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ckpts/universal/global_step40/zero/12.attention.query_key_value.weight/exp_avg.pt

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ckpts/universal/global_step40/zero/12.attention.query_key_value.weight/fp32.pt

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ckpts/universal/global_step40/zero/5.attention.query_key_value.weight/exp_avg_sq.pt

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+oid sha256:a4a982f870c12d4d6ad3c888be7a38add8529f91b462285165e3bfe72fabe2d4
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venv/lib/python3.10/site-packages/scipy/linalg/tests/test_basic.py

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+import itertools
+import warnings
+
+import numpy as np
+from numpy import (arange, array, dot, zeros, identity, conjugate, transpose,
+                   float32)
+from numpy.random import random
+
+from numpy.testing import (assert_equal, assert_almost_equal, assert_,
+                           assert_array_almost_equal, assert_allclose,
+                           assert_array_equal, suppress_warnings)
+import pytest
+from pytest import raises as assert_raises
+
+from scipy.linalg import (solve, inv, det, lstsq, pinv, pinvh, norm,
+                          solve_banded, solveh_banded, solve_triangular,
+                          solve_circulant, circulant, LinAlgError, block_diag,
+                          matrix_balance, qr, LinAlgWarning)
+
+from scipy.linalg._testutils import assert_no_overwrite
+from scipy._lib._testutils import check_free_memory, IS_MUSL
+from scipy.linalg.blas import HAS_ILP64
+from scipy._lib.deprecation import _NoValue
+
+REAL_DTYPES = (np.float32, np.float64, np.longdouble)
+COMPLEX_DTYPES = (np.complex64, np.complex128, np.clongdouble)
+DTYPES = REAL_DTYPES + COMPLEX_DTYPES
+
+
+def _eps_cast(dtyp):
+    """Get the epsilon for dtype, possibly downcast to BLAS types."""
+    dt = dtyp
+    if dt == np.longdouble:
+        dt = np.float64
+    elif dt == np.clongdouble:
+        dt = np.complex128
+    return np.finfo(dt).eps
+
+
+class TestSolveBanded:
+
+    def test_real(self):
+        a = array([[1.0, 20, 0, 0],
+                   [-30, 4, 6, 0],
+                   [2, 1, 20, 2],
+                   [0, -1, 7, 14]])
+        ab = array([[0.0, 20, 6, 2],
+                    [1, 4, 20, 14],
+                    [-30, 1, 7, 0],
+                    [2, -1, 0, 0]])
+        l, u = 2, 1
+        b4 = array([10.0, 0.0, 2.0, 14.0])
+        b4by1 = b4.reshape(-1, 1)
+        b4by2 = array([[2, 1],
+                       [-30, 4],
+                       [2, 3],
+                       [1, 3]])
+        b4by4 = array([[1, 0, 0, 0],
+                       [0, 0, 0, 1],
+                       [0, 1, 0, 0],
+                       [0, 1, 0, 0]])
+        for b in [b4, b4by1, b4by2, b4by4]:
+            x = solve_banded((l, u), ab, b)
+            assert_array_almost_equal(dot(a, x), b)
+
+    def test_complex(self):
+        a = array([[1.0, 20, 0, 0],
+                   [-30, 4, 6, 0],
+                   [2j, 1, 20, 2j],
+                   [0, -1, 7, 14]])
+        ab = array([[0.0, 20, 6, 2j],
+                    [1, 4, 20, 14],
+                    [-30, 1, 7, 0],
+                    [2j, -1, 0, 0]])
+        l, u = 2, 1
+        b4 = array([10.0, 0.0, 2.0, 14.0j])
+        b4by1 = b4.reshape(-1, 1)
+        b4by2 = array([[2, 1],
+                       [-30, 4],
+                       [2, 3],
+                       [1, 3]])
+        b4by4 = array([[1, 0, 0, 0],
+                       [0, 0, 0, 1j],
+                       [0, 1, 0, 0],
+                       [0, 1, 0, 0]])
+        for b in [b4, b4by1, b4by2, b4by4]:
+            x = solve_banded((l, u), ab, b)
+            assert_array_almost_equal(dot(a, x), b)
+
+    def test_tridiag_real(self):
+        ab = array([[0.0, 20, 6, 2],
+                   [1, 4, 20, 14],
+                   [-30, 1, 7, 0]])
+        a = np.diag(ab[0, 1:], 1) + np.diag(ab[1, :], 0) + np.diag(
+                                                                ab[2, :-1], -1)
+        b4 = array([10.0, 0.0, 2.0, 14.0])
+        b4by1 = b4.reshape(-1, 1)
+        b4by2 = array([[2, 1],
+                       [-30, 4],
+                       [2, 3],
+                       [1, 3]])
+        b4by4 = array([[1, 0, 0, 0],
+                       [0, 0, 0, 1],
+                       [0, 1, 0, 0],
+                       [0, 1, 0, 0]])
+        for b in [b4, b4by1, b4by2, b4by4]:
+            x = solve_banded((1, 1), ab, b)
+            assert_array_almost_equal(dot(a, x), b)
+
+    def test_tridiag_complex(self):
+        ab = array([[0.0, 20, 6, 2j],
+                   [1, 4, 20, 14],
+                   [-30, 1, 7, 0]])
+        a = np.diag(ab[0, 1:], 1) + np.diag(ab[1, :], 0) + np.diag(
+                                                               ab[2, :-1], -1)
+        b4 = array([10.0, 0.0, 2.0, 14.0j])
+        b4by1 = b4.reshape(-1, 1)
+        b4by2 = array([[2, 1],
+                       [-30, 4],
+                       [2, 3],
+                       [1, 3]])
+        b4by4 = array([[1, 0, 0, 0],
+                       [0, 0, 0, 1],
+                       [0, 1, 0, 0],
+                       [0, 1, 0, 0]])
+        for b in [b4, b4by1, b4by2, b4by4]:
+            x = solve_banded((1, 1), ab, b)
+            assert_array_almost_equal(dot(a, x), b)
+
+    def test_check_finite(self):
+        a = array([[1.0, 20, 0, 0],
+                   [-30, 4, 6, 0],
+                   [2, 1, 20, 2],
+                   [0, -1, 7, 14]])
+        ab = array([[0.0, 20, 6, 2],
+                    [1, 4, 20, 14],
+                    [-30, 1, 7, 0],
+                    [2, -1, 0, 0]])
+        l, u = 2, 1
+        b4 = array([10.0, 0.0, 2.0, 14.0])
+        x = solve_banded((l, u), ab, b4, check_finite=False)
+        assert_array_almost_equal(dot(a, x), b4)
+
+    def test_bad_shape(self):
+        ab = array([[0.0, 20, 6, 2],
+                    [1, 4, 20, 14],
+                    [-30, 1, 7, 0],
+                    [2, -1, 0, 0]])
+        l, u = 2, 1
+        bad = array([1.0, 2.0, 3.0, 4.0]).reshape(-1, 4)
+        assert_raises(ValueError, solve_banded, (l, u), ab, bad)
+        assert_raises(ValueError, solve_banded, (l, u), ab, [1.0, 2.0])
+
+        # Values of (l,u) are not compatible with ab.
+        assert_raises(ValueError, solve_banded, (1, 1), ab, [1.0, 2.0])
+
+    def test_1x1(self):
+        b = array([[1., 2., 3.]])
+        x = solve_banded((1, 1), [[0], [2], [0]], b)
+        assert_array_equal(x, [[0.5, 1.0, 1.5]])
+        assert_equal(x.dtype, np.dtype('f8'))
+        assert_array_equal(b, [[1.0, 2.0, 3.0]])
+
+    def test_native_list_arguments(self):
+        a = [[1.0, 20, 0, 0],
+             [-30, 4, 6, 0],
+             [2, 1, 20, 2],
+             [0, -1, 7, 14]]
+        ab = [[0.0, 20, 6, 2],
+              [1, 4, 20, 14],
+              [-30, 1, 7, 0],
+              [2, -1, 0, 0]]
+        l, u = 2, 1
+        b = [10.0, 0.0, 2.0, 14.0]
+        x = solve_banded((l, u), ab, b)
+        assert_array_almost_equal(dot(a, x), b)
+
+
+class TestSolveHBanded:
+
+    def test_01_upper(self):
+        # Solve
+        # [ 4 1 2 0]     [1]
+        # [ 1 4 1 2] X = [4]
+        # [ 2 1 4 1]     [1]
+        # [ 0 2 1 4]     [2]
+        # with the RHS as a 1D array.
+        ab = array([[0.0, 0.0, 2.0, 2.0],
+                    [-99, 1.0, 1.0, 1.0],
+                    [4.0, 4.0, 4.0, 4.0]])
+        b = array([1.0, 4.0, 1.0, 2.0])
+        x = solveh_banded(ab, b)
+        assert_array_almost_equal(x, [0.0, 1.0, 0.0, 0.0])
+
+    def test_02_upper(self):
+        # Solve
+        # [ 4 1 2 0]     [1 6]
+        # [ 1 4 1 2] X = [4 2]
+        # [ 2 1 4 1]     [1 6]
+        # [ 0 2 1 4]     [2 1]
+        #
+        ab = array([[0.0, 0.0, 2.0, 2.0],
+                    [-99, 1.0, 1.0, 1.0],
+                    [4.0, 4.0, 4.0, 4.0]])
+        b = array([[1.0, 6.0],
+                   [4.0, 2.0],
+                   [1.0, 6.0],
+                   [2.0, 1.0]])
+        x = solveh_banded(ab, b)
+        expected = array([[0.0, 1.0],
+                          [1.0, 0.0],
+                          [0.0, 1.0],
+                          [0.0, 0.0]])
+        assert_array_almost_equal(x, expected)
+
+    def test_03_upper(self):
+        # Solve
+        # [ 4 1 2 0]     [1]
+        # [ 1 4 1 2] X = [4]
+        # [ 2 1 4 1]     [1]
+        # [ 0 2 1 4]     [2]
+        # with the RHS as a 2D array with shape (3,1).
+        ab = array([[0.0, 0.0, 2.0, 2.0],
+                    [-99, 1.0, 1.0, 1.0],
+                    [4.0, 4.0, 4.0, 4.0]])
+        b = array([1.0, 4.0, 1.0, 2.0]).reshape(-1, 1)
+        x = solveh_banded(ab, b)
+        assert_array_almost_equal(x, array([0., 1., 0., 0.]).reshape(-1, 1))
+
+    def test_01_lower(self):
+        # Solve
+        # [ 4 1 2 0]     [1]
+        # [ 1 4 1 2] X = [4]
+        # [ 2 1 4 1]     [1]
+        # [ 0 2 1 4]     [2]
+        #
+        ab = array([[4.0, 4.0, 4.0, 4.0],
+                    [1.0, 1.0, 1.0, -99],
+                    [2.0, 2.0, 0.0, 0.0]])
+        b = array([1.0, 4.0, 1.0, 2.0])
+        x = solveh_banded(ab, b, lower=True)
+        assert_array_almost_equal(x, [0.0, 1.0, 0.0, 0.0])
+
+    def test_02_lower(self):
+        # Solve
+        # [ 4 1 2 0]     [1 6]
+        # [ 1 4 1 2] X = [4 2]
+        # [ 2 1 4 1]     [1 6]
+        # [ 0 2 1 4]     [2 1]
+        #
+        ab = array([[4.0, 4.0, 4.0, 4.0],
+                    [1.0, 1.0, 1.0, -99],
+                    [2.0, 2.0, 0.0, 0.0]])
+        b = array([[1.0, 6.0],
+                   [4.0, 2.0],
+                   [1.0, 6.0],
+                   [2.0, 1.0]])
+        x = solveh_banded(ab, b, lower=True)
+        expected = array([[0.0, 1.0],
+                          [1.0, 0.0],
+                          [0.0, 1.0],
+                          [0.0, 0.0]])
+        assert_array_almost_equal(x, expected)
+
+    def test_01_float32(self):
+        # Solve
+        # [ 4 1 2 0]     [1]
+        # [ 1 4 1 2] X = [4]
+        # [ 2 1 4 1]     [1]
+        # [ 0 2 1 4]     [2]
+        #
+        ab = array([[0.0, 0.0, 2.0, 2.0],
+                    [-99, 1.0, 1.0, 1.0],
+                    [4.0, 4.0, 4.0, 4.0]], dtype=float32)
+        b = array([1.0, 4.0, 1.0, 2.0], dtype=float32)
+        x = solveh_banded(ab, b)
+        assert_array_almost_equal(x, [0.0, 1.0, 0.0, 0.0])
+
+    def test_02_float32(self):
+        # Solve
+        # [ 4 1 2 0]     [1 6]
+        # [ 1 4 1 2] X = [4 2]
+        # [ 2 1 4 1]     [1 6]
+        # [ 0 2 1 4]     [2 1]
+        #
+        ab = array([[0.0, 0.0, 2.0, 2.0],
+                    [-99, 1.0, 1.0, 1.0],
+                    [4.0, 4.0, 4.0, 4.0]], dtype=float32)
+        b = array([[1.0, 6.0],
+                   [4.0, 2.0],
+                   [1.0, 6.0],
+                   [2.0, 1.0]], dtype=float32)
+        x = solveh_banded(ab, b)
+        expected = array([[0.0, 1.0],
+                          [1.0, 0.0],
+                          [0.0, 1.0],
+                          [0.0, 0.0]])
+        assert_array_almost_equal(x, expected)
+
+    def test_01_complex(self):
+        # Solve
+        # [ 4 -j  2  0]     [2-j]
+        # [ j  4 -j  2] X = [4-j]
+        # [ 2  j  4 -j]     [4+j]
+        # [ 0  2  j  4]     [2+j]
+        #
+        ab = array([[0.0, 0.0, 2.0, 2.0],
+                    [-99, -1.0j, -1.0j, -1.0j],
+                    [4.0, 4.0, 4.0, 4.0]])
+        b = array([2-1.0j, 4.0-1j, 4+1j, 2+1j])
+        x = solveh_banded(ab, b)
+        assert_array_almost_equal(x, [0.0, 1.0, 1.0, 0.0])
+
+    def test_02_complex(self):
+        # Solve
+        # [ 4 -j  2  0]     [2-j 2+4j]
+        # [ j  4 -j  2] X = [4-j -1-j]
+        # [ 2  j  4 -j]     [4+j 4+2j]
+        # [ 0  2  j  4]     [2+j j]
+        #
+        ab = array([[0.0, 0.0, 2.0, 2.0],
+                    [-99, -1.0j, -1.0j, -1.0j],
+                    [4.0, 4.0, 4.0, 4.0]])
+        b = array([[2-1j, 2+4j],
+                   [4.0-1j, -1-1j],
+                   [4.0+1j, 4+2j],
+                   [2+1j, 1j]])
+        x = solveh_banded(ab, b)
+        expected = array([[0.0, 1.0j],
+                          [1.0, 0.0],
+                          [1.0, 1.0],
+                          [0.0, 0.0]])
+        assert_array_almost_equal(x, expected)
+
+    def test_tridiag_01_upper(self):
+        # Solve
+        # [ 4 1 0]     [1]
+        # [ 1 4 1] X = [4]
+        # [ 0 1 4]     [1]
+        # with the RHS as a 1D array.
+        ab = array([[-99, 1.0, 1.0], [4.0, 4.0, 4.0]])
+        b = array([1.0, 4.0, 1.0])
+        x = solveh_banded(ab, b)
+        assert_array_almost_equal(x, [0.0, 1.0, 0.0])
+
+    def test_tridiag_02_upper(self):
+        # Solve
+        # [ 4 1 0]     [1 4]
+        # [ 1 4 1] X = [4 2]
+        # [ 0 1 4]     [1 4]
+        #
+        ab = array([[-99, 1.0, 1.0],
+                    [4.0, 4.0, 4.0]])
+        b = array([[1.0, 4.0],
+                   [4.0, 2.0],
+                   [1.0, 4.0]])
+        x = solveh_banded(ab, b)
+        expected = array([[0.0, 1.0],
+                          [1.0, 0.0],
+                          [0.0, 1.0]])
+        assert_array_almost_equal(x, expected)
+
+    def test_tridiag_03_upper(self):
+        # Solve
+        # [ 4 1 0]     [1]
+        # [ 1 4 1] X = [4]
+        # [ 0 1 4]     [1]
+        # with the RHS as a 2D array with shape (3,1).
