add doc for gallery

Author: rflamary

docs/source/auto_examples/auto_examples_jupyter.zip

@@ -0,0 +1,54 @@
+{
+  "nbformat_minor": 0, 
+  "nbformat": 4, 
+  "cells": [
+    {
+      "execution_count": null, 
+      "cell_type": "code", 
+      "source": [
+        "%matplotlib inline"
+      ], 
+      "outputs": [], 
+      "metadata": {
+        "collapsed": false
+      }
+    }, 
+    {
+      "source": [
+        "\nDemo for 1D optimal transport\n\n@author: rflamary\n\n"
+      ], 
+      "cell_type": "markdown", 
+      "metadata": {}
+    }, 
+    {
+      "execution_count": null, 
+      "cell_type": "code", 
+      "source": [
+        "import numpy as np\nimport matplotlib.pylab as pl\nimport ot\nfrom ot.datasets import get_1D_gauss as gauss\n\n\n#%% parameters\n\nn=100 # nb bins\n\n# bin positions\nx=np.arange(n,dtype=np.float64)\n\n# Gaussian distributions\na=gauss(n,m=n*.2,s=5) # m= mean, s= std\nb=gauss(n,m=n*.6,s=10)\n\n# loss matrix\nM=ot.dist(x.reshape((n,1)),x.reshape((n,1)))\nM/=M.max()\n\n#%% plot the distributions\n\npl.figure(1)\npl.plot(x,a,'b',label='Source distribution')\npl.plot(x,b,'r',label='Target distribution')\npl.legend()\n\n#%% plot distributions and loss matrix\n\npl.figure(2)\not.plot.plot1D_mat(a,b,M,'Cost matrix M')\n\n#%% EMD\n\nG0=ot.emd(a,b,M)\n\npl.figure(3)\not.plot.plot1D_mat(a,b,G0,'OT matrix G0')\n\n#%% Sinkhorn\n\nlambd=1e-3\nGs=ot.sinkhorn(a,b,M,lambd,verbose=True)\n\npl.figure(4)\not.plot.plot1D_mat(a,b,Gs,'OT matrix Sinkhorn')\n\n#%% Sinkhorn\n\nlambd=1e-4\nGss,log=ot.bregman.sinkhorn_stabilized(a,b,M,lambd,verbose=True,log=True)\nGss2,log2=ot.bregman.sinkhorn_stabilized(a,b,M,lambd,verbose=True,log=True,warmstart=log['warmstart'])\n\npl.figure(5)\not.plot.plot1D_mat(a,b,Gss,'OT matrix Sinkhorn stabilized')\n\n#%% Sinkhorn\n\nlambd=1e-11\nGss=ot.bregman.sinkhorn_epsilon_scaling(a,b,M,lambd,verbose=True)\n\npl.figure(5)\not.plot.plot1D_mat(a,b,Gss,'OT matrix Sinkhorn stabilized')"
+      ], 
+      "outputs": [], 
+      "metadata": {
+        "collapsed": false
+      }
+    }
+  ], 
+  "metadata": {
+    "kernelspec": {
+      "display_name": "Python 2", 
+      "name": "python2", 
+      "language": "python"
+    }, 
+    "language_info": {
+      "mimetype": "text/x-python", 
+      "nbconvert_exporter": "python", 
+      "name": "python", 
+      "file_extension": ".py", 
+      "version": "2.7.12", 
+      "pygments_lexer": "ipython2", 
+      "codemirror_mode": {
+        "version": 2, 
+        "name": "ipython"
+      }
+    }
+  }
+}

