From b202aad8d8e138d4c4cb8ccc590b87e1173f45bc Mon Sep 17 00:00:00 2001
From: Hameer Abbasi <einstein.edison@gmail.com>
Date: Wed, 29 Jan 2020 13:43:31 +0100
Subject: BUG: Fix for SVD not always sorted with hermitian=True

---
 numpy/linalg/linalg.py            | 21 +++++++++++++--------
 numpy/linalg/tests/test_linalg.py |  8 ++++++++
 2 files changed, 21 insertions(+), 8 deletions(-)

diff --git a/numpy/linalg/linalg.py b/numpy/linalg/linalg.py
index 0964e807b..1d572f876 100644
--- a/numpy/linalg/linalg.py
+++ b/numpy/linalg/linalg.py
@@ -24,7 +24,7 @@ from numpy.core import (
     add, multiply, sqrt, fastCopyAndTranspose, sum, isfinite,
     finfo, errstate, geterrobj, moveaxis, amin, amax, product, abs,
     atleast_2d, intp, asanyarray, object_, matmul,
-    swapaxes, divide, count_nonzero, isnan, sign
+    swapaxes, divide, count_nonzero, isnan, sign, argsort, sort
 )
 from numpy.core.multiarray import normalize_axis_index
 from numpy.core.overrides import set_module
@@ -1608,24 +1608,29 @@ def svd(a, full_matrices=True, compute_uv=True, hermitian=False):
     True
 
     """
+    import numpy as _nx
     a, wrap = _makearray(a)
 
     if hermitian:
-        # note: lapack returns eigenvalues in reverse order to our contract.
-        # reversing is cheap by design in numpy, so we do so to be consistent
+        # note: lapack svd returns eigenvalues with s ** 2 sorted descending,
+        # but eig returns s sorted ascending, so we re-order the eigenvalues
+        # and related arrays to have the correct order
         if compute_uv:
             s, u = eigh(a)
-            s = s[..., ::-1]
-            u = u[..., ::-1]
-            # singular values are unsigned, move the sign into v
-            vt = transpose(u * sign(s)[..., None, :]).conjugate()
+            sgn = sign(s)
             s = abs(s)
+            sidx = argsort(s)[..., ::-1]
+            sgn = _nx.take_along_axis(sgn, sidx, axis=-1)
+            s = _nx.take_along_axis(s, sidx, axis=-1)
+            u = _nx.take_along_axis(u, sidx[..., None, :], axis=-1)
+            # singular values are unsigned, move the sign into v
+            vt = transpose(u * sgn[..., None, :]).conjugate()
             return wrap(u), s, wrap(vt)
         else:
             s = eigvalsh(a)
             s = s[..., ::-1]
             s = abs(s)
-            return s
+            return sort(s)[..., ::-1]
 
     _assert_stacked_2d(a)
     t, result_t = _commonType(a)
diff --git a/numpy/linalg/tests/test_linalg.py b/numpy/linalg/tests/test_linalg.py
index 59c71d196..69352803e 100644
--- a/numpy/linalg/tests/test_linalg.py
+++ b/numpy/linalg/tests/test_linalg.py
@@ -680,6 +680,14 @@ class SVDHermitianCases(HermitianTestCase, HermitianGeneralizedTestCase):
         assert_allclose(a, dot_generalized(np.asarray(u) * np.asarray(s)[..., None, :],
                                            np.asarray(vt)),
                         rtol=get_rtol(u.dtype))
+        def hermitian(mat):
+            axes = list(range(mat.ndim))
+            axes[-1], axes[-2] = axes[-2], axes[-1]
+            return np.conj(np.transpose(mat, axes=axes))
+        
+        assert_almost_equal(np.matmul(u, hermitian(u)), np.broadcast_to(np.eye(u.shape[-1]), u.shape))
+        assert_almost_equal(np.matmul(vt, hermitian(vt)), np.broadcast_to(np.eye(vt.shape[-1]), vt.shape))
+        assert_equal(np.sort(s)[..., ::-1], s)
         assert_(consistent_subclass(u, a))
         assert_(consistent_subclass(vt, a))
 
-- 
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