From 905d06c5f1890f053b308854bb76698361807717 Mon Sep 17 00:00:00 2001 From: Mirko Date: Thu, 9 Apr 2020 15:34:20 -0400 Subject: [PATCH] added new versions for figures in paper --- .../CAN_Firing_Fields_3d.m | 116 + .../Create_Firing_Fields_CAN.ipynb | 297 ++ .../Figures/3d_field.png | Bin 0 -> 118013 bytes .../3D Firing Fields - CANs/src/plotting.py | 90 + .../src/twisted_attr.py | 84 + .../src/twisted_torus.py | 106 + .../3D Firing Fields - CANs/src/utils.py | 54 + .../3D Firing Fields - Idealized}/As.m | 16 +- .../Figures/3d_field_idealized2__id_0_.png | Bin 0 -> 58156 bytes .../Figures/example_bubbles.png | Bin 0 -> 59843 bytes .../Firing_Fields_3d.m | 207 ++ .../Capacity Figures/1D Capacity Figure.ipynb | 225 ++ .../Capacity Data Figures.ipynb | 372 +++ .../Figures/Fig3a_Capacity.pdf} | Bin 14059 -> 12978 bytes .../Figures/Fig3b_Capacity.pdf | Bin 0 -> 10615 bytes .../Figures/Fig4a_Trade_Off.pdf | Bin 0 -> 13001 bytes .../Figures/S1Fig_1d_bench.pdf} | Bin 13112 -> 11893 bytes .../Figures/S1Fig_1d_distr.pdf | Bin 0 -> 17973 bytes .../Capacity Figures/src}/prediction.py | 26 +- .../Capacity Figures/src/utils.py | 30 + experiments/Figure_Creation/README.md | 3 + ...lted Planes and 3d Fields-checkpoint.ipynb | 338 ++ .../Figures/2D_Field_Tilted_Plane.pdf | Bin 0 -> 37449 bytes .../Tilted Planes/Figures/3D_fields_lego.pdf | Bin 0 -> 56416 bytes .../Tilted Planes and 3d Fields.ipynb | 338 ++ .../Tilted Planes/src}/utils.py | 30 - .../_Figures/2D_Field_Tilted_Plane.pdf | Bin 0 -> 37449 bytes .../_Figures/3D_fields_lego.pdf | Bin 0 -> 56416 bytes .../Figure_Creation/_Figures/3d_field.png | Bin 0 -> 118013 bytes .../_Figures/Fig3a_Capacity.pdf | Bin 0 -> 12978 bytes .../_Figures/Fig3b_Capacity.pdf | Bin 0 -> 10615 bytes .../_Figures/Fig4a_Trade_Off.pdf | Bin 0 -> 13001 bytes .../_Figures/S1Fig_1d_bench.pdf | Bin 0 -> 11893 bytes .../_Figures/S1Fig_1d_distr.pdf | Bin 0 -> 17973 bytes .../_Figures/example_bubbles.png | Bin 0 -> 59843 bytes 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experiments/Figure_Creation/3D Firing Fields - CANs/src/plotting.py create mode 100644 experiments/Figure_Creation/3D Firing Fields - CANs/src/twisted_attr.py create mode 100644 experiments/Figure_Creation/3D Firing Fields - CANs/src/twisted_torus.py create mode 100644 experiments/Figure_Creation/3D Firing Fields - CANs/src/utils.py rename experiments/{MATLAB => Figure_Creation/3D Firing Fields - Idealized}/As.m (63%) create mode 100644 experiments/Figure_Creation/3D Firing Fields - Idealized/Figures/3d_field_idealized2__id_0_.png create mode 100644 experiments/Figure_Creation/3D Firing Fields - Idealized/Figures/example_bubbles.png create mode 100644 experiments/Figure_Creation/3D Firing Fields - Idealized/Firing_Fields_3d.m create mode 100644 experiments/Figure_Creation/Capacity Figures/1D Capacity Figure.ipynb create mode 100644 experiments/Figure_Creation/Capacity Figures/Capacity Data Figures.ipynb rename experiments/{Figures/Capacity_Figure_5a.pdf => Figure_Creation/Capacity Figures/Figures/Fig3a_Capacity.pdf} (54%) create mode 100644 experiments/Figure_Creation/Capacity Figures/Figures/Fig3b_Capacity.pdf create mode 100644 experiments/Figure_Creation/Capacity Figures/Figures/Fig4a_Trade_Off.pdf rename experiments/{Figures/Capacity_Figure_5b.pdf => Figure_Creation/Capacity Figures/Figures/S1Fig_1d_bench.pdf} (56%) create mode 100644 experiments/Figure_Creation/Capacity Figures/Figures/S1Fig_1d_distr.pdf rename experiments/{ => Figure_Creation/Capacity Figures/src}/prediction.py (73%) create mode 100644 experiments/Figure_Creation/Capacity Figures/src/utils.py create mode 100644 experiments/Figure_Creation/README.md create mode 100755 experiments/Figure_Creation/Tilted Planes/.ipynb_checkpoints/Tilted Planes and 3d Fields-checkpoint.ipynb create mode 100644 experiments/Figure_Creation/Tilted Planes/Figures/2D_Field_Tilted_Plane.pdf create mode 100644 experiments/Figure_Creation/Tilted Planes/Figures/3D_fields_lego.pdf create mode 100755 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hold on; + +thresh = 0.012 + + +b = data.b + + +x = -1:2./(b-1.):1.; + +y = x; +z = x; + +[x,y,z] = meshgrid(x,y,z); + +size(x) +size(f) + +% % +set(gca,'linewidth',4) +set(gca, 'XTickLabel', []) +set(gca, 'YTickLabel', []) +set(gca, 'ZTickLabel', []) +% +xticks([-1 0 1]) +yticks([-1 0 1]) +zticks([-1 0 1]) + +subplot(1,1,1); + + +isosurface(x, y, z, f, thresh); +isocaps(x, y, z, f, thresh, 'above'); + + + +azim = -25; +elev = 30; +lightangle(azim,elev); +daspect([1,1,1]); +camlight +lighting gouraud +grid on + + + + +view(22.5,15) + +% axis vis3d +colormap jet +% colormap copper + + + +v1 = [1 1 -1;1 -1 -1; -1 -1 -1; -1 1 -1]; +f1 = [1 2 3 4]; +patch('Faces',f1,'Vertices',v1,'FaceColor','black','FaceAlpha',.15, 'LineStyle','none'); + +v1 = [1 1 -1; + 1 1 1; + -1 1 1; + -1 1 -1]; +f1 = [1 2 3 4]; +patch('Faces',f1,'Vertices',v1,'FaceColor','black','FaceAlpha',.05, 'LineStyle','none'); + + +v1 = [-1 -1 -1; + -1 1 -1; + -1 1 1; + -1 -1 1]; +f1 = [1 2 3 4]; +patch('Faces',f1,'Vertices',v1,'FaceColor','black','FaceAlpha',.05, 'LineStyle','none'); + + + +v1 = [1 1 1;1 -1 1; -1 -1 1; -1 1 1]; +f1 = [1 2 3 4]; +patch('Faces',f1,'Vertices',v1,'FaceColor','black','FaceAlpha',0., 'LineWidth',4.); + +v1 = [1 -1 1;1 -1 -1;-1 -1 -1;-1 -1 1]; +f1 = [1 2 3 4]; +patch('Faces',f1,'Vertices',v1,'FaceColor','None','FaceAlpha',1., 'LineWidth',4.); + +v1 = [1 1 1 ; + 1 1 -1]; +f1 = [1 2]; +patch('Faces',f1,'Vertices',v1,'FaceColor','None','FaceAlpha',1., 'LineWidth',4.); + +v1 = [1 -1 -1 ; + 1 1 -1]; +f1 = [1 2]; +patch('Faces',f1,'Vertices',v1,'FaceColor','None','FaceAlpha',1., 'LineWidth',4.); + + + + +M = max(f,[],3); + +planeimg = mat2gray(reshape(M,100,100)); +size(planeimg) + + +% plot the image plane using surf. +surf([-1 1], [-1 1], repmat(-1, [2 2]), planeimg,'facecolor','texture') + + + +saveas(gcf, './Figures/3d_field.png'); + + diff --git a/experiments/Figure_Creation/3D Firing Fields - CANs/Create_Firing_Fields_CAN.ipynb b/experiments/Figure_Creation/3D Firing Fields - CANs/Create_Firing_Fields_CAN.ipynb new file mode 100644 index 0000000..89507c8 --- /dev/null +++ b/experiments/Figure_Creation/3D Firing Fields - CANs/Create_Firing_Fields_CAN.ipynb @@ -0,0 +1,297 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "%matplotlib inline\n", + "%load_ext autoreload\n", + "%autoreload 2" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import torch\n", + "from torch import nn\n", + "import torch.nn.functional as F\n", + "import matplotlib.pyplot as plt\n", + "\n", + "from src.twisted_attr import TwistedAttractor\n", + "from src.utils import MultiAttractor\n", + "from src.utils import get_path" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Torus attractors" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "m = 3\n", + "mec = MultiAttractor(m=m, dt=0.4)\n", + "W = mec.attr[0].W\n", + "print(W.shape)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "y0 = torch.zeros(m, 20, 20)\n", + "y0[:,0,0] = 10.\n", + "y0 = y0.view(m, 1, 400)\n", + "\n", + "mec.reset(y0)\n", + "\n", + "for t in range(1, 300):\n", + " b = 0.2*torch.ones(m,1,400)\n", + " y0 = mec(torch.zeros(m,1,2), b)\n", + " \n", + "\n", + "plt.imshow(y0.view(m*20,20))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Path Data" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "w=40\n", + "paths = [get_path(T=500, w=w, vmax=0.5) for _ in range(20)]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Path visualization" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "from src.plotting import scatter\n", + "\n", + "X,_ = paths[1]\n", + "scatter(X, mode=\"lines\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## path integration" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "A = torch.randn(m, 3, 2)\n", + "A = A/torch.norm(A, dim=1, keepdim=True)\n", + "A[0] = torch.eye(3)[:,:2]" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "model_input = []\n", + "\n", + "for x, v in paths:\n", + " model_input.append(4*v@A)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "model_output = []\n", + "\n", + "for i,v_ in enumerate(model_input):\n", + " T = v_.shape[1]\n", + " mec.reset(y0)\n", + " \n", + " if i%10 == 0: print(i, T)\n", + " \n", + " y = torch.zeros(T, m*400)\n", + " y[[0]] = y0.clone().view(1,m*400)\n", + " \n", + " for t in range(1, T):\n", + " b = .2*torch.ones(m,1,400)\n", + " \n", + " vel = v_[:,[t],:] + 0.3*torch.randn_like(v_[:,[t],:])\n", + " y[[t]] = mec(vel, b)\n", + " \n", + " model_output.append(y.clone())" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "x = torch.cat([x for x,v in paths], dim=0)\n", + "print(f\"x: {x.size()}\")\n", + "\n", + "y = torch.cat(model_output, dim=0)\n", + "y = y.view(-1, m,20,20)\n", + "print(f\"y: {y.size()}\")\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Look" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "from scipy.stats import binned_statistic_dd as binst\n", + "from scipy.ndimage.filters import gaussian_filter\n", + "from src.plotting import plot_3d_iso\n", + "from scipy.io import savemat" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "print(y.min(), y.max())\n", + "plt.imshow(y[10].view(m*20,20))" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "bins = 100\n", + "\n", + "vals = y[:,0,0,0].numpy() + \\\n", + " y[:,1,0,0].numpy() + \\\n", + " y[:,2,0,0].numpy() \n", + "\n", + "hist, be,_ = binst(x[:].numpy(), vals, bins=bins, statistic='mean')\n", + "hist = np.nan_to_num(hist)\n", + "print(hist.min(), hist.max())" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "values = gaussian_filter(hist, 3)\n", + "print(values.min(),values.max())" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "scrolled": false + }, + "outputs": [], + "source": [ + "X, Y, Z = np.mgrid[0:bins:1, 0:bins:1, 0:bins:1]\n", + "eps = .01\n", + "c = 0.001\n", + "\n", + "plot_3d_iso(X,Y,Z, values, c, eps)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "scipy.io.savemat('./data/data.mat', mdict={'arr': values, 'thresh': c, 'b': float(bins)})" + ] + } + ], + "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": "3.6.9" + }, + "toc": { + "base_numbering": 1, + "nav_menu": {}, + "number_sections": true, + "sideBar": true, + "skip_h1_title": false, + "title_cell": "Table of Contents", + "title_sidebar": "Contents", + "toc_cell": false, + "toc_position": { + "height": "calc(100% - 180px)", + "left": "10px", + "top": "150px", + "width": "165px" + }, + "toc_section_display": true, + "toc_window_display": true + } + }, + "nbformat": 4, + 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zYhyu=*nOCQ2JXzpy_^uNX)h)jxX{oFpsA_wUiW)5UczN5MQ z3TT8w_Z^Ka;Mu8c67F0a)PT@X+1W{VCHQ>FKkm#@rlN|zYE1vwlb-6fzPlk^V9?F8 zXn1jq3e|%=huWc7?%>I{ug+6>y)UC}2?Z9ym)An`QgZZ-O#i-%UMEH$f2^max(YM5 zOCv;w@dBdE%3qKM9x&2UJ4dC?M2yCj01r?-;K51(O bj", y, u) + + x_dot = -x + f(y + b) + + return x + dt*x_dot + + + def evolve(self, x, V, B, dt=None): + """ + Evolves the dynamical system for MULTIPLE time-steps with + initial condition `x`, and time dependent control signal `V`, + and time dependent feedforward input `B` + """ + T = V.size(0) + n = x.size(-1) + + Y = torch.zeros(T,n) + Y[0, :] = x + + for t in range(1,T): + Y[t,:] = self.forward(Y[t-1,:], V[t-1,:], B[t-1,:], dt) + + return Y + diff --git a/experiments/Figure_Creation/3D Firing Fields - CANs/src/twisted_torus.py b/experiments/Figure_Creation/3D Firing Fields - CANs/src/twisted_torus.py new file mode 100644 index 0000000..5884c40 --- /dev/null +++ b/experiments/Figure_Creation/3D Firing Fields - CANs/src/twisted_torus.py @@ -0,0 +1,106 @@ +#AUTOGENERATED! DO NOT EDIT! File to edit: dev/twisted_torus.ipynb (unless otherwise specified). + +__all__ = ['return_to_twisted_torus', 'twisted_distance', 'create_twisted_domain', 'create_twisted_inh_weights', + 'TwistedTorus', 't'] + +#Cell +import numpy as np +import torch +import matplotlib.pyplot as plt + +#Cell +def return_to_twisted_torus(x): + h = np.sqrt(3)/2. + x_ = torch.zeros_like(x) + + s = ((x[1]<0) + (x[1]>=h)).float() + + x_[0] = x[0] + s * 0.5 + x_[0] = x_[0]%1. + x_[1] = x[1]%h + + return x_ + +#Cell +def