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+
+
+.. _sphx_glr_auto_examples_plot_optim_OTreg.py:
+
+
+==================================
+Regularized OT with generic solver
+==================================
+
+Illustrates the use of the generic solver for regularized OT with
+user-designed regularization term. It uses Conditional gradient as in [6] and
+generalized Conditional Gradient as proposed in [5][7].
+
+
+[5] N. Courty; R. Flamary; D. Tuia; A. Rakotomamonjy, Optimal Transport for
+Domain Adaptation, in IEEE Transactions on Pattern Analysis and Machine
+Intelligence , vol.PP, no.99, pp.1-1.
+
+[6] Ferradans, S., Papadakis, N., Peyré, G., & Aujol, J. F. (2014).
+Regularized discrete optimal transport. SIAM Journal on Imaging Sciences,
+7(3), 1853-1882.
+
+[7] Rakotomamonjy, A., Flamary, R., & Courty, N. (2015). Generalized
+conditional gradient: analysis of convergence and applications.
+arXiv preprint arXiv:1510.06567.
+
+
+
+
+
+
+.. code-block:: python
+
+
+ import numpy as np
+ import matplotlib.pylab as pl
+ import ot
+ import ot.plot
+
+
+
+
+
+
+
+Generate data
+-------------
+
+
+
+.. code-block:: python
+
+
+ #%% parameters
+
+ n = 100 # nb bins
+
+ # bin positions
+ x = np.arange(n, dtype=np.float64)
+
+ # Gaussian distributions
+ a = ot.datasets.make_1D_gauss(n, m=20, s=5) # m= mean, s= std
+ b = ot.datasets.make_1D_gauss(n, m=60, s=10)
+
+ # loss matrix
+ M = ot.dist(x.reshape((n, 1)), x.reshape((n, 1)))
+ M /= M.max()
+
+
+
+
+
+
+
+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_optim_OTreg_003.png
+ :align: center
+
+
+
+
+Solve EMD with Frobenius norm regularization
+--------------------------------------------
+
+
+
+.. code-block:: python
+
+
+ #%% Example with Frobenius norm regularization
+
+
+ def f(G):
+ return 0.5 * np.sum(G**2)
+
+
+ def df(G):
+ return G
+
+
+ reg = 1e-1
+
+ Gl2 = ot.optim.cg(a, b, M, reg, f, df, verbose=True)
+
+ pl.figure(3)
+ ot.plot.plot1D_mat(a, b, Gl2, 'OT matrix Frob. reg')
+
+
+
+
+.. image:: /auto_examples/images/sphx_glr_plot_optim_OTreg_004.png
+ :align: center
+
+
+.. rst-class:: sphx-glr-script-out
+
+ Out::
+
+ It. |Loss |Delta loss
+ --------------------------------
+ 0|1.760578e-01|0.000000e+00
+ 1|1.669467e-01|-5.457501e-02
+ 2|1.665639e-01|-2.298130e-03
+ 3|1.664378e-01|-7.572776e-04
+ 4|1.664077e-01|-1.811855e-04
+ 5|1.663912e-01|-9.936787e-05
+ 6|1.663852e-01|-3.555826e-05