+        ab = array([[-99, 1.0, 1.0], [4.0, 4.0, 4.0]])
+        b = array([1.0, 4.0, 1.0]).reshape(-1, 1)
+        x = solveh_banded(ab, b)
+        assert_array_almost_equal(x, array([0.0, 1.0, 0.0]).reshape(-1, 1))
+
+    def test_tridiag_01_lower(self):
+        # Solve
+        # [ 4 1 0]     [1]
+        # [ 1 4 1] X = [4]
+        # [ 0 1 4]     [1]
+        #
+        ab = array([[4.0, 4.0, 4.0],
+                    [1.0, 1.0, -99]])
+        b = array([1.0, 4.0, 1.0])
+        x = solveh_banded(ab, b, lower=True)
+        assert_array_almost_equal(x, [0.0, 1.0, 0.0])
+
+    def test_tridiag_02_lower(self):
+        # Solve
+        # [ 4 1 0]     [1 4]
+        # [ 1 4 1] X = [4 2]
+        # [ 0 1 4]     [1 4]
+        #
+        ab = array([[4.0, 4.0, 4.0],
+                    [1.0, 1.0, -99]])
+        b = array([[1.0, 4.0],
+                   [4.0, 2.0],
+                   [1.0, 4.0]])
+        x = solveh_banded(ab, b, lower=True)
+        expected = array([[0.0, 1.0],
+                          [1.0, 0.0],
+                          [0.0, 1.0]])
+        assert_array_almost_equal(x, expected)
+
+    def test_tridiag_01_float32(self):
+        # Solve
+        # [ 4 1 0]     [1]
+        # [ 1 4 1] X = [4]
+        # [ 0 1 4]     [1]
+        #
+        ab = array([[-99, 1.0, 1.0], [4.0, 4.0, 4.0]], dtype=float32)
+        b = array([1.0, 4.0, 1.0], dtype=float32)
+        x = solveh_banded(ab, b)
+        assert_array_almost_equal(x, [0.0, 1.0, 0.0])
+
+    def test_tridiag_02_float32(self):
+        # Solve
+        # [ 4 1 0]     [1 4]
+        # [ 1 4 1] X = [4 2]
+        # [ 0 1 4]     [1 4]
+        #
+        ab = array([[-99, 1.0, 1.0],
+                    [4.0, 4.0, 4.0]], dtype=float32)
+        b = array([[1.0, 4.0],
+                   [4.0, 2.0],
+                   [1.0, 4.0]], dtype=float32)
+        x = solveh_banded(ab, b)
+        expected = array([[0.0, 1.0],
+                          [1.0, 0.0],
+                          [0.0, 1.0]])
+        assert_array_almost_equal(x, expected)
+
+    def test_tridiag_01_complex(self):
+        # Solve
+        # [ 4 -j 0]     [ -j]
+        # [ j 4 -j] X = [4-j]
+        # [ 0 j  4]     [4+j]
+        #
+        ab = array([[-99, -1.0j, -1.0j], [4.0, 4.0, 4.0]])
+        b = array([-1.0j, 4.0-1j, 4+1j])
+        x = solveh_banded(ab, b)
+        assert_array_almost_equal(x, [0.0, 1.0, 1.0])
+
+    def test_tridiag_02_complex(self):
+        # Solve
+        # [ 4 -j 0]     [ -j    4j]
+        # [ j 4 -j] X = [4-j  -1-j]
+        # [ 0 j  4]     [4+j   4  ]
+        #
+        ab = array([[-99, -1.0j, -1.0j],
+                    [4.0, 4.0, 4.0]])
+        b = array([[-1j, 4.0j],
+                   [4.0-1j, -1.0-1j],
+                   [4.0+1j, 4.0]])
+        x = solveh_banded(ab, b)
+        expected = array([[0.0, 1.0j],
+                          [1.0, 0.0],
+                          [1.0, 1.0]])
+        assert_array_almost_equal(x, expected)
+
+    def test_check_finite(self):
+        # Solve
+        # [ 4 1 0]     [1]
+        # [ 1 4 1] X = [4]
+        # [ 0 1 4]     [1]
+        # with the RHS as a 1D array.
+        ab = array([[-99, 1.0, 1.0], [4.0, 4.0, 4.0]])
+        b = array([1.0, 4.0, 1.0])
+        x = solveh_banded(ab, b, check_finite=False)
+        assert_array_almost_equal(x, [0.0, 1.0, 0.0])
+
+    def test_bad_shapes(self):
+        ab = array([[-99, 1.0, 1.0],
+                    [4.0, 4.0, 4.0]])
+        b = array([[1.0, 4.0],
+                   [4.0, 2.0]])
+        assert_raises(ValueError, solveh_banded, ab, b)
+        assert_raises(ValueError, solveh_banded, ab, [1.0, 2.0])
+        assert_raises(ValueError, solveh_banded, ab, [1.0])
+
+    def test_1x1(self):
+        x = solveh_banded([[1]], [[1, 2, 3]])
+        assert_array_equal(x, [[1.0, 2.0, 3.0]])
+        assert_equal(x.dtype, np.dtype('f8'))
+
+    def test_native_list_arguments(self):
+        # Same as test_01_upper, using python's native list.
+        ab = [[0.0, 0.0, 2.0, 2.0],
+              [-99, 1.0, 1.0, 1.0],
+              [4.0, 4.0, 4.0, 4.0]]
+        b = [1.0, 4.0, 1.0, 2.0]
+        x = solveh_banded(ab, b)
+        assert_array_almost_equal(x, [0.0, 1.0, 0.0, 0.0])
+
+
+class TestSolve:
+    def setup_method(self):
+        np.random.seed(1234)
+
+    def test_20Feb04_bug(self):
+        a = [[1, 1], [1.0, 0]]  # ok
+        x0 = solve(a, [1, 0j])
+        assert_array_almost_equal(dot(a, x0), [1, 0])
+
+        # gives failure with clapack.zgesv(..,rowmajor=0)
+        a = [[1, 1], [1.2, 0]]
+        b = [1, 0j]
+        x0 = solve(a, b)
+        assert_array_almost_equal(dot(a, x0), [1, 0])
+
+    def test_simple(self):
+        a = [[1, 20], [-30, 4]]
+        for b in ([[1, 0], [0, 1]],
+                  [1, 0],
+                  [[2, 1], [-30, 4]]
+                  ):
+            x = solve(a, b)
+            assert_array_almost_equal(dot(a, x), b)
+
+    def test_simple_complex(self):
+        a = array([[5, 2], [2j, 4]], 'D')
+        for b in ([1j, 0],
+                  [[1j, 1j], [0, 2]],
+                  [1, 0j],
+                  array([1, 0], 'D'),
+                  ):
+            x = solve(a, b)
+            assert_array_almost_equal(dot(a, x), b)
+
+    def test_simple_pos(self):
+        a = [[2, 3], [3, 5]]
+        for lower in [0, 1]:
+            for b in ([[1, 0], [0, 1]],
+                      [1, 0]
+                      ):
+                x = solve(a, b, assume_a='pos', lower=lower)
+                assert_array_almost_equal(dot(a, x), b)
+
+    def test_simple_pos_complexb(self):
+        a = [[5, 2], [2, 4]]
+        for b in ([1j, 0],
+                  [[1j, 1j], [0, 2]],
+                  ):
+            x = solve(a, b, assume_a='pos')
+            assert_array_almost_equal(dot(a, x), b)
+
+    def test_simple_sym(self):
+        a = [[2, 3], [3, -5]]
+        for lower in [0, 1]:
+            for b in ([[1, 0], [0, 1]],
+                      [1, 0]
+                      ):
+                x = solve(a, b, assume_a='sym', lower=lower)
+                assert_array_almost_equal(dot(a, x), b)
+
+    def test_simple_sym_complexb(self):
+        a = [[5, 2], [2, -4]]
+        for b in ([1j, 0],
+                  [[1j, 1j], [0, 2]]
+                  ):
+            x = solve(a, b, assume_a='sym')
+            assert_array_almost_equal(dot(a, x), b)
+
+    def test_simple_sym_complex(self):
+        a = [[5, 2+1j], [2+1j, -4]]
+        for b in ([1j, 0],
+                  [1, 0],
+                  [[1j, 1j], [0, 2]]
+                  ):
+            x = solve(a, b, assume_a='sym')
+            assert_array_almost_equal(dot(a, x), b)
+
+    def test_simple_her_actuallysym(self):
+        a = [[2, 3], [3, -5]]
+        for lower in [0, 1]:
+            for b in ([[1, 0], [0, 1]],
+                      [1, 0],
+                      [1j, 0],
+                      ):
+                x = solve(a, b, assume_a='her', lower=lower)
+                assert_array_almost_equal(dot(a, x), b)
+
+    def test_simple_her(self):
+        a = [[5, 2+1j], [2-1j, -4]]
+        for b in ([1j, 0],
+                  [1, 0],
+                  [[1j, 1j], [0, 2]]
+                  ):
+            x = solve(a, b, assume_a='her')
+            assert_array_almost_equal(dot(a, x), b)
+
+    def test_nils_20Feb04(self):
+        n = 2
+        A = random([n, n])+random([n, n])*1j
+        X = zeros((n, n), 'D')
+        Ainv = inv(A)
+        R = identity(n)+identity(n)*0j
+        for i in arange(0, n):
+            r = R[:, i]
+            X[:, i] = solve(A, r)
+        assert_array_almost_equal(X, Ainv)
+
+    def test_random(self):
+
+        n = 20
+        a = random([n, n])
+        for i in range(n):
+            a[i, i] = 20*(.1+a[i, i])
+        for i in range(4):
+            b = random([n, 3])
+            x = solve(a, b)
+            assert_array_almost_equal(dot(a, x), b)
+
+    def test_random_complex(self):
+        n = 20
+        a = random([n, n]) + 1j * random([n, n])
+        for i in range(n):
+            a[i, i] = 20*(.1+a[i, i])
+        for i in range(2):
+            b = random([n, 3])
+            x = solve(a, b)
+            assert_array_almost_equal(dot(a, x), b)
+
+    def test_random_sym(self):
+        n = 20
+        a = random([n, n])
+        for i in range(n):
+            a[i, i] = abs(20*(.1+a[i, i]))
+            for j in range(i):
+                a[i, j] = a[j, i]
+        for i in range(4):
+            b = random([n])
+            x = solve(a, b, assume_a="pos")
+            assert_array_almost_equal(dot(a, x), b)
+
+    def test_random_sym_complex(self):
+        n = 20
+        a = random([n, n])
+        a = a + 1j*random([n, n])
+        for i in range(n):
+            a[i, i] = abs(20*(.1+a[i, i]))
+            for j in range(i):
+                a[i, j] = conjugate(a[j, i])
+        b = random([n])+2j*random([n])
+        for i in range(2):
+            x = solve(a, b, assume_a="pos")
+            assert_array_almost_equal(dot(a, x), b)
+
+    def test_check_finite(self):
+        a = [[1, 20], [-30, 4]]
+        for b in ([[1, 0], [0, 1]], [1, 0],
+                  [[2, 1], [-30, 4]]):
+            x = solve(a, b, check_finite=False)
+            assert_array_almost_equal(dot(a, x), b)
+
+    def test_scalar_a_and_1D_b(self):
+        a = 1
+        b = [1, 2, 3]
+        x = solve(a, b)
+        assert_array_almost_equal(x.ravel(), b)
+        assert_(x.shape == (3,), 'Scalar_a_1D_b test returned wrong shape')
+
+    def test_simple2(self):
+        a = np.array([[1.80, 2.88, 2.05, -0.89],
+                      [525.00, -295.00, -95.00, -380.00],
+                      [1.58, -2.69, -2.90, -1.04],
+                      [-1.11, -0.66, -0.59, 0.80]])
+
+        b = np.array([[9.52, 18.47],
+                      [2435.00, 225.00],
+                      [0.77, -13.28],
+                      [-6.22, -6.21]])
+
+        x = solve(a, b)
+        assert_array_almost_equal(x, np.array([[1., -1, 3, -5],
+                                               [3, 2, 4, 1]]).T)
+
+    def test_simple_complex2(self):
+        a = np.array([[-1.34+2.55j, 0.28+3.17j, -6.39-2.20j, 0.72-0.92j],
+                      [-1.70-14.10j, 33.10-1.50j, -1.50+13.40j, 12.90+13.80j],
+                      [-3.29-2.39j, -1.91+4.42j, -0.14-1.35j, 1.72+1.35j],
+                      [2.41+0.39j, -0.56+1.47j, -0.83-0.69j, -1.96+0.67j]])
+
+        b = np.array([[26.26+51.78j, 31.32-6.70j],
+                      [64.30-86.80j, 158.60-14.20j],
+                      [-5.75+25.31j, -2.15+30.19j],
+                      [1.16+2.57j, -2.56+7.55j]])
+
+        x = solve(a, b)
+        assert_array_almost_equal(x, np. array([[1+1.j, -1-2.j],
+                                                [2-3.j, 5+1.j],
+                                                [-4-5.j, -3+4.j],
+                                                [6.j, 2-3.j]]))
+
+    def test_hermitian(self):
+        # An upper triangular matrix will be used for hermitian matrix a
+        a = np.array([[-1.84, 0.11-0.11j, -1.78-1.18j, 3.91-1.50j],
+                      [0, -4.63, -1.84+0.03j, 2.21+0.21j],
+                      [0, 0, -8.87, 1.58-0.90j],
+                      [0, 0, 0, -1.36]])
+        b = np.array([[2.98-10.18j, 28.68-39.89j],
+                      [-9.58+3.88j, -24.79-8.40j],
+                      [-0.77-16.05j, 4.23-70.02j],
+                      [7.79+5.48j, -35.39+18.01j]])
+        res = np.array([[2.+1j, -8+6j],
+                        [3.-2j, 7-2j],
+                        [-1+2j, -1+5j],
+                        [1.-1j, 3-4j]])
+        x = solve(a, b, assume_a='her')
+        assert_array_almost_equal(x, res)
+        # Also conjugate a and test for lower triangular data
+        x = solve(a.conj().T, b, assume_a='her', lower=True)
+        assert_array_almost_equal(x, res)
+
+    def test_pos_and_sym(self):
+        A = np.arange(1, 10).reshape(3, 3)
+        x = solve(np.tril(A)/9, np.ones(3), assume_a='pos')
+        assert_array_almost_equal(x, [9., 1.8, 1.])
+        x = solve(np.tril(A)/9, np.ones(3), assume_a='sym')
+        assert_array_almost_equal(x, [9., 1.8, 1.])