twisted_distance(X, Y): + h = np.sqrt(3)/2. + off = torch.tensor([ + [0 ,0], + [1 ,0], + [-1,0], + [0.5,h], + [-0.5,h], + [0.5,-h], + [-0.5,-h], + ]).t() + x = return_to_twisted_torus(X) + y = return_to_twisted_torus(Y) + + y = y.view(2,-1,1) + off.view(2,1,7) + + diff = x.view(2,1,-1, 1) - y.view(2,-1,1,7) + + norm = torch.norm(diff, dim=0) + dist, _ = torch.min(norm, dim=-1) + + return dist + + +#Cell +def create_twisted_domain(n): + h = np.sqrt(3)/2. + ticks = torch.arange(0,n, dtype=float)/n + m = torch.meshgrid([ticks, ticks]) + g = torch.stack(m).view(2,-1).float() + g[1] = g[1]*h + + return g + +#Cell +def create_twisted_inh_weights(x, y, sigma): + d = twisted_distance(x, y) + W = np.exp(-d**2/(2*sigma**2)) - 1. + W = W - torch.diag(W.diag()) + return W.float() + +#Cell + +class TwistedTorus(object): + def __init__(self, p=None, n = 10): + + h = int(np.sqrt(3)/2. * n) + self.shape = (h, n) +# self.c = np.stack(np.indices((h, n)), axis=2).reshape((-1,2)) + + m = torch.meshgrid([ + torch.arange(0,h, dtype=float)/h*np.sqrt(3)/2., + torch.arange(0,n, dtype=float)/n + ]) + + self.c = torch.stack(m).float().view(2,-1) + if p is None: + p = torch.rand(2) + p = p*torch.tensor([np.sqrt(3)/2., 1]) + + self.p = p + + def __call__(self, v=None): + if not v is None: + self.update(v) + + return self.cell_activity().view(*self.shape) + + def cell_activity(self): + d = twisted_distance(self.p, self.c) + print(d.shape) + return torch.exp(-d**2/0.01) + + def update(self,v): + p = self.p + p_ = p + v + p_ = return_to_twisted_torus(p_) + self.p = p_ + + return p_ + + diff --git a/experiments/Figure_Creation/3D Firing Fields - CANs/src/utils.py b/experiments/Figure_Creation/3D Firing Fields - CANs/src/utils.py new file mode 100644 index 0000000..7d20c15 --- /dev/null +++ b/experiments/Figure_Creation/3D Firing Fields - CANs/src/utils.py @@ -0,0 +1,54 @@ +import numpy as np +import torch +from torch import nn +import torch.nn.functional as F +from src.twisted_attr import TwistedAttractor + +class MultiAttractor: + def __init__(self, m=3, n=20, dt=0.4): + self.attr = [] + self.m = m + for i in range(self.m): + attr = TwistedAttractor( + n=n, + sigma=2., + dt=dt, + v=0.1, + cell_pos=None) + + self.attr.append(attr) + + self.reset() + + def reset(self, y=None): + if y is None: self.y = torch.rand(self.m, 1, 400)*0.01 + else: self.y = y.view(self.m, 1, 400).clone() + + def __call__(self, v, b, dt=None): + for i in range(self.m): + self.y[i] = self.attr[i](self.y[i], v[i], b[i], dt) + + return self.y.view(1, self.m*400) + + + +def get_path(T=1000, w=35, vmax=0.4): + x = torch.zeros(T, 3) + x[0] = w/2. + + v = torch.zeros(T, 3) + v[0] = torch.randn(3) + v = torch.clamp(v, -vmax, vmax) + + + for t in range(1,T): + a = torch.randn(3)*0.05 + for i in range(3): + if x[t-1,i] <= 0: a[i] = 0.2 + if x[t-1,i] >= w: a[i] = -0.2 + + v[t] = v[t-1] + a + v[t] = torch.clamp(v[t], -vmax, vmax) + x[t] = x[t-1] + v[t] + + return x, v \ No newline at end of file diff --git a/experiments/MATLAB/As.m b/experiments/Figure_Creation/3D Firing Fields - Idealized/As.m similarity index 63% rename from experiments/MATLAB/As.m rename to experiments/Figure_Creation/3D Firing Fields - Idealized/As.m index d395112..b46f769 100644 --- a/experiments/MATLAB/As.m +++ b/experiments/Figure_Creation/3D Firing Fields - Idealized/As.m @@ -1,28 +1,28 @@ A1 = [ -1.3791 0.6494 0.0606 - 0.1599 -1.3973 -0.5910] + 0.1599 -1.3973 -0.5910]; A2 = [ 0.6827 -0.9140 -0.6783 - 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zvfgI35u-ge;`o68h^Weg_&AfTXLNgB9!QQvE{BYIsUk#FQ{dHCjBt@yCk+y)8iT5z zQ2<$)c|7cEKK2IQ%>X}Q_!_`1^&xmmC+RPCMEn5Qc6vP=l!ri!GynhZ{{afD?R%w5 Vo4HEm>jR!cZfWYn2{&w?{|hfqgSP+x literal 0 HcmV?d00001 diff --git a/experiments/Figure_Creation/3D Firing Fields - Idealized/Firing_Fields_3d.m b/experiments/Figure_Creation/3D Firing Fields - Idealized/Firing_Fields_3d.m new file mode 100644 index 0000000..4e75231 --- /dev/null +++ b/experiments/Figure_Creation/3D Firing Fields - Idealized/Firing_Fields_3d.m @@ -0,0 +1,207 @@ + +x = -1:0.02:1.; +y = x; +z = x; +[x,y,z] = meshgrid(x,y,z); +sz = size(x); + +x_ = reshape(x,1,[]); +y_ = reshape(y,1,[]); +z_ = reshape(z,1,[]); +X = vertcat(x_,y_,z_); + + +m = 2 +f = get_bubbles(m, X); +f = reshape(f, sz); + +R = 0.9; +min_f=min(f, [],'all'); +max_f=max(f, [],'all'); +thresh=(1 - R)*min_f + R*max_f; + + + +set(gca,'linewidth',4) +set(gca, 'XTickLabel', []) +set(gca, 'YTickLabel', []) +set(gca, 'ZTickLabel', []) +xticks([-1 0 1]) +yticks([-1 0 1]) +zticks([-1 0 1]) + + +subplot(1,1,1); +% ------------- +isosurface(x, y, z, f, thresh); +isocaps(x, y, z, f, thresh, 'above'); + +xlim([-1 1]); +ylim([-1 1]); +zlim([-1 1]); + +azim = -25; +elev = 30; +lightangle(azim,elev); +daspect([1,1,1]); +camlight +lighting gouraud +grid on +view(22.5,15) +colormap jet + +v1 = [1 1 -1;1 -1 -1; -1 -1 -1; -1 1 -1]; +f1 = [1 2 3 4]; +patch('Faces',f1,'Vertices',v1,'FaceColor','black','FaceAlpha',.15, 'LineStyle','none'); +v1 = [1 1 -1; + 1 1 1; + -1 1 1; + -1 1 -1]; +f1 = [1 2 3 4]; +patch('Faces',f1,'Vertices',v1,'FaceColor','black','FaceAlpha',.05, 'LineStyle','none'); + +v1 = [-1 -1 -1; + -1 1 -1; + -1 1 1; + -1 -1 1]; +f1 = [1 2 3 4]; +patch('Faces',f1,'Vertices',v1,'FaceColor','black','FaceAlpha',.05, 'LineStyle','none'); + +v1 = [1 1 1;1 -1 1; -1 -1 1; -1 1 1]; +f1 = [1 2 3 4]; +patch('Faces',f1,'Vertices',v1,'FaceColor','black','FaceAlpha',0., 'LineWidth',4.); + +v1 = [1 -1 1;1 -1 -1;-1 -1 -1;-1 -1 1]; +f1 = [1 2 3 4]; +patch('Faces',f1,'Vertices',v1,'FaceColor','None','FaceAlpha',1., 'LineWidth',4.); + +v1 = [1 1 1; + 1 1 -1]; +f1 = [1 2]; +patch('Faces',f1,'Vertices',v1,'FaceColor','None','FaceAlpha',1., 'LineWidth',4.); + +v1 = [1 -1 -1; + 1 1 -1]; +f1 = [1 2]; +patch('Faces',f1,'Vertices',v1,'FaceColor','None','FaceAlpha',1., 'LineWidth',4.); + +r = 0 +saveas(gcf,['./Figures/3d_field_idealized' num2str(m) '__id_' num2str(r) '_.png']); + +% ------------------------------------------------------------- +% ------------------------------------------------------------- + +function d = can_distance(X, Y) + global Rhom + Z = mod(X - Y,1); + Z = Rhom(:,[1; 3])*Z; + n1 = vecnorm(Z - Rhom(:,1), 2, 1); + n2 = vecnorm(Z - Rhom(:,2), 2, 1); + n3 = vecnorm(Z - Rhom(:,3), 2, 1); + n4 = vecnorm(Z - Rhom(:,4), 2, 1); + D = vertcat(n1,n2,n3,n4); + d = min(D,[],1); +end + + +function g = normalize(f) + g_ = f - min(f,[],'all'); + g_ = g_./max(g_, [],'all'); + g = g_; +end + +function M=RandOrthMat(n, tol) +% M = RANDORTHMAT(n) +% generates a random n x n orthogonal real matrix. +% +% M = RANDORTHMAT(n,tol) +% explicitly specifies a thresh value that measures linear dependence +% of a newly formed column with the existing columns. Defaults to 1e-6. +% +% In this version the generated matrix distribution *is* uniform over the manifold +% O(n) w.r.t. the induced R^(n^2) Lebesgue measure, at a slight computational +% overhead (randn + normalization, as opposed to rand ). +% +% (c) Ofek Shilon , 2006. + if nargin==1 + tol=1e-6; + end + + M = zeros(n); % prealloc + + % gram-schmidt on random column vectors + + vi = randn(n,1); + + % the n-dimensional normal distribution has spherical symmetry, which implies + % that after normalization the drawn vectors would be uniformly distributed on the + % n-dimensional unit sphere. + M(:,1) = vi ./ norm(vi); + + for i=2:n + nrm = 0; + while nrm" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.rc(\"font\",**{\"family\": \"sans-serif\",\"sans-serif\": [\"Arial\"],\"size\": 8})\n", + "fig, axs = plt.subplots(figsize=(2., 2.), ncols=1, nrows=8, sharex=True, tight_layout = {\"pad\": 0})\n", + "\n", + "axs[7].set_xlabel(\"Coding Range\")\n", + "axs[0].set_title(\"N = 1\")\n", + "for m_ in range(8):\n", + " m = m_ + 1\n", + " \n", + " ax = axs[7 - m_]\n", + " ax.spines['right'].set_visible(False)\n", + " ax.spines['top'].set_visible(False)\n", + " ax.spines['bottom'].set_visible(False)\n", + " ax.spines['left'].set_visible(False)\n", + " ylabel = ax.set_ylabel(\"M={}\".format(m))\n", + " ylabel.set_rotation(0)\n", + " ax.set_yticks([])\n", + " ax.set_xscale(\"log\")\n", + " \n", + " h,_ = np.histogram(X[m_,:], bins=np.exp(x))\n", + "\n", + " ax.plot(np.exp(x[:-1]), h, alpha=1., color=\"black\", linewidth=1.)\n", + " ax.fill_between(np.exp(x[:-1]), h, y2=0, color=\"C2\", alpha=.4)\n", + "\n", + "\n", + "plt.savefig(\"./Figures/S1Fig_1d_distr.pdf\", dpi=300, transparent=True)" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.rc(\"font\",**{\"family\": \"sans-serif\",\"sans-serif\": [\"Arial\"],\"size\": 8})\n", + "\n", + "fig, ax = plt.subplots(figsize=(2.5, 2.), ncols=1, nrows=1, sharex=True, tight_layout = {\"pad\": 0})\n", + "\n", + "ax.set_ylabel(\"Coding Range\")\n", + "\n", + "ms = np.arange(1,9)\n", + "ax.set_title(\"N = 1\")\n", + "ax.set_xticks(ms)\n", + "ax.spines['right'].set_visible(False)\n", + "ax.spines['top'].set_visible(False)\n", + "ax.set_xlabel(\"M\")\n", + "ax.set_yscale(\"log\")\n", + "\n", + "ax.set_xticks(ms)\n", + "ax.set_xlim(0.5,ms[-1]+.5)\n", + "\n", + "\n", + "\n", + "\n", + "k = 1\n", + "k_ = k - 1\n", + "valid = np.where(2*ms>=k)[0] \n", + "a = np.exp(log_mean - 2*log_std)[valid,k_]\n", + "b = np.exp(log_mean)[valid,k_]\n", + "c = np.exp(log_mean + 2*log_std)[valid,k_]\n", + "\n", + "\n", + "p = 0.2 * (1./(0.2**2))**ms\n", + "\n", + "\n", + "\n", + "ax.plot(ms[valid], p[valid], \n", + " color=\"black\",\n", + " linewidth= 3,\n", + " linestyle=\"-\",\n", + " alpha=1.,\n", + " marker=\"None\", markersize=8 , markerfacecolor=\"cyan\") \n", + "\n", + "ax.plot( [ms[valid],ms[valid]] ,[a,c], linewidth=1.,color=\"C0\",linestyle=\"-\", alpha=1.)\n", + "ax.plot(ms[valid], b, \n", + " marker=\"s\", color=\"C0\", \n", + " markerfacecolor= \"white\",\n", + " markersize=6,\n", + " markeredgewidth=1.,\n", + " linewidth=1., \n", + " linestyle=\"none\")\n", + " \n", + "plt.savefig(\"./Figures/S1Fig_1d_bench.pdf\", dpi=300, transparent=True)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "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": "3.6.9" + }, + "toc": { + "base_numbering": 1, + "nav_menu": {}, + "number_sections": true, + "sideBar": true, + "skip_h1_title": false, + "title_cell": "Table of Contents", + "title_sidebar": "Contents", + "toc_cell": false, + "toc_position": {}, + "toc_section_display": true, + "toc_window_display": false + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/experiments/Figure_Creation/Capacity Figures/Capacity Data Figures.ipynb b/experiments/Figure_Creation/Capacity Figures/Capacity Data Figures.ipynb new file mode 100644 index 0000000..077b7b1 --- /dev/null +++ b/experiments/Figure_Creation/Capacity Figures/Capacity Data Figures.ipynb @@ -0,0 +1,372 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The autoreload extension is already loaded. To reload it, use:\n", + " %reload_ext autoreload\n" + ] + } + ], + "source": [ + "%load_ext autoreload\n", + "%autoreload 2" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [], + "source": [ + "%matplotlib inline\n", + "import matplotlib.pyplot as plt\n", + "from scipy.stats import skewnorm\n", + "from scipy.stats import norm\n", + "\n", + "import numpy as np\n", + "import pickle\n", + "\n", + "from src.prediction import construct_predictions\n", + "from src.utils import gather_data\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Load ND data we want to analyse\n", + "\n", + "- **Width** data is a 4D array \"indexed\" by\n", + "(delta, module, dimension, trial)\n", + " - Here data for *one* delta only \n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "W shape is (9, 4, 60) indexed by module number, dimension, trial\n" + ] + } + ], + "source": [ + "\"\"\"\n", + " Load the ND data, \n", + " which we want to analyze\n", + "\"\"\" \n", + "\n", + "path_to_data = \"./data/m_k_normal\"\n", + "W = gather_data(path_to_data, \"width\")\n", + "\n", + "\n", + "\n", + "\n", + "W = W[0,:,:,:]\n", + "log_mean = np.mean(np.log(W), axis=2)\n", + "log_std = np.std(np.log(W), axis=2)\n", + "\n", + "print(f\"W shape is {W.shape} indexed by module number, dimension, trial\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Construct