docs/source/auto_examples/auto_examples_python.zip

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+# -*- coding: utf-8 -*-
+"""
+Demo for 1D optimal transport
+
+@author: rflamary
+"""
+
+import numpy as np
+import matplotlib.pylab as pl
+import ot
+from ot.datasets import get_1D_gauss as gauss
+
+
+#%% parameters
+
+n=100 # nb bins
+
+# bin positions
+x=np.arange(n,dtype=np.float64)
+
+# Gaussian distributions
+a=gauss(n,m=n*.2,s=5) # m= mean, s= std
+b=gauss(n,m=n*.6,s=10)
+
+# loss matrix
+M=ot.dist(x.reshape((n,1)),x.reshape((n,1)))
+M/=M.max()
+
+#%% plot the distributions
+
+pl.figure(1)
+pl.plot(x,a,'b',label='Source distribution')
+pl.plot(x,b,'r',label='Target distribution')
+pl.legend()
+
+#%% plot distributions and loss matrix
+
+pl.figure(2)
+ot.plot.plot1D_mat(a,b,M,'Cost matrix M')
+
+#%% EMD
+
+G0=ot.emd(a,b,M)
+
+pl.figure(3)
+ot.plot.plot1D_mat(a,b,G0,'OT matrix G0')
+
+#%% Sinkhorn
+
+lambd=1e-3
+Gs=ot.sinkhorn(a,b,M,lambd,verbose=True)
+
+pl.figure(4)
+ot.plot.plot1D_mat(a,b,Gs,'OT matrix Sinkhorn')
+
+#%% Sinkhorn
+
+lambd=1e-4
+Gss,log=ot.bregman.sinkhorn_stabilized(a,b,M,lambd,verbose=True,log=True)
+Gss2,log2=ot.bregman.sinkhorn_stabilized(a,b,M,lambd,verbose=True,log=True,warmstart=log['warmstart'])
+
+pl.figure(5)
+ot.plot.plot1D_mat(a,b,Gss,'OT matrix Sinkhorn stabilized')
+
+#%% Sinkhorn
+
+lambd=1e-11
+Gss=ot.bregman.sinkhorn_epsilon_scaling(a,b,M,lambd,verbose=True)
+
+pl.figure(5)
+ot.plot.plot1D_mat(a,b,Gss,'OT matrix Sinkhorn stabilized')

docs/source/auto_examples/demo_OT_1D_test.ipynb

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+
+
+.. _sphx_glr_auto_examples_demo_OT_1D_test.py:
+
+
+Demo for 1D optimal transport
+
+@author: rflamary
+
+
+
+.. code-block:: python
+
+
+    import numpy as np
+    import matplotlib.pylab as pl
+    import ot
+    from ot.datasets import get_1D_gauss as gauss
+
+
+    #%% parameters
+
+    n=100 # nb bins
+
+    # bin positions
+    x=np.arange(n,dtype=np.float64)
+
+    # Gaussian distributions
+    a=gauss(n,m=n*.2,s=5) # m= mean, s= std
+    b=gauss(n,m=n*.6,s=10)
+
+    # loss matrix
+    M=ot.dist(x.reshape((n,1)),x.reshape((n,1)))
+    M/=M.max()
+
+    #%% plot the distributions
+
+    pl.figure(1)
+    pl.plot(x,a,'b',label='Source distribution')
+    pl.plot(x,b,'r',label='Target distribution')
+    pl.legend()
+
+    #%% plot distributions and loss matrix
+
+    pl.figure(2)
+    ot.plot.plot1D_mat(a,b,M,'Cost matrix M')
+
+    #%% EMD
+
+    G0=ot.emd(a,b,M)
+
+    pl.figure(3)
+    ot.plot.plot1D_mat(a,b,G0,'OT matrix G0')
+
+    #%% Sinkhorn
+
+    lambd=1e-3
+    Gs=ot.sinkhorn(a,b,M,lambd,verbose=True)
+
+    pl.figure(4)
+    ot.plot.plot1D_mat(a,b,Gs,'OT matrix Sinkhorn')
+
+    #%% Sinkhorn
+
+    lambd=1e-4
+    Gss,log=ot.bregman.sinkhorn_stabilized(a,b,M,lambd,verbose=True,log=True)
+    Gss2,log2=ot.bregman.sinkhorn_stabilized(a,b,M,lambd,verbose=True,log=True,warmstart=log['warmstart'])
+
+    pl.figure(5)
+    ot.plot.plot1D_mat(a,b,Gss,'OT matrix Sinkhorn stabilized')
+
+    #%% Sinkhorn
+
+    lambd=1e-11
+    Gss=ot.bregman.sinkhorn_epsilon_scaling(a,b,M,lambd,verbose=True)
+
+    pl.figure(5)
+    ot.plot.plot1D_mat(a,b,Gss,'OT matrix Sinkhorn stabilized')
+
+**Total running time of the script:** ( 0 minutes  0.000 seconds)
+
+
+
+.. container:: sphx-glr-footer
+
+
+  .. container:: sphx-glr-download
+
+     :download:`Download Python source code: demo_OT_1D_test.py <demo_OT_1D_test.py>`
+
+
+
+  .. container:: sphx-glr-download
+
+     :download:`Download Jupyter notebook: demo_OT_1D_test.ipynb <demo_OT_1D_test.ipynb>`
+
+.. rst-class:: sphx-glr-signature
+
+    `Generated by Sphinx-Gallery <http://sphinx-gallery.readthedocs.io>`_

