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-rw-r--r--docs/source/auto_examples/plot_OT_L1_vs_L2.py280
1 files changed, 187 insertions, 93 deletions
diff --git a/docs/source/auto_examples/plot_OT_L1_vs_L2.py b/docs/source/auto_examples/plot_OT_L1_vs_L2.py
index dfc9462..77bde22 100644
--- a/docs/source/auto_examples/plot_OT_L1_vs_L2.py
+++ b/docs/source/auto_examples/plot_OT_L1_vs_L2.py
@@ -4,6 +4,8 @@
2D Optimal transport for different metrics
==========================================
+2D OT on empirical distributio with different gound metric.
+
Stole the figure idea from Fig. 1 and 2 in
https://arxiv.org/pdf/1706.07650.pdf
@@ -18,98 +20,190 @@ import numpy as np
import matplotlib.pylab as pl
import ot
-#%% parameters and data generation
-
-for data in range(2):
-
- if data:
- n = 20 # nb samples
- xs = np.zeros((n, 2))
- xs[:, 0] = np.arange(n) + 1
- xs[:, 1] = (np.arange(n) + 1) * -0.001 # to make it strictly convex...
-
- xt = np.zeros((n, 2))
- xt[:, 1] = np.arange(n) + 1
- else:
-
- n = 50 # nb samples
- xtot = np.zeros((n + 1, 2))
- xtot[:, 0] = np.cos(
- (np.arange(n + 1) + 1.0) * 0.9 / (n + 2) * 2 * np.pi)
- xtot[:, 1] = np.sin(
- (np.arange(n + 1) + 1.0) * 0.9 / (n + 2) * 2 * np.pi)
-
- xs = xtot[:n, :]
- xt = xtot[1:, :]
-
- a, b = ot.unif(n), ot.unif(n) # uniform distribution on samples
-
- # loss matrix
- M1 = ot.dist(xs, xt, metric='euclidean')
- M1 /= M1.max()
-
- # loss matrix
- M2 = ot.dist(xs, xt, metric='sqeuclidean')
- M2 /= M2.max()
-
- # loss matrix
- Mp = np.sqrt(ot.dist(xs, xt, metric='euclidean'))
- Mp /= Mp.max()
-
- #%% plot samples
-
- pl.figure(1 + 3 * data, figsize=(7, 3))
- pl.clf()
- pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')
- pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')
- pl.axis('equal')
- pl.title('Source and traget distributions')
-
- pl.figure(2 + 3 * data, figsize=(7, 3))
-
- pl.subplot(1, 3, 1)
- pl.imshow(M1, interpolation='nearest')
- pl.title('Euclidean cost')
-
- pl.subplot(1, 3, 2)
- pl.imshow(M2, interpolation='nearest')
- pl.title('Squared Euclidean cost')
-
- pl.subplot(1, 3, 3)
- pl.imshow(Mp, interpolation='nearest')
- pl.title('Sqrt Euclidean cost')
- pl.tight_layout()
-
- #%% EMD
- G1 = ot.emd(a, b, M1)
- G2 = ot.emd(a, b, M2)
- Gp = ot.emd(a, b, Mp)
-
- pl.figure(3 + 3 * data, figsize=(7, 3))
-
- pl.subplot(1, 3, 1)
- ot.plot.plot2D_samples_mat(xs, xt, G1, c=[.5, .5, 1])
- pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')
- pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')
- pl.axis('equal')
- # pl.legend(loc=0)
- pl.title('OT Euclidean')
-
- pl.subplot(1, 3, 2)
- ot.plot.plot2D_samples_mat(xs, xt, G2, c=[.5, .5, 1])
- pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')
- pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')
- pl.axis('equal')
- # pl.legend(loc=0)
- pl.title('OT squared Euclidean')
-
- pl.subplot(1, 3, 3)
- ot.plot.plot2D_samples_mat(xs, xt, Gp, c=[.5, .5, 1])
- pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')
- pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')
- pl.axis('equal')
- # pl.legend(loc=0)
- pl.title('OT sqrt Euclidean')
- pl.tight_layout()
+##############################################################################
+# Dataset 1 : uniform sampling
+##############################################################################
+
+n = 20 # nb samples
+xs = np.zeros((n, 2))
+xs[:, 0] = np.arange(n) + 1
+xs[:, 1] = (np.arange(n) + 1) * -0.001 # to make it strictly convex...
