Projection to closed curves

.deepsource.toml

@@ -5,4 +5,12 @@ name = "python"
 enabled = true
 
   [analyzers.meta]
-  runtime_version = "3.x.x"
+  runtime_version = "3.x.x"
+
+[[transformers]]
+name = "isort"
+enabled = true
+
+[[transformers]]
+name = "black"
+enabled = true

README.rst

@@ -185,8 +185,8 @@ This work is supported by:
    :target: https://twitter.com/geomstats
 .. |PyPI version| image:: https://badge.fury.io/py/geomstats.svg
    :target: https://badge.fury.io/py/geomstats
-.. |Build Status| image:: https://travis-ci.org/geomstats/geomstats.svg?branch=master
-   :target: https://travis-ci.org/geomstats/geomstats
+.. |Build Status| image:: https://github.com/geomstats/geomstats/actions/workflows/build.yml/badge.svg
+   :target: https://github.com/geomstats/geomstats/actions/workflows/build.yml
 .. |Slack| image:: https://img.shields.io/badge/Slack-Join-yellow
    :target: https://geomstats.slack.com/
 .. |Coverage Status np| image:: https://codecov.io/gh/geomstats/geomstats/branch/master/graph/badge.svg?flag=numpy

examples/learning_graph_embedding_and_predicting.py

@@ -55,10 +55,9 @@ def main():
     kmeans = RiemannianKMeans(
         metric=hyperbolic_embedding.manifold.metric,
         n_clusters=n_clusters,
-        init='random',
-        mean_method='frechet-poincare-ball')
+        init='random')
 
-    centroids = kmeans.fit(X=embeddings, max_iter=100)
+    centroids = kmeans.fit(X=embeddings)
     labels = kmeans.predict(X=embeddings)
 
     colors = ['g', 'c', 'm']

examples/plot_expectation_maximization_manifolds.py → examples/plot_expectation_maximization_ball.py

@@ -14,7 +14,8 @@
 
 import geomstats.backend as gs
 from geomstats.geometry.poincare_ball import PoincareBall
-from geomstats.learning.expectation_maximization import RiemannianEM
+from geomstats.learning.expectation_maximization import RiemannianEM, \
+    weighted_gmm_pdf
 
 DEFAULT_PLOT_PRECISION = 100
 
@@ -41,13 +42,12 @@ def plot_gaussian_mixture_distribution(data,
             gs.expand_dims(y_axis_samples[z_index], -1)),
             axis=-1)
 
-        mesh_probabilities = PoincareBall.\
-            weighted_gmm_pdf(
-                mixture_coefficients,
-                x_y_plane_mesh,
-                means,
-                variances,
-                metric)
+        mesh_probabilities = weighted_gmm_pdf(
+            mixture_coefficients,
+            x_y_plane_mesh,
+            means,
+            variances,
+            metric)
 
         z_axis_samples[z_index] = mesh_probabilities.sum(-1)
 
@@ -122,12 +122,9 @@ def expectation_maximisation_poincare_ball():
 
     EM = RiemannianEM(n_gaussians=n_clusters,
                       metric=metric,
-                      initialisation_method='random',
-                      mean_method='frechet-poincare-ball')
+                      initialisation_method='random')
 
-    means, variances, mixture_coefficients = EM.fit(
-        data=data,
-        max_iter=100)
+    means, variances, mixture_coefficients = EM.fit(data=data)
 
     # Plot result
     plot = plot_gaussian_mixture_distribution(data,

examples/plot_geodesics_poincare_polydisk.py

@@ -52,7 +52,7 @@ def main():
     vector = gs.array([3.5, 0.6, 0.8])
     stack_vector = gs.stack([vector] * N_DISKS, axis=0)
     vector = gs.to_ndarray(stack_vector, to_ndim=3)
-    initial_tangent_vec = POINCARE_POLYDISK.projection_to_tangent_space(
+    initial_tangent_vec = POINCARE_POLYDISK.to_tangent(
         vector=vector, base_point=initial_point)
     fig = plt.figure()
     plot_geodesic_between_two_points(

examples/plot_kmeans_manifolds.py

@@ -33,11 +33,9 @@ def kmean_poincare_ball():
 
     kmeans = RiemannianKMeans(metric=metric,
                               n_clusters=n_clusters,
-                              init='random',
-                              mean_method='frechet-poincare-ball'
-                              )
+                              init='random')
 
-    centroids = kmeans.fit(X=data, max_iter=100)
+    centroids = kmeans.fit(X=data)
     labels = kmeans.predict(X=data)
 
     plt.figure(1)
@@ -86,8 +84,7 @@ def kmean_hypersphere():
 
     # Generate data on south pole
     cluster_2 = manifold.random_von_mises_fisher(kappa=50, n_samples=n_samples)
-    for point in cluster_2:
-        point[2] = -point[2]
+    cluster_2 = - cluster_2
 
     data = gs.concatenate((cluster_1, cluster_2), axis=0)
 
@@ -122,7 +119,7 @@ def kmean_hypersphere():
         s=200,
         color='green')
 