+
+    def test_singularity(self):
+        a = np.array([[1, 0, 0, 0, 0, 0, 1, 0, 1],
+                      [1, 1, 1, 0, 0, 0, 1, 0, 1],
+                      [0, 1, 1, 0, 0, 0, 1, 0, 1],
+                      [1, 0, 1, 1, 1, 1, 0, 0, 0],
+                      [1, 0, 1, 1, 1, 1, 0, 0, 0],
+                      [1, 0, 1, 1, 1, 1, 0, 0, 0],
+                      [1, 0, 1, 1, 1, 1, 0, 0, 0],
+                      [1, 1, 1, 1, 1, 1, 1, 1, 1],
+                      [1, 1, 1, 1, 1, 1, 1, 1, 1]])
+        b = np.arange(9)[:, None]
+        assert_raises(LinAlgError, solve, a, b)
+
+    def test_ill_condition_warning(self):
+        a = np.array([[1, 1], [1+1e-16, 1-1e-16]])
+        b = np.ones(2)
+        with warnings.catch_warnings():
+            warnings.simplefilter('error')
+            assert_raises(LinAlgWarning, solve, a, b)
+
+    def test_empty_rhs(self):
+        a = np.eye(2)
+        b = [[], []]
+        x = solve(a, b)
+        assert_(x.size == 0, 'Returned array is not empty')
+        assert_(x.shape == (2, 0), 'Returned empty array shape is wrong')
+
+    def test_multiple_rhs(self):
+        a = np.eye(2)
+        b = np.random.rand(2, 3, 4)
+        x = solve(a, b)
+        assert_array_almost_equal(x, b)
+
+    def test_transposed_keyword(self):
+        A = np.arange(9).reshape(3, 3) + 1
+        x = solve(np.tril(A)/9, np.ones(3), transposed=True)
+        assert_array_almost_equal(x, [1.2, 0.2, 1])
+        x = solve(np.tril(A)/9, np.ones(3), transposed=False)
+        assert_array_almost_equal(x, [9, -5.4, -1.2])
+
+    def test_transposed_notimplemented(self):
+        a = np.eye(3).astype(complex)
+        with assert_raises(NotImplementedError):
+            solve(a, a, transposed=True)
+
+    def test_nonsquare_a(self):
+        assert_raises(ValueError, solve, [1, 2], 1)
+
+    def test_size_mismatch_with_1D_b(self):
+        assert_array_almost_equal(solve(np.eye(3), np.ones(3)), np.ones(3))
+        assert_raises(ValueError, solve, np.eye(3), np.ones(4))
+
+    def test_assume_a_keyword(self):
+        assert_raises(ValueError, solve, 1, 1, assume_a='zxcv')
+
+    @pytest.mark.skip(reason="Failure on OS X (gh-7500), "
+                             "crash on Windows (gh-8064)")
+    def test_all_type_size_routine_combinations(self):
+        sizes = [10, 100]
+        assume_as = ['gen', 'sym', 'pos', 'her']
+        dtypes = [np.float32, np.float64, np.complex64, np.complex128]
+        for size, assume_a, dtype in itertools.product(sizes, assume_as,
+                                                       dtypes):
+            is_complex = dtype in (np.complex64, np.complex128)
+            if assume_a == 'her' and not is_complex:
+                continue
+
+            err_msg = (f"Failed for size: {size}, assume_a: {assume_a},"
+                       f"dtype: {dtype}")
+
+            a = np.random.randn(size, size).astype(dtype)
+            b = np.random.randn(size).astype(dtype)
+            if is_complex:
+                a = a + (1j*np.random.randn(size, size)).astype(dtype)
+
+            if assume_a == 'sym':  # Can still be complex but only symmetric
+                a = a + a.T
+            elif assume_a == 'her':  # Handle hermitian matrices here instead
+                a = a + a.T.conj()
+            elif assume_a == 'pos':
+                a = a.conj().T.dot(a) + 0.1*np.eye(size)
+
+            tol = 1e-12 if dtype in (np.float64, np.complex128) else 1e-6
+
+            if assume_a in ['gen', 'sym', 'her']:
+                # We revert the tolerance from before
+                #   4b4a6e7c34fa4060533db38f9a819b98fa81476c
+                if dtype in (np.float32, np.complex64):
+                    tol *= 10
+
+            x = solve(a, b, assume_a=assume_a)
+            assert_allclose(a.dot(x), b,
+                            atol=tol * size,
+                            rtol=tol * size,
+                            err_msg=err_msg)
+
+            if assume_a == 'sym' and dtype not in (np.complex64,
+                                                   np.complex128):
+                x = solve(a, b, assume_a=assume_a, transposed=True)
+                assert_allclose(a.dot(x), b,
+                                atol=tol * size,
+                                rtol=tol * size,
+                                err_msg=err_msg)
+
+
+class TestSolveTriangular:
+
+    def test_simple(self):
+        """
+        solve_triangular on a simple 2x2 matrix.
+        """
+        A = array([[1, 0], [1, 2]])
+        b = [1, 1]
+        sol = solve_triangular(A, b, lower=True)
+        assert_array_almost_equal(sol, [1, 0])
+
+        # check that it works also for non-contiguous matrices
+        sol = solve_triangular(A.T, b, lower=False)
+        assert_array_almost_equal(sol, [.5, .5])
+
+        # and that it gives the same result as trans=1
+        sol = solve_triangular(A, b, lower=True, trans=1)
+        assert_array_almost_equal(sol, [.5, .5])
+
+        b = identity(2)
+        sol = solve_triangular(A, b, lower=True, trans=1)
+        assert_array_almost_equal(sol, [[1., -.5], [0, 0.5]])
+
+    def test_simple_complex(self):
+        """
+        solve_triangular on a simple 2x2 complex matrix
+        """
+        A = array([[1+1j, 0], [1j, 2]])
+        b = identity(2)
+        sol = solve_triangular(A, b, lower=True, trans=1)
+        assert_array_almost_equal(sol, [[.5-.5j, -.25-.25j], [0, 0.5]])
+
+        # check other option combinations with complex rhs
+        b = np.diag([1+1j, 1+2j])
+        sol = solve_triangular(A, b, lower=True, trans=0)
+        assert_array_almost_equal(sol, [[1, 0], [-0.5j, 0.5+1j]])
+
+        sol = solve_triangular(A, b, lower=True, trans=1)
+        assert_array_almost_equal(sol, [[1, 0.25-0.75j], [0, 0.5+1j]])
+
+        sol = solve_triangular(A, b, lower=True, trans=2)
+        assert_array_almost_equal(sol, [[1j, -0.75-0.25j], [0, 0.5+1j]])
+
+        sol = solve_triangular(A.T, b, lower=False, trans=0)
+        assert_array_almost_equal(sol, [[1, 0.25-0.75j], [0, 0.5+1j]])
+
+        sol = solve_triangular(A.T, b, lower=False, trans=1)
+        assert_array_almost_equal(sol, [[1, 0], [-0.5j, 0.5+1j]])
+
+        sol = solve_triangular(A.T, b, lower=False, trans=2)
+        assert_array_almost_equal(sol, [[1j, 0], [-0.5, 0.5+1j]])
+
+    def test_check_finite(self):
+        """
+        solve_triangular on a simple 2x2 matrix.
+        """
+        A = array([[1, 0], [1, 2]])
+        b = [1, 1]
+        sol = solve_triangular(A, b, lower=True, check_finite=False)
+        assert_array_almost_equal(sol, [1, 0])
+
+
+class TestInv:
+    def setup_method(self):
+        np.random.seed(1234)
+
+    def test_simple(self):
+        a = [[1, 2], [3, 4]]
+        a_inv = inv(a)
+        assert_array_almost_equal(dot(a, a_inv), np.eye(2))
+        a = [[1, 2, 3], [4, 5, 6], [7, 8, 10]]
+        a_inv = inv(a)
+        assert_array_almost_equal(dot(a, a_inv), np.eye(3))
+
+    def test_random(self):
+        n = 20
+        for i in range(4):
+            a = random([n, n])
+            for i in range(n):
+                a[i, i] = 20*(.1+a[i, i])
+            a_inv = inv(a)
+            assert_array_almost_equal(dot(a, a_inv),
+                                      identity(n))
+
+    def test_simple_complex(self):
+        a = [[1, 2], [3, 4j]]
+        a_inv = inv(a)
+        assert_array_almost_equal(dot(a, a_inv), [[1, 0], [0, 1]])
+
+    def test_random_complex(self):
+        n = 20
+        for i in range(4):
+            a = random([n, n])+2j*random([n, n])
+            for i in range(n):
+                a[i, i] = 20*(.1+a[i, i])
+            a_inv = inv(a)
+            assert_array_almost_equal(dot(a, a_inv),
+                                      identity(n))
+
+    def test_check_finite(self):
+        a = [[1, 2], [3, 4]]
+        a_inv = inv(a, check_finite=False)
+        assert_array_almost_equal(dot(a, a_inv), [[1, 0], [0, 1]])
+
+
+class TestDet:
+    def setup_method(self):
+        self.rng = np.random.default_rng(1680305949878959)
+
+    def test_1x1_all_singleton_dims(self):
+        a = np.array([[1]])
+        deta = det(a)
+        assert deta.dtype.char == 'd'
+        assert np.isscalar(deta)
+        assert deta == 1.
+        a = np.array([[[[1]]]], dtype='f')
+        deta = det(a)
+        assert deta.dtype.char == 'd'
+        assert np.isscalar(deta)
+        assert deta == 1.
+        a = np.array([[[1 + 3.j]]], dtype=np.complex64)
+        deta = det(a)
+        assert deta.dtype.char == 'D'
+        assert np.isscalar(deta)
+        assert deta == 1.+3.j
+
+    def test_1by1_stacked_input_output(self):
+        a = self.rng.random([4, 5, 1, 1], dtype=np.float32)
+        deta = det(a)
+        assert deta.dtype.char == 'd'
+        assert deta.shape == (4, 5)
+        assert_allclose(deta, np.squeeze(a))
+
+        a = self.rng.random([4, 5, 1, 1], dtype=np.float32)*np.complex64(1.j)
+        deta = det(a)
+        assert deta.dtype.char == 'D'
+        assert deta.shape == (4, 5)
+        assert_allclose(deta, np.squeeze(a))
+
+    @pytest.mark.parametrize('shape', [[2, 2], [20, 20], [3, 2, 20, 20]])
+    def test_simple_det_shapes_real_complex(self, shape):
+        a = self.rng.uniform(-1., 1., size=shape)
+        d1, d2 = det(a), np.linalg.det(a)
+        assert_allclose(d1, d2)
+
+        b = self.rng.uniform(-1., 1., size=shape)*1j
+        b += self.rng.uniform(-0.5, 0.5, size=shape)
+        d3, d4 = det(b), np.linalg.det(b)
+        assert_allclose(d3, d4)
+
+    def test_for_known_det_values(self):
+        # Hadamard8
+        a = np.array([[1, 1, 1, 1, 1, 1, 1, 1],
+                      [1, -1, 1, -1, 1, -1, 1, -1],
+                      [1, 1, -1, -1, 1, 1, -1, -1],
+                      [1, -1, -1, 1, 1, -1, -1, 1],
+                      [1, 1, 1, 1, -1, -1, -1, -1],
+                      [1, -1, 1, -1, -1, 1, -1, 1],
+                      [1, 1, -1, -1, -1, -1, 1, 1],
+                      [1, -1, -1, 1, -1, 1, 1, -1]])
+        assert_allclose(det(a), 4096.)
+
+        # consecutive number array always singular
+        assert_allclose(det(np.arange(25).reshape(5, 5)), 0.)
+
+        # simple anti-diagonal block array
+        # Upper right has det (-2+1j) and lower right has (-2-1j)
+        # det(a) = - (-2+1j) (-2-1j) = 5.
+        a = np.array([[0.+0.j, 0.+0.j, 0.-1.j, 1.-1.j],
+                      [0.+0.j, 0.+0.j, 1.+0.j, 0.-1.j],
+                      [0.+1.j, 1.+1.j, 0.+0.j, 0.+0.j],
+                      [1.+0.j, 0.+1.j, 0.+0.j, 0.+0.j]], dtype=np.complex64)
+        assert_allclose(det(a), 5.+0.j)
+
+        # Fiedler companion complexified
+        # >>> a = scipy.linalg.fiedler_companion(np.arange(1, 10))
+        a = np.array([[-2., -3., 1., 0., 0., 0., 0., 0.],
+                      [1., 0., 0., 0., 0., 0., 0., 0.],
+                      [0., -4., 0., -5., 1., 0., 0., 0.],
+                      [0., 1., 0., 0., 0., 0., 0., 0.],
+                      [0., 0., 0., -6., 0., -7., 1., 0.],
+                      [0., 0., 0., 1., 0., 0., 0., 0.],
+                      [0., 0., 0., 0., 0., -8., 0., -9.],
+                      [0., 0., 0., 0., 0., 1., 0., 0.]])*1.j
+        assert_allclose(det(a), 9.)
+
+    # g and G dtypes are handled differently in windows and other platforms
+    @pytest.mark.parametrize('typ', [x for x in np.typecodes['All'][:20]
+                                     if x not in 'gG'])
+    def test_sample_compatible_dtype_input(self, typ):
+        n = 4
+        a = self.rng.random([n, n]).astype(typ)  # value is not important
+        assert isinstance(det(a), (np.float64, np.complex128))
+
+    def test_incompatible_dtype_input(self):
+        # Double backslashes needed for escaping pytest regex.
+        msg = 'cannot be cast to float\\(32, 64\\)'
+
+        for c, t in zip('SUO', ['bytes8', 'str32', 'object']):
+            with assert_raises(TypeError, match=msg):
+                det(np.array([['a', 'b']]*2, dtype=c))
+        with assert_raises(TypeError, match=msg):
+            det(np.array([[b'a', b'b']]*2, dtype='V'))
+        with assert_raises(TypeError, match=msg):
+            det(np.array([[100, 200]]*2, dtype='datetime64[s]'))
+        with assert_raises(TypeError, match=msg):
+            det(np.array([[100, 200]]*2, dtype='timedelta64[s]'))
+
+    def test_empty_edge_cases(self):
+        assert_allclose(det(np.empty([0, 0])), 1.)
+        assert_allclose(det(np.empty([0, 0, 0])), np.array([]))
+        assert_allclose(det(np.empty([3, 0, 0])), np.array([1., 1., 1.]))
+        with assert_raises(ValueError, match='Last 2 dimensions'):
+            det(np.empty([0, 0, 3]))
+        with assert_raises(ValueError, match='at least two-dimensional'):
+            det(np.array([]))
+        with assert_raises(ValueError, match='Last 2 dimensions'):
+            det(np.array([[]]))
+        with assert_raises(ValueError, match='Last 2 dimensions'):
+            det(np.array([[[]]]))
+
+    def test_overwrite_a(self):
+        # If all conditions are met then input should be overwritten;
+        #   - dtype is one of 'fdFD'
+        #   - C-contiguous
+        #   - writeable
+        a = np.arange(9).reshape(3, 3).astype(np.float32)
+        ac = a.copy()
+        deta = det(ac, overwrite_a=True)
+        assert_allclose(deta, 0.)
+        assert not (a == ac).all()
+
+    def test_readonly_array(self):
+        a = np.array([[2., 0., 1.], [5., 3., -1.], [1., 1., 1.]])
+        a.setflags(write=False)
+        # overwrite_a will be overridden
+        assert_allclose(det(a, overwrite_a=True), 10.)
