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‎master/_downloads/07fcc19ba03226cd3d83d4e40ec44385/auto_examples_python.zip

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‎master/_downloads/8ef8fd4d251060babb7f94a1610a6880/plot_solve_variants.ipynb

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{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"\n# Optimal Transport solvers comparison\n\nThis example illustrates the solutions returns for diffrent variants of exact,\nregularized and unbalanced OT solvers.\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"# Author: Remi Flamary <[email protected]>\n#\n# License: MIT License\n# sphinx_gallery_thumbnail_number = 3"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"import numpy as np\nimport matplotlib.pylab as pl\nimport ot\nimport ot.plot\nfrom ot.datasets import make_1D_gauss as gauss"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Generate data\n\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"n = 50 # nb bins\n\n# bin positions\nx = np.arange(n, dtype=np.float64)\n\n# Gaussian distributions\na = 0.6 * gauss(n, m=15, s=5) + 0.4 * gauss(n, m=35, s=5) # m= mean, s= std\nb = gauss(n, m=25, s=5)\n\n# loss matrix\nM = ot.dist(x.reshape((n, 1)), x.reshape((n, 1)))\nM /= M.max()"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Plot distributions and loss matrix\n\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"pl.figure(1, figsize=(6.4, 3))\npl.plot(x, a, 'b', label='Source distribution')\npl.plot(x, b, 'r', label='Target distribution')\npl.legend()"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"pl.figure(2, figsize=(5, 5))\not.plot.plot1D_mat(a, b, M, 'Cost matrix M')"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Define Group lasso regularization and gradient\nThe groups are the first and second half of the columns of G\n\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"def reg_gl(G): # group lasso + small l2 reg\n G1 = G[:n // 2, :]**2\n G2 = G[n // 2:, :]**2\n gl1 = np.sum(np.sqrt(np.sum(G1, 0)))\n gl2 = np.sum(np.sqrt(np.sum(G2, 0)))\n return gl1 + gl2 + 0.1 * np.sum(G**2)\n\n\ndef grad_gl(G): # gradient of group lasso + small l2 reg\n G1 = G[:n // 2, :]\n G2 = G[n // 2:, :]\n gl1 = G1 / np.sqrt(np.sum(G1**2, 0, keepdims=True) + 1e-8)\n gl2 = G2 / np.sqrt(np.sum(G2**2, 0, keepdims=True) + 1e-8)\n return np.concatenate((gl1, gl2), axis=0) + 0.2 * G\n\n\nreg_type_gl = (reg_gl, grad_gl)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Set up parameters for solvers and solve\n\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"lst_regs = [\"No Reg.\", \"Entropic\", \"L2\", \"Group Lasso + L2\"]\nlst_unbalanced = [\"Balanced\", \"Unbalanced KL\", 'Unbalanced L2', 'Unb. TV (Partial)'] # [\"Balanced\", \"Unb. KL\", \"Unb. L2\", \"Unb L1 (partial)\"]\n\nlst_solvers = [ # name, param for ot.solve function\n # balanced OT\n ('Exact OT', dict()),\n ('Entropic Reg. OT', dict(reg=0.005)),\n ('L2 Reg OT', dict(reg=1, reg_type='l2')),\n ('Group Lasso Reg. OT', dict(reg=0.1, reg_type=reg_type_gl)),\n\n\n # unbalanced OT KL\n ('Unbalanced KL No Reg.', dict(unbalanced=0.005)),\n ('Unbalanced KL wit KL Reg.', dict(reg=0.0005, unbalanced=0.005, unbalanced_type='kl', reg_type='kl')),\n ('Unbalanced KL with L2 Reg.', dict(reg=0.5, reg_type='l2', unbalanced=0.005, unbalanced_type='kl')),\n ('Unbalanced KL with Group Lasso Reg.', dict(reg=0.1, reg_type=reg_type_gl, unbalanced=0.05, unbalanced_type='kl')),\n\n # unbalanced OT L2\n ('Unbalanced L2 No Reg.', dict(unbalanced=0.5, unbalanced_type='l2')),\n ('Unbalanced L2 with KL Reg.', dict(reg=0.001, unbalanced=0.2, unbalanced_type='l2')),\n ('Unbalanced L2 with L2 Reg.', dict(reg=0.1, reg_type='l2', unbalanced=0.2, unbalanced_type='l2')),\n ('Unbalanced L2 with Group Lasso Reg.', dict(reg=0.05, reg_type=reg_type_gl, unbalanced=0.7, unbalanced_type='l2')),\n\n # unbalanced OT TV\n ('Unbalanced TV No Reg.', dict(unbalanced=0.1, unbalanced_type='tv')),\n ('Unbalanced TV with KL Reg.', dict(reg=0.001, unbalanced=0.01, unbalanced_type='tv')),\n ('Unbalanced TV with L2 Reg.', dict(reg=0.1, reg_type='l2', unbalanced=0.01, unbalanced_type='tv')),\n ('Unbalanced TV with Group Lasso Reg.', dict(reg=0.02, reg_type=reg_type_gl, unbalanced=0.01, unbalanced_type='tv')),\n\n]\n\nlst_plans = []\nfor (name, param) in lst_solvers:\n G = ot.solve(M, a, b, **param).plan\n lst_plans.append(G)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Plot plans\n\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"pl.figure(3, figsize=(9, 9))\n\nfor i, bname in enumerate(lst_unbalanced):\n for j, rname in enumerate(lst_regs):\n pl.subplot(len(lst_unbalanced), len(lst_regs), i * len(lst_regs) + j + 1)\n\n plan = lst_plans[i * len(lst_regs) + j]\n m2 = plan.sum(0)\n m1 = plan.sum(1)\n m1, m2 = m1 / a.max(), m2 / b.max()\n pl.imshow(plan, cmap='Greys')\n pl.plot(x, m2 * 10, 'r')\n pl.plot(m1 * 10, x, 'b')\n pl.plot(x, b / b.max() * 10, 'r', alpha=0.3)\n pl.plot(a / a.max() * 10, x, 'b', alpha=0.3)\n #pl.axis('off')\n pl.tick_params(left=False, right=False, labelleft=False,\n labelbottom=False, bottom=False)\n if i == 0:\n pl.title(rname)\n if j == 0:\n pl.ylabel(bname, fontsize=14)"
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]
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.10.14"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 0
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}

