ENH: Allow use of svd on empty arrays

part of #8654

3 files changed, 25 insertions, 17 deletions

diff --git a/numpy/linalg/linalg.py b/numpy/linalg/linalg.py
index 90dc2e657..8e7ad70cd 100644
--- a/numpy/linalg/linalg.py
+++ b/numpy/linalg/linalg.py
@@ -1527,7 +1527,6 @@ def svd(a, full_matrices=True, compute_uv=True):
 
     """
     a, wrap = _makearray(a)
-    _assertNoEmpty2d(a)
     _assertRankAtLeast2(a)
     t, result_t = _commonType(a)
 
@@ -1644,6 +1643,7 @@ def cond(x, p=None):
 
     """
     x = asarray(x)  # in case we have a matrix
+    _assertNoEmpty2d(x)
     if p is None or p == 2 or p == -2:
         s = svd(x, compute_uv=False)
         with errstate(all='ignore'):
diff --git a/numpy/linalg/tests/test_linalg.py b/numpy/linalg/tests/test_linalg.py
index 87dfe988a..1c24f1e04 100644
--- a/numpy/linalg/tests/test_linalg.py
+++ b/numpy/linalg/tests/test_linalg.py
@@ -644,10 +644,6 @@ class TestEig(EigCases):
 class SVDCases(LinalgSquareTestCase, LinalgGeneralizedSquareTestCase):
 
     def do(self, a, b, tags):
-        if 'size-0' in tags:
-            assert_raises(LinAlgError, linalg.svd, a, 0)
-            return
-
         u, s, vt = linalg.svd(a, 0)
         assert_allclose(a, dot_generalized(np.asarray(u) * np.asarray(s)[..., None, :],
                                            np.asarray(vt)),
@@ -670,15 +666,19 @@ class TestSVD(SVDCases):
         for dtype in [single, double, csingle, cdouble]:
             check(dtype)
 
-    def test_0_size(self):
-        # These raise errors currently
-        # (which does not mean that it may not make sense)
-        a = np.zeros((0, 0), dtype=np.complex64)
-        assert_raises(linalg.LinAlgError, linalg.svd, a)
-        a = np.zeros((0, 1), dtype=np.complex64)
-        assert_raises(linalg.LinAlgError, linalg.svd, a)
-        a = np.zeros((1, 0), dtype=np.complex64)
-        assert_raises(linalg.LinAlgError, linalg.svd, a)
+    def test_empty_identity(self):
+        """ Empty input should put an identity matrix in u or vh """
+        x = np.empty((4, 0))
+        u, s, vh = linalg.svd(x, compute_uv=True)
+        assert_equal(u.shape, (4, 4))
+        assert_equal(vh.shape, (0, 0))
+        assert_equal(u, np.eye(4))
+
+        x = np.empty((0, 4))
+        u, s, vh = linalg.svd(x, compute_uv=True)
+        assert_equal(u.shape, (0, 0))
+        assert_equal(vh.shape, (4, 4))
+        assert_equal(vh, np.eye(4))
 
 
 class CondCases(LinalgSquareTestCase, LinalgGeneralizedSquareTestCase):
diff --git a/numpy/linalg/umath_linalg.c.src b/numpy/linalg/umath_linalg.c.src
index 7dc1cb0cb..9fc68a7aa 100644
--- a/numpy/linalg/umath_linalg.c.src
+++ b/numpy/linalg/umath_linalg.c.src
@@ -2735,19 +2735,18 @@ static NPY_INLINE void
                            (fortran_int)dimensions[0],
                            (fortran_int)dimensions[1])) {
         LINEARIZE_DATA_t a_in, u_out, s_out, v_out;
+        fortran_int min_m_n = params.M < params.N ? params.M : params.N;
 
         init_linearize_data(&a_in, params.N, params.M, steps[1], steps[0]);
         if ('N' == params.JOBZ) {
             /* only the singular values are wanted */
-            fortran_int min_m_n = params.M < params.N? params.M : params.N;
             init_linearize_data(&s_out, 1, min_m_n, 0, steps[2]);
         } else {
             fortran_int u_columns, v_rows;
-            fortran_int min_m_n = params.M < params.N? params.M : params.N;
             if ('S' == params.JOBZ) {
                 u_columns = min_m_n;
                 v_rows = min_m_n;
-            } else {
+            } else { /* JOBZ == 'A' */
                 u_columns = params.M;
                 v_rows = params.N;
             }
@@ -2771,6 +2770,15 @@ static NPY_INLINE void
                 if ('N' == params.JOBZ) {
                     delinearize_@REALTYPE@_matrix(args[1], params.S, &s_out);
                 } else {
+                    if ('A' == params.JOBZ && min_m_n == 0) {
+                        /* Lapack has betrayed us and left these uninitialized,
+                         * so produce an identity matrix for whichever of u
+                         * and v is not empty.
+                         */
+                        identity_@TYPE@_matrix(params.U, params.M);
+                        identity_@TYPE@_matrix(params.VT, params.N);
+                    }
+
                     delinearize_@TYPE@_matrix(args[1], params.U, &u_out);
                     delinearize_@REALTYPE@_matrix(args[2], params.S, &s_out);
                     delinearize_@TYPE@_matrix(args[3], params.VT, &v_out);