diff options
author | RĂ©mi Flamary <remi.flamary@gmail.com> | 2017-09-15 14:54:21 +0200 |
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committer | GitHub <noreply@github.com> | 2017-09-15 14:54:21 +0200 |
commit | 81b2796226f3abde29fc024752728444da77509a (patch) | |
tree | c52cec3c38552f9f8c15361758aa9a80c30c3ef3 /docs/source/auto_examples/plot_barycenter_1D.ipynb | |
parent | e70d5420204db78691af2d0fbe04cc3d4416a8f4 (diff) | |
parent | 7fea2cd3e8ad29bf3fa442d7642bae124ee2bab0 (diff) |
Merge pull request #27 from rflamary/autonb
auto notebooks + release update (fixes #16)
Diffstat (limited to 'docs/source/auto_examples/plot_barycenter_1D.ipynb')
-rw-r--r-- | docs/source/auto_examples/plot_barycenter_1D.ipynb | 76 |
1 files changed, 74 insertions, 2 deletions
diff --git a/docs/source/auto_examples/plot_barycenter_1D.ipynb b/docs/source/auto_examples/plot_barycenter_1D.ipynb index 36f3975..a19e0fd 100644 --- a/docs/source/auto_examples/plot_barycenter_1D.ipynb +++ b/docs/source/auto_examples/plot_barycenter_1D.ipynb @@ -15,7 +15,7 @@ }, { "source": [ - "\n# 1D Wasserstein barycenter demo\n\n\n\n@author: rflamary\n\n" + "\n# 1D Wasserstein barycenter demo\n\n\nThis example illustrates the computation of regularized Wassersyein Barycenter\nas proposed in [3].\n\n\n[3] Benamou, J. D., Carlier, G., Cuturi, M., Nenna, L., & Peyr\u00e9, G. (2015).\nIterative Bregman projections for regularized transportation problems\nSIAM Journal on Scientific Computing, 37(2), A1111-A1138.\n\n\n" ], "cell_type": "markdown", "metadata": {} @@ -24,7 +24,79 @@ "execution_count": null, "cell_type": "code", "source": [ - "import numpy as np\nimport matplotlib.pylab as pl\nimport ot\nfrom mpl_toolkits.mplot3d import Axes3D #necessary for 3d plot even if not used\nfrom matplotlib.collections import PolyCollection\n\n\n#%% parameters\n\nn=100 # nb bins\n\n# bin positions\nx=np.arange(n,dtype=np.float64)\n\n# Gaussian distributions\na1=ot.datasets.get_1D_gauss(n,m=20,s=5) # m= mean, s= std\na2=ot.datasets.get_1D_gauss(n,m=60,s=8)\n\n# creating matrix A containing all distributions\nA=np.vstack((a1,a2)).T\nnbd=A.shape[1]\n\n# loss matrix + normalization\nM=ot.utils.dist0(n)\nM/=M.max()\n\n#%% plot the distributions\n\npl.figure(1)\nfor i in range(nbd):\n pl.plot(x,A[:,i])\npl.title('Distributions')\n\n#%% barycenter computation\n\nalpha=0.2 # 0<=alpha<=1\nweights=np.array([1-alpha,alpha])\n\n# l2bary\nbary_l2=A.dot(weights)\n\n# wasserstein\nreg=1e-3\nbary_wass=ot.bregman.barycenter(A,M,reg,weights)\n\npl.figure(2)\npl.clf()\npl.subplot(2,1,1)\nfor i in range(nbd):\n pl.plot(x,A[:,i])\npl.title('Distributions')\n\npl.subplot(2,1,2)\npl.plot(x,bary_l2,'r',label='l2')\npl.plot(x,bary_wass,'g',label='Wasserstein')\npl.legend()\npl.title('Barycenters')\n\n\n#%% barycenter interpolation\n\nnbalpha=11\nalphalist=np.linspace(0,1,nbalpha)\n\n\nB_l2=np.zeros((n,nbalpha))\n\nB_wass=np.copy(B_l2)\n\nfor i in range(0,nbalpha):\n alpha=alphalist[i]\n weights=np.array([1-alpha,alpha])\n B_l2[:,i]=A.dot(weights)\n B_wass[:,i]=ot.bregman.barycenter(A,M,reg,weights)\n\n#%% plot interpolation\n\npl.figure(3,(10,5))\n\n#pl.subplot(1,2,1)\ncmap=pl.cm.get_cmap('viridis')\nverts = []\nzs = alphalist\nfor i,z in enumerate(zs):\n ys = B_l2[:,i]\n verts.append(list(zip(x, ys)))\n\nax = pl.gcf().gca(projection='3d')\n\npoly = PolyCollection(verts,facecolors=[cmap(a) for a in alphalist])\npoly.set_alpha(0.7)\nax.add_collection3d(poly, zs=zs, zdir='y')\n\nax.set_xlabel('x')\nax.set_xlim3d(0, n)\nax.set_ylabel('$\\\\alpha$')\nax.set_ylim3d(0,1)\nax.set_zlabel('')\nax.set_zlim3d(0, B_l2.max()*1.01)\npl.title('Barycenter interpolation with l2')\n\npl.show()\n\npl.figure(4,(10,5))\n\n#pl.subplot(1,2,1)\ncmap=pl.cm.get_cmap('viridis')\nverts = []\nzs = alphalist\nfor i,z in enumerate(zs):\n ys = B_wass[:,i]\n verts.append(list(zip(x, ys)))\n\nax = pl.gcf().gca(projection='3d')\n\npoly = PolyCollection(verts,facecolors=[cmap(a) for a in alphalist])\npoly.set_alpha(0.7)\nax.add_collection3d(poly, zs=zs, zdir='y')\n\nax.set_xlabel('x')\nax.set_xlim3d(0, n)\nax.set_ylabel('$\\\\alpha$')\nax.set_ylim3d(0,1)\nax.set_zlabel('')\nax.set_zlim3d(0, B_l2.max()*1.01)\npl.title('Barycenter