‎master/_downloads/e0aaac1e7374a0c77ff58b5403e88b4e/plot_solve_variants.py

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# -*- coding: utf-8 -*-
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"""
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======================================
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Optimal Transport solvers comparison
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======================================
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This example illustrates the solutions returns for diffrent variants of exact,
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regularized and unbalanced OT solvers.
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"""
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# Author: Remi Flamary <[email protected]>
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#
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# License: MIT License
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# sphinx_gallery_thumbnail_number = 3
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#%%
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import numpy as np
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import matplotlib.pylab as pl
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import ot
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import ot.plot
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from ot.datasets import make_1D_gauss as gauss
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##############################################################################
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# Generate data
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# -------------
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#%% parameters
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n = 50 # nb bins
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# bin positions
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x = np.arange(n, dtype=np.float64)
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# Gaussian distributions
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a = 0.6 * gauss(n, m=15, s=5) + 0.4 * gauss(n, m=35, s=5) # m= mean, s= std
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b = gauss(n, m=25, s=5)
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# loss matrix
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M = ot.dist(x.reshape((n, 1)), x.reshape((n, 1)))
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M /= M.max()
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##############################################################################
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# Plot distributions and loss matrix
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# ----------------------------------
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#%% plot the distributions
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pl.figure(1, figsize=(6.4, 3))
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pl.plot(x, a, 'b', label='Source distribution')
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pl.plot(x, b, 'r', label='Target distribution')
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pl.legend()
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#%% plot distributions and loss matrix
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pl.figure(2, figsize=(5, 5))
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ot.plot.plot1D_mat(a, b, M, 'Cost matrix M')
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##############################################################################
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# Define Group lasso regularization and gradient
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# ------------------------------------------------
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# The groups are the first and second half of the columns of G
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def reg_gl(G): # group lasso + small l2 reg
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G1 = G[:n // 2, :]**2
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G2 = G[n // 2:, :]**2
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gl1 = np.sum(np.sqrt(np.sum(G1, 0)))
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gl2 = np.sum(np.sqrt(np.sum(G2, 0)))
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return gl1 + gl2 + 0.1 * np.sum(G**2)
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def grad_gl(G): # gradient of group lasso + small l2 reg
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G1 = G[:n // 2, :]
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G2 = G[n // 2:, :]
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gl1 = G1 / np.sqrt(np.sum(G1**2, 0, keepdims=True) + 1e-8)
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gl2 = G2 / np.sqrt(np.sum(G2**2, 0, keepdims=True) + 1e-8)
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return np.concatenate((gl1, gl2), axis=0) + 0.2 * G
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reg_type_gl = (reg_gl, grad_gl)
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# %%
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# Set up parameters for solvers and solve
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# ---------------------------------------