predictions from 1d data\n", + "\n", + "- **Width** data for prediction again is a 4D array \"indexed\" by\n", + "(delta, module, dimension, trial)\n", + " - Here we need data for 1D only \n", + "- **Prediction** is computed from log 1D data and will spit out a 3D array \"indexed\" by (modules, dimensions, delta)" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "scrolled": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Prediction shape is (9, 7, 5)\n" + ] + } + ], + "source": [ + "path_to_data = \"./data/benchmark_normal\"\n", + "\n", + "X = gather_data(path_to_data)\n", + "X = X[:, :, 0, :]\n", + "X = np.swapaxes(X, 0, 1)\n", + "\n", + "logX = np.log(X)\n", + "prediction = construct_predictions(logX[:,:], \n", + " ms=range(1,9 + 1), #No. of modules\n", + " ks=range(1,7 + 1), #Input dim\n", + " ps=range(5), #Index into phase resolution subarray\n", + " raw=False)\n", + "\n", + "print(f\"Prediction shape is {prediction.shape}\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Figure 3a, 3b" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": { + "scrolled": false + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.rc(\"font\",**{\"family\": \"sans-serif\",\"sans-serif\": [\"Arial\"],\"size\": 8})\n", + "fig, axes = plt.subplots(figsize=(5., 1.25), ncols=4, sharey=False, tight_layout = {\"pad\": 0})\n", + "\n", + "ms = np.arange(1,10)\n", + "ks = np.array([3,4,5,6])\n", + "\n", + "axes[0].set_ylabel(\"Range\")\n", + "for i,ax in enumerate(axes):\n", + "\n", + " ax.set_title(\"N = {}\".format(ks[i]))\n", + " ax.set_xticks(ms)\n", + " ax.spines['right'].set_visible(False)\n", + " ax.spines['top'].set_visible(False)\n", + " ax.set_xlabel(\"M\")\n", + " ax.set_yscale(\"log\")\n", + "\n", + " ax.set_xticks(ms)\n", + " ax.set_xlim(0.5,ms[-1]+.5)\n", + "\n", + " \n", + " k = ks[i]\n", + " k_ = i\n", + "\n", + " \n", + " valid = np.where(ms>=k)[0]\n", + "\n", + " \n", + " ax.plot(ms[valid], prediction[valid,k - 1,1], \n", + " color=\"black\",\n", + " linewidth= 3,\n", + " linestyle=\"-\",\n", + " alpha=1.,\n", + " marker=\"None\", markersize=8 , markerfacecolor=\"cyan\") \n", + "\n", + " valid = np.where(2*ms>=k)[0] \n", + " a = np.exp(log_mean - 2*log_std)[valid,k_]\n", + " b = np.exp(log_mean)[valid,k_]\n", + " c = np.exp(log_mean + 2*log_std)[valid,k_]\n", + " \n", + " ax.plot( [ms[valid],ms[valid]] ,[a,c], linewidth=1.,color=\"C0\",linestyle=\"-\", alpha=1.)\n", + " ax.plot(ms[valid], b, \n", + " marker=\"s\", color=\"C0\", \n", + " markerfacecolor= \"white\",\n", + " markersize=4,\n", + " markeredgewidth=1.,\n", + " linewidth=.5, \n", + " linestyle=\"none\")\n", + " \n", + "\n", + "plt.savefig(\"./Figures/Fig3a_Capacity.pdf\", dpi=300, transparent=False)\n" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.rc(\"font\",**{\"family\": \"sans-serif\",\"sans-serif\": [\"Arial\"],\"size\": 8})\n", + "fig, axes = plt.subplots(figsize=(3., 1.25), ncols=2, sharey=False, tight_layout = {\"pad\": 0})\n", + "\n", + "ms = np.arange(1,10)\n", + "ks = np.array([5,6])\n", + "\n", + "axes[0].set_ylabel(\"Range\")\n", + "for i,ax in enumerate(axes):\n", + "\n", + " ax.set_title(\"N = {}\".format(ks[i]))\n", + " ax.set_xticks(ms)\n", + " ax.spines['right'].set_visible(False)\n", + " ax.spines['top'].set_visible(False)\n", + " ax.set_xlabel(\"M\")\n", + " ax.set_yscale(\"log\")\n", + " ax.set_xticks(ms)\n", + " ax.set_xlim(0.5,ms[-1]+.5)\n", + "\n", + " \n", + " k = ks[i]\n", + " valid = np.where(ms>=k)[0]\n", + " for d in range(1,5):\n", + " l = 3. if d == 1 else 1\n", + " c = \"black\" \n", + " ax.plot(ms[valid], prediction[valid,k - 1,d], \n", + " color=c,\n", + " linewidth= l,\n", + " linestyle=\"-\",\n", + " marker=\"None\", markersize=2 , markerfacecolor=\"black\") \n", + "\n", + "\n", + "plt.savefig(\"./Figures/Fig3b_Capacity.pdf\", dpi=300, transparent=False)\n" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.rc(\"font\",**{\"family\": \"sans-serif\",\"sans-serif\": [\"Arial\"],\"size\": 8})\n", + "fig, ax = plt.subplots(figsize=(2., 1.25), ncols=1, sharey=False, tight_layout = {\"pad\": 0})\n", + "\n", + "\n", + "m = 9\n", + "ks = np.array([3,4,5,6])\n", + "\n", + "\n", + "ax.set_title(\"M={}\".format(m))\n", + "ax.spines['right'].set_visible(False)\n", + "ax.spines['top'].set_visible(False)\n", + "ax.set_xlabel(\"N\")\n", + "ax.set_ylabel(\"Range\")\n", + "ax.set_yscale(\"log\")\n", + "\n", + "ax.set_xticks(1 - 1./ks)\n", + "ax.set_xticklabels(ks)\n", + "\n", + "\n", + "\n", + "\n", + "p = prediction[m - 1,ks-1,1]\n", + "f = W[m-1,:,:]\n", + "\n", + "\n", + "ax.plot(1 - 1./ks, p, \n", + " color=\"black\",\n", + " linestyle=\"-\",\n", + " marker=\"None\", linewidth=3,\n", + " alpha=1., zorder=1000)\n", + "\n", + "\n", + "for t in range(50,60):\n", + " ax.plot(1 - 1./ks, f[:,t], \n", + " color=\"C1\",\n", + " linestyle=\"-\",\n", + " marker=\"o\",\n", + " markerfacecolor=\"white\",\n", + " markeredgewidth=0.5,\n", + " markersize=3,\n", + " linewidth=0.5,\n", + " alpha=1., zorder=-1000)\n", + "\n", + "\n", + "plt.savefig(\"./Figures/Fig4a_Trade_Off.pdf\", dpi=300, transparent=False)\n", + "\n", + " " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "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": "3.6.9" + }, + "toc": { + "base_numbering": 1, + "nav_menu": {}, + "number_sections": true, + "sideBar": true, + "skip_h1_title": false, + "title_cell": "Table of Contents", + 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zj`lEfOSt{n=Urs1O@Or#c~K)5e;XU*T5wiYHFpPYIlk?