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"\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"
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"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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