docs/source/auto_examples/demo_OT_1D_test.py

@@ -0,0 +1,54 @@
+{
+  "nbformat_minor": 0, 
+  "nbformat": 4, 
+  "cells": [
+    {
+      "execution_count": null, 
+      "cell_type": "code", 
+      "source": [
+        "%matplotlib inline"
+      ], 
+      "outputs": [], 
+      "metadata": {
+        "collapsed": false
+      }
+    }, 
+    {
+      "source": [
+        "\nDemo for 2D Optimal transport between empirical distributions\n\n@author: rflamary\n\n"
+      ], 
+      "cell_type": "markdown", 
+      "metadata": {}
+    }, 
+    {
+      "execution_count": null, 
+      "cell_type": "code", 
+      "source": [
+        "import numpy as np\nimport matplotlib.pylab as pl\nimport ot\n\n#%% parameters and data generation\n\nn=5000 # nb samples\n\nmu_s=np.array([0,0])\ncov_s=np.array([[1,0],[0,1]])\n\nmu_t=np.array([4,4])\ncov_t=np.array([[1,-.8],[-.8,1]])\n\nxs=ot.datasets.get_2D_samples_gauss(n,mu_s,cov_s)\nxt=ot.datasets.get_2D_samples_gauss(n,mu_t,cov_t)\n\na,b = ot.unif(n),ot.unif(n) # uniform distribution on samples\n\n# loss matrix\nM=ot.dist(xs,xt)\nM/=M.max()\n\n#%% plot samples\n\n#pl.figure(1)\n#pl.plot(xs[:,0],xs[:,1],'+b',label='Source samples')\n#pl.plot(xt[:,0],xt[:,1],'xr',label='Target samples')\n#pl.legend(loc=0)\n#pl.title('Source and traget distributions')\n#\n#pl.figure(2)\n#pl.imshow(M,interpolation='nearest')\n#pl.title('Cost matrix M')\n#\n\n#%% EMD\n\nG0=ot.emd(a,b,M)\n\n#pl.figure(3)\n#pl.imshow(G0,interpolation='nearest')\n#pl.title('OT matrix G0')\n#\n#pl.figure(4)\n#ot.plot.plot2D_samples_mat(xs,xt,G0,c=[.5,.5,1])\n#pl.plot(xs[:,0],xs[:,1],'+b',label='Source samples')\n#pl.plot(xt[:,0],xt[:,1],'xr',label='Target samples')\n#pl.legend(loc=0)\n#pl.title('OT matrix with samples')\n\n\n#%% sinkhorn\n\n# reg term\nlambd=5e-3\n\nGs=ot.sinkhorn(a,b,M,lambd)\n\n#pl.figure(5)\n#pl.imshow(Gs,interpolation='nearest')\n#pl.title('OT matrix sinkhorn')\n#\n#pl.figure(6)\n#ot.plot.plot2D_samples_mat(xs,xt,Gs,color=[.5,.5,1])\n#pl.plot(xs[:,0],xs[:,1],'+b',label='Source samples')\n#pl.plot(xt[:,0],xt[:,1],'xr',label='Target samples')\n#pl.legend(loc=0)\n#pl.title('OT matrix Sinkhorn with samples')\n#"
+      ], 
+      "outputs": [], 
+      "metadata": {
+        "collapsed": false
+      }
+    }
+  ], 
+  "metadata": {
+    "kernelspec": {
+      "display_name": "Python 2", 
+      "name": "python2", 
+      "language": "python"
+    }, 
+    "language_info": {
+      "mimetype": "text/x-python", 
+      "nbconvert_exporter": "python", 
+      "name": "python", 
+      "file_extension": ".py", 
+      "version": "2.7.12", 
+      "pygments_lexer": "ipython2", 
+      "codemirror_mode": {
+        "version": 2, 
+        "name": "ipython"
+      }
+    }
+  }
+}