%!R#H+E-x@QJ1++YEv" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "fig = plt.figure(figsize=(22,4))\n", + "\n", + "thresh = 0.7\n", + "for i in range(1,5):\n", + " ax = fig.add_subplot(1, 4, i, projection='3d')\n", + " ax.set_title(\"M={}\".format(i))\n", + " ax.set_xticklabels([])\n", + " ax.set_yticklabels([])\n", + " ax.set_zticklabels([])\n", + " g = f[i]\n", + " voxels = g > np.amax(g)*thresh\n", + " ax.voxels(voxels, edgecolor='k')\n", + " \n", + "plt.savefig(\"./Figures/3D_fields_lego.pdf\", dpi=300, transparent=False)" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "from scipy.signal import correlate2d\n", + "\n", + "step_size = 0.02\n", + "env_size = 2\n", + "b = int(env_size/step_size)\n", + "\n", + "X = np.mgrid[0:env_size:step_size, 0:env_size:step_size]\n", + "X = X.reshape((2,-1)).T\n", + "X = X - env_size*0.5\n", + "\n", + "\n", + "Plane_base = np.array([\n", + " [np.cos(-np.pi/4.),0,np.sin(-np.pi/4.)],\n", + " [0,1,0]\n", + "])\n", + "\n", + "X_ = np.dot(X, Plane_base)\n", + "\n", + "\n", + "i = 1\n", + "img = create_firing_field(X_, A[i])\n", + "img = img.reshape((b,b))\n", + "\n", + "corr = correlate2d(img,img, mode=\"full\")" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "\n", + "\n", + "fig = plt.figure(figsize=(4,2))\n", + "ax = fig.add_subplot(1,2,1)\n", + "ax.axis(\"off\")\n", + "ax.imshow(img.T, cmap=\"jet\")\n", + "\n", + "ax = fig.add_subplot(1,2,2)\n", + "ax.axis(\"off\")\n", + "ax.imshow(corr.T, cmap=\"jet\")\n", + "\n", + "plt.savefig(\"./Figures/2D_Field_Tilted_Plane.pdf\", dpi=300, transparent=False)" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "80\n", + "[[ 1.25 -0.72168784 0. ]\n", + " [ 0. 1.44337567 0. ]]\n" + ] + } + ], + "source": [ + "\n", + "step_size = 0.05\n", + "env_size = 4.\n", + "b = int(env_size/step_size)\n", + "\n", + "X = np.mgrid[0:env_size:step_size, 0:env_size:step_size]\n", + "X = X.reshape((2,-1)).T\n", + "X = X - env_size*0.5\n", + "\n", + "angle = np.pi*0.5\n", + "rot = 0.0\n", + "\n", + "Plane_base = np.array([\n", + " [np.cos(rot), np.sin(rot), 0],\n", + " [np.cos(angle)*np.cos(rot + np.pi/2.),np.cos(angle)*np.sin(rot + np.pi/2.), np.sin(angle)]\n", + "])\n", + "\n", + "\n", + "PL2 = np.array([\n", + " [1,0, 0],\n", + " [0,1, 0]\n", + "])\n", + "\n", + "\n", + "\n", + "X_ = np.dot(X, Plane_base)\n", + "\n", + "\n", + "\n", + "X_2 = np.dot(X, PL2)\n", + "\n", + "img = create_firing_field(X_, A)\n", + "img = img.reshape((b,b))\n", + "\n", + "thresh = 0.7\n", + "voxels = g > np.amax(g)*thresh" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", 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+ "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "import scipy\n", + "\n", + "\n", + "def get_3dA(s):\n", + " B = np.zeros((3,3))\n", + " B[:2,:2] = lattice(np.random.sample()*np.pi*2.,np.pi/3.)\n", + " B[:2,2] = np.random.randn(2)*0.05\n", + " B[2,2] = 1 + np.random.randn()*0.1\n", + " A = np.zeros((2,3))\n", + " A = np.linalg.inv(s*B)[:2]\n", + " return A\n", + "\n", + "\n", + "for _ in range(3):\n", + " A = get_3dA(s=0.8)\n", + " \n", + " img = create_firing_field(X_ + np.random.randn(3), A)\n", + " img2 = create_firing_field(X_2, A)\n", + " img = img.reshape((b,b))\n", + " img2 = img2.reshape((b,b))\n", + " \n", + " f = img\n", + " f2 = img2\n", + " f = f - np.median(f)\n", + " f = f/np.std(f)\n", + " \n", + " f2 = f2 - np.median(f2)\n", + " f2 = f2/np.std(f2)\n", + " \n", + " corr = scipy.signal.correlate2d(f,f, mode=\"full\")\n", + "\n", + " fig = plt.figure(figsize=(2,1))\n", + " ax = fig.add_subplot(1,2,1)\n", + " ax.axis(\"off\")\n", + " ax.imshow(f.T, cmap=\"jet\")\n", + "\n", + " ax = fig.add_subplot(1,2,2)\n", + " ax.axis(\"off\")\n", + " ax.imshow(corr.T, cmap=\"jet\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "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": "3.6.9" + }, + "toc": { + "base_numbering": 1, + "nav_menu": {}, + "number_sections": true, + "sideBar": true, + "skip_h1_title": false, + "title_cell": "Table of Contents", + "title_sidebar": "Contents", + "toc_cell": false, + "toc_position": {}, + "toc_section_display": true, + "toc_window_display": false + } + }, + 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@@ -0,0 +1,338 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "%load_ext autoreload\n", + "%autoreload 2" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "%matplotlib inline\n", + "import numpy as np\n", + "from scipy.stats import ortho_group\n", + "import matplotlib.pyplot as plt\n", + "from mpl_toolkits.mplot3d import Axes3D \n", + "from src.utils import create_firing_field, get_3dA, lattice" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "step_size = 0.1\n", + "env_size = 2\n", + "b = int(env_size/step_size)\n", + "\n", + "X = np.mgrid[0:env_size:step_size, 0:env_size:step_size, 0:env_size:step_size]\n", + "X = X.reshape((3,-1)).T\n", + "X = X - env_size*0.5\n", + "\n", + "\n", + "f = np.ones((5, b,b,b))\n", + "A = np.zeros((5,2,3))\n", + "for i in range(1,5): \n", + "\n", + " if i==1:\n", + " Q = np.eye(3)\n", + " else:\n", + " Q = ortho_group.rvs(3)\n", + "\n", + " A[i-1] = np.dot( get_3dA(s=1.), Q)\n", + " \n", + " g = create_firing_field(X, A[i-1])\n", + " g = g.reshape((b,b,b))\n", + " f[i] = f[i-1]*g" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "

" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "fig = plt.figure(figsize=(22,4))\n", + "\n", + "thresh = 0.7\n", + "for i in range(1,5):\n", + " ax = fig.add_subplot(1, 4, i, projection='3d')\n", + " ax.set_title(\"M={}\".format(i))\n", + " ax.set_xticklabels([])\n", + " ax.set_yticklabels([])\n", + " ax.set_zticklabels([])\n", + " g = f[i]\n", + " voxels = g > np.amax(g)*thresh\n", + " ax.voxels(voxels, edgecolor='k')\n", + " \n", + "plt.savefig(\"./Figures/3D_fields_lego.pdf\", dpi=300, transparent=False)" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "from scipy.signal import correlate2d\n", + "\n", + "step_size = 0.02\n", + "env_size = 2\n", + "b = int(env_size/step_size)\n", + "\n", + "X = np.mgrid[0:env_size:step_size, 0:env_size:step_size]\n", + "X = X.reshape((2,-1)).T\n", + "X = X - env_size*0.5\n", + "\n", + "\n", + "Plane_base = np.array([\n", + " [np.cos(-np.pi/4.),0,np.sin(-np.pi/4.)],\n", + " [0,1,0]\n", + "])\n", + "\n", + "X_ = np.dot(X, Plane_base)\n", + "\n", + "\n", + "i = 1\n", + "img = create_firing_field(X_, A[i])\n", + "img = img.reshape((b,b))\n", + "\n", + "corr = correlate2d(img,img, mode=\"full\")" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "\n", + "\n", + "fig = plt.figure(figsize=(4,2))\n", + "ax = fig.add_subplot(1,2,1)\n", + "ax.axis(\"off\")\n", + "ax.imshow(img.T, cmap=\"jet\")\n", + "\n", + "ax = fig.add_subplot(1,2,2)\n", + "ax.axis(\"off\")\n", + "ax.imshow(corr.T, cmap=\"jet\")\n", + "\n", + "plt.savefig(\"./Figures/2D_Field_Tilted_Plane.pdf\", dpi=300, transparent=False)" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "80\n", + "[[ 1.25 -0.72168784 0. ]\n", + " [ 0. 