+
+    def test_simple_check_finite(self):
+        a = [[1, 2], [3, np.inf]]
+        with assert_raises(ValueError, match='array must not contain'):
+            det(a)
+
+
+def direct_lstsq(a, b, cmplx=0):
+    at = transpose(a)
+    if cmplx:
+        at = conjugate(at)
+    a1 = dot(at, a)
+    b1 = dot(at, b)
+    return solve(a1, b1)
+
+
+class TestLstsq:
+    lapack_drivers = ('gelsd', 'gelss', 'gelsy', None)
+
+    def test_simple_exact(self):
+        for dtype in REAL_DTYPES:
+            a = np.array([[1, 20], [-30, 4]], dtype=dtype)
+            for lapack_driver in TestLstsq.lapack_drivers:
+                for overwrite in (True, False):
+                    for bt in (((1, 0), (0, 1)), (1, 0),
+                               ((2, 1), (-30, 4))):
+                        # Store values in case they are overwritten
+                        # later
+                        a1 = a.copy()
+                        b = np.array(bt, dtype=dtype)
+                        b1 = b.copy()
+                        out = lstsq(a1, b1,
+                                    lapack_driver=lapack_driver,
+                                    overwrite_a=overwrite,
+                                    overwrite_b=overwrite)
+                        x = out[0]
+                        r = out[2]
+                        assert_(r == 2,
+                                'expected efficient rank 2, got %s' % r)
+                        assert_allclose(dot(a, x), b,
+                                        atol=25 * _eps_cast(a1.dtype),
+                                        rtol=25 * _eps_cast(a1.dtype),
+                                        err_msg="driver: %s" % lapack_driver)
+
+    def test_simple_overdet(self):
+        for dtype in REAL_DTYPES:
+            a = np.array([[1, 2], [4, 5], [3, 4]], dtype=dtype)
+            b = np.array([1, 2, 3], dtype=dtype)
+            for lapack_driver in TestLstsq.lapack_drivers:
+                for overwrite in (True, False):
+                    # Store values in case they are overwritten later
+                    a1 = a.copy()
+                    b1 = b.copy()
+                    out = lstsq(a1, b1, lapack_driver=lapack_driver,
+                                overwrite_a=overwrite,
+                                overwrite_b=overwrite)
+                    x = out[0]
+                    if lapack_driver == 'gelsy':
+                        residuals = np.sum((b - a.dot(x))**2)
+                    else:
+                        residuals = out[1]
+                    r = out[2]
+                    assert_(r == 2, 'expected efficient rank 2, got %s' % r)
+                    assert_allclose(abs((dot(a, x) - b)**2).sum(axis=0),
+                                    residuals,
+                                    rtol=25 * _eps_cast(a1.dtype),
+                                    atol=25 * _eps_cast(a1.dtype),
+                                    err_msg="driver: %s" % lapack_driver)
+                    assert_allclose(x, (-0.428571428571429, 0.85714285714285),
+                                    rtol=25 * _eps_cast(a1.dtype),
+                                    atol=25 * _eps_cast(a1.dtype),
+                                    err_msg="driver: %s" % lapack_driver)
+
+    def test_simple_overdet_complex(self):
+        for dtype in COMPLEX_DTYPES:
+            a = np.array([[1+2j, 2], [4, 5], [3, 4]], dtype=dtype)
+            b = np.array([1, 2+4j, 3], dtype=dtype)
+            for lapack_driver in TestLstsq.lapack_drivers:
+                for overwrite in (True, False):
+                    # Store values in case they are overwritten later
+                    a1 = a.copy()
+                    b1 = b.copy()
+                    out = lstsq(a1, b1, lapack_driver=lapack_driver,
+                                overwrite_a=overwrite,
+                                overwrite_b=overwrite)
+
+                    x = out[0]
+                    if lapack_driver == 'gelsy':
+                        res = b - a.dot(x)
+                        residuals = np.sum(res * res.conj())
+                    else:
+                        residuals = out[1]
+                    r = out[2]
+                    assert_(r == 2, 'expected efficient rank 2, got %s' % r)
+                    assert_allclose(abs((dot(a, x) - b)**2).sum(axis=0),
+                                    residuals,
+                                    rtol=25 * _eps_cast(a1.dtype),
+                                    atol=25 * _eps_cast(a1.dtype),
+                                    err_msg="driver: %s" % lapack_driver)
+                    assert_allclose(
+                                x, (-0.4831460674157303 + 0.258426966292135j,
+                                    0.921348314606741 + 0.292134831460674j),
+                                rtol=25 * _eps_cast(a1.dtype),
+                                atol=25 * _eps_cast(a1.dtype),
+                                err_msg="driver: %s" % lapack_driver)
+
+    def test_simple_underdet(self):
+        for dtype in REAL_DTYPES:
+            a = np.array([[1, 2, 3], [4, 5, 6]], dtype=dtype)
+            b = np.array([1, 2], dtype=dtype)
+            for lapack_driver in TestLstsq.lapack_drivers:
+                for overwrite in (True, False):
+                    # Store values in case they are overwritten later
+                    a1 = a.copy()
+                    b1 = b.copy()
+                    out = lstsq(a1, b1, lapack_driver=lapack_driver,
+                                overwrite_a=overwrite,
+                                overwrite_b=overwrite)
+
+                    x = out[0]
+                    r = out[2]
+                    assert_(r == 2, 'expected efficient rank 2, got %s' % r)
+                    assert_allclose(x, (-0.055555555555555, 0.111111111111111,
+                                        0.277777777777777),
+                                    rtol=25 * _eps_cast(a1.dtype),
+                                    atol=25 * _eps_cast(a1.dtype),
+                                    err_msg="driver: %s" % lapack_driver)
+
+    def test_random_exact(self):
+        rng = np.random.RandomState(1234)
+        for dtype in REAL_DTYPES:
+            for n in (20, 200):
+                for lapack_driver in TestLstsq.lapack_drivers:
+                    for overwrite in (True, False):
+                        a = np.asarray(rng.random([n, n]), dtype=dtype)
+                        for i in range(n):
+                            a[i, i] = 20 * (0.1 + a[i, i])
+                        for i in range(4):
+                            b = np.asarray(rng.random([n, 3]), dtype=dtype)
+                            # Store values in case they are overwritten later
+                            a1 = a.copy()
+                            b1 = b.copy()
+                            out = lstsq(a1, b1,
+                                        lapack_driver=lapack_driver,
+                                        overwrite_a=overwrite,
+                                        overwrite_b=overwrite)
+                            x = out[0]
+                            r = out[2]
+                            assert_(r == n, f'expected efficient rank {n}, '
+                                    f'got {r}')
+                            if dtype is np.float32:
+                                assert_allclose(
+                                          dot(a, x), b,
+                                          rtol=500 * _eps_cast(a1.dtype),
+                                          atol=500 * _eps_cast(a1.dtype),
+                                          err_msg="driver: %s" % lapack_driver)
+                            else:
+                                assert_allclose(
+                                          dot(a, x), b,
+                                          rtol=1000 * _eps_cast(a1.dtype),
+                                          atol=1000 * _eps_cast(a1.dtype),
+                                          err_msg="driver: %s" % lapack_driver)
+
+    @pytest.mark.skipif(IS_MUSL, reason="may segfault on Alpine, see gh-17630")
+    def test_random_complex_exact(self):
+        rng = np.random.RandomState(1234)
+        for dtype in COMPLEX_DTYPES:
+            for n in (20, 200):
+                for lapack_driver in TestLstsq.lapack_drivers:
+                    for overwrite in (True, False):
+                        a = np.asarray(rng.random([n, n]) + 1j*rng.random([n, n]),
+                                       dtype=dtype)
+                        for i in range(n):
+                            a[i, i] = 20 * (0.1 + a[i, i])
+                        for i in range(2):
+                            b = np.asarray(rng.random([n, 3]), dtype=dtype)
+                            # Store values in case they are overwritten later
+                            a1 = a.copy()
+                            b1 = b.copy()
+                            out = lstsq(a1, b1, lapack_driver=lapack_driver,
+                                        overwrite_a=overwrite,
+                                        overwrite_b=overwrite)
+                            x = out[0]
+                            r = out[2]
+                            assert_(r == n, f'expected efficient rank {n}, '
+                                    f'got {r}')
+                            if dtype is np.complex64:
+                                assert_allclose(
+                                          dot(a, x), b,
+                                          rtol=400 * _eps_cast(a1.dtype),
+                                          atol=400 * _eps_cast(a1.dtype),
+                                          err_msg="driver: %s" % lapack_driver)
+                            else:
+                                assert_allclose(
+                                          dot(a, x), b,
+                                          rtol=1000 * _eps_cast(a1.dtype),
+                                          atol=1000 * _eps_cast(a1.dtype),
+                                          err_msg="driver: %s" % lapack_driver)
+
+    def test_random_overdet(self):
+        rng = np.random.RandomState(1234)
+        for dtype in REAL_DTYPES:
+            for (n, m) in ((20, 15), (200, 2)):
+                for lapack_driver in TestLstsq.lapack_drivers:
+                    for overwrite in (True, False):
+                        a = np.asarray(rng.random([n, m]), dtype=dtype)
+                        for i in range(m):
+                            a[i, i] = 20 * (0.1 + a[i, i])
+                        for i in range(4):
+                            b = np.asarray(rng.random([n, 3]), dtype=dtype)
+                            # Store values in case they are overwritten later
+                            a1 = a.copy()
+                            b1 = b.copy()
+                            out = lstsq(a1, b1,
+                                        lapack_driver=lapack_driver,
+                                        overwrite_a=overwrite,
+                                        overwrite_b=overwrite)
+                            x = out[0]
+                            r = out[2]
+                            assert_(r == m, f'expected efficient rank {m}, '
+                                    f'got {r}')
+                            assert_allclose(
+                                          x, direct_lstsq(a, b, cmplx=0),
+                                          rtol=25 * _eps_cast(a1.dtype),
+                                          atol=25 * _eps_cast(a1.dtype),
+                                          err_msg="driver: %s" % lapack_driver)
+
+    def test_random_complex_overdet(self):
+        rng = np.random.RandomState(1234)
+        for dtype in COMPLEX_DTYPES:
+            for (n, m) in ((20, 15), (200, 2)):
+                for lapack_driver in TestLstsq.lapack_drivers:
+                    for overwrite in (True, False):
+                        a = np.asarray(rng.random([n, m]) + 1j*rng.random([n, m]),
+                                       dtype=dtype)
+                        for i in range(m):
+                            a[i, i] = 20 * (0.1 + a[i, i])
+                        for i in range(2):
+                            b = np.asarray(rng.random([n, 3]), dtype=dtype)
+                            # Store values in case they are overwritten
+                            # later
+                            a1 = a.copy()
+                            b1 = b.copy()
+                            out = lstsq(a1, b1,
+                                        lapack_driver=lapack_driver,
+                                        overwrite_a=overwrite,
+                                        overwrite_b=overwrite)
+                            x = out[0]
+                            r = out[2]
+                            assert_(r == m, f'expected efficient rank {m}, '
+                                    f'got {r}')
+                            assert_allclose(
+                                      x, direct_lstsq(a, b, cmplx=1),
+                                      rtol=25 * _eps_cast(a1.dtype),
+                                      atol=25 * _eps_cast(a1.dtype),
+                                      err_msg="driver: %s" % lapack_driver)
+
+    def test_check_finite(self):
+        with suppress_warnings() as sup:
+            # On (some) OSX this tests triggers a warning (gh-7538)
+            sup.filter(RuntimeWarning,
+                       "internal gelsd driver lwork query error,.*"
+                       "Falling back to 'gelss' driver.")
+
+        at = np.array(((1, 20), (-30, 4)))
+        for dtype, bt, lapack_driver, overwrite, check_finite in \
+            itertools.product(REAL_DTYPES,
+                              (((1, 0), (0, 1)), (1, 0), ((2, 1), (-30, 4))),
+                              TestLstsq.lapack_drivers,
+                              (True, False),
+                              (True, False)):
+
+            a = at.astype(dtype)
+            b = np.array(bt, dtype=dtype)
+            # Store values in case they are overwritten
+            # later
+            a1 = a.copy()
+            b1 = b.copy()
+            out = lstsq(a1, b1, lapack_driver=lapack_driver,
+                        check_finite=check_finite, overwrite_a=overwrite,
+                        overwrite_b=overwrite)
+            x = out[0]
+            r = out[2]
+            assert_(r == 2, 'expected efficient rank 2, got %s' % r)
+            assert_allclose(dot(a, x), b,
+                            rtol=25 * _eps_cast(a.dtype),
+                            atol=25 * _eps_cast(a.dtype),
+                            err_msg="driver: %s" % lapack_driver)
+
+    def test_zero_size(self):
+        for a_shape, b_shape in (((0, 2), (0,)),
+                                 ((0, 4), (0, 2)),
+                                 ((4, 0), (4,)),
+                                 ((4, 0), (4, 2))):
+            b = np.ones(b_shape)
+            x, residues, rank, s = lstsq(np.zeros(a_shape), b)
+            assert_equal(x, np.zeros((a_shape[1],) + b_shape[1:]))
+            residues_should_be = (np.empty((0,)) if a_shape[1]
+                                  else np.linalg.norm(b, axis=0)**2)
+            assert_equal(residues, residues_should_be)
+            assert_(rank == 0, 'expected rank 0')
+            assert_equal(s, np.empty((0,)))
+
+
+class TestPinv:
+    def setup_method(self):
+        np.random.seed(1234)
+
+    def test_simple_real(self):
+        a = array([[1, 2, 3], [4, 5, 6], [7, 8, 10]], dtype=float)
+        a_pinv = pinv(a)
+        assert_array_almost_equal(dot(a, a_pinv), np.eye(3))
+
+    def test_simple_complex(self):
+        a = (array([[1, 2, 3], [4, 5, 6], [7, 8, 10]],
+             dtype=float) + 1j * array([[10, 8, 7], [6, 5, 4], [3, 2, 1]],
+                                       dtype=float))
+        a_pinv = pinv(a)
+        assert_array_almost_equal(dot(a, a_pinv), np.eye(3))
+
+    def test_simple_singular(self):
+        a = array([[1, 2, 3], [4, 5, 6], [7, 8, 9]], dtype=float)
+        a_pinv = pinv(a)
+        expected = array([[-6.38888889e-01, -1.66666667e-01, 3.05555556e-01],
+                          [-5.55555556e-02, 1.30136518e-16, 5.55555556e-02],
+                          [5.27777778e-01, 1.66666667e-01, -1.94444444e-01]])
+        assert_array_almost_equal(a_pinv, expected)
+
+    def test_simple_cols(self):
+        a = array([[1, 2, 3], [4, 5, 6]], dtype=float)
+        a_pinv = pinv(a)
+        expected = array([[-0.94444444, 0.44444444],
+                          [-0.11111111, 0.11111111],
+                          [0.72222222, -0.22222222]])
+        assert_array_almost_equal(a_pinv, expected)
+
+    def test_simple_rows(self):
+        a = array([[1, 2], [3, 4], [5, 6]], dtype=float)
+        a_pinv = pinv(a)
+        expected = array([[-1.33333333, -0.33333333, 0.66666667],
+                          [1.08333333, 0.33333333, -0.41666667]])
+        assert_array_almost_equal(a_pinv, expected)
+
+    def test_check_finite(self):
+        a = array([[1, 2, 3], [4, 5, 6.], [7, 8, 10]])
+        a_pinv = pinv(a, check_finite=False)
+        assert_array_almost_equal(dot(a, a_pinv), np.eye(3))
+
+    def test_native_list_argument(self):
+        a = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]
+        a_pinv = pinv(a)
+        expected = array([[-6.38888889e-01, -1.66666667e-01, 3.05555556e-01],
+                          [-5.55555556e-02, 1.30136518e-16, 5.55555556e-02],
+                          [5.27777778e-01, 1.66666667e-01, -1.94444444e-01]])
+        assert_array_almost_equal(a_pinv, expected)
+
+    def test_atol_rtol(self):
+        n = 12
+        # get a random ortho matrix for shuffling
+        q, _ = qr(np.random.rand(n, n))
+        a_m = np.arange(35.0).reshape(7, 5)
+        a = a_m.copy()
+        a[0, 0] = 0.001
+        atol = 1e-5
+        rtol = 0.05
+        # svds of a_m is ~ [116.906, 4.234, tiny, tiny, tiny]
+        # svds of a is ~ [116.906, 4.234, 4.62959e-04, tiny, tiny]
+        # Just abs cutoff such that we arrive at a_modified
+        a_p = pinv(a_m, atol=atol, rtol=0.)
