venv/lib/python3.11/site-packages/scipy/sparse/tests/test_construct.py

"""test sparse matrix construction functions"""

import numpy as np
from numpy import array
from numpy.testing import (assert_equal, assert_,
        assert_array_equal, assert_array_almost_equal_nulp)
import pytest
from pytest import raises as assert_raises
from scipy._lib._testutils import check_free_memory

from scipy.sparse import (csr_matrix, coo_matrix,
                          csr_array, coo_array,
                          csc_array, bsr_array,
                          dia_array, dok_array,
                          lil_array, csc_matrix,
                          bsr_matrix, dia_matrix,
                          lil_matrix, sparray, spmatrix,
                          _construct as construct)
from scipy.sparse._construct import rand as sprand

sparse_formats = ['csr','csc','coo','bsr','dia','lil','dok']

#TODO check whether format=XXX is respected


def _sprandn(m, n, density=0.01, format="coo", dtype=None, rng=None):
    # Helper function for testing.
    rng = np.random.default_rng(rng)
    data_rvs = rng.standard_normal
    return construct.random(m, n, density, format, dtype, rng, data_rvs)


def _sprandn_array(m, n, density=0.01, format="coo", dtype=None, rng=None):
    # Helper function for testing.
    rng = np.random.default_rng(rng)
    data_sampler = rng.standard_normal
    return construct.random_array((m, n), density=density, format=format, dtype=dtype,
                                  rng=rng, data_sampler=data_sampler)


class TestConstructUtils:

    @pytest.mark.parametrize("cls", [
        csc_array, csr_array, coo_array, bsr_array,
        dia_array, dok_array, lil_array
    ])
    def test_singleton_array_constructor(self, cls):
        with pytest.raises(
            ValueError,
            match=(
                'scipy sparse array classes do not support '
                'instantiation from a scalar'
            )
        ):
            cls(0)

    @pytest.mark.parametrize("cls", [
        csc_matrix, csr_matrix, coo_matrix,
        bsr_matrix, dia_matrix, lil_matrix
    ])
    def test_singleton_matrix_constructor(self, cls):
        """
        This test is for backwards compatibility post scipy 1.13.
        The behavior observed here is what is to be expected
        with the older matrix classes. This test comes with the
        exception of dok_matrix, which was not working pre scipy1.12
        (unlike the rest of these).
        """
        assert cls(0).shape == (1, 1)

    def test_spdiags(self):
        diags1 = array([[1, 2, 3, 4, 5]])
        diags2 = array([[1, 2, 3, 4, 5],
                         [6, 7, 8, 9,10]])
        diags3 = array([[1, 2, 3, 4, 5],
                         [6, 7, 8, 9,10],
                         [11,12,13,14,15]])

        cases = []
        cases.append((diags1, 0, 1, 1, [[1]]))
        cases.append((diags1, [0], 1, 1, [[1]]))
        cases.append((diags1, [0], 2, 1, [[1],[0]]))
        cases.append((diags1, [0], 1, 2, [[1,0]]))
        cases.append((diags1, [1], 1, 2, [[0,2]]))
        cases.append((diags1,[-1], 1, 2, [[0,0]]))
        cases.append((diags1, [0], 2, 2, [[1,0],[0,2]]))
        cases.append((diags1,[-1], 2, 2, [[0,0],[1,0]]))
        cases.append((diags1, [3], 2, 2, [[0,0],[0,0]]))
        cases.append((diags1, [0], 3, 4, [[1,0,0,0],[0,2,0,0],[0,0,3,0]]))
        cases.append((diags1, [1], 3, 4, [[0,2,0,0],[0,0,3,0],[0,0,0,4]]))
        cases.append((diags1, [2], 3, 5, [[0,0,3,0,0],[0,0,0,4,0],[0,0,0,0,5]]))

        cases.append((diags2, [0,2], 3, 3, [[1,0,8],[0,2,0],[0,0,3]]))
        cases.append((diags2, [-1,0], 3, 4, [[6,0,0,0],[1,7,0,0],[0,2,8,0]]))
        cases.append((diags2, [2,-3], 6, 6, [[0,0,3,0,0,0],
                                              [0,0,0,4,0,0],
                                              [0,0,0,0,5,0],
                                              [6,0,0,0,0,0],
                                              [0,7,0,0,0,0],
                                              [0,0,8,0,0,0]]))

