diff options
Diffstat (limited to 'docs/source/auto_examples/plot_OT_2D_samples.rst')
| -rw-r--r-- | docs/source/auto_examples/plot_OT_2D_samples.rst | 172 |
1 files changed, 116 insertions, 56 deletions
diff --git a/docs/source/auto_examples/plot_OT_2D_samples.rst b/docs/source/auto_examples/plot_OT_2D_samples.rst index e05e591..5565c54 100644 --- a/docs/source/auto_examples/plot_OT_2D_samples.rst +++ b/docs/source/auto_examples/plot_OT_2D_samples.rst @@ -7,131 +7,191 @@ 2D Optimal transport between empirical distributions ==================================================== -@author: rflamary +Illustration of 2D optimal transport between discributions that are weighted +sum of diracs. The OT matrix is plotted with the samples. -.. rst-class:: sphx-glr-horizontal +.. code-block:: python - * + # Author: Remi Flamary <remi.flamary@unice.fr> + # + # License: MIT License - .. image:: /auto_examples/images/sphx_glr_plot_OT_2D_samples_001.png - :scale: 47 + import numpy as np + import matplotlib.pylab as pl + import ot - * - .. image:: /auto_examples/images/sphx_glr_plot_OT_2D_samples_002.png - :scale: 47 - * - .. image:: /auto_examples/images/sphx_glr_plot_OT_2D_samples_003.png - :scale: 47 - * - .. image:: /auto_examples/images/sphx_glr_plot_OT_2D_samples_004.png - :scale: 47 - * +Generate data +------------- - .. image:: /auto_examples/images/sphx_glr_plot_OT_2D_samples_005.png - :scale: 47 - * - .. image:: /auto_examples/images/sphx_glr_plot_OT_2D_samples_006.png - :scale: 47 +.. code-block:: python -.. rst-class:: sphx-glr-script-out + #%% parameters and data generation - Out:: + n = 50 # nb samples - ('Warning: numerical errors at iteration', 0) + 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 = np.ones((n,)) / n, np.ones((n,)) / n # uniform distribution on samples -| + # loss matrix + M = ot.dist(xs, xt) + M /= M.max() -.. code-block:: python - import numpy as np - import matplotlib.pylab as pl - import ot - #%% parameters and data generation - n=50 # nb samples - mu_s=np.array([0,0]) - cov_s=np.array([[1,0],[0,1]]) +Plot data +--------- - 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 +.. code-block:: python - # 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.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.title('Source and target distributions') pl.figure(2) - pl.imshow(M,interpolation='nearest') + pl.imshow(M, interpolation='nearest') pl.title('Cost matrix M') + + +.. rst-class:: sphx-glr-horizontal + + + * + + .. image:: /auto_examples/images/sphx_glr_plot_OT_2D_samples_001.png + :scale: 47 + + * + + .. image:: /auto_examples/images/sphx_glr_plot_OT_2D_samples_002.png + :scale: 47 + + + + +Compute EMD +----------- + + + +.. code-block:: python + + #%% EMD - G0=ot.emd(a,b,M) + G0 = ot.emd(a, b, M) pl.figure(3) - pl.imshow(G0,interpolation='nearest') + 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') + 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') + + + +.. rst-class:: sphx-glr-horizontal + + + * + + .. image:: /auto_examples/images/sphx_glr_plot_OT_2D_samples_005.png + :scale: 47 + + * + + .. image:: /auto_examples/images/sphx_glr_plot_OT_2D_samples_006.png + :scale: 47 + + + + +Compute Sinkhorn +---------------- + + + +.. code-block:: python + + #%% sinkhorn # reg term - lambd=5e-4 + lambd = 1e-3 - Gs=ot.sinkhorn(a,b,M,lambd) + Gs = ot.sinkhorn(a, b, M, lambd) pl.figure(5) - pl.imshow(Gs,interpolation='nearest') + 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') + 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') -**Total running time of the script:** ( 0 minutes 0.623 seconds) + pl.show() + + + +.. rst-class:: sphx-glr-horizontal + + + * + + .. image:: /auto_examples/images/sphx_glr_plot_OT_2D_samples_009.png + :scale: 47 + + * + + .. image:: /auto_examples/images/sphx_glr_plot_OT_2D_samples_010.png + :scale: 47 + + + + +**Total running time of the script:** ( 0 minutes 3.380 seconds) |