+ 7|1.663814e-01|-2.305693e-05
+ 8|1.663785e-01|-1.760450e-05
+ 9|1.663767e-01|-1.078011e-05
+ 10|1.663751e-01|-9.525192e-06
+ 11|1.663737e-01|-8.396466e-06
+ 12|1.663727e-01|-6.086938e-06
+ 13|1.663720e-01|-4.042609e-06
+ 14|1.663713e-01|-4.160914e-06
+ 15|1.663707e-01|-3.823502e-06
+ 16|1.663702e-01|-3.022440e-06
+ 17|1.663697e-01|-3.181249e-06
+ 18|1.663692e-01|-2.698532e-06
+ 19|1.663687e-01|-3.258253e-06
+ It. |Loss |Delta loss
+ --------------------------------
+ 20|1.663682e-01|-2.741118e-06
+ 21|1.663678e-01|-2.624135e-06
+ 22|1.663673e-01|-2.645179e-06
+ 23|1.663670e-01|-1.957237e-06
+ 24|1.663666e-01|-2.261541e-06
+ 25|1.663663e-01|-1.851305e-06
+ 26|1.663660e-01|-1.942296e-06
+ 27|1.663657e-01|-2.092896e-06
+ 28|1.663653e-01|-1.924361e-06
+ 29|1.663651e-01|-1.625455e-06
+ 30|1.663648e-01|-1.641123e-06
+ 31|1.663645e-01|-1.566666e-06
+ 32|1.663643e-01|-1.338514e-06
+ 33|1.663641e-01|-1.222711e-06
+ 34|1.663639e-01|-1.221805e-06
+ 35|1.663637e-01|-1.440781e-06
+ 36|1.663634e-01|-1.520091e-06
+ 37|1.663632e-01|-1.288193e-06
+ 38|1.663630e-01|-1.123055e-06
+ 39|1.663628e-01|-1.024487e-06
+ It. |Loss |Delta loss
+ --------------------------------
+ 40|1.663627e-01|-1.079606e-06
+ 41|1.663625e-01|-1.172093e-06
+ 42|1.663623e-01|-1.047880e-06
+ 43|1.663621e-01|-1.010577e-06
+ 44|1.663619e-01|-1.064438e-06
+ 45|1.663618e-01|-9.882375e-07
+ 46|1.663616e-01|-8.532647e-07
+ 47|1.663615e-01|-9.930189e-07
+ 48|1.663613e-01|-8.728955e-07
+ 49|1.663612e-01|-9.524214e-07
+ 50|1.663610e-01|-9.088418e-07
+ 51|1.663609e-01|-7.639430e-07
+ 52|1.663608e-01|-6.662611e-07
+ 53|1.663607e-01|-7.133700e-07
+ 54|1.663605e-01|-7.648141e-07
+ 55|1.663604e-01|-6.557516e-07
+ 56|1.663603e-01|-7.304213e-07
+ 57|1.663602e-01|-6.353809e-07
+ 58|1.663601e-01|-7.968279e-07
+ 59|1.663600e-01|-6.367159e-07
+ It. |Loss |Delta loss
+ --------------------------------
+ 60|1.663599e-01|-5.610790e-07
+ 61|1.663598e-01|-5.787466e-07
+ 62|1.663596e-01|-6.937777e-07
+ 63|1.663596e-01|-5.599432e-07
+ 64|1.663595e-01|-5.813048e-07
+ 65|1.663594e-01|-5.724600e-07
+ 66|1.663593e-01|-6.081892e-07
+ 67|1.663592e-01|-5.948732e-07
+ 68|1.663591e-01|-4.941833e-07
+ 69|1.663590e-01|-5.213739e-07
+ 70|1.663589e-01|-5.127355e-07
+ 71|1.663588e-01|-4.349251e-07
+ 72|1.663588e-01|-5.007084e-07
+ 73|1.663587e-01|-4.880265e-07
+ 74|1.663586e-01|-4.931950e-07
+ 75|1.663585e-01|-4.981309e-07
