8000 Start fixing inheritance in Product/NFold/Landmarks/Curves Spaces by ninamiolane · Pull Request #1581 · geomstats/geomstats · GitHub
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Start fixing inheritance in Product/NFold/Landmarks/Curves Spaces #1581

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merged 2 commits into from
Jun 14, 2022
Merged

Start fixing inheritance in Product/NFold/Landmarks/Curves Spaces #1581

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89f4de4
Put NFoldMetric in product_riemannian_metric
ninamiolane Jun 14, 2022
1b6aa2f
Correctly import NFoldMetric in tests
ninamiolane Jun 14, 2022
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131 changes: 4 additions & 127 deletions geomstats/geometry/product_manifold.py
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Original file line number Diff line number Diff line change
Expand Up @@ -8,8 +8,10 @@
import geomstats.backend as gs
import geomstats.errors
from geomstats.geometry.manifold import Manifold
from geomstats.geometry.product_riemannian_metric import ProductRiemannianMetric
from geomstats.geometry.riemannian_metric import RiemannianMetric
from geomstats.geometry.product_riemannian_metric import (
NFoldMetric,
ProductRiemannianMetric,
)


class ProductManifold(Manifold):
Expand Down Expand Up @@ -487,128 +489,3 @@ def projection(self, point):
raise NotImplementedError(
"The base manifold does not implement a projection " "method."
)


class NFoldMetric(RiemannianMetric):
r"""Class for an n-fold product manifold :math:`M^n`.

Define a manifold as the product manifold of n copies of a given base manifold M.

Parameters
----------
base_metric : RiemannianMetric
Base metric.
n_copies : int
Number of replication of the base metric.
"""

def __init__(self, base_metric, n_copies):
geomstats.errors.check_integer(n_copies, "n_copies")
dim = n_copies * base_metric.dim
base_shape = base_metric.shape
super(NFoldMetric, self).__init__(dim=dim, shape=(n_copies, *base_shape))
self.base_shape = base_shape
self.base_metric = base_metric
self.n_copies = n_copies

def metric_matrix(self, base_point=None):
"""Compute the matrix of the inner-product.

Matrix of the inner-product defined by the Riemmanian metric
at point base_point of the manifold.

Parameters
----------
base_point : array-like, shape=[..., n_copies, *base_shape]
Point on the manifold at which to compute the inner-product matrix.
Optional, default: None.

Returns
-------
matrix : array-like, shape=[..., n_copies, dim, dim]
Matrix of the inner-product at the base point.
"""
point_ = gs.reshape(base_point, (-1, *self.base_shape))
matrices = self.base_metric.metric_matrix(point_)
dim = self.base_metric.dim
reshaped = gs.reshape(matrices, (-1, self.n_copies, dim, dim))
return gs.squeeze(reshaped)

def inner_product(self, tangent_vec_a, tangent_vec_b, base_point):
"""Compute the inner-product of two tangent vectors at a base point.

Inner product defined by the Riemannian metric at point `base_point`
between tangent vectors `tangent_vec_a` and `tangent_vec_b`.

Parameters
----------
tangent_vec_a : array-like, shape=[..., n_copies, *base_shape]
First tangent vector at base point.
tangent_vec_b : array-like, shape=[..., n_copies, *base_shape]
Second tangent vector at base point.
base_point : array-like, shape=[..., n_copies, *base_shape]
Point on the manifold.
Optional, default: None.

Returns
-------
inner_prod : array-like, shape=[...,]
Inner-product of the two tangent vectors.
"""
tangent_vec_a_, tangent_vec_b_, point_ = gs.broadcast_arrays(
tangent_vec_a, tangent_vec_b, base_point
)
point_ = gs.reshape(point_, (-1, *self.base_shape))
vector_a = gs.reshape(tangent_vec_a_, (-1, *self.base_shape))
vector_b = gs.reshape(tangent_vec_b_, (-1, *self.base_shape))
inner_each = self.base_metric.inner_product(vector_a, vector_b, point_)
reshaped = gs.reshape(inner_each, (-1, self.n_copies))
return gs.squeeze(gs.sum(reshaped, axis=-1))

def exp(self, tangent_vec, base_point, **kwargs):
"""Compute the Riemannian exponential of a tangent vector.

