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authorRémi Flamary <remi.flamary@gmail.com>2017-08-30 17:01:01 +0200
committerRémi Flamary <remi.flamary@gmail.com>2017-08-30 17:01:01 +0200
commitdc8737a30cb6d9f1305173eb8d16fe6716fd1231 (patch)
tree1f03384de2af88ed07a1e850e0871db826ed53e7 /docs/source/auto_examples/plot_barycenter_1D.ipynb
parentc2a7a1f3ab4ba5c4f5adeca0fa22d8d6b4fc079d (diff)
wroking make!
Diffstat (limited to 'docs/source/auto_examples/plot_barycenter_1D.ipynb')
-rw-r--r--docs/source/auto_examples/plot_barycenter_1D.ipynb4
1 files changed, 2 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..239b8b8 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\n\n"
],
"cell_type": "markdown",
"metadata": {}
@@ -24,7 +24,7 @@
"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\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\nn_distributions = 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, figsize=(6.4, 3))\nfor i in range(n_distributions):\n pl.plot(x, A[:, i])\npl.title('Distributions')\npl.tight_layout()\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(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()\n\n#%% 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": {