+        adiff1 = a @ a_p @ a - a
+        adiff2 = a_m @ a_p @ a_m - a_m
+        # Now adiff1 should be around atol value while adiff2 should be
+        # relatively tiny
+        assert_allclose(np.linalg.norm(adiff1), 5e-4, atol=5.e-4)
+        assert_allclose(np.linalg.norm(adiff2), 5e-14, atol=5.e-14)
+
+        # Now do the same but remove another sv ~4.234 via rtol
+        a_p = pinv(a_m, atol=atol, rtol=rtol)
+        adiff1 = a @ a_p @ a - a
+        adiff2 = a_m @ a_p @ a_m - a_m
+        assert_allclose(np.linalg.norm(adiff1), 4.233, rtol=0.01)
+        assert_allclose(np.linalg.norm(adiff2), 4.233, rtol=0.01)
+
+    @pytest.mark.parametrize("cond", [1, None, _NoValue])
+    @pytest.mark.parametrize("rcond", [1, None, _NoValue])
+    def test_cond_rcond_deprecation(self, cond, rcond):
+        if cond is _NoValue and rcond is _NoValue:
+            # the defaults if cond/rcond aren't set -> no warning
+            pinv(np.ones((2,2)), cond=cond, rcond=rcond)
+        else:
+            # at least one of cond/rcond has a user-supplied value -> warn
+            with pytest.deprecated_call(match='"cond" and "rcond"'):
+                pinv(np.ones((2,2)), cond=cond, rcond=rcond)
+
+    def test_positional_deprecation(self):
+        with pytest.deprecated_call(match="use keyword arguments"):
+            pinv(np.ones((2,2)), 0., 1e-10)
+
+
+class TestPinvSymmetric:
+
+    def setup_method(self):
+        np.random.seed(1234)
+
+    def test_simple_real(self):
+        a = array([[1, 2, 3], [4, 5, 6], [7, 8, 10]], dtype=float)
+        a = np.dot(a, a.T)
+        a_pinv = pinvh(a)
+        assert_array_almost_equal(np.dot(a, a_pinv), np.eye(3))
+
+    def test_nonpositive(self):
+        a = array([[1, 2, 3], [4, 5, 6], [7, 8, 9]], dtype=float)
+        a = np.dot(a, a.T)
+        u, s, vt = np.linalg.svd(a)
+        s[0] *= -1
+        a = np.dot(u * s, vt)  # a is now symmetric non-positive and singular
+        a_pinv = pinv(a)
+        a_pinvh = pinvh(a)
+        assert_array_almost_equal(a_pinv, a_pinvh)
+
+    def test_simple_complex(self):
+        a = (array([[1, 2, 3], [4, 5, 6], [7, 8, 10]],
+             dtype=float) + 1j * array([[10, 8, 7], [6, 5, 4], [3, 2, 1]],
+                                       dtype=float))
+        a = np.dot(a, a.conj().T)
+        a_pinv = pinvh(a)
+        assert_array_almost_equal(np.dot(a, a_pinv), np.eye(3))
+
+    def test_native_list_argument(self):
+        a = array([[1, 2, 3], [4, 5, 6], [7, 8, 10]], dtype=float)
+        a = np.dot(a, a.T)
+        a_pinv = pinvh(a.tolist())
+        assert_array_almost_equal(np.dot(a, a_pinv), np.eye(3))
+
+    def test_atol_rtol(self):
+        n = 12
+        # get a random ortho matrix for shuffling
+        q, _ = qr(np.random.rand(n, n))
+        a = np.diag([4, 3, 2, 1, 0.99e-4, 0.99e-5] + [0.99e-6]*(n-6))
+        a = q.T @ a @ q
+        a_m = np.diag([4, 3, 2, 1, 0.99e-4, 0.] + [0.]*(n-6))
+        a_m = q.T @ a_m @ q
+        atol = 1e-5
+        rtol = (4.01e-4 - 4e-5)/4
+        # Just abs cutoff such that we arrive at a_modified
+        a_p = pinvh(a, atol=atol, rtol=0.)
+        adiff1 = a @ a_p @ a - a
+        adiff2 = a_m @ a_p @ a_m - a_m
+        # Now adiff1 should dance around atol value since truncation
+        # while adiff2 should be relatively tiny
+        assert_allclose(norm(adiff1), atol, rtol=0.1)
+        assert_allclose(norm(adiff2), 1e-12, atol=1e-11)
+
+        # Now do the same but through rtol cancelling atol value
+        a_p = pinvh(a, atol=atol, rtol=rtol)
+        adiff1 = a @ a_p @ a - a
+        adiff2 = a_m @ a_p @ a_m - a_m
+        # adiff1 and adiff2 should be elevated to ~1e-4 due to mismatch
+        assert_allclose(norm(adiff1), 1e-4, rtol=0.1)
+        assert_allclose(norm(adiff2), 1e-4, rtol=0.1)
+
+
+@pytest.mark.parametrize('scale', (1e-20, 1., 1e20))
+@pytest.mark.parametrize('pinv_', (pinv, pinvh))
+def test_auto_rcond(scale, pinv_):
+    x = np.array([[1, 0], [0, 1e-10]]) * scale
+    expected = np.diag(1. / np.diag(x))
+    x_inv = pinv_(x)
+    assert_allclose(x_inv, expected)
+
+
+class TestVectorNorms:
+
+    def test_types(self):
+        for dtype in np.typecodes['AllFloat']:
+            x = np.array([1, 2, 3], dtype=dtype)
+            tol = max(1e-15, np.finfo(dtype).eps.real * 20)
+            assert_allclose(norm(x), np.sqrt(14), rtol=tol)
+            assert_allclose(norm(x, 2), np.sqrt(14), rtol=tol)
+
+        for dtype in np.typecodes['Complex']:
+            x = np.array([1j, 2j, 3j], dtype=dtype)
+            tol = max(1e-15, np.finfo(dtype).eps.real * 20)
+            assert_allclose(norm(x), np.sqrt(14), rtol=tol)
+            assert_allclose(norm(x, 2), np.sqrt(14), rtol=tol)
+
+    def test_overflow(self):
+        # unlike numpy's norm, this one is
+        # safer on overflow
+        a = array([1e20], dtype=float32)
+        assert_almost_equal(norm(a), a)
+
+    def test_stable(self):
+        # more stable than numpy's norm
+        a = array([1e4] + [1]*10000, dtype=float32)
+        try:
+            # snrm in double precision; we obtain the same as for float64
+            # -- large atol needed due to varying blas implementations
+            assert_allclose(norm(a) - 1e4, 0.5, atol=1e-2)
+        except AssertionError:
+            # snrm implemented in single precision, == np.linalg.norm result
+            msg = ": Result should equal either 0.0 or 0.5 (depending on " \
+                  "implementation of snrm2)."
+            assert_almost_equal(norm(a) - 1e4, 0.0, err_msg=msg)
+
+    def test_zero_norm(self):
+        assert_equal(norm([1, 0, 3], 0), 2)
+        assert_equal(norm([1, 2, 3], 0), 3)
+
+    def test_axis_kwd(self):
+        a = np.array([[[2, 1], [3, 4]]] * 2, 'd')
+        assert_allclose(norm(a, axis=1), [[3.60555128, 4.12310563]] * 2)
+        assert_allclose(norm(a, 1, axis=1), [[5.] * 2] * 2)
+
+    def test_keepdims_kwd(self):
+        a = np.array([[[2, 1], [3, 4]]] * 2, 'd')
+        b = norm(a, axis=1, keepdims=True)
+        assert_allclose(b, [[[3.60555128, 4.12310563]]] * 2)
+        assert_(b.shape == (2, 1, 2))
+        assert_allclose(norm(a, 1, axis=2, keepdims=True), [[[3.], [7.]]] * 2)
+
+    @pytest.mark.skipif(not HAS_ILP64, reason="64-bit BLAS required")
+    def test_large_vector(self):
+        check_free_memory(free_mb=17000)
+        x = np.zeros([2**31], dtype=np.float64)
+        x[-1] = 1
+        res = norm(x)
+        del x
+        assert_allclose(res, 1.0)
+
+
+class TestMatrixNorms:
+
+    def test_matrix_norms(self):
+        # Not all of these are matrix norms in the most technical sense.
+        np.random.seed(1234)
+        for n, m in (1, 1), (1, 3), (3, 1), (4, 4), (4, 5), (5, 4):
+            for t in np.float32, np.float64, np.complex64, np.complex128, np.int64:
+                A = 10 * np.random.randn(n, m).astype(t)
+                if np.issubdtype(A.dtype, np.complexfloating):
+                    A = (A + 10j * np.random.randn(n, m)).astype(t)
+                    t_high = np.complex128
+                else:
+                    t_high = np.float64
+                for order in (None, 'fro', 1, -1, 2, -2, np.inf, -np.inf):
+                    actual = norm(A, ord=order)
+                    desired = np.linalg.norm(A, ord=order)
+                    # SciPy may return higher precision matrix norms.
+                    # This is a consequence of using LAPACK.
+                    if not np.allclose(actual, desired):
+                        desired = np.linalg.norm(A.astype(t_high), ord=order)
+                        assert_allclose(actual, desired)
+
+    def test_axis_kwd(self):
+        a = np.array([[[2, 1], [3, 4]]] * 2, 'd')
+        b = norm(a, ord=np.inf, axis=(1, 0))
+        c = norm(np.swapaxes(a, 0, 1), ord=np.inf, axis=(0, 1))
+        d = norm(a, ord=1, axis=(0, 1))
+        assert_allclose(b, c)
+        assert_allclose(c, d)
+        assert_allclose(b, d)
+        assert_(b.shape == c.shape == d.shape)
+        b = norm(a, ord=1, axis=(1, 0))
+        c = norm(np.swapaxes(a, 0, 1), ord=1, axis=(0, 1))
+        d = norm(a, ord=np.inf, axis=(0, 1))
+        assert_allclose(b, c)
+        assert_allclose(c, d)
+        assert_allclose(b, d)
+        assert_(b.shape == c.shape == d.shape)
+
+    def test_keepdims_kwd(self):
+        a = np.arange(120, dtype='d').reshape(2, 3, 4, 5)
+        b = norm(a, ord=np.inf, axis=(1, 0), keepdims=True)
+        c = norm(a, ord=1, axis=(0, 1), keepdims=True)
+        assert_allclose(b, c)
+        assert_(b.shape == c.shape)
+
+
+class TestOverwrite:
+    def test_solve(self):
+        assert_no_overwrite(solve, [(3, 3), (3,)])
+
+    def test_solve_triangular(self):
+        assert_no_overwrite(solve_triangular, [(3, 3), (3,)])
+
+    def test_solve_banded(self):
+        assert_no_overwrite(lambda ab, b: solve_banded((2, 1), ab, b),
+                            [(4, 6), (6,)])
+
+    def test_solveh_banded(self):
+        assert_no_overwrite(solveh_banded, [(2, 6), (6,)])
+
+    def test_inv(self):
+        assert_no_overwrite(inv, [(3, 3)])
+
+    def test_det(self):
+        assert_no_overwrite(det, [(3, 3)])
+
+    def test_lstsq(self):
+        assert_no_overwrite(lstsq, [(3, 2), (3,)])
+
+    def test_pinv(self):
+        assert_no_overwrite(pinv, [(3, 3)])
+
+    def test_pinvh(self):
+        assert_no_overwrite(pinvh, [(3, 3)])
+
+
+class TestSolveCirculant:
+
+    def test_basic1(self):
+        c = np.array([1, 2, 3, 5])
+        b = np.array([1, -1, 1, 0])
+        x = solve_circulant(c, b)
+        y = solve(circulant(c), b)
+        assert_allclose(x, y)
+
+    def test_basic2(self):
+        # b is a 2-d matrix.
+        c = np.array([1, 2, -3, -5])
+        b = np.arange(12).reshape(4, 3)
+        x = solve_circulant(c, b)
+        y = solve(circulant(c), b)
+        assert_allclose(x, y)
+
+    def test_basic3(self):
+        # b is a 3-d matrix.
+        c = np.array([1, 2, -3, -5])
+        b = np.arange(24).reshape(4, 3, 2)
+        x = solve_circulant(c, b)
+        y = solve(circulant(c), b)
+        assert_allclose(x, y)
+
+    def test_complex(self):
+        # Complex b and c
+        c = np.array([1+2j, -3, 4j, 5])
+        b = np.arange(8).reshape(4, 2) + 0.5j
+        x = solve_circulant(c, b)
+        y = solve(circulant(c), b)
+        assert_allclose(x, y)
+
+    def test_random_b_and_c(self):
+        # Random b and c
+        np.random.seed(54321)
+        c = np.random.randn(50)
+        b = np.random.randn(50)
+        x = solve_circulant(c, b)
+        y = solve(circulant(c), b)
+        assert_allclose(x, y)
+
+    def test_singular(self):
+        # c gives a singular circulant matrix.
+        c = np.array([1, 1, 0, 0])
+        b = np.array([1, 2, 3, 4])
+        x = solve_circulant(c, b, singular='lstsq')
+        y, res, rnk, s = lstsq(circulant(c), b)
+        assert_allclose(x, y)
+        assert_raises(LinAlgError, solve_circulant, x, y)
+
+    def test_axis_args(self):
+        # Test use of caxis, baxis and outaxis.
+
+        # c has shape (2, 1, 4)
+        c = np.array([[[-1, 2.5, 3, 3.5]], [[1, 6, 6, 6.5]]])
+
+        # b has shape (3, 4)
+        b = np.array([[0, 0, 1, 1], [1, 1, 0, 0], [1, -1, 0, 0]])
+
+        x = solve_circulant(c, b, baxis=1)
+        assert_equal(x.shape, (4, 2, 3))
+        expected = np.empty_like(x)
+        expected[:, 0, :] = solve(circulant(c[0]), b.T)
+        expected[:, 1, :] = solve(circulant(c[1]), b.T)
+        assert_allclose(x, expected)
+
+        x = solve_circulant(c, b, baxis=1, outaxis=-1)
+        assert_equal(x.shape, (2, 3, 4))
+        assert_allclose(np.moveaxis(x, -1, 0), expected)
+
+        # np.swapaxes(c, 1, 2) has shape (2, 4, 1); b.T has shape (4, 3).
+        x = solve_circulant(np.swapaxes(c, 1, 2), b.T, caxis=1)
+        assert_equal(x.shape, (4, 2, 3))
+        assert_allclose(x, expected)
+
+    def test_native_list_arguments(self):
+        # Same as test_basic1 using python's native list.
+        c = [1, 2, 3, 5]
+        b = [1, -1, 1, 0]
+        x = solve_circulant(c, b)
+        y = solve(circulant(c), b)
+        assert_allclose(x, y)
+
+
+class TestMatrix_Balance:
+
+    def test_string_arg(self):
+        assert_raises(ValueError, matrix_balance, 'Some string for fail')
+
+    def test_infnan_arg(self):
+        assert_raises(ValueError, matrix_balance,
+                      np.array([[1, 2], [3, np.inf]]))
+        assert_raises(ValueError, matrix_balance,
+                      np.array([[1, 2], [3, np.nan]]))
+
+    def test_scaling(self):
+        _, y = matrix_balance(np.array([[1000, 1], [1000, 0]]))
+        # Pre/post LAPACK 3.5.0 gives the same result up to an offset
+        # since in each case col norm is x1000 greater and
+        # 1000 / 32 ~= 1 * 32 hence balanced with 2 ** 5.
+        assert_allclose(np.diff(np.log2(np.diag(y))), [5])
+
+    def test_scaling_order(self):
+        A = np.array([[1, 0, 1e-4], [1, 1, 1e-2], [1e4, 1e2, 1]])
+        x, y = matrix_balance(A)
+        assert_allclose(solve(y, A).dot(y), x)
+
+    def test_separate(self):
+        _, (y, z) = matrix_balance(np.array([[1000, 1], [1000, 0]]),
+                                   separate=1)
+        assert_equal(np.diff(np.log2(y)), [5])
+        assert_allclose(z, np.arange(2))
+
+    def test_permutation(self):
+        A = block_diag(np.ones((2, 2)), np.tril(np.ones((2, 2))),
+                       np.ones((3, 3)))
+        x, (y, z) = matrix_balance(A, separate=1)
+        assert_allclose(y, np.ones_like(y))
+        assert_allclose(z, np.array([0, 1, 6, 5, 4, 3, 2]))
+
+    def test_perm_and_scaling(self):
+        # Matrix with its diagonal removed
+        cases = (  # Case 0
+                 np.array([[0., 0., 0., 0., 0.000002],
+                           [0., 0., 0., 0., 0.],
+                           [2., 2., 0., 0., 0.],
+                           [2., 2., 0., 0., 0.],
+                           [0., 0., 0.000002, 0., 0.]]),
+                 #  Case 1 user reported GH-7258
+                 np.array([[-0.5, 0., 0., 0.],
+                           [0., -1., 0., 0.],
+                           [1., 0., -0.5, 0.],
+                           [0., 1., 0., -1.]]),
+                 #  Case 2 user reported GH-7258
+                 np.array([[-3., 0., 1., 0.],
+                           [-1., -1., -0., 1.],
+                           [-3., -0., -0., 0.],
+                           [-1., -0., 1., -1.]])