interpolation with Wasserstein')\n\npl.show()" + "# Author: Remi Flamary <remi.flamary@unice.fr>\n#\n# License: MIT License\n\nimport numpy as np\nimport matplotlib.pylab as pl\nimport ot\n# necessary for 3d plot even if not used\nfrom mpl_toolkits.mplot3d import Axes3D # noqa\nfrom matplotlib.collections import PolyCollection" + ], + "outputs": [], + "metadata": { + "collapsed": false + } + }, + { + "source": [ + "Generate data\n-------------\n\n" + ], + "cell_type": "markdown", + "metadata": {} + }, + { + "execution_count": null, + "cell_type": "code", + "source": [ + "#%% parameters\n\nn = 100 # nb bins\n\n# bin positions\nx = np.arange(n, dtype=np.float64)\n\n# Gaussian distributions\na1 = ot.datasets.get_1D_gauss(n, m=20, s=5) # m= mean, s= std\na2 = ot.datasets.get_1D_gauss(n, m=60, s=8)\n\n# creating matrix A containing all distributions\nA = np.vstack((a1, a2)).T\nn_distributions = A.shape[1]\n\n# loss matrix + normalization\nM = ot.utils.dist0(n)\nM /= M.max()" + ], + "outputs": [], + "metadata": { + "collapsed": false + } + }, + { + "source": [ + "Plot data\n---------\n\n" + ], + "cell_type": "markdown", + "metadata": {} + }, + { + "execution_count": null, + "cell_type": "code", + "source": [ + "#%% plot the distributions\n\npl.figure(1, figsize=(6.4, 3))\nfor i in range(n_distributions):\n pl.plot(x, A[:, i])\npl.title('Distributions')\npl.tight_layout()" + ], + "outputs": [], + "metadata": { + "collapsed": false + } + }, + { + "source": [ + "Barycenter computation\n----------------------\n\n" + ], + "cell_type": "markdown", + "metadata": {} + }, + { + "execution_count": null, + "cell_type": "code", + "source": [ + "#%% barycenter computation\n\nalpha = 0.2 # 0<=alpha<=1\nweights = np.array([1 - alpha, alpha])\n\n# l2bary\nbary_l2 = A.dot(weights)\n\n# wasserstein\nreg = 1e-3\nbary_wass = ot.bregman.barycenter(A, M, reg, weights)\n\npl.figure(2)\npl.clf()\npl.subplot(2, 1, 1)\nfor i in range(n_distributions):\n pl.plot(x, A[:, i])\npl.title('Distributions')\n\npl.subplot(2, 1, 2)\npl.plot(x, bary_l2, 'r', label='l2')\npl.plot(x, bary_wass, 'g', label='Wasserstein')\npl.legend()\npl.title('Barycenters')\npl.tight_layout()" + ], + "outputs": [], + "metadata": { + "collapsed": false + } + }, + { + "source": [ + "Barycentric interpolation\n-------------------------\n\n" + ], + "cell_type": "markdown", + "metadata": {} + }, + { + "execution_count": null, + "cell_type": "code", + "source": [ + "#%% barycenter interpolation\n\nn_alpha = 11\nalpha_list = np.linspace(0, 1, n_alpha)\n\n\nB_l2 = np.zeros((n, n_alpha))\n\nB_wass = np.copy(B_l2)\n\nfor i in range(0, n_alpha):\n alpha = alpha_list[i]\n weights = np.array([1 - alpha, alpha])\n B_l2[:, i] = A.dot(weights)\n B_wass[:, i] = ot.bregman.barycenter(A, M, reg, weights)\n\n#%% plot interpolation\n\npl.figure(3)\n\ncmap = pl.cm.get_cmap('viridis')\nverts = []\nzs = alpha_list\nfor i, z in enumerate(zs):\n ys = B_l2[:, i]\n verts.append(list(zip(x, ys)))\n\nax = pl.gcf().gca(projection='3d')\n\npoly = PolyCollection(verts, facecolors=[cmap(a) for a in alpha_list])\npoly.set_alpha(0.7)\nax.add_collection3d(poly, zs=zs, zdir='y')\nax.set_xlabel('x')\nax.set_xlim3d(0, n)\nax.set_ylabel('$\\\\alpha$')\nax.set_ylim3d(0, 1)\nax.set_zlabel('')\nax.set_zlim3d(0, B_l2.max() * 1.01)\npl.title('Barycenter interpolation with l2')\npl.tight_layout()\n\npl.figure(4)\ncmap = pl.cm.get_cmap('viridis')\nverts = []\nzs = alpha_list\nfor i, z in enumerate(zs):\n ys = B_wass[:, i]\n verts.append(list(zip(x, ys)))\n\nax = pl.gcf().gca(projection='3d')\n\npoly = PolyCollection(verts, facecolors=[cmap(a) for a in alpha_list])\npoly.set_alpha(0.7)\nax.add_collection3d(poly, zs=zs, zdir='y')\nax.set_xlabel('x')\nax.set_xlim3d(0, n)\nax.set_ylabel('$\\\\alpha$')\nax.set_ylim3d(0, 1)\nax.set_zlabel('')\nax.set_zlim3d(0, B_l2.max() * 1.01)\npl.title('Barycenter interpolation with Wasserstein')\npl.tight_layout()\n\npl.show()" ], "outputs": [], "metadata": { |