1.44337567 0. ]]\n" + ] + } + ], + "source": [ + "\n", + "step_size = 0.05\n", + "env_size = 4.\n", + "b = int(env_size/step_size)\n", + "\n", + "X = np.mgrid[0:env_size:step_size, 0:env_size:step_size]\n", + "X = X.reshape((2,-1)).T\n", + "X = X - env_size*0.5\n", + "\n", + "angle = np.pi*0.5\n", + "rot = 0.0\n", + "\n", + "Plane_base = np.array([\n", + " [np.cos(rot), np.sin(rot), 0],\n", + " [np.cos(angle)*np.cos(rot + np.pi/2.),np.cos(angle)*np.sin(rot + np.pi/2.), np.sin(angle)]\n", + "])\n", + "\n", + "\n", + "PL2 = np.array([\n", + " [1,0, 0],\n", + " [0,1, 0]\n", + "])\n", + "\n", + "\n", + "\n", + "X_ = np.dot(X, Plane_base)\n", + "\n", + "\n", + "\n", + "X_2 = np.dot(X, PL2)\n", + "\n", + "img = create_firing_field(X_, A)\n", + "img = img.reshape((b,b))\n", + "\n", + "thresh = 0.7\n", + "voxels = g > np.amax(g)*thresh" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "import scipy\n", + "\n", + "\n", + "def get_3dA(s):\n", + " B = np.zeros((3,3))\n", + " B[:2,:2] = lattice(np.random.sample()*np.pi*2.,np.pi/3.)\n", + " B[:2,2] = np.random.randn(2)*0.05\n", + " B[2,2] = 1 + np.random.randn()*0.1\n", + " A = np.zeros((2,3))\n", + " A = np.linalg.inv(s*B)[:2]\n", + " return A\n", + "\n", + "\n", + "for _ in range(3):\n", + " A = get_3dA(s=0.8)\n", + " \n", + " img = create_firing_field(X_ + np.random.randn(3), A)\n", + " img2 = create_firing_field(X_2, A)\n", + " img = img.reshape((b,b))\n", + " img2 = img2.reshape((b,b))\n", + " \n", + " f = img\n", + " f2 = img2\n", + " f = f - np.median(f)\n", + " f = f/np.std(f)\n", + " \n", + " f2 = f2 - np.median(f2)\n", + " f2 = f2/np.std(f2)\n", + " \n", + " corr = scipy.signal.correlate2d(f,f, mode=\"full\")\n", + "\n", + " fig = plt.figure(figsize=(2,1))\n", + " ax = fig.add_subplot(1,2,1)\n", + " ax.axis(\"off\")\n", + " ax.imshow(f.T, cmap=\"jet\")\n", + "\n", + " ax = fig.add_subplot(1,2,2)\n", + " ax.axis(\"off\")\n", + " ax.imshow(corr.T, cmap=\"jet\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "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": "3.6.9" + }, + "toc": { + "base_numbering": 1, + "nav_menu": {}, + "number_sections": true, + "sideBar": true, + "skip_h1_title": false, + "title_cell": "Table of Contents", + "title_sidebar": "Contents", + "toc_cell": false, + "toc_position": {}, + "toc_section_display": true, + "toc_window_display": false + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/experiments/utils.py b/experiments/Figure_Creation/Tilted Planes/src/utils.py similarity index 60% rename from experiments/utils.py rename to experiments/Figure_Creation/Tilted Planes/src/utils.py index 5608140..7f8bb2e 100644 --- a/experiments/utils.py +++ b/experiments/Figure_Creation/Tilted Planes/src/utils.py @@ -1,35 +1,7 @@ import numpy as np -import pickle -from os import listdir -from os.path import isfile, join from scipy.stats import ortho_group -def gather_data(mypath, key="width"): - """ - Loads trials from a folder and - returns an array indexed by: m, k, t. - """ - filenames = [join(mypath, f) for f in listdir(mypath) if isfile(join(mypath, f))] - filenames = [f for f in filenames if f.endswith(".p")] - W = [] - for filename in filenames: - with open(filename, 'r') as f: - data = pickle.load(f) - W.append(np.expand_dims(data[key], axis=-1) ) - - W = np.concatenate(W, axis=-1) - return W - - -def normalized_histogram(data, bins=200): - h, b = np.histogram(data, bins=bins) - h = h.astype(float) - h= h/np.amax(h) - return h, b[:-1] - - - hex_base = np.array([ [1., np.cos(np.pi/3.)], [0., np.sin(np.pi/3.)]]) @@ -79,5 +51,3 @@ def create_firing_field(X, A): - - diff --git a/experiments/Figure_Creation/_Figures/2D_Field_Tilted_Plane.pdf b/experiments/Figure_Creation/_Figures/2D_Field_Tilted_Plane.pdf new file mode 100644 index 0000000000000000000000000000000000000000..8ce39a1df6389f81846482f5224db0dc51115f08 GIT binary patch literal 37449 zcmd43Wk6JG_dbjwq9CD%0R#yVPzGtF8AQ5s=oX~A2L==*96)KLyJJ*3hVBkw=#rsB za%ldep7VGff6u4))BAzV-oxyD-}hSAx>nsA24!(c77kW!Jcgoa+QJ$<4qA3vdlM@> zAt72eWn*(QXIf6oC#tk;>Yff}v}|I=F2*+Y=CmLXo|&ELk1z85>jnuA7b!ItV;3`8 z?q4@a+S|F%a{W42Hg<6_bF!m-_Tv(dP1(u*rJ9)wtuAI9aY@Yc%{*La*<@@nW4`$N zx7gpmWoY$j+0-nIO)c%rX?cF#uBBvRW%kmAmiOnwe@};l9rM9I3lO!lvv+aE41u{{ z3^NroJIodTuLnpu*}FQ>{#d4%8ZDc+nVaQHGgT?f(3mTACu2Kj2V*BQyO*B-to+ya 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- -sz = size(x); -x_ = reshape(x,1,[]); -y_ = reshape(y,1,[]); -z_ = reshape(z,1,[]); -X = vertcat(x_,y_,z_); - - -n = 4; - - -A = zeros(n, 2, 3); -B = zeros(n, 3, 3); -size(A); -for i = 1:n -% --------------------- - -B(i,[1;2],[1;2]) = Rhom(:,[1; 3]); -% B(i,:,3) = [0;0;1]; - -B(i,[1;2],3) = randn(2,1); -B(i,3,3)=1; -B = B.*1.; -Ai = inv(reshape(B(i,1:3,1:3),3,3)); -A(i,:,:) = Ai(1:2,:)*RandOrthMat(3); - -% --------------------- -end - - -clf; -for i = 2:n -% --------------------- - -Ai = reshape(A(i,:,:), 2,3); -f = can_distance(Ai*X, zeros(2,size(X,2)) ); -f = exp(-f.