+ 76|1.663584e-01|-3.952959e-07
+ 77|1.663584e-01|-4.544857e-07
+ 78|1.663583e-01|-4.237579e-07
+ 79|1.663582e-01|-4.382386e-07
+ It. |Loss |Delta loss
+ --------------------------------
+ 80|1.663582e-01|-3.646051e-07
+ 81|1.663581e-01|-4.197994e-07
+ 82|1.663580e-01|-4.072764e-07
+ 83|1.663580e-01|-3.994645e-07
+ 84|1.663579e-01|-4.842721e-07
+ 85|1.663578e-01|-3.276486e-07
+ 86|1.663578e-01|-3.737346e-07
+ 87|1.663577e-01|-4.282043e-07
+ 88|1.663576e-01|-4.020937e-07
+ 89|1.663576e-01|-3.431951e-07
+ 90|1.663575e-01|-3.052335e-07
+ 91|1.663575e-01|-3.500538e-07
+ 92|1.663574e-01|-3.063176e-07
+ 93|1.663573e-01|-3.576367e-07
+ 94|1.663573e-01|-3.224681e-07
+ 95|1.663572e-01|-3.673221e-07
+ 96|1.663572e-01|-3.635561e-07
+ 97|1.663571e-01|-3.527236e-07
+ 98|1.663571e-01|-2.788548e-07
+ 99|1.663570e-01|-2.727141e-07
+ It. |Loss |Delta loss
+ --------------------------------
+ 100|1.663570e-01|-3.127278e-07
+ 101|1.663569e-01|-2.637504e-07
+ 102|1.663569e-01|-2.922750e-07
+ 103|1.663568e-01|-3.076454e-07
+ 104|1.663568e-01|-2.911509e-07
+ 105|1.663567e-01|-2.403398e-07
+ 106|1.663567e-01|-2.439790e-07
+ 107|1.663567e-01|-2.634542e-07
+ 108|1.663566e-01|-2.452203e-07
+ 109|1.663566e-01|-2.852991e-07
+ 110|1.663565e-01|-2.165490e-07
+ 111|1.663565e-01|-2.450250e-07
+ 112|1.663564e-01|-2.685294e-07
+ 113|1.663564e-01|-2.821800e-07
+ 114|1.663564e-01|-2.237390e-07
+ 115|1.663563e-01|-1.992842e-07
+ 116|1.663563e-01|-2.166739e-07
+ 117|1.663563e-01|-2.086064e-07
+ 118|1.663562e-01|-2.435945e-07
+ 119|1.663562e-01|-2.292497e-07
+ It. |Loss |Delta loss
+ --------------------------------
+ 120|1.663561e-01|-2.366209e-07
+ 121|1.663561e-01|-2.138746e-07
+ 122|1.663561e-01|-2.009637e-07
+ 123|1.663560e-01|-2.386258e-07
+ 124|1.663560e-01|-1.927442e-07
+ 125|1.663560e-01|-2.081681e-07
+ 126|1.663559e-01|-1.759123e-07
+ 127|1.663559e-01|-1.890771e-07
+ 128|1.663559e-01|-1.971315e-07
+ 129|1.663558e-01|-2.101983e-07
+ 130|1.663558e-01|-2.035645e-07
+ 131|1.663558e-01|-1.984492e-07
+ 132|1.663557e-01|-1.849064e-07
+ 133|1.663557e-01|-1.795703e-07
+ 134|1.663557e-01|-1.624087e-07
+ 135|1.663557e-01|-1.689557e-07
+ 136|1.663556e-01|-1.644308e-07
+ 137|1.663556e-01|-1.618007e-07
+ 138|1.663556e-01|-1.483013e-07
+ 139|1.663555e-01|-1.708771e-07
+ It. |Loss |Delta loss
+ --------------------------------
+ 140|1.663555e-01|-2.013847e-07
+ 141|1.663555e-01|-1.721217e-07