Parameters
----------
tangent_vec : array-like, shape=[..., n_copies, *base_shape]
Tangent vector at a base point.
base_point : array-like, shape=[..., n_copies, *base_shape]
Point on the manifold.
Optional, default: None.

Returns
-------
exp : array-like, shape=[..., n_copies, *base_shape]
Point on the manifold equal to the Riemannian exponential
of tangent_vec at the base point.
"""
tangent_vec, point_ = gs.broadcast_arrays(tangent_vec, base_point)
point_ = gs.reshape(point_, (-1, *self.base_shape))
vector_ = gs.reshape(tangent_vec, (-1, *self.base_shape))
each_exp = self.base_metric.exp(vector_, point_)
reshaped = gs.reshape(each_exp, (-1, self.n_copies) + self.base_shape)
return gs.squeeze(reshaped)

def log(self, point, base_point, **kwargs):
"""Compute the Riemannian logarithm of a point.

Parameters
----------
point : array-like, shape=[..., n_copies, *base_shape]
Point on the manifold.
base_point : array-like, shape=[..., n_copies, *base_shape]
Point on the manifold.
Optional, default: None.

Returns
-------
log : array-like, shape=[..., n_copies, *base_shape]
Tangent vector at the base point equal to the Riemannian logarithm
of point at the base point.
"""
point_, base_point_ = gs.broadcast_arrays(point, base_point)
base_point_ = gs.reshape(base_point_, (-1, *self.base_shape))
point_ = gs.reshape(point_, (-1, *self.base_shape))
each_log = self.base_metric.log(point_, base_point_)
reshaped = gs.reshape(each_log, (-1, self.n_copies) + self.base_shape)
return gs.squeeze(reshaped)
125 changes: 125 additions & 0 deletions geomstats/geometry/product_riemannian_metric.py
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Original file line number Diff line number Diff line change
Expand Up @@ -287,3 +287,128 @@ def log(self, point, base_point=None, point_type=None, **kwargs):
axis=-2,
)
return logs


class NFoldMetric(RiemannianMetric):
r"""Class for an n-fold product manifold :math:`M^n`.

Define a manifold as the product manifold of n copies of a given base manifold M.

Parameters
----------
base_metric : RiemannianMetric
Base metric.
n_copies : int
Number of replication of the base metric.
"""

def __init__(self, base_metric, n_copies):
geomstats.errors.check_integer(n_copies, "n_copies")
dim = n_copies * base_metric.dim
base_shape = base_metric.shape
super(NFoldMetric, self).__init__(dim=dim, shape=(n_copies, *base_shape))
self.base_shape = base_shape
self.base_metric = base_metric
self.n_copies = n_copies

def metric_matrix(self, base_point=None):
"""Compute the matrix of the inner-product.

Matrix of the inner-product defined by the Riemmanian metric
at point base_point of the manifold.

Parameters
----------
base_point : array-like, shape=[..., n_copies, *base_shape]
Point on the manifold at which to compute the inner-product matrix.
Optional, default: None.

Returns
-------
matrix : array-like, shape=[..., n_copies, dim, dim]
Matrix of the inner-product at the base point.
"""
point_ = gs.reshape(base_point, (-1, *self.base_shape))
matrices = self.base_metric.metric_matrix(point_)
dim = self.base_metric.dim
reshaped = gs.reshape(matrices, (-1, self.n_copies, dim, dim))
return gs.squeeze(reshaped)

def inner_product(self, tangent_vec_a, tangent_vec_b, base_point):
"""Compute the inner-product of two tangent vectors at a base point.

