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Diffstat (limited to 'docs/source/auto_examples/plot_OT_1D.rst')
| -rw-r--r-- | docs/source/auto_examples/plot_OT_1D.rst | 173 |
1 files changed, 116 insertions, 57 deletions
diff --git a/docs/source/auto_examples/plot_OT_1D.rst b/docs/source/auto_examples/plot_OT_1D.rst index 44b715b..975a923 100644 --- a/docs/source/auto_examples/plot_OT_1D.rst +++ b/docs/source/auto_examples/plot_OT_1D.rst @@ -7,7 +7,80 @@ 1D optimal transport ==================== -@author: rflamary +This example illustrates the computation of EMD and Sinkhorn transport plans +and their visualization. + + + + +.. code-block:: python + + + # Author: Remi Flamary <remi.flamary@unice.fr> + # + # License: MIT License + + import numpy as np + import matplotlib.pylab as pl + import ot + from ot.datasets import get_1D_gauss as gauss + + + + + + + +Generate data +------------- + + + +.. code-block:: python + + + + #%% parameters + + n = 100 # nb bins + + # bin positions + x = np.arange(n, dtype=np.float64) + + # Gaussian distributions + a = gauss(n, m=20, s=5) # m= mean, s= std + b = gauss(n, m=60, s=10) + + # loss matrix + M = ot.dist(x.reshape((n, 1)), x.reshape((n, 1))) + M /= M.max() + + + + + + + + +Plot distributions and loss matrix +---------------------------------- + + + +.. code-block:: python + + + #%% plot the distributions + + pl.figure(1, figsize=(6.4, 3)) + 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, figsize=(5, 5)) + ot.plot.plot1D_mat(a, b, M, 'Cost matrix M') @@ -25,94 +98,80 @@ .. image:: /auto_examples/images/sphx_glr_plot_OT_1D_002.png :scale: 47 - * - .. image:: /auto_examples/images/sphx_glr_plot_OT_1D_003.png - :scale: 47 - * - .. image:: /auto_examples/images/sphx_glr_plot_OT_1D_004.png - :scale: 47 +Solve EMD +--------- -.. rst-class:: sphx-glr-script-out - Out:: +.. code-block:: python - It. |Err - ------------------- - 0|8.187970e-02| - 10|3.460174e-02| - 20|6.633335e-03| - 30|9.797798e-04| - 40|1.389606e-04| - 50|1.959016e-05| - 60|2.759079e-06| - 70|3.885166e-07| - 80|5.470605e-08| - 90|7.702918e-09| - 100|1.084609e-09| - 110|1.527180e-10| + #%% EMD + G0 = ot.emd(a, b, M) -| + pl.figure(3, figsize=(5, 5)) + ot.plot.plot1D_mat(a, b, G0, 'OT matrix G0') -.. code-block:: python - import numpy as np - import matplotlib.pylab as pl - import ot - from ot.datasets import get_1D_gauss as gauss +.. image:: /auto_examples/images/sphx_glr_plot_OT_1D_005.png + :align: center - #%% parameters - n=100 # nb bins - # bin positions - x=np.arange(n,dtype=np.float64) +Solve Sinkhorn +-------------- - # Gaussian distributions - a=gauss(n,m=20,s=5) # m= mean, s= std - b=gauss(n,m=60,s=10) - # loss matrix - M=ot.dist(x.reshape((n,1)),x.reshape((n,1))) - M/=M.max() - #%% plot the distributions +.. code-block:: python - 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') + #%% Sinkhorn - #%% EMD + lambd = 1e-3 + Gs = ot.sinkhorn(a, b, M, lambd, verbose=True) - G0=ot.emd(a,b,M) + pl.figure(4, figsize=(5, 5)) + ot.plot.plot1D_mat(a, b, Gs, 'OT matrix Sinkhorn') - pl.figure(3) - ot.plot.plot1D_mat(a,b,G0,'OT matrix G0') + pl.show() - #%% 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') +.. image:: /auto_examples/images/sphx_glr_plot_OT_1D_007.png + :align: center + + +.. rst-class:: sphx-glr-script-out + + Out:: + + It. |Err + ------------------- + 0|8.187970e-02| + 10|3.460174e-02| + 20|6.633335e-03| + 30|9.797798e-04| + 40|1.389606e-04| + 50|1.959016e-05| + 60|2.759079e-06| + 70|3.885166e-07| + 80|5.470605e-08| + 90|7.702918e-09| + 100|1.084609e-09| + 110|1.527180e-10| + -**Total running time of the script:** ( 0 minutes 0.674 seconds) +**Total running time of the script:** ( 0 minutes 1.198 seconds) |