+ 142|1.663554e-01|-2.027911e-07
+ 143|1.663554e-01|-1.764565e-07
+ 144|1.663554e-01|-1.677151e-07
+ 145|1.663554e-01|-1.351982e-07
+ 146|1.663553e-01|-1.423360e-07
+ 147|1.663553e-01|-1.541112e-07
+ 148|1.663553e-01|-1.491601e-07
+ 149|1.663553e-01|-1.466407e-07
+ 150|1.663552e-01|-1.801524e-07
+ 151|1.663552e-01|-1.714107e-07
+ 152|1.663552e-01|-1.491257e-07
+ 153|1.663552e-01|-1.513799e-07
+ 154|1.663551e-01|-1.354539e-07
+ 155|1.663551e-01|-1.233818e-07
+ 156|1.663551e-01|-1.576219e-07
+ 157|1.663551e-01|-1.452791e-07
+ 158|1.663550e-01|-1.262867e-07
+ 159|1.663550e-01|-1.316379e-07
+ It. |Loss |Delta loss
+ --------------------------------
+ 160|1.663550e-01|-1.295447e-07
+ 161|1.663550e-01|-1.283286e-07
+ 162|1.663550e-01|-1.569222e-07
+ 163|1.663549e-01|-1.172942e-07
+ 164|1.663549e-01|-1.399809e-07
+ 165|1.663549e-01|-1.229432e-07
+ 166|1.663549e-01|-1.326191e-07
+ 167|1.663548e-01|-1.209694e-07
+ 168|1.663548e-01|-1.372136e-07
+ 169|1.663548e-01|-1.338395e-07
+ 170|1.663548e-01|-1.416497e-07
+ 171|1.663548e-01|-1.298576e-07
+ 172|1.663547e-01|-1.190590e-07
+ 173|1.663547e-01|-1.167083e-07
+ 174|1.663547e-01|-1.069425e-07
+ 175|1.663547e-01|-1.217780e-07
+ 176|1.663547e-01|-1.140754e-07
+ 177|1.663546e-01|-1.160707e-07
+ 178|1.663546e-01|-1.101798e-07
+ 179|1.663546e-01|-1.114904e-07
+ It. |Loss |Delta loss
+ --------------------------------
+ 180|1.663546e-01|-1.064022e-07
+ 181|1.663546e-01|-9.258231e-08
+ 182|1.663546e-01|-1.213120e-07
+ 183|1.663545e-01|-1.164296e-07
+ 184|1.663545e-01|-1.188762e-07
+ 185|1.663545e-01|-9.394153e-08
+ 186|1.663545e-01|-1.028656e-07
+ 187|1.663545e-01|-1.115348e-07
+ 188|1.663544e-01|-9.768310e-08
+ 189|1.663544e-01|-1.021806e-07
+ 190|1.663544e-01|-1.086303e-07
+ 191|1.663544e-01|-9.879008e-08
+ 192|1.663544e-01|-1.050210e-07
+ 193|1.663544e-01|-1.002463e-07
+ 194|1.663543e-01|-1.062747e-07
+ 195|1.663543e-01|-9.348538e-08
+ 196|1.663543e-01|-7.992512e-08
+ 197|1.663543e-01|-9.558020e-08
+ 198|1.663543e-01|-9.993772e-08
+ 199|1.663543e-01|-8.588499e-08
+ It. |Loss |Delta loss
+ --------------------------------
+ 200|1.663543e-01|-8.737134e-08
+
+
+Solve EMD with entropic regularization
+--------------------------------------
+
+
+
+.. code-block:: python
+
+
+ #%% Example with entropic regularization
+
+
+ def f(G):
+ return np.sum(G * np.log(G))
+
+
+ def df(G):
+ return np.log(G) + 1.