Inner product defined by the Riemannian metric at point `base_point`
between tangent vectors `tangent_vec_a` and `tangent_vec_b`.

Parameters
----------
tangent_vec_a : array-like, shape=[..., n_copies, *base_shape]
First tangent vector at base point.
tangent_vec_b : array-like, shape=[..., n_copies, *base_shape]
Second tangent vector at base point.
base_point : array-like, shape=[..., n_copies, *base_shape]
Point on the manifold.
Optional, default: None.

Returns
-------
inner_prod : array-like, shape=[...,]
Inner-product of the two tangent vectors.
"""
tangent_vec_a_, tangent_vec_b_, point_ = gs.broadcast_arrays(
tangent_vec_a, tangent_vec_b, base_point
)
point_ = gs.reshape(point_, (-1, *self.base_shape))
vector_a = gs.reshape(tangent_vec_a_, (-1, *self.base_shape))
vector_b = gs.reshape(tangent_vec_b_, (-1, *self.base_shape))
inner_each = self.base_metric.inner_product(vector_a, vector_b, point_)
reshaped = gs.reshape(inner_each, (-1, self.n_copies))
return gs.squeeze(gs.sum(reshaped, axis=-1))

def exp(self, tangent_vec, base_point, **kwargs):
"""Compute the Riemannian exponential of a tangent vector.

Parameters
----------
tangent_vec : array-like, shape=[..., n_copies, *base_shape]
Tangent vector at a base point.
base_point : array-like, shape=[..., n_copies, *base_shape]
Point on the manifold.
Optional, default: None.

Returns
-------
exp : array-like, shape=[..., n_copies, *base_shape]
Point on the manifold equal to the Riemannian exponential
of tangent_vec at the base point.
"""
tangent_vec, point_ = gs.broadcast_arrays(tangent_vec, base_point)
point_ = gs.reshape(point_, (-1, *self.base_shape))
vector_ = gs.reshape(tangent_vec, (-1, *self.base_shape))
each_exp = self.base_metric.exp(vector_, point_)
reshaped = gs.reshape(each_exp, (-1, self.n_copies) + self.base_shape)
return gs.squeeze(reshaped)

def log(self, point, base_point, **kwargs):
"""Compute the Riemannian logarithm of a point.

Parameters
----------
point : array-like, shape=[..., n_copies, *base_shape]
Point on the manifold.
base_point : array-like, shape=[..., n_copies, *base_shape]
Point on the manifold.
Optional, default: None.

Returns
-------
log : array-like, shape=[..., n_copies, *base_shape]
Tangent vector at the base point equal to the Riemannian logarithm
of point at the base point.
"""
point_, base_point_ = gs.broadcast_arrays(point, base_point)
base_point_ = gs.reshape(base_point_, (-1, *self.base_shape))
point_ = gs.reshape(point_, (-1, *self.base_shape))
each_log = self.base_metric.log(point_, base_point_)
reshaped = gs.reshape(each_log, (-1, self.n_copies) + self.base_shape)
return gs.squeeze(reshaped)
7 changes: 3 additions & 4 deletions tests/tests_geomstats/test_product_manifold.py
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Original file line number Diff line number Diff line change
Expand Up @@ -4,12 +4,11 @@
import geomstats.tests
from geomstats.geometry.euclidean import Euclidean
from geomstats.geometry.minkowski import Minkowski
from geomstats.geometry.product_manifold import (
NFoldManifold,
from geomstats.geometry.product_manifold import NFoldManifold, ProductManifold
from geomstats.geometry.product_riemannian_metric import (
NFoldMetric,
ProductManifold,
ProductRiemannianMetric,
)
from geomstats.geometry.product_riemannian_metric import ProductRiemannianMetric
from tests.conftest import Parametrizer
from tests.data.product_manifold_data import (
NFoldManifoldTestData,
Expand Down
0