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lst_regs = ["No Reg.", "Entropic", "L2", "Group Lasso + L2"]
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lst_unbalanced = ["Balanced", "Unbalanced KL", 'Unbalanced L2', 'Unb. TV (Partial)'] # ["Balanced", "Unb. KL", "Unb. L2", "Unb L1 (partial)"]
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lst_solvers = [ # name, param for ot.solve function
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# balanced OT
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('Exact OT', dict()),
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('Entropic Reg. OT', dict(reg=0.005)),
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('L2 Reg OT', dict(reg=1, reg_type='l2')),
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('Group Lasso Reg. OT', dict(reg=0.1, reg_type=reg_type_gl)),
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# unbalanced OT KL
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('Unbalanced KL No Reg.', dict(unbalanced=0.005)),
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('Unbalanced KL wit KL Reg.', dict(reg=0.0005, unbalanced=0.005, unbalanced_type='kl', reg_type='kl')),
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('Unbalanced KL with L2 Reg.', dict(reg=0.5, reg_type='l2', unbalanced=0.005, unbalanced_type='kl')),
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('Unbalanced KL with Group Lasso Reg.', dict(reg=0.1, reg_type=reg_type_gl, unbalanced=0.05, unbalanced_type='kl')),
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# unbalanced OT L2
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('Unbalanced L2 No Reg.', dict(unbalanced=0.5, unbalanced_type='l2')),
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('Unbalanced L2 with KL Reg.', dict(reg=0.001, unbalanced=0.2, unbalanced_type='l2')),
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('Unbalanced L2 with L2 Reg.', dict(reg=0.1, reg_type='l2', unbalanced=0.2, unbalanced_type='l2')),
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('Unbalanced L2 with Group Lasso Reg.', dict(reg=0.05, reg_type=reg_type_gl, unbalanced=0.7, unbalanced_type='l2')),
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# unbalanced OT TV
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('Unbalanced TV No Reg.', dict(unbalanced=0.1, unbalanced_type='tv')),
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('Unbalanced TV with KL Reg.', dict(reg=0.001, unbalanced=0.01, unbalanced_type='tv')),
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('Unbalanced TV with L2 Reg.', dict(reg=0.1, reg_type='l2', unbalanced=0.01, unbalanced_type='tv')),
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('Unbalanced TV with Group Lasso Reg.', dict(reg=0.02, reg_type=reg_type_gl, unbalanced=0.01, unbalanced_type='tv')),
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]
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lst_plans = []
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for (name, param) in lst_solvers:
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G = ot.solve(M, a, b, **param).plan
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lst_plans.append(G)
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##############################################################################
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# Plot plans
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# ----------
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pl.figure(3, figsize=(9, 9))
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for i, bname in enumerate(lst_unbalanced):
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for j, rname in enumerate(lst_regs):
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pl.subplot(len(lst_unbalanced), len(lst_regs), i * len(lst_regs) + j + 1)
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plan = lst_plans[i * len(lst_regs) + j]
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m2 = plan.sum(0)
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m1 = plan.sum(1)
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m1, m2 = m1 / a.max(), m2 / b.max()
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pl.imshow(plan, cmap='Greys')
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pl.plot(x, m2 * 10, 'r')
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pl.plot(m1 * 10, x, 'b')
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pl.plot(x, b / b.max() * 10, 'r', alpha=0.3)
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pl.plot(a / a.max() * 10, x, 'b', alpha=0.3)
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#pl.axis('off')
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pl.tick_params(left=False, right=False, labelleft=False,
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labelbottom=False, bottom=False)
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if i == 0:
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pl.title(rname)
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if j == 0:
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pl.ylabel(bname, fontsize=14)

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0.9.4dev
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<title>ot.backend &mdash; POT Python Optimal Transport 0.9.4dev documentation</title>
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<link rel="stylesheet" type="text/css" href="../../_static/pygments.css?v=80d5e7a1" />
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