+
+
+ reg = 1e-3
+
+ Ge = ot.optim.cg(a, b, M, reg, f, df, verbose=True)
+
+ pl.figure(4, figsize=(5, 5))
+ ot.plot.plot1D_mat(a, b, Ge, 'OT matrix Entrop. reg')
+
+
+
+
+.. image:: /auto_examples/images/sphx_glr_plot_optim_OTreg_006.png
+ :align: center
+
+
+.. rst-class:: sphx-glr-script-out
+
+ Out::
+
+ It. |Loss |Delta loss
+ --------------------------------
+ 0|1.692289e-01|0.000000e+00
+ 1|1.617643e-01|-4.614437e-02
+ 2|1.612639e-01|-3.102965e-03
+ 3|1.611291e-01|-8.371098e-04
+ 4|1.610468e-01|-5.110558e-04
+ 5|1.610198e-01|-1.672927e-04
+ 6|1.610130e-01|-4.232417e-05
+ 7|1.610090e-01|-2.513455e-05
+ 8|1.610002e-01|-5.443507e-05
+ 9|1.609996e-01|-3.657071e-06
+ 10|1.609948e-01|-2.998735e-05
+ 11|1.609695e-01|-1.569217e-04
+ 12|1.609533e-01|-1.010779e-04
+ 13|1.609520e-01|-8.043897e-06
+ 14|1.609465e-01|-3.415246e-05
+ 15|1.609386e-01|-4.898605e-05
+ 16|1.609324e-01|-3.837052e-05
+ 17|1.609298e-01|-1.617826e-05
+ 18|1.609184e-01|-7.080015e-05
+ 19|1.609083e-01|-6.273206e-05
+ It. |Loss |Delta loss
+ --------------------------------
+ 20|1.608988e-01|-5.940805e-05
+ 21|1.608853e-01|-8.380030e-05
+ 22|1.608844e-01|-5.185045e-06
+ 23|1.608824e-01|-1.279113e-05
+ 24|1.608819e-01|-3.156821e-06
+ 25|1.608783e-01|-2.205746e-05
+ 26|1.608764e-01|-1.189894e-05
+ 27|1.608755e-01|-5.474607e-06
+ 28|1.608737e-01|-1.144227e-05
+ 29|1.608676e-01|-3.775335e-05
+ 30|1.608638e-01|-2.348020e-05
+ 31|1.608627e-01|-6.863136e-06
+ 32|1.608529e-01|-6.110230e-05
+ 33|1.608487e-01|-2.641106e-05
+ 34|1.608409e-01|-4.823638e-05
+ 35|1.608373e-01|-2.256641e-05
+ 36|1.608338e-01|-2.132444e-05
+ 37|1.608310e-01|-1.786649e-05
+ 38|1.608260e-01|-3.103848e-05
+ 39|1.608206e-01|-3.321265e-05
+ It. |Loss |Delta loss
+ --------------------------------
+ 40|1.608201e-01|-3.054747e-06
+ 41|1.608195e-01|-4.198335e-06
+ 42|1.608193e-01|-8.458736e-07
+ 43|1.608159e-01|-2.153759e-05
+ 44|1.608115e-01|-2.738314e-05
+ 45|1.608108e-01|-3.960032e-06
+ 46|1.608081e-01|-1.675447e-05
+ 47|1.608072e-01|-5.976340e-06
+ 48|1.608046e-01|-1.604130e-05
+ 49|1.608020e-01|-1.617036e-05
+ 50|1.608014e-01|-3.957795e-06
+ 51|1.608011e-01|-1.292411e-06
+ 52|1.607998e-01|-8.431795e-06
+ 53|1.607964e-01|-2.127054e-05
+ 54|1.607947e-01|-1.021878e-05
+ 55|1.607947e-01|-3.560621e-07
+ 56|1.607900e-01|-2.929781e-05
+ 57|1.607890e-01|-5.740229e-06
+ 58|1.607858e-01|-2.039550e-05
+ 59|1.607836e-01|-1.319545e-05
+ It. |Loss |Delta loss
+ --------------------------------
+ 60|1.607826e-01|-6.378947e-06
+ 61|1.607808e-01|-1.145102e-05
+ 62|1.607776e-01|-1.941743e-05
+ 63|1.607743e-01|-2.087422e-05
+ 64|1.607741e-01|-1.310249e-06
+ 65|1.607738e-01|-1.682752e-06