        cases.append((diags3, [-1,0,1], 6, 6, [[6,12, 0, 0, 0, 0],
                                                [1, 7,13, 0, 0, 0],
                                                [0, 2, 8,14, 0, 0],
                                                [0, 0, 3, 9,15, 0],
                                                [0, 0, 0, 4,10, 0],
                                                [0, 0, 0, 0, 5, 0]]))
        cases.append((diags3, [-4,2,-1], 6, 5, [[0, 0, 8, 0, 0],
                                                 [11, 0, 0, 9, 0],
                                                 [0,12, 0, 0,10],
                                                 [0, 0,13, 0, 0],
                                                 [1, 0, 0,14, 0],
                                                 [0, 2, 0, 0,15]]))
        cases.append((diags3, [-1, 1, 2], len(diags3[0]), len(diags3[0]),
                      [[0, 7, 13, 0, 0],
                       [1, 0, 8, 14, 0],
                       [0, 2, 0, 9, 15],
                       [0, 0, 3, 0, 10],
                       [0, 0, 0, 4, 0]]))

        for d, o, m, n, result in cases:
            if len(d[0]) == m and m == n:
                assert_equal(construct.spdiags(d, o).toarray(), result)
            assert_equal(construct.spdiags(d, o, m, n).toarray(), result)
            assert_equal(construct.spdiags(d, o, (m, n)).toarray(), result)

    def test_diags(self):
        a = array([1, 2, 3, 4, 5])
        b = array([6, 7, 8, 9, 10])
        c = array([11, 12, 13, 14, 15])

        cases = []
        cases.append((a[:1], 0, (1, 1), [[1]]))
        cases.append(([a[:1]], [0], (1, 1), [[1]]))
        cases.append(([a[:1]], [0], (2, 1), [[1],[0]]))
        cases.append(([a[:1]], [0], (1, 2), [[1,0]]))
        cases.append(([a[:1]], [1], (1, 2), [[0,1]]))
        cases.append(([a[:2]], [0], (2, 2), [[1,0],[0,2]]))
        cases.append(([a[:1]],[-1], (2, 2), [[0,0],[1,0]]))
        cases.append(([a[:3]], [0], (3, 4), [[1,0,0,0],[0,2,0,0],[0,0,3,0]]))
        cases.append(([a[:3]], [1], (3, 4), [[0,1,0,0],[0,0,2,0],[0,0,0,3]]))
        cases.append(([a[:1]], [-2], (3, 5), [[0,0,0,0,0],[0,0,0,0,0],[1,0,0,0,0]]))
        cases.append(([a[:2]], [-1], (3, 5), [[0,0,0,0,0],[1,0,0,0,0],[0,2,0,0,0]]))
        cases.append(([a[:3]], [0], (3, 5), [[1,0,0,0,0],[0,2,0,0,0],[0,0,3,0,0]]))
        cases.append(([a[:3]], [1], (3, 5), [[0,1,0,0,0],[0,0,2,0,0],[0,0,0,3,0]]))
        cases.append(([a[:3]], [2], (3, 5), [[0,0,1,0,0],[0,0,0,2,0],[0,0,0,0,3]]))
        cases.append(([a[:2]], [3], (3, 5), [[0,0,0,1,0],[0,0,0,0,2],[0,0,0,0,0]]))
        cases.append(([a[:1]], [4], (3, 5), [[0,0,0,0,1],[0,0,0,0,0],[0,0,0,0,0]]))
        cases.append(([a[:1]], [-4], (5, 3), [[0,0,0],[0,0,0],[0,0,0],[0,0,0],[1,0,0]]))
        cases.append(([a[:2]], [-3], (5, 3), [[0,0,0],[0,0,0],[0,0,0],[1,0,0],[0,2,0]]))
        cases.append(([a[:3]], [-2], (5, 3), [[0,0,0],[0,0,0],[1,0,0],[0,2,0],[0,0,3]]))
        cases.append(([a[:3]], [-1], (5, 3), [[0,0,0],[1,0,0],[0,2,0],[0,0,3],[0,0,0]]))
        cases.append(([a[:3]], [0], (5, 3), [[1,0,0],[0,2,0],[0,0,3],[0,0,0],[0,0,0]]))
        cases.append(([a[:2]], [1], (5, 3), [[0,1,0],[0,0,2],[0,0,0],[0,0,0],[0,0,0]]))
        cases.append(([a[:1]], [2], (5, 3), [[0,0,1],[0,0,0],[0,0,0],[0,0,0],[0,0,0]]))