docs/source/auto_examples/demo_OT_1D_test.rst

@@ -0,0 +1,78 @@
+# -*- coding: utf-8 -*-
+"""
+Demo for 2D Optimal transport between empirical distributions
+
+@author: rflamary
+"""
+
+import numpy as np
+import matplotlib.pylab as pl
+import ot
+
+#%% parameters and data generation
+
+n=5000 # nb samples
+
+mu_s=np.array([0,0])
+cov_s=np.array([[1,0],[0,1]])
+
+mu_t=np.array([4,4])
+cov_t=np.array([[1,-.8],[-.8,1]])
+
+xs=ot.datasets.get_2D_samples_gauss(n,mu_s,cov_s)
+xt=ot.datasets.get_2D_samples_gauss(n,mu_t,cov_t)
+
+a,b = ot.unif(n),ot.unif(n) # uniform distribution on samples
+
+# loss matrix
+M=ot.dist(xs,xt)
+M/=M.max()
+
+#%% plot samples
+
+#pl.figure(1)
+#pl.plot(xs[:,0],xs[:,1],'+b',label='Source samples')
+#pl.plot(xt[:,0],xt[:,1],'xr',label='Target samples')
+#pl.legend(loc=0)
+#pl.title('Source and traget distributions')
+#
+#pl.figure(2)
+#pl.imshow(M,interpolation='nearest')
+#pl.title('Cost matrix M')
+#
+
+#%% EMD
+
+G0=ot.emd(a,b,M)
+
+#pl.figure(3)
+#pl.imshow(G0,interpolation='nearest')
+#pl.title('OT matrix G0')
+#
+#pl.figure(4)
+#ot.plot.plot2D_samples_mat(xs,xt,G0,c=[.5,.5,1])
+#pl.plot(xs[:,0],xs[:,1],'+b',label='Source samples')
+#pl.plot(xt[:,0],xt[:,1],'xr',label='Target samples')
+#pl.legend(loc=0)
+#pl.title('OT matrix with samples')
+
+
+#%% sinkhorn
+
+# reg term
+lambd=5e-3
+
+Gs=ot.sinkhorn(a,b,M,lambd)
+
+#pl.figure(5)
+#pl.imshow(Gs,interpolation='nearest')
+#pl.title('OT matrix sinkhorn')
+#
+#pl.figure(6)
+#ot.plot.plot2D_samples_mat(xs,xt,Gs,color=[.5,.5,1])
+#pl.plot(xs[:,0],xs[:,1],'+b',label='Source samples')
+#pl.plot(xt[:,0],xt[:,1],'xr',label='Target samples')
+#pl.legend(loc=0)
+#pl.title('OT matrix Sinkhorn with samples')
+#
+