+ 66|1.607691e-01|-2.913936e-05
+ 67|1.607671e-01|-1.288855e-05
+ 68|1.607654e-01|-1.002448e-05
+ 69|1.607641e-01|-8.209492e-06
+ 70|1.607632e-01|-5.588467e-06
+ 71|1.607619e-01|-8.050388e-06
+ 72|1.607618e-01|-9.417493e-07
+ 73|1.607598e-01|-1.210509e-05
+ 74|1.607591e-01|-4.392914e-06
+ 75|1.607579e-01|-7.759587e-06
+ 76|1.607574e-01|-2.760280e-06
+ 77|1.607556e-01|-1.146469e-05
+ 78|1.607550e-01|-3.689456e-06
+ 79|1.607550e-01|-4.065631e-08
+ It. |Loss |Delta loss
+ --------------------------------
+ 80|1.607539e-01|-6.555681e-06
+ 81|1.607528e-01|-7.177470e-06
+ 82|1.607527e-01|-5.306068e-07
+ 83|1.607514e-01|-7.816045e-06
+ 84|1.607511e-01|-2.301970e-06
+ 85|1.607504e-01|-4.281072e-06
+ 86|1.607503e-01|-7.821886e-07
+ 87|1.607480e-01|-1.403013e-05
+ 88|1.607480e-01|-1.169298e-08
+ 89|1.607473e-01|-4.235982e-06
+ 90|1.607470e-01|-1.717105e-06
+ 91|1.607470e-01|-6.148402e-09
+ 92|1.607462e-01|-5.396481e-06
+ 93|1.607461e-01|-5.194954e-07
+ 94|1.607450e-01|-6.525707e-06
+ 95|1.607442e-01|-5.332060e-06
+ 96|1.607439e-01|-1.682093e-06
+ 97|1.607437e-01|-1.594796e-06
+ 98|1.607435e-01|-7.923812e-07
+ 99|1.607420e-01|-9.738552e-06
+ It. |Loss |Delta loss
+ --------------------------------
+ 100|1.607419e-01|-1.022448e-07
+ 101|1.607419e-01|-4.865999e-07
+ 102|1.607418e-01|-7.092012e-07
+ 103|1.607408e-01|-5.861815e-06
+ 104|1.607402e-01|-3.953266e-06
+ 105|1.607395e-01|-3.969572e-06
+ 106|1.607390e-01|-3.612075e-06
+ 107|1.607377e-01|-7.683735e-06
+ 108|1.607365e-01|-7.777599e-06
+ 109|1.607364e-01|-2.335096e-07
+ 110|1.607364e-01|-4.562036e-07
+ 111|1.607360e-01|-2.089538e-06
+ 112|1.607356e-01|-2.755355e-06
+ 113|1.607349e-01|-4.501960e-06
+ 114|1.607347e-01|-1.160544e-06
+ 115|1.607346e-01|-6.289450e-07
+ 116|1.607345e-01|-2.092146e-07
+ 117|1.607336e-01|-5.990866e-06
+ 118|1.607330e-01|-3.348498e-06
+ 119|1.607328e-01|-1.256222e-06
+ It. |Loss |Delta loss
+ --------------------------------
+ 120|1.607320e-01|-5.418353e-06
+ 121|1.607318e-01|-8.296189e-07
+ 122|1.607311e-01|-4.381608e-06
+ 123|1.607310e-01|-8.913901e-07
+ 124|1.607309e-01|-3.808821e-07
+ 125|1.607302e-01|-4.608994e-06
+ 126|1.607294e-01|-5.063777e-06
+ 127|1.607290e-01|-2.532835e-06
+ 128|1.607285e-01|-2.870049e-06
+ 129|1.607284e-01|-4.892812e-07
+ 130|1.607281e-01|-1.760452e-06
+ 131|1.607279e-01|-1.727139e-06
+ 132|1.607275e-01|-2.220706e-06
+ 133|1.607271e-01|-2.516930e-06
+ 134|1.607269e-01|-1.201434e-06
+ 135|1.607269e-01|-2.183459e-09
+ 136|1.607262e-01|-4.223011e-06
+ 137|1.607258e-01|-2.530202e-06
+ 138|1.607258e-01|-1.857260e-07
+ 139|1.607256e-01|-1.401957e-06
+ It. |Loss |Delta loss
+ --------------------------------