+
+xt = np.zeros((n, 2))
+xt[:, 1] = np.arange(n) + 1
+
+a, b = ot.unif(n), ot.unif(n) # uniform distribution on samples
+
+# loss matrix
+M1 = ot.dist(xs, xt, metric='euclidean')
+M1 /= M1.max()
+
+# loss matrix
+M2 = ot.dist(xs, xt, metric='sqeuclidean')
+M2 /= M2.max()
+
+# loss matrix
+Mp = np.sqrt(ot.dist(xs, xt, metric='euclidean'))
+Mp /= Mp.max()
+
+# Data
+pl.figure(1, figsize=(7, 3))
+pl.clf()
+pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')
+pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')
+pl.axis('equal')
+pl.title('Source and traget distributions')
+
+
+# Cost matrices
+pl.figure(2, figsize=(7, 3))
+
+pl.subplot(1, 3, 1)
+pl.imshow(M1, interpolation='nearest')
+pl.title('Euclidean cost')
+
+pl.subplot(1, 3, 2)
+pl.imshow(M2, interpolation='nearest')
+pl.title('Squared Euclidean cost')
+
+pl.subplot(1, 3, 3)
+pl.imshow(Mp, interpolation='nearest')
+pl.title('Sqrt Euclidean cost')
+pl.tight_layout()
+
+##############################################################################
+# Dataset 1 : Plot OT Matrices
+##############################################################################
+
+
+
+#%% EMD
+G1 = ot.emd(a, b, M1)
+G2 = ot.emd(a, b, M2)
+Gp = ot.emd(a, b, Mp)
+
+# OT matrices
+pl.figure(3, figsize=(7, 3))
+
+pl.subplot(1, 3, 1)
+ot.plot.plot2D_samples_mat(xs, xt, G1, c=[.5, .5, 1])
+pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')
+pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')
+pl.axis('equal')
+# pl.legend(loc=0)
+pl.title('OT Euclidean')
+
+pl.subplot(1, 3, 2)
+ot.plot.plot2D_samples_mat(xs, xt, G2, c=[.5, .5, 1])
+pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')
+pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')
+pl.axis('equal')
+# pl.legend(loc=0)
+pl.title('OT squared Euclidean')
+
+pl.subplot(1, 3, 3)
+ot.plot.plot2D_samples_mat(xs, xt, Gp, c=[.5, .5, 1])
+pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')
+pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')
+pl.axis('equal')
+# pl.legend(loc=0)
+pl.title('OT sqrt Euclidean')
+pl.tight_layout()
+
+pl.show()
+
+
+##############################################################################
+# Dataset 2 : Partial circle
+##############################################################################
+
+n = 50 # nb samples
+xtot = np.zeros((n + 1, 2))
+xtot[:, 0] = np.cos(
+ (np.arange(n + 1) + 1.0) * 0.9 / (n + 2) * 2 * np.pi)
+xtot[:, 1] = np.sin(
+ (np.arange(n + 1) + 1.0) * 0.9 / (n + 2) * 2 * np.pi)
+
+xs = xtot[:n, :]
+xt = xtot[1:, :]
+
+a, b = ot.unif(n), ot.unif(n) # uniform distribution on samples
+
+# loss matrix
+M1 = ot.dist(xs, xt, metric='euclidean')
+M1 /= M1.max()
+
+# loss matrix
+M2 = ot.dist(xs, xt, metric='sqeuclidean')
+M2 /= M2.max()
+
+# loss matrix
+Mp = np.sqrt(ot.dist(xs, xt, metric='euclidean'))
+Mp /= Mp.max()
+
+
+# Data
+pl.figure(4, figsize=(7, 3))
+pl.clf()
+pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')
+pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')
+pl.axis('equal')
+pl.title('Source and traget distributions')
+
+
+# Cost matrices
+pl.figure(5, figsize=(7, 3))
+
+pl.subplot(1, 3, 1)
+pl.imshow(M1, interpolation='nearest')
+pl.title('Euclidean cost')
+
+pl.subplot(1, 3, 2)
+pl.imshow(M2, interpolation='nearest')
+pl.title('Squared Euclidean cost')
+
+pl.subplot(1, 3, 3)
+pl.imshow(Mp, interpolation='nearest')
+pl.title('Sqrt Euclidean cost')
+pl.tight_layout()
+
+##############################################################################
+# Dataset 2 : Plot OT Matrices
+##############################################################################
+
+
+
+#%% EMD
+G1 = ot.emd(a, b, M1)
+G2 = ot.emd(a, b, M2)
+Gp = ot.emd(a, b, Mp)
+
+# OT matrices
+pl.figure(6, figsize=(7, 3))
+
+pl.subplot(1, 3, 1)
+ot.plot.plot2D_samples_mat(xs, xt, G1, c=[.5, .5, 1])
+pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')
+pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')
+pl.axis('equal')
+# pl.legend(loc=0)
+pl.title('OT Euclidean')
+
+pl.subplot(1, 3, 2)
+ot.plot.plot2D_samples_mat(xs, xt, G2, c=[.5, .5, 1])
+pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')
+pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')
+pl.axis('equal')
+# pl.legend(loc=0)
+pl.title('OT squared Euclidean')
+
+pl.subplot(1, 3, 3)
+ot.plot.plot2D_samples_mat(xs, xt, Gp, c=[.5, .5, 1])
+pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')
+pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')
+pl.axis('equal')
+# pl.legend(loc=0)
+pl.title('OT sqrt Euclidean')
+pl.tight_layout()
pl.show()
generated by cgit v1.2.3 (git 2.39.1) at 2024-06-02 22:05:14 +0000