        cases.append(([a[:3],b[:1]], [0,2], (3, 3), [[1,0,6],[0,2,0],[0,0,3]]))
        cases.append(([a[:2],b[:3]], [-1,0], (3, 4), [[6,0,0,0],[1,7,0,0],[0,2,8,0]]))
        cases.append(([a[:4],b[:3]], [2,-3], (6, 6), [[0,0,1,0,0,0],
                                                     [0,0,0,2,0,0],
                                                     [0,0,0,0,3,0],
                                                     [6,0,0,0,0,4],
                                                     [0,7,0,0,0,0],
                                                     [0,0,8,0,0,0]]))

        cases.append(([a[:4],b,c[:4]], [-1,0,1], (5, 5), [[6,11, 0, 0, 0],
                                                            [1, 7,12, 0, 0],
                                                            [0, 2, 8,13, 0],
                                                            [0, 0, 3, 9,14],
                                                            [0, 0, 0, 4,10]]))
        cases.append(([a[:2],b[:3],c], [-4,2,-1], (6, 5), [[0, 0, 6, 0, 0],
                                                          [11, 0, 0, 7, 0],
                                                          [0,12, 0, 0, 8],
                                                          [0, 0,13, 0, 0],
                                                          [1, 0, 0,14, 0],
                                                          [0, 2, 0, 0,15]]))

        # too long arrays are OK
        cases.append(([a], [0], (1, 1), [[1]]))
        cases.append(([a[:3],b], [0,2], (3, 3), [[1, 0, 6], [0, 2, 0], [0, 0, 3]]))
        cases.append((
            np.array([[1, 2, 3], [4, 5, 6]]),
            [0,-1],
            (3, 3),
            [[1, 0, 0], [4, 2, 0], [0, 5, 3]]
        ))

        # scalar case: broadcasting
        cases.append(([1,-2,1], [1,0,-1], (3, 3), [[-2, 1, 0],
                                                    [1, -2, 1],
                                                    [0, 1, -2]]))

        for d, o, shape, result in cases:
            err_msg = f"{d!r} {o!r} {shape!r} {result!r}"
            assert_equal(construct.diags(d, offsets=o, shape=shape).toarray(),
                         result, err_msg=err_msg)

            if (shape[0] == shape[1]
                and hasattr(d[0], '__len__')
                and len(d[0]) <= max(shape)):
                # should be able to find the shape automatically
                assert_equal(construct.diags(d, offsets=o).toarray(), result,
                             err_msg=err_msg)

    def test_diags_default(self):
        a = array([1, 2, 3, 4, 5])
        assert_equal(construct.diags(a).toarray(), np.diag(a))

    def test_diags_default_bad(self):
        a = array([[1, 2, 3, 4, 5], [2, 3, 4, 5, 6]])
        assert_raises(ValueError, construct.diags, a)

    def test_diags_bad(self):
        a = array([1, 2, 3, 4, 5])
        b = array([6, 7, 8, 9, 10])
        c = array([11, 12, 13, 14, 15])

        cases = []
        cases.append(([a[:0]], 0, (1, 1)))
        cases.append(([a[:4],b,c[:3]], [-1,0,1], (5, 5)))
        cases.append(([a[:2],c,b[:3]], [-4,2,-1], (6, 5)))
        cases.append(([a[:2],c,b[:3]], [-4,2,-1], None))
        cases.append(([], [-4,2,-1], None))
        cases.append(([1], [-5], (4, 4)))
        cases.append(([a], 0, None))

        for d, o, shape in cases:
            assert_raises(ValueError, construct.diags, d, offsets=o, shape=shape)

        assert_raises(TypeError, construct.diags, [[None]], offsets=[0])