+                 )
+
+        for A in cases:
+            x, y = matrix_balance(A)
+            x, (s, p) = matrix_balance(A, separate=1)
+            ip = np.empty_like(p)
+            ip[p] = np.arange(A.shape[0])
+            assert_allclose(y, np.diag(s)[ip, :])
+            assert_allclose(solve(y, A).dot(y), x)

venv/lib/python3.10/site-packages/scipy/linalg/tests/test_blas.py

@@ -0,0 +1,1114 @@
+#
+# Created by: Pearu Peterson, April 2002
+#
+
+import math
+import pytest
+import numpy as np
+from numpy.testing import (assert_equal, assert_almost_equal, assert_,
+                           assert_array_almost_equal, assert_allclose)
+from pytest import raises as assert_raises
+
+from numpy import float32, float64, complex64, complex128, arange, triu, \
+                  tril, zeros, tril_indices, ones, mod, diag, append, eye, \
+                  nonzero
+
+from numpy.random import rand, seed
+import scipy
+from scipy.linalg import _fblas as fblas, get_blas_funcs, toeplitz, solve
+
+try:
+    from scipy.linalg import _cblas as cblas
+except ImportError:
+    cblas = None
+
+REAL_DTYPES = [float32, float64]
+COMPLEX_DTYPES = [complex64, complex128]
+DTYPES = REAL_DTYPES + COMPLEX_DTYPES
+
+
+def test_get_blas_funcs():
+    # check that it returns Fortran code for arrays that are
+    # fortran-ordered
+    f1, f2, f3 = get_blas_funcs(
+        ('axpy', 'axpy', 'axpy'),
+        (np.empty((2, 2), dtype=np.complex64, order='F'),
+         np.empty((2, 2), dtype=np.complex128, order='C'))
+        )
+
+    # get_blas_funcs will choose libraries depending on most generic
+    # array
+    assert_equal(f1.typecode, 'z')
+    assert_equal(f2.typecode, 'z')
+    if cblas is not None:
+        assert_equal(f1.module_name, 'cblas')
+        assert_equal(f2.module_name, 'cblas')
+
+    # check defaults.
+    f1 = get_blas_funcs('rotg')
+    assert_equal(f1.typecode, 'd')
+
+    # check also dtype interface
+    f1 = get_blas_funcs('gemm', dtype=np.complex64)
+    assert_equal(f1.typecode, 'c')
+    f1 = get_blas_funcs('gemm', dtype='F')
+    assert_equal(f1.typecode, 'c')
+
+    # extended precision complex
+    f1 = get_blas_funcs('gemm', dtype=np.clongdouble)
+    assert_equal(f1.typecode, 'z')
+
+    # check safe complex upcasting
+    f1 = get_blas_funcs('axpy',
+                        (np.empty((2, 2), dtype=np.float64),
+                         np.empty((2, 2), dtype=np.complex64))
+                        )
+    assert_equal(f1.typecode, 'z')
+
+
+def test_get_blas_funcs_alias():
+    # check alias for get_blas_funcs
+    f, g = get_blas_funcs(('nrm2', 'dot'), dtype=np.complex64)
+    assert f.typecode == 'c'
+    assert g.typecode == 'c'
+
+    f, g, h = get_blas_funcs(('dot', 'dotc', 'dotu'), dtype=np.float64)
+    assert f is g
+    assert f is h
+
+
+class TestCBLAS1Simple:
+
+    def test_axpy(self):
+        for p in 'sd':
+            f = getattr(cblas, p+'axpy', None)
+            if f is None:
+                continue
+            assert_array_almost_equal(f([1, 2, 3], [2, -1, 3], a=5),
+                                      [7, 9, 18])
+        for p in 'cz':
+            f = getattr(cblas, p+'axpy', None)
+            if f is None:
+                continue
+            assert_array_almost_equal(f([1, 2j, 3], [2, -1, 3], a=5),
+                                      [7, 10j-1, 18])
+
+
+class TestFBLAS1Simple:
+
+    def test_axpy(self):
+        for p in 'sd':
+            f = getattr(fblas, p+'axpy', None)
+            if f is None:
+                continue
+            assert_array_almost_equal(f([1, 2, 3], [2, -1, 3], a=5),
+                                      [7, 9, 18])
+        for p in 'cz':
+            f = getattr(fblas, p+'axpy', None)
+            if f is None:
+                continue
+            assert_array_almost_equal(f([1, 2j, 3], [2, -1, 3], a=5),
+                                      [7, 10j-1, 18])
+
+    def test_copy(self):
+        for p in 'sd':
+            f = getattr(fblas, p+'copy', None)
+            if f is None:
+                continue
+            assert_array_almost_equal(f([3, 4, 5], [8]*3), [3, 4, 5])
+        for p in 'cz':
+            f = getattr(fblas, p+'copy', None)
+            if f is None:
+                continue
+            assert_array_almost_equal(f([3, 4j, 5+3j], [8]*3), [3, 4j, 5+3j])
+
+    def test_asum(self):
+        for p in 'sd':
+            f = getattr(fblas, p+'asum', None)
+            if f is None:
+                continue
+            assert_almost_equal(f([3, -4, 5]), 12)
+        for p in ['sc', 'dz']:
+            f = getattr(fblas, p+'asum', None)
+            if f is None:
+                continue
+            assert_almost_equal(f([3j, -4, 3-4j]), 14)
+
+    def test_dot(self):
+        for p in 'sd':
+            f = getattr(fblas, p+'dot', None)
+            if f is None:
+                continue
+            assert_almost_equal(f([3, -4, 5], [2, 5, 1]), -9)
+
+    def test_complex_dotu(self):
+        for p in 'cz':
+            f = getattr(fblas, p+'dotu', None)
+            if f is None:
+                continue
+            assert_almost_equal(f([3j, -4, 3-4j], [2, 3, 1]), -9+2j)
+
+    def test_complex_dotc(self):
+        for p in 'cz':
+            f = getattr(fblas, p+'dotc', None)
+            if f is None:
+                continue
+            assert_almost_equal(f([3j, -4, 3-4j], [2, 3j, 1]), 3-14j)
+
+    def test_nrm2(self):
+        for p in 'sd':
+            f = getattr(fblas, p+'nrm2', None)
+            if f is None:
+                continue
+            assert_almost_equal(f([3, -4, 5]), math.sqrt(50))
+        for p in ['c', 'z', 'sc', 'dz']:
+            f = getattr(fblas, p+'nrm2', None)
+            if f is None:
+                continue
+            assert_almost_equal(f([3j, -4, 3-4j]), math.sqrt(50))
+
+    def test_scal(self):
+        for p in 'sd':
+            f = getattr(fblas, p+'scal', None)
+            if f is None:
+                continue
+            assert_array_almost_equal(f(2, [3, -4, 5]), [6, -8, 10])
+        for p in 'cz':
+            f = getattr(fblas, p+'scal', None)
+            if f is None:
+                continue
+            assert_array_almost_equal(f(3j, [3j, -4, 3-4j]), [-9, -12j, 12+9j])
+        for p in ['cs', 'zd']:
+            f = getattr(fblas, p+'scal', None)
+            if f is None:
+                continue
+            assert_array_almost_equal(f(3, [3j, -4, 3-4j]), [9j, -12, 9-12j])
+
+    def test_swap(self):
+        for p in 'sd':
+            f = getattr(fblas, p+'swap', None)
+            if f is None:
+                continue
+            x, y = [2, 3, 1], [-2, 3, 7]
+            x1, y1 = f(x, y)
+            assert_array_almost_equal(x1, y)
+            assert_array_almost_equal(y1, x)
+        for p in 'cz':
+            f = getattr(fblas, p+'swap', None)
+            if f is None:
+                continue
+            x, y = [2, 3j, 1], [-2, 3, 7-3j]
+            x1, y1 = f(x, y)
+            assert_array_almost_equal(x1, y)
+            assert_array_almost_equal(y1, x)
+
+    def test_amax(self):
+        for p in 'sd':
+            f = getattr(fblas, 'i'+p+'amax')
+            assert_equal(f([-2, 4, 3]), 1)
+        for p in 'cz':
+            f = getattr(fblas, 'i'+p+'amax')
+            assert_equal(f([-5, 4+3j, 6]), 1)
+    # XXX: need tests for rot,rotm,rotg,rotmg
+
+
+class TestFBLAS2Simple:
+
+    def test_gemv(self):
+        for p in 'sd':
+            f = getattr(fblas, p+'gemv', None)
+            if f is None:
+                continue
+            assert_array_almost_equal(f(3, [[3]], [-4]), [-36])
+            assert_array_almost_equal(f(3, [[3]], [-4], 3, [5]), [-21])
+        for p in 'cz':
+            f = getattr(fblas, p+'gemv', None)
+            if f is None:
+                continue
+            assert_array_almost_equal(f(3j, [[3-4j]], [-4]), [-48-36j])
+            assert_array_almost_equal(f(3j, [[3-4j]], [-4], 3, [5j]),
+                                      [-48-21j])
+
+    def test_ger(self):
+
+        for p in 'sd':
+            f = getattr(fblas, p+'ger', None)
+            if f is None:
+                continue
+            assert_array_almost_equal(f(1, [1, 2], [3, 4]), [[3, 4], [6, 8]])
+            assert_array_almost_equal(f(2, [1, 2, 3], [3, 4]),
+                                      [[6, 8], [12, 16], [18, 24]])
+
+            assert_array_almost_equal(f(1, [1, 2], [3, 4],
+                                        a=[[1, 2], [3, 4]]), [[4, 6], [9, 12]])
+
+        for p in 'cz':
+            f = getattr(fblas, p+'geru', None)
+            if f is None:
+                continue
+            assert_array_almost_equal(f(1, [1j, 2], [3, 4]),
+                                      [[3j, 4j], [6, 8]])
+            assert_array_almost_equal(f(-2, [1j, 2j, 3j], [3j, 4j]),
+                                      [[6, 8], [12, 16], [18, 24]])
+
+        for p in 'cz':
+            for name in ('ger', 'gerc'):
+                f = getattr(fblas, p+name, None)
+                if f is None:
+                    continue
+                assert_array_almost_equal(f(1, [1j, 2], [3, 4]),
+                                          [[3j, 4j], [6, 8]])
+                assert_array_almost_equal(f(2, [1j, 2j, 3j], [3j, 4j]),
+                                          [[6, 8], [12, 16], [18, 24]])
+
+    def test_syr_her(self):
+        x = np.arange(1, 5, dtype='d')
+        resx = np.triu(x[:, np.newaxis] * x)
+        resx_reverse = np.triu(x[::-1, np.newaxis] * x[::-1])
+
+        y = np.linspace(0, 8.5, 17, endpoint=False)
+
+        z = np.arange(1, 9, dtype='d').view('D')
+        resz = np.triu(z[:, np.newaxis] * z)
+        resz_reverse = np.triu(z[::-1, np.newaxis] * z[::-1])
+        rehz = np.triu(z[:, np.newaxis] * z.conj())
+        rehz_reverse = np.triu(z[::-1, np.newaxis] * z[::-1].conj())
+
+        w = np.c_[np.zeros(4), z, np.zeros(4)].ravel()
+
+        for p, rtol in zip('sd', [1e-7, 1e-14]):
+            f = getattr(fblas, p+'syr', None)
+            if f is None:
+                continue
+            assert_allclose(f(1.0, x), resx, rtol=rtol)
+            assert_allclose(f(1.0, x, lower=True), resx.T, rtol=rtol)
+            assert_allclose(f(1.0, y, incx=2, offx=2, n=4), resx, rtol=rtol)
+            # negative increments imply reversed vectors in blas
+            assert_allclose(f(1.0, y, incx=-2, offx=2, n=4),
+                            resx_reverse, rtol=rtol)
+
+            a = np.zeros((4, 4), 'f' if p == 's' else 'd', 'F')
+            b = f(1.0, x, a=a, overwrite_a=True)
+            assert_allclose(a, resx, rtol=rtol)
+
+            b = f(2.0, x, a=a)
+            assert_(a is not b)
+            assert_allclose(b, 3*resx, rtol=rtol)
+
+            assert_raises(Exception, f, 1.0, x, incx=0)
+            assert_raises(Exception, f, 1.0, x, offx=5)
+            assert_raises(Exception, f, 1.0, x, offx=-2)
+            assert_raises(Exception, f, 1.0, x, n=-2)
+            assert_raises(Exception, f, 1.0, x, n=5)
+            assert_raises(Exception, f, 1.0, x, lower=2)
+            assert_raises(Exception, f, 1.0, x, a=np.zeros((2, 2), 'd', 'F'))
+
+        for p, rtol in zip('cz', [1e-7, 1e-14]):
+            f = getattr(fblas, p+'syr', None)
+            if f is None:
+                continue
+            assert_allclose(f(1.0, z), resz, rtol=rtol)
+            assert_allclose(f(1.0, z, lower=True), resz.T, rtol=rtol)
+            assert_allclose(f(1.0, w, incx=3, offx=1, n=4), resz, rtol=rtol)
+            # negative increments imply reversed vectors in blas
+            assert_allclose(f(1.0, w, incx=-3, offx=1, n=4),
+                            resz_reverse, rtol=rtol)
+
+            a = np.zeros((4, 4), 'F' if p == 'c' else 'D', 'F')
+            b = f(1.0, z, a=a, overwrite_a=True)
+            assert_allclose(a, resz, rtol=rtol)
+
+            b = f(2.0, z, a=a)
+            assert_(a is not b)
+            assert_allclose(b, 3*resz, rtol=rtol)
+
+            assert_raises(Exception, f, 1.0, x, incx=0)
+            assert_raises(Exception, f, 1.0, x, offx=5)
+            assert_raises(Exception, f, 1.0, x, offx=-2)
+            assert_raises(Exception, f, 1.0, x, n=-2)
+            assert_raises(Exception, f, 1.0, x, n=5)
+            assert_raises(Exception, f, 1.0, x, lower=2)
+            assert_raises(Exception, f, 1.0, x, a=np.zeros((2, 2), 'd', 'F'))
+
+        for p, rtol in zip('cz', [1e-7, 1e-14]):
+            f = getattr(fblas, p+'her', None)
+            if f is None:
+                continue
+            assert_allclose(f(1.0, z), rehz, rtol=rtol)
+            assert_allclose(f(1.0, z, lower=True), rehz.T.conj(), rtol=rtol)
+            assert_allclose(f(1.0, w, incx=3, offx=1, n=4), rehz, rtol=rtol)
+            # negative increments imply reversed vectors in blas
+            assert_allclose(f(1.0, w, incx=-3, offx=1, n=4),
+                            rehz_reverse, rtol=rtol)
+
+            a = np.zeros((4, 4), 'F' if p == 'c' else 'D', 'F')
+            b = f(1.0, z, a=a, overwrite_a=True)
+            assert_allclose(a, rehz, rtol=rtol)
+
+            b = f(2.0, z, a=a)
+            assert_(a is not b)
+            assert_allclose(b, 3*rehz, rtol=rtol)
+
+            assert_raises(Exception, f, 1.0, x, incx=0)
+            assert_raises(Exception, f, 1.0, x, offx=5)
+            assert_raises(Exception, f, 1.0, x, offx=-2)
+            assert_raises(Exception, f, 1.0, x, n=-2)
+            assert_raises(Exception, f, 1.0, x, n=5)
+            assert_raises(Exception, f, 1.0, x, lower=2)
+            assert_raises(Exception, f, 1.0, x, a=np.zeros((2, 2), 'd', 'F'))
+
+    def test_syr2(self):
+        x = np.arange(1, 5, dtype='d')
+        y = np.arange(5, 9, dtype='d')
+        resxy = np.triu(x[:, np.newaxis] * y + y[:, np.newaxis] * x)
+        resxy_reverse = np.triu(x[::-1, np.newaxis] * y[::-1]
+                                + y[::-1, np.newaxis] * x[::-1])
+
+        q = np.linspace(0, 8.5, 17, endpoint=False)
+
+        for p, rtol in zip('sd', [1e-7, 1e-14]):
+            f = getattr(fblas, p+'syr2', None)
+            if f is None:
+                continue
+            assert_allclose(f(1.0, x, y), resxy, rtol=rtol)
+            assert_allclose(f(1.0, x, y, n=3), resxy[:3, :3], rtol=rtol)
+            assert_allclose(f(1.0, x, y, lower=True), resxy.T, rtol=rtol)
+
+            assert_allclose(f(1.0, q, q, incx=2, offx=2, incy=2, offy=10),
+                            resxy, rtol=rtol)
+            assert_allclose(f(1.0, q, q, incx=2, offx=2, incy=2, offy=10, n=3),
+                            resxy[:3, :3], rtol=rtol)
+            # negative increments imply reversed vectors in blas
+            assert_allclose(f(1.0, q, q, incx=-2, offx=2, incy=-2, offy=10),
+                            resxy_reverse, rtol=rtol)
+
+            a = np.zeros((4, 4), 'f' if p == 's' else 'd', 'F')
+            b = f(1.0, x, y, a=a, overwrite_a=True)
+            assert_allclose(a, resxy, rtol=rtol)
+
+            b = f(2.0, x, y, a=a)
+            assert_(a is not b)
+            assert_allclose(b, 3*resxy, rtol=rtol)
+
+            assert_raises(Exception, f, 1.0, x, y, incx=0)
+            assert_raises(Exception, f, 1.0, x, y, offx=5)
+            assert_raises(Exception, f, 1.0, x, y, offx=-2)
+            assert_raises(Exception, f, 1.0, x, y, incy=0)
+            assert_raises(Exception, f, 1.0, x, y, offy=5)
