x}$ and $\\eta_x \\sim \\mathcal{N}(0,1/2)$ and Var($E_{1x}$) $=\\frac{1}{2}$. We used that $(1-r)^2 + (1-r^2) = 2-2r$.\n", - "\n", - "For a centric structure factor, we likewise obtain $Var(\\Delta E)=2(1-r)$.\n", - "\n", - "For centrics, that essentially settles why $Var(\\Delta |E|) \\leq 2(1-r)$, with the inequality coming from us not taking absolute values in the above equation. That is, $\\left||E_1| - |E_2|\\right| \\leq \\left|E_1 - E_2\\right|$. As long as $r$ is fairly close to 1, $E_1$ and $E_2$ will be very likely to have the same phase, in which case equality holds.\n", - "\n", - "For acentrics, the argument is more complicated. We can choose radial and transverse directions, apply the above argument to the radial dimension, and observe that the radial difference dominates the difference in absolute value, as long as $r$ is fairly close to 1. " - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.8.8" - }, - "toc": { - "base_numbering": 1, - "nav_menu": {}, - "number_sections": true, - "sideBar": false, - "skip_h1_title": false, - "title_cell": "Table of Contents", - "title_sidebar": "Contents", - "toc_cell": false, - "toc_position": { - "height": "831px", - "left": "25px", - "top": "110px", - "width": "340px" - }, - "toc_section_display": true, - "toc_window_display": false - } - }, - "nbformat": 4, - "nbformat_minor": 4 -}