    def test_diags_vs_diag(self):
        # Check that
        #
        #    diags([a, b, ...], [i, j, ...]) == diag(a, i) + diag(b, j) + ...
        #

        rng = np.random.RandomState(1234)

        for n_diags in [1, 2, 3, 4, 5, 10]:
            n = 1 + n_diags//2 + rng.randint(0, 10)

            offsets = np.arange(-n+1, n-1)
            rng.shuffle(offsets)
            offsets = offsets[:n_diags]

            diagonals = [rng.rand(n - abs(q)) for q in offsets]

            mat = construct.diags(diagonals, offsets=offsets)
            dense_mat = sum([np.diag(x, j) for x, j in zip(diagonals, offsets)])

            assert_array_almost_equal_nulp(mat.toarray(), dense_mat)

            if len(offsets) == 1:
                mat = construct.diags(diagonals[0], offsets=offsets[0])
                dense_mat = np.diag(diagonals[0], offsets[0])
                assert_array_almost_equal_nulp(mat.toarray(), dense_mat)

    def test_diags_dtype(self):
        x = construct.diags([2.2], offsets=[0], shape=(2, 2), dtype=int)
        assert_equal(x.dtype, int)
        assert_equal(x.toarray(), [[2, 0], [0, 2]])

    def test_diags_one_diagonal(self):
        d = list(range(5))
        for k in range(-5, 6):
            assert_equal(construct.diags(d, offsets=k).toarray(),
                         construct.diags([d], offsets=[k]).toarray())

    def test_diags_empty(self):
        x = construct.diags([])
        assert_equal(x.shape, (0, 0))

    @pytest.mark.parametrize("identity", [construct.identity, construct.eye_array])
    def test_identity(self, identity):
        assert_equal(identity(1).toarray(), [[1]])
        assert_equal(identity(2).toarray(), [[1,0],[0,1]])

        I = identity(3, dtype='int8', format='dia')
        assert_equal(I.dtype, np.dtype('int8'))
        assert_equal(I.format, 'dia')

        for fmt in sparse_formats:
            I = identity(3, format=fmt)
            assert_equal(I.format, fmt)
            assert_equal(I.toarray(), [[1,0,0],[0,1,0],[0,0,1]])

    @pytest.mark.parametrize("eye", [construct.eye, construct.eye_array])
    def test_eye(self, eye):
        assert_equal(eye(1,1).toarray(), [[1]])
        assert_equal(eye(2,3).toarray(), [[1,0,0],[0,1,0]])
        assert_equal(eye(3,2).toarray(), [[1,0],[0,1],[0,0]])
        assert_equal(eye(3,3).toarray(), [[1,0,0],[0,1,0],[0,0,1]])

        assert_equal(eye(3,3,dtype='int16').dtype, np.dtype('int16'))

        for m in [3, 5]:
            for n in [3, 5]:
                for k in range(-5,6):
                    # scipy.sparse.eye deviates from np.eye here. np.eye will
                    # create arrays of all 0's when the diagonal offset is
                    # greater than the size of the array. For sparse arrays
                    # this makes less sense, especially as it results in dia
                    # arrays with negative diagonals. Therefore sp.sparse.eye
                    # validates that diagonal offsets fall within the shape of
                    # the array. See gh-18555.
                    if (k > 0 and k > n) or (k < 0 and abs(k) > m):
                        with pytest.raises(
                            ValueError, match="Offset.*out of bounds"
                        ):
                            eye(m, n, k=k)

                    else:
                        assert_equal(
                            eye(m, n, k=k).toarray(),
                            np.eye(m, n, k=k)
                        )
                        if m == n:
                            assert_equal(
                                eye(m, k=k).toarray(),
                                np.eye(m, n, k=k)
                            )

    @pytest.mark.parametrize("eye", [construct.eye, construct.eye_array])
    def test_eye_one(self, eye):
        assert_equal(eye(1).toarray(), [[1]])
        assert_equal(eye(2).toarray(), [[1,0],[0,1]])