-    ax.set_title('Kmeans on Hypersphere Manifold')
+    ax.set_title('Kmeans on the sphere')
 
     return plt
 

examples/plot_square_h2_klein_disk.py

@@ -9,7 +9,7 @@
 H2 = Hyperboloid(dim=2)
 METRIC = H2.metric
 
-SQUARE_SIZE = 20
+SQUARE_SIZE = 10
 
 
 def main():

examples/plot_square_h2_poincare_disk.py

@@ -9,7 +9,7 @@
 H2 = Hyperboloid(dim=2)
 METRIC = H2.metric
 
-SQUARE_SIZE = 20
+SQUARE_SIZE = 10
 
 
 def main():

examples/plot_square_h2_poincare_half_plane.py

@@ -9,7 +9,7 @@
 H2 = Hyperboloid(dim=2)
 METRIC = H2.metric
 
-SQUARE_SIZE = 20
+SQUARE_SIZE = 10
 
 
 def main():

geomstats/_backend/__init__.py

@@ -38,12 +38,14 @@
         'clip',
         'concatenate',
         'convert_to_wider_dtype',
+        'comb',
         'copy',
         'cos',
         'cosh',
         'cross',
         'cumprod',
         'cumsum',
+        'diag_indices',
         'diagonal',
         'divide',
         'dot',
@@ -63,6 +65,7 @@
         'greater',
         'hsplit',
         'hstack',
+        'imag',
         'isclose',
         'isnan',
         'less',
@@ -71,6 +74,7 @@
         'log',
         'logical_and',
         'logical_or',
+        'mat_from_diag_triu_tril',
         'matmul',
         'maximum',
         'mean',
@@ -83,6 +87,8 @@
         'outer',
         'polygamma',
         'power',
+        'prod',
+        'real',
         'repeat',
         'reshape',
         'rtol',

geomstats/_backend/numpy/__init__.py

@@ -1,5 +1,7 @@
 """Numpy based computation backend."""
 
+import math
+
 import autograd # NOQA
 import autograd.numpy as np
 from autograd.numpy import (  # NOQA
@@ -28,10 +30,11 @@
     cross,
     cumprod,
     cumsum,
+    diag_indices,
     diagonal,
     divide,
     dot,
-    dtype,
+    dtype as ndtype,
     einsum,
     empty,
     empty_like,
@@ -48,6 +51,7 @@
     hstack,
     int32,
     int64,
+    imag,
     isclose,
     isnan,
     less,
@@ -65,6 +69,8 @@
     ones_like,
     outer,
     power,
+    prod,
+    real,
     repeat,
     reshape,
     shape,
@@ -92,7 +98,7 @@
     zeros,
     zeros_like
 )
-from autograd.scipy.special import polygamma # NOQA
+from autograd.scipy.special import erf, polygamma # NOQA
 from scipy.sparse import coo_matrix
 
 from . import linalg  # NOQA
@@ -101,16 +107,20 @@
 from ..constants import np_atol, np_rtol
 
 DTYPES = {
-    dtype('int32'): 0,
-    dtype('int64'): 1,
-    dtype('float32'): 2,
-    dtype('float64'): 3}
+    ndtype('int32'): 0,
+    ndtype('int64'): 1,
+    ndtype('float32'): 2,
+    ndtype('float64'): 3}
 
 
 atol = np_atol
 rtol = np_rtol
 
 
+def comb(n, k):
+    return math.factorial(n) // math.factorial(k) // math.factorial(n - k)
+
+
 def to_numpy(x):
     return x
 
@@ -366,16 +376,33 @@ def array_from_sparse(indices, data, target_shape):
         coo_matrix((data, list(zip(*indices))), target_shape).todense())
 
 
-def erf(x):
-    cst_erf = 8.0 / (3.0 * np.pi) * (np.pi - 3.0) / (4.0 - np.pi)
-    return \
-        np.sign(x) * \
-        np.sqrt(1 - np.exp(-x * x *
-                           (4 / np.pi + cst_erf * x * x) /
-                           (1 + cst_erf * x * x)))
-
-
 def triu_to_vec(x, k=0):
     n = x.shape[-1]
     rows, cols = triu_indices(n, k=k)
     return x[..., rows, cols]
+
+
+def mat_from_diag_triu_tril(diag, tri_upp, tri_low):
+    """Build matrix from given components.
+
+    Forms a matrix from diagonal, strictly upper triangular and
+    strictly lower traingular parts.
+
+    Parameters
+    ----------
+    diag : array_like, shape=[..., n]
+    tri_upp : array_like, shape=[..., (n * (n - 1)) / 2]
+    tri_low : array_like, shape=[..., (n * (n - 1)) / 2]
+
+    Returns
+    -------
+    mat : array_like, shape=[..., n, n]
+    """
+    n = diag.shape[-1]
+    i, = np.diag_indices(n, ndim=1)
+    j, k = np.triu_indices(n, k=1)
+    mat = np.zeros(diag.shape + (n, ))
+    mat[..., i, i] = diag
+    mat[..., j, k] = tri_upp
+    mat[..., k, j] = tri_low
+    return mat