Do not segfault in svd(a) with VT.size > INT_MAX

scipy/linalg/_decomp_svd.py

@@ -116,6 +116,20 @@ def svd(a, full_matrices=True, compute_uv=True, overwrite_a=False,
     if lapack_driver not in ('gesdd', 'gesvd'):
         message = f'lapack_driver must be "gesdd" or "gesvd", not "{lapack_driver}"'
         raise ValueError(message)
+
+    if lapack_driver == 'gesdd' and compute_uv:
+        # XXX: revisit int32 when ILP64 lapack becomes a thing
+        max_mn, min_mn = (m, n) if m > n else (n, m)
+        if full_matrices:
+            if max_mn*max_mn > numpy.iinfo(numpy.int32).max:
+                raise ValueError(f"Indexing a matrix size {max_mn} x {max_mn} "
+                                 f" would incur integer overflow in LAPACK.")
+        else:
+            sz = max(m * min_mn, n * min_mn)
+            if max(m * min_mn, n * min_mn) > numpy.iinfo(numpy.int32).max:
+                raise ValueError(f"Indexing a matrix of {sz} elements would "
+                                  "incur an in integer overflow in LAPACK.")
+
     funcs = (lapack_driver, lapack_driver + '_lwork')
     gesXd, gesXd_lwork = get_lapack_funcs(funcs, (a1,), ilp64='preferred')
 

scipy/linalg/tests/test_decomp.py

@@ -1089,6 +1089,14 @@ class TestSVD_GESVD(TestSVD_GESDD):
     lapack_driver = 'gesvd'
 
 
+def test_svd_gesdd_nofegfault():
+    # svd(a) with {U,VT}.size > INT_MAX does not segfault
+    # cf https://github.com/scipy/scipy/issues/14001
+    df=np.ones((4799, 53130), dtype=np.float64)
+    with assert_raises(ValueError):
+        svd(df)
+
+
 class TestSVDVals:
 
     def test_empty(self):