Merge pull request #125 from antoinecollas/complex_valued_manifolds

Add Complex valued manifolds.

src/pymanopt/manifolds/__init__.py

@@ -3,8 +3,11 @@
     "ComplexGrassmann",
     "Elliptope",
     "Euclidean",
+    "ComplexEuclidean",
     "FixedRankEmbedded",
     "Grassmann",
+    "HermitianPositiveDefinite",
+    "SpecialHermitianPositiveDefinite",
     "Oblique",
     "PSDFixedRank",
     "PSDFixedRankComplex",
@@ -23,14 +26,18 @@
 ]
 
 from .complex_circle import ComplexCircle
-from .euclidean import Euclidean, SkewSymmetric, Symmetric
+from .euclidean import ComplexEuclidean, Euclidean, SkewSymmetric, Symmetric
 from .fixed_rank import FixedRankEmbedded
 from .grassmann import ComplexGrassmann, Grassmann
 from .group import SpecialOrthogonalGroup, UnitaryGroup
 from .hyperbolic import PoincareBall
 from .oblique import Oblique
 from .positive import Positive
-from .positive_definite import SymmetricPositiveDefinite
+from .positive_definite import (
+    HermitianPositiveDefinite,
+    SpecialHermitianPositiveDefinite,
+    SymmetricPositiveDefinite,
+)
 from .product import Product
 from .psd import Elliptope, PSDFixedRank, PSDFixedRankComplex
 from .sphere import (

src/pymanopt/manifolds/euclidean.py

@@ -15,8 +15,12 @@ def typical_dist(self):
 
     def inner_product(self, point, tangent_vector_a, tangent_vector_b):
         return float(
-            np.tensordot(
-                tangent_vector_a, tangent_vector_b, axes=tangent_vector_a.ndim
+            np.real(
+                np.tensordot(
+                    tangent_vector_a.conj(),
+                    tangent_vector_b,
+                    axes=tangent_vector_a.ndim,
+                )
             )
         )
 
@@ -92,6 +96,45 @@ def __init__(self, *shape: int):
         super().__init__(name, dimension, *shape)
 
 
+class ComplexEuclidean(_Euclidean):
+    r"""Complex Euclidean manifold.
+
+    Args:
+        shape: Shape of points on the manifold.
+
+    Note:
+        If ``shape == (n,)``, this is the manifold of vectors with the
+        standard Euclidean inner product, i.e., :math:`\C^n`.
+        For ``shape == (m, n)``, it corresponds to the manifold of ``m x n``
+        matrices equipped with the standard trace inner product.
+        For ``shape == (n1, n2, ..., nk)``, the class represents the manifold
+        of tensors of shape ``n1 x n2 x ... x nk`` with the inner product
+        corresponding to the usual tensor dot product.
+    """
+
+    def __init__(self, *shape):
+        if len(shape) == 0:
+            raise TypeError("Need shape parameters")
+        if len(shape) == 1:
+            (n1,) = shape
+            name = f"Complex Euclidean manifold of {n1}-vectors"
+        elif len(shape) == 2:
+            n1, n2 = shape
+            name = f"Complex Euclidean manifold of {n1}x{n2} matrices"
+        else:
+            name = f"Complex Euclidean manifold of shape {shape} tensors"
+        dimension = 2 * np.prod(shape)
+        super().__init__(name, dimension, *shape)
+
+    def random_point(self):
+        return np.random.randn(*self._shape) + 1j * np.random.randn(
+            *self._shape
+        )
+
+    def zero_vector(self, point):
+        return np.zeros(self._shape, dtype=complex)
+
+
 class Symmetric(_Euclidean):
     """(Product) manifold of symmetric matrices.
 

src/pymanopt/manifolds/manifold.py

@@ -6,7 +6,7 @@
 import numpy as np
 
 
-def _raise_not_implemented_error(method):
+def raise_not_implemented_error(method):
     @functools.wraps(method)
     def wrapper(self, *args, **kwargs):
         raise NotImplementedError(
@@ -206,7 +206,7 @@ def zero_vector(self, point):
 
     # Methods which are only required by certain optimizers.
 
-    @_raise_not_implemented_error
+    @raise_not_implemented_error
     def dist(self, point_a, point_b):
         """The geodesic distance between two points on the manifold.
 
@@ -218,7 +218,7 @@ def dist(self, point_a, point_b):
             The distance between ``point_a`` and ``point_b`` on the manifold.
         """
 
-    @_raise_not_implemented_error
+    @raise_not_implemented_error
     def euclidean_to_riemannian_gradient(self, point, euclidean_gradient):
         """Converts the Euclidean to the Riemannian gradient.
 
@@ -233,7 +233,7 @@ def euclidean_to_riemannian_gradient(self, point, euclidean_gradient):
             This must be a tangent vector at ``point``.
         """
 
-    @_raise_not_implemented_error
+    @raise_not_implemented_error
     def euclidean_to_riemannian_hessian(
         self, point, euclidean_gradient, euclidean_hessian, tangent_vector
     ):
@@ -257,7 +257,7 @@ def euclidean_to_riemannian_hessian(
             The Riemannian Hessian as a tangent vector at ``point``.
         """
 
-    @_raise_not_implemented_error
+    @raise_not_implemented_error
     def retraction(self, point, tangent_vector):
         """Retracts a tangent vector back to the manifold.
 
@@ -275,7 +275,7 @@ def retraction(self, point, tangent_vector):
             the direction of ``tangent_vector``.
         """
 
-    @_raise_not_implemented_error
+    @raise_not_implemented_error
     def exp(self, point, tangent_vector):
         """Computes the exponential map on the manifold.
 
@@ -288,7 +288,7 @@ def exp(self, point, tangent_vector):
             along a geodesic in the direction of ``tangent_vector``.
         """
 
-    @_raise_not_implemented_error
+    @raise_not_implemented_error
     def log(self, point_a, point_b):
         """Computes the logarithmic map on the manifold.
 
@@ -306,7 +306,7 @@ def log(self, point_a, point_b):
             A tangent vector in the tangent space at ``point_a``.
         """
 
-    @_raise_not_implemented_error
+    @raise_not_implemented_error
     def transport(self, point_a, point_b, tangent_vector_a):
         """Compute transport of tangent vectors between tangent spaces.
 
@@ -326,7 +326,7 @@ def transport(self, point_a, point_b, tangent_vector_a):
             A tangent vector at ``point_b``.
         """
 
-    @_raise_not_implemented_error
+    @raise_not_implemented_error
     def pair_mean(self, point_a, point_b):
         """Computes the intrinsic mean of two points on the manifold.
 
@@ -342,7 +342,7 @@ def pair_mean(self, point_a, point_b):
             The mid-way point between ``point_a`` and ``point_b``.
         """
 
-    @_raise_not_implemented_error
+    @raise_not_implemented_error
     def to_tangent_space(self, point, vector):
         """Re-tangentialize a vector.
 
@@ -411,7 +411,7 @@ class RiemannianSubmanifold(Manifold, metaclass=abc.ABCMeta):
         the notes in section 5.11 of [Bou2020]_.
     """
 
-    @_raise_not_implemented_error
+    @raise_not_implemented_error
     def weingarten(self, point, tangent_vector, normal_vector):
         """Compute the Weingarten map of the manifold.