{
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    {
      "execution_count": null, 
      "cell_type": "code", 
      "source": [
        "%matplotlib inline"
      ], 
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      "source": [
        "\n# 2D Optimal transport for different metrics\n\n\nStole the figure idea from Fig. 1 and 2 in \nhttps://arxiv.org/pdf/1706.07650.pdf\n\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\nfor data in range(2):\n\n    if data:\n        n=20 # nb samples\n        xs=np.zeros((n,2))\n        xs[:,0]=np.arange(n)+1\n        xs[:,1]=(np.arange(n)+1)*-0.001 # to make it strictly convex...\n        \n        xt=np.zeros((n,2))\n        xt[:,1]=np.arange(n)+1\n    else:\n        \n        n=50 # nb samples\n        xtot=np.zeros((n+1,2))\n        xtot[:,0]=np.cos((np.arange(n+1)+1.0)*0.9/(n+2)*2*np.pi)\n        xtot[:,1]=np.sin((np.arange(n+1)+1.0)*0.9/(n+2)*2*np.pi)\n        \n        xs=xtot[:n,:]\n        xt=xtot[1:,:]\n        \n        \n    \n    a,b = ot.unif(n),ot.unif(n) # uniform distribution on samples\n    \n    # loss matrix\n    M1=ot.dist(xs,xt,metric='euclidean')\n    M1/=M1.max()\n    \n    # loss matrix\n    M2=ot.dist(xs,xt,metric='sqeuclidean')\n    M2/=M2.max()\n    \n    # loss matrix\n    Mp=np.sqrt(ot.dist(xs,xt,metric='euclidean'))\n    Mp/=Mp.max()\n    \n    #%% plot samples\n    \n    pl.figure(1+3*data)\n    pl.clf()\n    pl.plot(xs[:,0],xs[:,1],'+b',label='Source samples')\n    pl.plot(xt[:,0],xt[:,1],'xr',label='Target samples')\n    pl.axis('equal')\n    pl.title('Source and traget distributions')\n    \n    pl.figure(2+3*data,(15,5))\n    pl.subplot(1,3,1)\n    pl.imshow(M1,interpolation='nearest')\n    pl.title('Eucidean cost')\n    pl.subplot(1,3,2)\n    pl.imshow(M2,interpolation='nearest')\n    pl.title('Squared Euclidean cost')\n    \n    pl.subplot(1,3,3)\n    pl.imshow(Mp,interpolation='nearest')\n    pl.title('Sqrt Euclidean cost')\n    #%% EMD\n    \n    G1=ot.emd(a,b,M1)\n    G2=ot.emd(a,b,M2)\n    Gp=ot.emd(a,b,Mp)\n    \n    pl.figure(3+3*data,(15,5))\n    \n    pl.subplot(1,3,1)\n    ot.plot.plot2D_samples_mat(xs,xt,G1,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.axis('equal')\n    #pl.legend(loc=0)\n    pl.title('OT Euclidean')\n    \n    pl.subplot(1,3,2)\n    \n    ot.plot.plot2D_samples_mat(xs,xt,G2,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.axis('equal')\n    #pl.legend(loc=0)\n    pl.title('OT squared Euclidean')\n    \n    pl.subplot(1,3,3)\n    \n    ot.plot.plot2D_samples_mat(xs,xt,Gp,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.axis('equal')\n    #pl.legend(loc=0)\n    pl.title('OT sqrt Euclidean')"
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