+ 140|1.607250e-01|-3.242751e-06
+ 141|1.607247e-01|-2.308071e-06
+ 142|1.607247e-01|-4.730700e-08
+ 143|1.607246e-01|-4.240229e-07
+ 144|1.607242e-01|-2.484810e-06
+ 145|1.607238e-01|-2.539206e-06
+ 146|1.607234e-01|-2.535574e-06
+ 147|1.607231e-01|-1.954802e-06
+ 148|1.607228e-01|-1.765447e-06
+ 149|1.607228e-01|-1.620007e-08
+ 150|1.607222e-01|-3.615783e-06
+ 151|1.607222e-01|-8.668516e-08
+ 152|1.607215e-01|-4.000673e-06
+ 153|1.607213e-01|-1.774103e-06
+ 154|1.607213e-01|-6.328834e-09
+ 155|1.607209e-01|-2.418783e-06
+ 156|1.607208e-01|-2.848492e-07
+ 157|1.607207e-01|-8.836043e-07
+ 158|1.607205e-01|-1.192836e-06
+ 159|1.607202e-01|-1.638022e-06
+ It. |Loss |Delta loss
+ --------------------------------
+ 160|1.607202e-01|-3.670914e-08
+ 161|1.607197e-01|-3.153709e-06
+ 162|1.607197e-01|-2.419565e-09
+ 163|1.607194e-01|-2.136882e-06
+ 164|1.607194e-01|-1.173754e-09
+ 165|1.607192e-01|-8.169238e-07
+ 166|1.607191e-01|-9.218755e-07
+ 167|1.607189e-01|-9.459255e-07
+ 168|1.607187e-01|-1.294835e-06
+ 169|1.607186e-01|-5.797668e-07
+ 170|1.607186e-01|-4.706272e-08
+ 171|1.607183e-01|-1.753383e-06
+ 172|1.607183e-01|-1.681573e-07
+ 173|1.607183e-01|-2.563971e-10
+
+
+Solve EMD with Frobenius norm + entropic regularization
+-------------------------------------------------------
+
+
+
+.. code-block:: python
+
+
+ #%% Example with Frobenius norm + entropic regularization with gcg
+
+
+ def f(G):
+ return 0.5 * np.sum(G**2)
+
+
+ def df(G):
+ return G
+
+
+ reg1 = 1e-3
+ reg2 = 1e-1
+
+ Gel2 = ot.optim.gcg(a, b, M, reg1, reg2, f, df, verbose=True)
+
+ pl.figure(5, figsize=(5, 5))
+ ot.plot.plot1D_mat(a, b, Gel2, 'OT entropic + matrix Frob. reg')
+ pl.show()
+
+
+
+.. image:: /auto_examples/images/sphx_glr_plot_optim_OTreg_008.png
+ :align: center
+
+
+.. rst-class:: sphx-glr-script-out
+
+ Out::
+
+ It. |Loss |Delta loss
+ --------------------------------
+ 0|1.693084e-01|0.000000e+00
+ 1|1.610121e-01|-5.152589e-02
+ 2|1.609378e-01|-4.622297e-04
+ 3|1.609284e-01|-5.830043e-05
+ 4|1.609284e-01|-1.111407e-12
+
+
+**Total running time of the script:** ( 0 minutes 1.990 seconds)
+
+
+
+.. only :: html
+
+ .. container:: sphx-glr-footer
+
+
+ .. container:: sphx-glr-download
+
+ :download:`Download Python source code: plot_optim_OTreg.py <plot_optim_OTreg.py>`
+
+
+
+ .. container:: sphx-glr-download
+
+ :download:`Download Jupyter notebook: plot_optim_OTreg.ipynb <plot_optim_OTreg.ipynb>`
+
+
+.. only:: html
+
+ .. rst-class:: sphx-glr-signature
+
+ `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.readthedocs.io>`_
generated by cgit v1.2.3 (git 2.39.1) at 2024-06-17 17:56:58 +0000