+            assert_raises(Exception, f, 1.0, x, y, offy=-2)
+            assert_raises(Exception, f, 1.0, x, y, n=-2)
+            assert_raises(Exception, f, 1.0, x, y, n=5)
+            assert_raises(Exception, f, 1.0, x, y, lower=2)
+            assert_raises(Exception, f, 1.0, x, y,
+                          a=np.zeros((2, 2), 'd', 'F'))
+
+    def test_her2(self):
+        x = np.arange(1, 9, dtype='d').view('D')
+        y = np.arange(9, 17, dtype='d').view('D')
+        resxy = x[:, np.newaxis] * y.conj() + y[:, np.newaxis] * x.conj()
+        resxy = np.triu(resxy)
+
+        resxy_reverse = x[::-1, np.newaxis] * y[::-1].conj()
+        resxy_reverse += y[::-1, np.newaxis] * x[::-1].conj()
+        resxy_reverse = np.triu(resxy_reverse)
+
+        u = np.c_[np.zeros(4), x, np.zeros(4)].ravel()
+        v = np.c_[np.zeros(4), y, np.zeros(4)].ravel()
+
+        for p, rtol in zip('cz', [1e-7, 1e-14]):
+            f = getattr(fblas, p+'her2', None)
+            if f is None:
+                continue
+            assert_allclose(f(1.0, x, y), resxy, rtol=rtol)
+            assert_allclose(f(1.0, x, y, n=3), resxy[:3, :3], rtol=rtol)
+            assert_allclose(f(1.0, x, y, lower=True), resxy.T.conj(),
+                            rtol=rtol)
+
+            assert_allclose(f(1.0, u, v, incx=3, offx=1, incy=3, offy=1),
+                            resxy, rtol=rtol)
+            assert_allclose(f(1.0, u, v, incx=3, offx=1, incy=3, offy=1, n=3),
+                            resxy[:3, :3], rtol=rtol)
+            # negative increments imply reversed vectors in blas
+            assert_allclose(f(1.0, u, v, incx=-3, offx=1, incy=-3, offy=1),
+                            resxy_reverse, rtol=rtol)
+
+            a = np.zeros((4, 4), 'F' if p == 'c' else 'D', 'F')
+            b = f(1.0, x, y, a=a, overwrite_a=True)
+            assert_allclose(a, resxy, rtol=rtol)
+
+            b = f(2.0, x, y, a=a)
+            assert_(a is not b)
+            assert_allclose(b, 3*resxy, rtol=rtol)
+
+            assert_raises(Exception, f, 1.0, x, y, incx=0)
+            assert_raises(Exception, f, 1.0, x, y, offx=5)
+            assert_raises(Exception, f, 1.0, x, y, offx=-2)
+            assert_raises(Exception, f, 1.0, x, y, incy=0)
+            assert_raises(Exception, f, 1.0, x, y, offy=5)
+            assert_raises(Exception, f, 1.0, x, y, offy=-2)
+            assert_raises(Exception, f, 1.0, x, y, n=-2)
+            assert_raises(Exception, f, 1.0, x, y, n=5)
+            assert_raises(Exception, f, 1.0, x, y, lower=2)
+            assert_raises(Exception, f, 1.0, x, y,
+                          a=np.zeros((2, 2), 'd', 'F'))
+
+    def test_gbmv(self):
+        seed(1234)
+        for ind, dtype in enumerate(DTYPES):
+            n = 7
+            m = 5
+            kl = 1
+            ku = 2
+            # fake a banded matrix via toeplitz
+            A = toeplitz(append(rand(kl+1), zeros(m-kl-1)),
+                         append(rand(ku+1), zeros(n-ku-1)))
+            A = A.astype(dtype)
+            Ab = zeros((kl+ku+1, n), dtype=dtype)
+
+            # Form the banded storage
+            Ab[2, :5] = A[0, 0]  # diag
+            Ab[1, 1:6] = A[0, 1]  # sup1
+            Ab[0, 2:7] = A[0, 2]  # sup2
+            Ab[3, :4] = A[1, 0]  # sub1
+
+            x = rand(n).astype(dtype)
+            y = rand(m).astype(dtype)
+            alpha, beta = dtype(3), dtype(-5)
+
+            func, = get_blas_funcs(('gbmv',), dtype=dtype)
+            y1 = func(m=m, n=n, ku=ku, kl=kl, alpha=alpha, a=Ab,
+                      x=x, y=y, beta=beta)
+            y2 = alpha * A.dot(x) + beta * y
+            assert_array_almost_equal(y1, y2)
+
+            y1 = func(m=m, n=n, ku=ku, kl=kl, alpha=alpha, a=Ab,
+                      x=y, y=x, beta=beta, trans=1)
+            y2 = alpha * A.T.dot(y) + beta * x
+            assert_array_almost_equal(y1, y2)
+
+    def test_sbmv_hbmv(self):
+        seed(1234)
+        for ind, dtype in enumerate(DTYPES):
+            n = 6
+            k = 2
+            A = zeros((n, n), dtype=dtype)
+            Ab = zeros((k+1, n), dtype=dtype)
+
+            # Form the array and its packed banded storage
+            A[arange(n), arange(n)] = rand(n)
+            for ind2 in range(1, k+1):
+                temp = rand(n-ind2)
+                A[arange(n-ind2), arange(ind2, n)] = temp
+                Ab[-1-ind2, ind2:] = temp
+            A = A.astype(dtype)
+            A = A + A.T if ind < 2 else A + A.conj().T
+            Ab[-1, :] = diag(A)
+            x = rand(n).astype(dtype)
+            y = rand(n).astype(dtype)
+            alpha, beta = dtype(1.25), dtype(3)
+
+            if ind > 1:
+                func, = get_blas_funcs(('hbmv',), dtype=dtype)
+            else:
+                func, = get_blas_funcs(('sbmv',), dtype=dtype)
+            y1 = func(k=k, alpha=alpha, a=Ab, x=x, y=y, beta=beta)
+            y2 = alpha * A.dot(x) + beta * y
+            assert_array_almost_equal(y1, y2)
+
+    def test_spmv_hpmv(self):
+        seed(1234)
+        for ind, dtype in enumerate(DTYPES+COMPLEX_DTYPES):
+            n = 3
+            A = rand(n, n).astype(dtype)
+            if ind > 1:
+                A += rand(n, n)*1j
+            A = A.astype(dtype)
+            A = A + A.T if ind < 4 else A + A.conj().T
+            c, r = tril_indices(n)
+            Ap = A[r, c]
+            x = rand(n).astype(dtype)
+            y = rand(n).astype(dtype)
+            xlong = arange(2*n).astype(dtype)
+            ylong = ones(2*n).astype(dtype)
+            alpha, beta = dtype(1.25), dtype(2)
+
+            if ind > 3:
+                func, = get_blas_funcs(('hpmv',), dtype=dtype)
+            else:
+                func, = get_blas_funcs(('spmv',), dtype=dtype)
+            y1 = func(n=n, alpha=alpha, ap=Ap, x=x, y=y, beta=beta)
+            y2 = alpha * A.dot(x) + beta * y
+            assert_array_almost_equal(y1, y2)
+
+            # Test inc and offsets
+            y1 = func(n=n-1, alpha=alpha, beta=beta, x=xlong, y=ylong, ap=Ap,
+                      incx=2, incy=2, offx=n, offy=n)
+            y2 = (alpha * A[:-1, :-1]).dot(xlong[3::2]) + beta * ylong[3::2]
+            assert_array_almost_equal(y1[3::2], y2)
+            assert_almost_equal(y1[4], ylong[4])
+
+    def test_spr_hpr(self):
+        seed(1234)
+        for ind, dtype in enumerate(DTYPES+COMPLEX_DTYPES):
+            n = 3
+            A = rand(n, n).astype(dtype)
+            if ind > 1:
+                A += rand(n, n)*1j
+            A = A.astype(dtype)
+            A = A + A.T if ind < 4 else A + A.conj().T
+            c, r = tril_indices(n)
+            Ap = A[r, c]
+            x = rand(n).astype(dtype)
+            alpha = (DTYPES+COMPLEX_DTYPES)[mod(ind, 4)](2.5)
+
+            if ind > 3:
+                func, = get_blas_funcs(('hpr',), dtype=dtype)
+                y2 = alpha * x[:, None].dot(x[None, :].conj()) + A
+            else:
+                func, = get_blas_funcs(('spr',), dtype=dtype)
+                y2 = alpha * x[:, None].dot(x[None, :]) + A
+
+            y1 = func(n=n, alpha=alpha, ap=Ap, x=x)
+            y1f = zeros((3, 3), dtype=dtype)
+            y1f[r, c] = y1
+            y1f[c, r] = y1.conj() if ind > 3 else y1
+            assert_array_almost_equal(y1f, y2)
+
+    def test_spr2_hpr2(self):
+        seed(1234)
+        for ind, dtype in enumerate(DTYPES):
+            n = 3
+            A = rand(n, n).astype(dtype)
+            if ind > 1:
+                A += rand(n, n)*1j
+            A = A.astype(dtype)
+            A = A + A.T if ind < 2 else A + A.conj().T
+            c, r = tril_indices(n)
+            Ap = A[r, c]
+            x = rand(n).astype(dtype)
+            y = rand(n).astype(dtype)
+            alpha = dtype(2)
+
+            if ind > 1:
+                func, = get_blas_funcs(('hpr2',), dtype=dtype)
+            else:
+                func, = get_blas_funcs(('spr2',), dtype=dtype)
+
+            u = alpha.conj() * x[:, None].dot(y[None, :].conj())
+            y2 = A + u + u.conj().T
+            y1 = func(n=n, alpha=alpha, x=x, y=y, ap=Ap)
+            y1f = zeros((3, 3), dtype=dtype)
+            y1f[r, c] = y1
+            y1f[[1, 2, 2], [0, 0, 1]] = y1[[1, 3, 4]].conj()
+            assert_array_almost_equal(y1f, y2)
+
+    def test_tbmv(self):
+        seed(1234)
+        for ind, dtype in enumerate(DTYPES):
+            n = 10
+            k = 3
+            x = rand(n).astype(dtype)
+            A = zeros((n, n), dtype=dtype)
+            # Banded upper triangular array
+            for sup in range(k+1):
+                A[arange(n-sup), arange(sup, n)] = rand(n-sup)
+
+            # Add complex parts for c,z
+            if ind > 1:
+                A[nonzero(A)] += 1j * rand((k+1)*n-(k*(k+1)//2)).astype(dtype)
+
+            # Form the banded storage
+            Ab = zeros((k+1, n), dtype=dtype)
+            for row in range(k+1):
+                Ab[-row-1, row:] = diag(A, k=row)
+            func, = get_blas_funcs(('tbmv',), dtype=dtype)
+
+            y1 = func(k=k, a=Ab, x=x)
+            y2 = A.dot(x)
+            assert_array_almost_equal(y1, y2)
+
+            y1 = func(k=k, a=Ab, x=x, diag=1)
+            A[arange(n), arange(n)] = dtype(1)
+            y2 = A.dot(x)
+            assert_array_almost_equal(y1, y2)
+
+            y1 = func(k=k, a=Ab, x=x, diag=1, trans=1)
+            y2 = A.T.dot(x)
+            assert_array_almost_equal(y1, y2)
+
+            y1 = func(k=k, a=Ab, x=x, diag=1, trans=2)
+            y2 = A.conj().T.dot(x)
+            assert_array_almost_equal(y1, y2)
+
+    def test_tbsv(self):
+        seed(1234)
+        for ind, dtype in enumerate(DTYPES):
+            n = 6
+            k = 3
+            x = rand(n).astype(dtype)
+            A = zeros((n, n), dtype=dtype)
+            # Banded upper triangular array
+            for sup in range(k+1):
+                A[arange(n-sup), arange(sup, n)] = rand(n-sup)
+
+            # Add complex parts for c,z
+            if ind > 1:
+                A[nonzero(A)] += 1j * rand((k+1)*n-(k*(k+1)//2)).astype(dtype)
+
+            # Form the banded storage
+            Ab = zeros((k+1, n), dtype=dtype)
+            for row in range(k+1):
+                Ab[-row-1, row:] = diag(A, k=row)
+            func, = get_blas_funcs(('tbsv',), dtype=dtype)
+
+            y1 = func(k=k, a=Ab, x=x)
+            y2 = solve(A, x)
+            assert_array_almost_equal(y1, y2)
+
+            y1 = func(k=k, a=Ab, x=x, diag=1)
+            A[arange(n), arange(n)] = dtype(1)
+            y2 = solve(A, x)
+            assert_array_almost_equal(y1, y2)
+
+            y1 = func(k=k, a=Ab, x=x, diag=1, trans=1)
+            y2 = solve(A.T, x)
+            assert_array_almost_equal(y1, y2)
+
+            y1 = func(k=k, a=Ab, x=x, diag=1, trans=2)
+            y2 = solve(A.conj().T, x)
+            assert_array_almost_equal(y1, y2)
+
+    def test_tpmv(self):
+        seed(1234)
+        for ind, dtype in enumerate(DTYPES):
+            n = 10
+            x = rand(n).astype(dtype)
+            # Upper triangular array
+            A = triu(rand(n, n)) if ind < 2 else triu(rand(n, n)+rand(n, n)*1j)
+            # Form the packed storage
+            c, r = tril_indices(n)
+            Ap = A[r, c]
+            func, = get_blas_funcs(('tpmv',), dtype=dtype)
+
+            y1 = func(n=n, ap=Ap, x=x)
+            y2 = A.dot(x)
+            assert_array_almost_equal(y1, y2)
+
+            y1 = func(n=n, ap=Ap, x=x, diag=1)
+            A[arange(n), arange(n)] = dtype(1)
+            y2 = A.dot(x)
+            assert_array_almost_equal(y1, y2)
+
+            y1 = func(n=n, ap=Ap, x=x, diag=1, trans=1)
+            y2 = A.T.dot(x)
+            assert_array_almost_equal(y1, y2)
+
+            y1 = func(n=n, ap=Ap, x=x, diag=1, trans=2)
+            y2 = A.conj().T.dot(x)
+            assert_array_almost_equal(y1, y2)
+
+    def test_tpsv(self):
+        seed(1234)
+        for ind, dtype in enumerate(DTYPES):
+            n = 10
+            x = rand(n).astype(dtype)
+            # Upper triangular array
+            A = triu(rand(n, n)) if ind < 2 else triu(rand(n, n)+rand(n, n)*1j)
+            A += eye(n)
+            # Form the packed storage
+            c, r = tril_indices(n)
+            Ap = A[r, c]
+            func, = get_blas_funcs(('tpsv',), dtype=dtype)
+
+            y1 = func(n=n, ap=Ap, x=x)
+            y2 = solve(A, x)
+            assert_array_almost_equal(y1, y2)
+
+            y1 = func(n=n, ap=Ap, x=x, diag=1)
+            A[arange(n), arange(n)] = dtype(1)
+            y2 = solve(A, x)
+            assert_array_almost_equal(y1, y2)
+
+            y1 = func(n=n, ap=Ap, x=x, diag=1, trans=1)
+            y2 = solve(A.T, x)
+            assert_array_almost_equal(y1, y2)
+
+            y1 = func(n=n, ap=Ap, x=x, diag=1, trans=2)
+            y2 = solve(A.conj().T, x)
+            assert_array_almost_equal(y1, y2)
+
+    def test_trmv(self):
+        seed(1234)
+        for ind, dtype in enumerate(DTYPES):
+            n = 3
+            A = (rand(n, n)+eye(n)).astype(dtype)
+            x = rand(3).astype(dtype)
+            func, = get_blas_funcs(('trmv',), dtype=dtype)
+
+            y1 = func(a=A, x=x)
+            y2 = triu(A).dot(x)
+            assert_array_almost_equal(y1, y2)
+
+            y1 = func(a=A, x=x, diag=1)
+            A[arange(n), arange(n)] = dtype(1)
+            y2 = triu(A).dot(x)
+            assert_array_almost_equal(y1, y2)
+
+            y1 = func(a=A, x=x, diag=1, trans=1)
+            y2 = triu(A).T.dot(x)
+            assert_array_almost_equal(y1, y2)
+
+            y1 = func(a=A, x=x, diag=1, trans=2)
+            y2 = triu(A).conj().T.dot(x)
+            assert_array_almost_equal(y1, y2)
+
+    def test_trsv(self):
+        seed(1234)
+        for ind, dtype in enumerate(DTYPES):
+            n = 15
+            A = (rand(n, n)+eye(n)).astype(dtype)
+            x = rand(n).astype(dtype)
+            func, = get_blas_funcs(('trsv',), dtype=dtype)
+
+            y1 = func(a=A, x=x)
+            y2 = solve(triu(A), x)
+            assert_array_almost_equal(y1, y2)
+
+            y1 = func(a=A, x=x, lower=1)
+            y2 = solve(tril(A), x)
+            assert_array_almost_equal(y1, y2)
+
+            y1 = func(a=A, x=x, diag=1)
+            A[arange(n), arange(n)] = dtype(1)
+            y2 = solve(triu(A), x)
+            assert_array_almost_equal(y1, y2)
+
+            y1 = func(a=A, x=x, diag=1, trans=1)
+            y2 = solve(triu(A).T, x)
+            assert_array_almost_equal(y1, y2)
+
+            y1 = func(a=A, x=x, diag=1, trans=2)
+            y2 = solve(triu(A).conj().T, x)
+            assert_array_almost_equal(y1, y2)
+
+
+class TestFBLAS3Simple:
+
+    def test_gemm(self):
+        for p in 'sd':
+            f = getattr(fblas, p+'gemm', None)
+            if f is None:
+                continue
+            assert_array_almost_equal(f(3, [3], [-4]), [[-36]])
+            assert_array_almost_equal(f(3, [3], [-4], 3, [5]), [-21])
+        for p in 'cz':
+            f = getattr(fblas, p+'gemm', None)
+            if f is None:
+                continue
+            assert_array_almost_equal(f(3j, [3-4j], [-4]), [[-48-36j]])
+            assert_array_almost_equal(f(3j, [3-4j], [-4], 3, [5j]), [-48-21j])
+
+
+def _get_func(func, ps='sdzc'):
+    """Just a helper: return a specified BLAS function w/typecode."""
