diff options
Diffstat (limited to 'docs/source/auto_examples/plot_OT_1D_smooth.rst')
-rw-r--r-- | docs/source/auto_examples/plot_OT_1D_smooth.rst | 242 |
1 files changed, 242 insertions, 0 deletions
diff --git a/docs/source/auto_examples/plot_OT_1D_smooth.rst b/docs/source/auto_examples/plot_OT_1D_smooth.rst new file mode 100644 index 0000000..5a0ebd3 --- /dev/null +++ b/docs/source/auto_examples/plot_OT_1D_smooth.rst @@ -0,0 +1,242 @@ + + +.. _sphx_glr_auto_examples_plot_OT_1D_smooth.py: + + +=========================== +1D smooth optimal transport +=========================== + +This example illustrates the computation of EMD, Sinkhorn and smooth OT 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 + import ot.plot + from ot.datasets import make_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') + + + + +.. rst-class:: sphx-glr-horizontal + + + * + + .. image:: /auto_examples/images/sphx_glr_plot_OT_1D_smooth_001.png + :scale: 47 + + * + + .. image:: /auto_examples/images/sphx_glr_plot_OT_1D_smooth_002.png + :scale: 47 + + + + +Solve EMD +--------- + + + +.. code-block:: python + + + + #%% EMD + + G0 = ot.emd(a, b, M) + + pl.figure(3, figsize=(5, 5)) + ot.plot.plot1D_mat(a, b, G0, 'OT matrix G0') + + + + +.. image:: /auto_examples/images/sphx_glr_plot_OT_1D_smooth_005.png + :align: center + + + + +Solve Sinkhorn +-------------- + + + +.. code-block:: python + + + + #%% Sinkhorn + + lambd = 2e-3 + Gs = ot.sinkhorn(a, b, M, lambd, verbose=True) + + pl.figure(4, figsize=(5, 5)) + ot.plot.plot1D_mat(a, b, Gs, 'OT matrix Sinkhorn') + + pl.show() + + + + +.. image:: /auto_examples/images/sphx_glr_plot_OT_1D_smooth_007.png + :align: center + + +.. rst-class:: sphx-glr-script-out + + Out:: + + It. |Err + ------------------- + 0|7.958844e-02| + 10|5.921715e-03| + 20|1.238266e-04| + 30|2.469780e-06| + 40|4.919966e-08| + 50|9.800197e-10| + + +Solve Smooth OT +-------------- + + + +.. code-block:: python + + + + #%% Smooth OT with KL regularization + + lambd = 2e-3 + Gsm = ot.smooth.smooth_ot_dual(a, b, M, lambd, reg_type='kl') + + pl.figure(5, figsize=(5, 5)) + ot.plot.plot1D_mat(a, b, Gsm, 'OT matrix Smooth OT KL reg.') + + pl.show() + + + #%% Smooth OT with KL regularization + + lambd = 1e-1 + Gsm = ot.smooth.smooth_ot_dual(a, b, M, lambd, reg_type='l2') + + pl.figure(6, figsize=(5, 5)) + ot.plot.plot1D_mat(a, b, Gsm, 'OT matrix Smooth OT l2 reg.') + + pl.show() + + + +.. rst-class:: sphx-glr-horizontal + + + * + + .. image:: /auto_examples/images/sphx_glr_plot_OT_1D_smooth_009.png + :scale: 47 + + * + + .. image:: /auto_examples/images/sphx_glr_plot_OT_1D_smooth_010.png + :scale: 47 + + + + +**Total running time of the script:** ( 0 minutes 1.053 seconds) + + + +.. only :: html + + .. container:: sphx-glr-footer + + + .. container:: sphx-glr-download + + :download:`Download Python source code: plot_OT_1D_smooth.py <plot_OT_1D_smooth.py>` + + + + .. container:: sphx-glr-download + + :download:`Download Jupyter notebook: plot_OT_1D_smooth.ipynb <plot_OT_1D_smooth.ipynb>` + + +.. only:: html + + .. rst-class:: sphx-glr-signature + + `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.readthedocs.io>`_ |