^2/.1); -f = reshape(f, sz); -colormap jet - -thresh=0.8; - - -azim = 0; -elev = 45; - -subplot(2,n,n+i); - - -a=.5; b=-.0;c=1;d=0; -[x_ y_] = meshgrid(-1:0.01:1); % Generate x and y data -z_ = -1/c*(a*x_ + b*y_ + d); % Solve for z data -h =slice(x,y,z,f,x_,y_,z_, 'linear'); -set(h,'edgecolor','none'); -xlim([-1 1]) -ylim([-1 1]) -zlim([-1 1]) - -lightangle(azim,elev); -daspect([1,1,1]); -camlight -lighting gouraud -grid on -view(20,20) -set(gca, 'XTickLabel', []) -set(gca, 'YTickLabel', []) -set(gca, 'ZTickLabel', []) - - - -subplot(2,n,i); -isosurface(x, y, z, f, thresh); -isocaps(x, y, z, f, thresh, 'above'); -xlim([-1 1]) -ylim([-1 1]) -zlim([-1 1]) - -lightangle(azim,elev); -daspect([1,1,1]); -camlight -lighting gouraud -grid on -view(20,20) - -set(gca, 'XTickLabel', []) -set(gca, 'YTickLabel', []) -set(gca, 'ZTickLabel', []) -% --------------------- -end - - -h = subplot(2,n,1); - - -vert = [0 0 0;1 0 0;1 1 0;0 1 0;0 0 1;1 0 1;1 1 1;0 1 1]; -fac = [1 2 6 5;2 3 7 6;3 4 8 7;4 1 5 8;1 2 3 4;5 6 7 8]; -patch('Vertices',vert,'Faces',fac,... - 'FaceVertexCData',hsv(6), 'FaceAlpha', 0.2); - - -lightangle(azim,elev); -daspect([1,1,1]); -camlight -grid on -view(20,20) - -set(gca, 'XTickLabel', []) -set(gca, 'YTickLabel', []) -set(gca, 'ZTickLabel', []) - - -h = subplot(2,n,n+1); -a=.5; b=-.0;c=1;d=0; -[x_ y_] = meshgrid(-1:0.01:1); % Generate x and y data -z_ = -1/c*(a*x_ + b*y_ + d); % Solve for z data -surf(x_,y_,z_, 'EdgeColor', 'none', 'FaceColor', [0,0,0],... - 'FaceLighting', 'flat',... - 'FaceAlpha', 0.3); - -xlim([-1 1]) -ylim([-1 1]) -zlim([-1 1]) -lightangle(azim,elev); -daspect([1,1,1]); -camlight -grid on -view(20,20) - -set(gca, 'XTickLabel', []) -set(gca, 'YTickLabel', []) -set(gca, 'ZTickLabel', []) - -print('tuning', '-dpng', '-r300'); - - -save('mydata', "A","B") - - -function d = can_distance(X, Y) - global Rhom - Z = mod(X - Y,1); - Z = Rhom(:,[1; 3])*Z; - n1 = vecnorm(Z - Rhom(:,1), 2, 1); - n2 = vecnorm(Z - Rhom(:,2), 2, 1); - n3 = vecnorm(Z - Rhom(:,3), 2, 1); - n4 = vecnorm(Z - Rhom(:,4), 2, 1); - D = vertcat(n1,n2,n3,n4); - d = min(D,[],1); -end - - -function g = normalize(f) - g_ = f - min(f,[],'all'); - g_ = g_./max(g_, [],'all'); - g = 1 - g_; -end - -function M=RandOrthMat(n, tol) -% M = RANDORTHMAT(n) -% generates a random n x n orthogonal real matrix. -% -% M = RANDORTHMAT(n,tol) -% explicitly specifies a thresh value that measures linear dependence 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-B([1;2],[1;2]) = Rhom(:,[1; 3]); -B(:,3) = [0;0;1]; -% B([1;2],3) = randn(2,1); -% B(3,3)=1; - - - -A = inv(B); - -A1 = 1.2*A(1:2,:)*RandOrthMat(3); - -% B = zeros(3,3); -% B([1;2],[1;2]) = Rhom(:,[1; 3]); -% % B(:,3) = [0;0;1]; -% B([1;2],3) = randn(2,1); -% B(3,3)=1; - - - -A = inv(B); - -A2 = 1.*A(1:2,:)*RandOrthMat(3); - - - -r = pi/2.; -% A = [cos(r) sin(r); -sin(r) cos(r)]*A; - - - - -f1 = can_distance(A1*X, zeros(2,size(X,2)) ); -f2 = can_distance(A2*X, zeros(2,size(X,2)) ); - -f1 = reshape(f1, sz); -f2 = reshape(f2, sz); - -% f1 = normalize(f1); -% f2 = normalize(f2); - -f1 = exp(-f1.^2/.03); -f2 = exp(-f2.^2); -clf; - - -g = f1.*f2; - -colormap jet - - -thresh=0.2; - - -subplot(1,3,1); - - -a=.5; b=-.0;c=1;d=0; - -[x_ y_] = meshgrid(-1:0.1:1); % Generate x and y data -z_ = -1/c*(a*x_ + b*y_ + d); % Solve for z data -h =slice(x,y,z,f1,x_,y_,z_, 'linear') -set(h,'edgecolor','none') - -isosurface(x, y, z, f1, thresh); -isocaps(x, y, z, f1, thresh, 'above'); -xlim([-1 1]) -ylim([-1 1]) -zlim([-1 1]) -azim = 0; -elev = 45; -lightangle(azim,elev); -daspect([1,1,1]); -camlight -lighting gouraud -grid on -view(20,20) -set(gca, 'XTickLabel', []) -set(gca, 'YTickLabel', []) -set(gca, 'ZTickLabel', []) - - - - - - - - - -subplot(1,3,2); -isosurface(x, y, z, f2, thresh); -isocaps(x, y, z, f2, thresh, 'above'); - -xlim([-1 1]) -ylim([-1 1]) -zlim([-1 1]) -azim = 0; -elev = 45; -lightangle(azim,elev); -daspect([1,1,1]); -camlight -lighting gouraud -grid on -view(20,20) -set(gca, 'XTickLabel', []) -set(gca, 'YTickLabel', []) -set(gca, 'ZTickLabel', []) - - - -subplot(1,3,3); - -gthresh=0.96; -% for n = 1:4 -% isosurface(x, y, z,g, gthresh + n*0.01); -% -% end -isosurface(x, y, z,g, gthresh ); - -isocaps(x, y, z, g, gthresh, 'above'); -alpha(1.); - -view(20,20) - -xlim([-1 1]) -ylim([-1 1]) -zlim([-1 1]) -azim = 0; -elev = 45; -lightangle(azim,elev); -daspect([1,1,1]); -camlight -lighting gouraud -grid on; -xslice= []; -yslice= []; -zslice= []; -yslice = [0.]; - -% contourslice(x,y,z,g,xslice,yslice,zslice) - - -set(gca, 'XTickLabel', []) -set(gca, 'YTickLabel', []) -set(gca, 'ZTickLabel', []) -print('tuning', '-dpng', '-r300'); - -% figure(2) -% -% -% pr = reshape(exp(-f1).*exp(-f2)./sum(exp(-f1).*exp(-f2)),1, []); -% % pr = reshape( (f1+f2)./sum(f1+f2),1, []); -% plot(pr); -% xlim([0 size(pr,2)]) -% box off; -% -% fig = gcf; -% fig.PaperUnits = 'inches'; -% fig.PaperPosition = [0 0 3 2]; -% % set(gcf, 'PaperSize', [2 1]); -% set(gca,'FontSize',12) -% set(gca,'xtick',[]) -% set(gca,'xticklabel',[]) -% set(gca,'ytick',[]) -% set(gca,'yticklabel',[]) -% -% -% xlabel('Position') -% ylabel('Pr') - -print('pr','-dpng','-r0') - - - - - -function d = can_distance(X, Y) - global Rhom - Z = mod(X - Y,1); - Z = Rhom(:,[1; 3])*Z; - n1 = vecnorm(Z - Rhom(:,1), 2, 1); - n2 = vecnorm(Z - Rhom(:,2), 2, 1); - n3 = vecnorm(Z - Rhom(:,3), 2, 1); - n4 = vecnorm(Z - Rhom(:,4), 2, 1); - D = vertcat(n1,n2,n3,n4); - d = min(D,[],1); -end - - -function g = normalize(f) - g_ = f - min(f,[],'all'); - g_ = g_./max(g_, [],'all'); - g = 1 - g_; -end - -function M=RandOrthMat(n, tol) -% M = RANDORTHMAT(n) -% generates a random n x n orthogonal real matrix. -% -% M = RANDORTHMAT(n,tol) -% explicitly specifies a thresh value that measures linear dependence -% of a newly formed column with the existing columns. Defaults to 1e-6. -% -% In this version the generated matrix distribution *is* uniform over the manifold -% O(n) w.r.t. the induced R^(n^2) Lebesgue measure, at a slight computational -% overhead (randn + normalization, as opposed to rand ). -% -% (c) Ofek Shilon , 2006. - if nargin==1 - tol=1e-6; - end - - M = zeros(n); % prealloc - - % gram-schmidt on random column vectors - - vi = randn(n,1); - % the n-dimensional normal distribution has spherical symmetry, which implies - % that after normalization the drawn vectors would be uniformly distributed on the - % n-dimensional unit sphere. - M(:,1) = vi ./ norm(vi); - - for i=2:n - nrm = 0; - while nrm;4b-H!G0gtV2#_=9#^p{p>yO4fQpduCQI9qM~Bbdj8ai zis~{a6&2msB^uyLv-+)1z}sc7=a#-yRAM}Tf2aeYs{X)5dOt0_XY}(lS1&%2!N?-G zflIu8&n*0mJ)QjmUivsu={+{lef&h^u8FJDUA>onuI8RTZoVRSwIB{+N*07W!2S3C z-mmWC^wRIOC*-clYY!)?N0Oo%POn5I9zK%4EAdD{N?t))%4o^~MMZU&O6%!klfaw} zLfB^l>G8}lHtdULLYKocncAWU_#bz=y>E6($GolST6$@HslB%W%4?`~q4~2IZ;mJ- 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