DOC: Improved documentation of matrix_normal.

scipy/stats/_multivariate.py

@@ -669,7 +669,7 @@ class matrix_normal_gen(multi_rv_generic):
     A matrix normal random variable.
 
     The `mean` keyword specifies the mean. The `rowcov` keyword specifies the
-    among-row covariance matrix. The 'colcov' keyword specified the
+    among-row covariance matrix. The 'colcov' keyword specifies the
     among-column covariance matrix.
 
     Methods
@@ -700,10 +700,10 @@ class matrix_normal_gen(multi_rv_generic):
     -----
     %(_matnorm_doc_callparams_note)s
 
-    The covariance matrices `rowcov` and `colcov` must be (symmetric) positive
-    definite. If the samples in `X` are :math:`m \times n`, then `rowcov`
-    must be :math:`m \times m` and `colcov` must be :math:`n \times n`.
-    `mean` must be the same shape as `X`.
+    The covariance matrices specified by `rowcov` and `colcov` must be
+    (symmetric) positive definite. If the samples in `X` are
+    :math:`m \times n`, then `rowcov` must be :math:`m \times m` and
+    `colcov` must be :math:`n \times n`. `mean` must be the same shape as `X`.
 
     The probability density function for `matrix_normal` is
 
@@ -720,6 +720,12 @@ class matrix_normal_gen(multi_rv_generic):
     distribution is not currently supported. Covariance matrices must be
     full rank.
 
+    The `matrix_normal` distribution is closely related to the
+    `multivariate_normal` distribution. Specifically, :math:`\mathrm{Vec}(X)`
+    (the vectorisation of :math:`X`) has a multivariate normal distribution
+    with mean :math:`\mathrm{Vec}(M)` and covariance :math:`V \otimes U`
+    (where :math:`\otimes` is the Kronecker product).
+
     .. versionadded:: 0.17.0
 
     Examples
@@ -744,6 +750,14 @@ class matrix_normal_gen(multi_rv_generic):
            [ 4.1,  5.1]])
     >>> matrix_normal.pdf(X, mean=M, rowcov=U, colcov=V)
     0.023410202050005054
+       
+    >>> # Equivalent multivariate normal
+    >>> from scipy.stats import multivariate_normal
+    >>> vectorised_X = X.T.flatten()
+    >>> equiv_mean = M.T.flatten()
+    >>> equiv_cov = np.kron(V,U)
+    >>> multivariate_normal.pdf(vectorised_X, mean=equiv_mean, cov=equiv_cov)
+    0.023410202050005054
     """
 
     def __init__(self, seed=None):
@@ -966,6 +980,7 @@ def rvs(self, mean=None, rowcov=1, colcov=1, size=1, random_state=None):
 
 matrix_normal = matrix_normal_gen()
 
+
 class matrix_normal_frozen(multi_rv_frozen):
     def __init__(self, mean=None, rowcov=1, colcov=1, seed=None):
         """
@@ -1013,6 +1028,7 @@ def rvs(self, size=1, random_state=None):
         return self._dist.rvs(self.mean, self.rowcov, self.colcov, size,
                               random_state)
 
+
 # Set frozen generator docstrings from corresponding docstrings in
 # matrix_normal_gen and fill in default strings in class docstrings
 for name in ['logpdf', 'pdf', 'rvs']:

scipy/stats/tests/test_multivariate.py

@@ -475,27 +475,6 @@ def test_matches_multivariate(self):
                 assert_allclose(pdf1, pdf2, rtol=1E-10)
                 assert_allclose(logpdf1, logpdf2, rtol=1E-10)
 
-    def test_equivalent_multivariate(self):
-        # Check that the equivalent multivariate distribution matches
-        for i in range(1,5):
-            for j in range(1,5):
-                M = 0.3 * np.ones((i,j))
-                U = 0.5 * np.identity(i) + 0.5 * np.ones((i,i))
-                V = 0.7 * np.identity(j) + 0.3 * np.ones((j,j))
-
-                frozen = matrix_normal(mean=M, rowcov=U, colcov=V)
-                X = frozen.rvs(random_state=1234)
-                pdf1 = frozen.pdf(X)
-                logpdf1 = frozen.logpdf(X)
-
-                mvn = frozen.equivalent_multivariate_normal()
-                vecX = X.T.flatten()
-                pdf2 = mvn.pdf(vecX)
-                logpdf2 = mvn.logpdf(vecX)
-
-                assert_allclose(pdf1, pdf2, rtol=1E-10)
-                assert_allclose(logpdf1, logpdf2, rtol=1E-10)
-
     def test_array_input(self):
         # Check array of inputs has the same output as the separate entries.
         num_rows = 4