+    for p in ps:
+        f = getattr(fblas, p+func, None)
+        if f is None:
+            continue
+        yield f
+
+
+class TestBLAS3Symm:
+
+    def setup_method(self):
+        self.a = np.array([[1., 2.],
+                           [0., 1.]])
+        self.b = np.array([[1., 0., 3.],
+                           [0., -1., 2.]])
+        self.c = np.ones((2, 3))
+        self.t = np.array([[2., -1., 8.],
+                           [3., 0., 9.]])
+
+    def test_symm(self):
+        for f in _get_func('symm'):
+            res = f(a=self.a, b=self.b, c=self.c, alpha=1., beta=1.)
+            assert_array_almost_equal(res, self.t)
+
+            res = f(a=self.a.T, b=self.b, lower=1, c=self.c, alpha=1., beta=1.)
+            assert_array_almost_equal(res, self.t)
+
+            res = f(a=self.a, b=self.b.T, side=1, c=self.c.T,
+                    alpha=1., beta=1.)
+            assert_array_almost_equal(res, self.t.T)
+
+    def test_summ_wrong_side(self):
+        f = getattr(fblas, 'dsymm', None)
+        if f is not None:
+            assert_raises(Exception, f, **{'a': self.a, 'b': self.b,
+                                           'alpha': 1, 'side': 1})
+            # `side=1` means C <- B*A, hence shapes of A and B are to be
+            #  compatible. Otherwise, f2py exception is raised
+
+    def test_symm_wrong_uplo(self):
+        """SYMM only considers the upper/lower part of A. Hence setting
+        wrong value for `lower` (default is lower=0, meaning upper triangle)
+        gives a wrong result.
+        """
+        f = getattr(fblas, 'dsymm', None)
+        if f is not None:
+            res = f(a=self.a, b=self.b, c=self.c, alpha=1., beta=1.)
+            assert np.allclose(res, self.t)
+
+            res = f(a=self.a, b=self.b, lower=1, c=self.c, alpha=1., beta=1.)
+            assert not np.allclose(res, self.t)
+
+
+class TestBLAS3Syrk:
+    def setup_method(self):
+        self.a = np.array([[1., 0.],
+                           [0., -2.],
+                           [2., 3.]])
+        self.t = np.array([[1., 0., 2.],
+                           [0., 4., -6.],
+                           [2., -6., 13.]])
+        self.tt = np.array([[5., 6.],
+                            [6., 13.]])
+
+    def test_syrk(self):
+        for f in _get_func('syrk'):
+            c = f(a=self.a, alpha=1.)
+            assert_array_almost_equal(np.triu(c), np.triu(self.t))
+
+            c = f(a=self.a, alpha=1., lower=1)
+            assert_array_almost_equal(np.tril(c), np.tril(self.t))
+
+            c0 = np.ones(self.t.shape)
+            c = f(a=self.a, alpha=1., beta=1., c=c0)
+            assert_array_almost_equal(np.triu(c), np.triu(self.t+c0))
+
+            c = f(a=self.a, alpha=1., trans=1)
+            assert_array_almost_equal(np.triu(c), np.triu(self.tt))
+
+    # prints '0-th dimension must be fixed to 3 but got 5',
+    # FIXME: suppress?
+    # FIXME: how to catch the _fblas.error?
+    def test_syrk_wrong_c(self):
+        f = getattr(fblas, 'dsyrk', None)
+        if f is not None:
+            assert_raises(Exception, f, **{'a': self.a, 'alpha': 1.,
+                                           'c': np.ones((5, 8))})
+        # if C is supplied, it must have compatible dimensions
+
+
+class TestBLAS3Syr2k:
+    def setup_method(self):
+        self.a = np.array([[1., 0.],
+                           [0., -2.],
+                           [2., 3.]])
+        self.b = np.array([[0., 1.],
+                           [1., 0.],
+                           [0, 1.]])
+        self.t = np.array([[0., -1., 3.],
+                           [-1., 0., 0.],
+                           [3., 0., 6.]])
+        self.tt = np.array([[0., 1.],
+                            [1., 6]])
+
+    def test_syr2k(self):
+        for f in _get_func('syr2k'):
+            c = f(a=self.a, b=self.b, alpha=1.)
+            assert_array_almost_equal(np.triu(c), np.triu(self.t))
+
+            c = f(a=self.a, b=self.b, alpha=1., lower=1)
+            assert_array_almost_equal(np.tril(c), np.tril(self.t))
+
+            c0 = np.ones(self.t.shape)
+            c = f(a=self.a, b=self.b, alpha=1., beta=1., c=c0)
+            assert_array_almost_equal(np.triu(c), np.triu(self.t+c0))
+
+            c = f(a=self.a, b=self.b, alpha=1., trans=1)
+            assert_array_almost_equal(np.triu(c), np.triu(self.tt))
+
+    # prints '0-th dimension must be fixed to 3 but got 5', FIXME: suppress?
+    def test_syr2k_wrong_c(self):
+        f = getattr(fblas, 'dsyr2k', None)
+        if f is not None:
+            assert_raises(Exception, f, **{'a': self.a,
+                                           'b': self.b,
+                                           'alpha': 1.,
+                                           'c': np.zeros((15, 8))})
+        # if C is supplied, it must have compatible dimensions
+
+
+class TestSyHe:
+    """Quick and simple tests for (zc)-symm, syrk, syr2k."""
+
+    def setup_method(self):
+        self.sigma_y = np.array([[0., -1.j],
+                                 [1.j, 0.]])
+
+    def test_symm_zc(self):
+        for f in _get_func('symm', 'zc'):
+            # NB: a is symmetric w/upper diag of ONLY
+            res = f(a=self.sigma_y, b=self.sigma_y, alpha=1.)
+            assert_array_almost_equal(np.triu(res), np.diag([1, -1]))
+
+    def test_hemm_zc(self):
+        for f in _get_func('hemm', 'zc'):
+            # NB: a is hermitian w/upper diag of ONLY
+            res = f(a=self.sigma_y, b=self.sigma_y, alpha=1.)
+            assert_array_almost_equal(np.triu(res), np.diag([1, 1]))
+
+    def test_syrk_zr(self):
+        for f in _get_func('syrk', 'zc'):
+            res = f(a=self.sigma_y, alpha=1.)
+            assert_array_almost_equal(np.triu(res), np.diag([-1, -1]))
+
+    def test_herk_zr(self):
+        for f in _get_func('herk', 'zc'):
+            res = f(a=self.sigma_y, alpha=1.)
+            assert_array_almost_equal(np.triu(res), np.diag([1, 1]))
+
+    def test_syr2k_zr(self):
+        for f in _get_func('syr2k', 'zc'):
+            res = f(a=self.sigma_y, b=self.sigma_y, alpha=1.)
+            assert_array_almost_equal(np.triu(res), 2.*np.diag([-1, -1]))
+
+    def test_her2k_zr(self):
+        for f in _get_func('her2k', 'zc'):
+            res = f(a=self.sigma_y, b=self.sigma_y, alpha=1.)
+            assert_array_almost_equal(np.triu(res), 2.*np.diag([1, 1]))
+
+
+class TestTRMM:
+    """Quick and simple tests for dtrmm."""
+
+    def setup_method(self):
+        self.a = np.array([[1., 2., ],
+                           [-2., 1.]])
+        self.b = np.array([[3., 4., -1.],
+                           [5., 6., -2.]])
+
+        self.a2 = np.array([[1, 1, 2, 3],
+                            [0, 1, 4, 5],
+                            [0, 0, 1, 6],
+                            [0, 0, 0, 1]], order="f")
+        self.b2 = np.array([[1, 4], [2, 5], [3, 6], [7, 8], [9, 10]],
+                           order="f")
+
+    @pytest.mark.parametrize("dtype_", DTYPES)
+    def test_side(self, dtype_):
+        trmm = get_blas_funcs("trmm", dtype=dtype_)
+        # Provide large A array that works for side=1 but not 0 (see gh-10841)
+        assert_raises(Exception, trmm, 1.0, self.a2, self.b2)
+        res = trmm(1.0, self.a2.astype(dtype_), self.b2.astype(dtype_),
+                   side=1)
+        k = self.b2.shape[1]
+        assert_allclose(res, self.b2 @ self.a2[:k, :k], rtol=0.,
+                        atol=100*np.finfo(dtype_).eps)
+
+    def test_ab(self):
+        f = getattr(fblas, 'dtrmm', None)
+        if f is not None:
+            result = f(1., self.a, self.b)
+            # default a is upper triangular
+            expected = np.array([[13., 16., -5.],
+                                 [5., 6., -2.]])
+            assert_array_almost_equal(result, expected)
+
+    def test_ab_lower(self):
+        f = getattr(fblas, 'dtrmm', None)
+        if f is not None:
+            result = f(1., self.a, self.b, lower=True)
+            expected = np.array([[3., 4., -1.],
+                                 [-1., -2., 0.]])  # now a is lower triangular
+            assert_array_almost_equal(result, expected)
+
+    def test_b_overwrites(self):
+        # BLAS dtrmm modifies B argument in-place.
+        # Here the default is to copy, but this can be overridden
+        f = getattr(fblas, 'dtrmm', None)
+        if f is not None:
+            for overwr in [True, False]:
+                bcopy = self.b.copy()
+                result = f(1., self.a, bcopy, overwrite_b=overwr)
+                # C-contiguous arrays are copied
+                assert_(bcopy.flags.f_contiguous is False and
+                        np.may_share_memory(bcopy, result) is False)
+                assert_equal(bcopy, self.b)
+
+            bcopy = np.asfortranarray(self.b.copy())  # or just transpose it
+            result = f(1., self.a, bcopy, overwrite_b=True)
+            assert_(bcopy.flags.f_contiguous is True and
+                    np.may_share_memory(bcopy, result) is True)
+            assert_array_almost_equal(bcopy, result)
+
+
+def test_trsm():
+    seed(1234)
+    for ind, dtype in enumerate(DTYPES):
+        tol = np.finfo(dtype).eps*1000
+        func, = get_blas_funcs(('trsm',), dtype=dtype)
+
+        # Test protection against size mismatches
+        A = rand(4, 5).astype(dtype)
+        B = rand(4, 4).astype(dtype)
+        alpha = dtype(1)
+        assert_raises(Exception, func, alpha, A, B)
+        assert_raises(Exception, func, alpha, A.T, B)
+
+        n = 8
+        m = 7
+        alpha = dtype(-2.5)
+        A = (rand(m, m) if ind < 2 else rand(m, m) + rand(m, m)*1j) + eye(m)
+        A = A.astype(dtype)
+        Au = triu(A)
+        Al = tril(A)
+        B1 = rand(m, n).astype(dtype)
+        B2 = rand(n, m).astype(dtype)
+
+        x1 = func(alpha=alpha, a=A, b=B1)
+        assert_equal(B1.shape, x1.shape)
+        x2 = solve(Au, alpha*B1)
+        assert_allclose(x1, x2, atol=tol)
+
+        x1 = func(alpha=alpha, a=A, b=B1, trans_a=1)
+        x2 = solve(Au.T, alpha*B1)
+        assert_allclose(x1, x2, atol=tol)
+
+        x1 = func(alpha=alpha, a=A, b=B1, trans_a=2)
+        x2 = solve(Au.conj().T, alpha*B1)
+        assert_allclose(x1, x2, atol=tol)
+
+        x1 = func(alpha=alpha, a=A, b=B1, diag=1)
+        Au[arange(m), arange(m)] = dtype(1)
+        x2 = solve(Au, alpha*B1)
+        assert_allclose(x1, x2, atol=tol)
+
+        x1 = func(alpha=alpha, a=A, b=B2, diag=1, side=1)
+        x2 = solve(Au.conj().T, alpha*B2.conj().T)
+        assert_allclose(x1, x2.conj().T, atol=tol)
+
+        x1 = func(alpha=alpha, a=A, b=B2, diag=1, side=1, lower=1)
+        Al[arange(m), arange(m)] = dtype(1)
+        x2 = solve(Al.conj().T, alpha*B2.conj().T)
+        assert_allclose(x1, x2.conj().T, atol=tol)
+
+
+@pytest.mark.xfail(run=False,
+                   reason="gh-16930")
+def test_gh_169309():
+    x = np.repeat(10, 9)
+    actual = scipy.linalg.blas.dnrm2(x, 5, 3, -1)
+    expected = math.sqrt(500)
+    assert_allclose(actual, expected)
+
+
+def test_dnrm2_neg_incx():
+    # check that dnrm2(..., incx < 0) raises
+    # XXX: remove the test after the lowest supported BLAS implements
+    # negative incx (new in LAPACK 3.10)
+    x = np.repeat(10, 9)
+    incx = -1
+    with assert_raises(fblas.__fblas_error):
+        scipy.linalg.blas.dnrm2(x, 5, 3, incx)