        I = eye(3, dtype='int8', format='dia')
        assert_equal(I.dtype, np.dtype('int8'))
        assert_equal(I.format, 'dia')

        for fmt in sparse_formats:
            I = eye(3, format=fmt)
            assert_equal(I.format, fmt)
            assert_equal(I.toarray(), [[1,0,0],[0,1,0],[0,0,1]])

    def test_eye_array_vs_matrix(self):
        assert isinstance(construct.eye_array(3), sparray)
        assert not isinstance(construct.eye(3), sparray)

    def test_kron(self):
        cases = []

        cases.append(array([[0]]))
        cases.append(array([[-1]]))
        cases.append(array([[4]]))
        cases.append(array([[10]]))
        cases.append(array([[0],[0]]))
        cases.append(array([[0,0]]))
        cases.append(array([[1,2],[3,4]]))
        cases.append(array([[0,2],[5,0]]))
        cases.append(array([[0,2,-6],[8,0,14]]))
        cases.append(array([[5,4],[0,0],[6,0]]))
        cases.append(array([[5,4,4],[1,0,0],[6,0,8]]))
        cases.append(array([[0,1,0,2,0,5,8]]))
        cases.append(array([[0.5,0.125,0,3.25],[0,2.5,0,0]]))

        # test all cases with some formats
        for a in cases:
            ca = csr_array(a)
            for b in cases:
                cb = csr_array(b)
                expected = np.kron(a, b)
                for fmt in sparse_formats[1:4]:
                    result = construct.kron(ca, cb, format=fmt)
                    assert_equal(result.format, fmt)
                    assert_array_equal(result.toarray(), expected)
                    assert isinstance(result, sparray)

        # test one case with all formats
        a = cases[-1]
        b = cases[-3]
        ca = csr_array(a)
        cb = csr_array(b)

        expected = np.kron(a, b)
        for fmt in sparse_formats:
            result = construct.kron(ca, cb, format=fmt)
            assert_equal(result.format, fmt)
            assert_array_equal(result.toarray(), expected)
            assert isinstance(result, sparray)

        # check that spmatrix returned when both inputs are spmatrix
        result = construct.kron(csr_matrix(a), csr_matrix(b), format=fmt)
        assert_equal(result.format, fmt)
        assert_array_equal(result.toarray(), expected)
        assert isinstance(result, spmatrix)

    def test_kron_ndim_exceptions(self):
        with pytest.raises(ValueError, match='requires 2D input'):
            construct.kron([[0], [1]], csr_array([0, 1]))
        with pytest.raises(ValueError, match='requires 2D input'):
            construct.kron(csr_array([0, 1]), [[0], [1]])
        # no exception if sparse arrays are not input (spmatrix inferred)
        construct.kron([[0], [1]], [0, 1])

    def test_kron_large(self):
        n = 2**16
        a = construct.diags_array([1], shape=(1, n), offsets=n-1)
        b = construct.diags_array([1], shape=(n, 1), offsets=1-n)

        construct.kron(a, a)
        construct.kron(b, b)

    def test_kronsum(self):
        cases = []

        cases.append(array([[0]]))
        cases.append(array([[-1]]))
        cases.append(array([[4]]))
        cases.append(array([[10]]))
        cases.append(array([[1,2],[3,4]]))
        cases.append(array([[0,2],[5,0]]))
        cases.append(array([[0,2,-6],[8,0,14],[0,3,0]]))
        cases.append(array([[1,0,0],[0,5,-1],[4,-2,8]]))

        # test all cases with default format
        for a in cases:
            for b in cases:
                result = construct.kronsum(csr_array(a), csr_array(b)).toarray()
                expected = (np.kron(np.eye(b.shape[0]), a)
                            + np.kron(b, np.eye(a.shape[0])))
                assert_array_equal(result, expected)

        # check that spmatrix returned when both inputs are spmatrix
        result = construct.kronsum(csr_matrix(a), csr_matrix(b)).toarray()
        assert_array_equal(result, expected)

    def test_kronsum_ndim_exceptions(self):
        with pytest.raises(ValueError, match='requires 2D input'):
            construct.kronsum([[0], [1]], csr_array([0, 1]))
        with pytest.raises(ValueError, match='requires 2D input'):
            construct.kronsum(csr_array([0, 1]), [[0], [1]])
        # no exception if sparse arrays are not input (spmatrix inferred)
        construct.kronsum([[0, 1], [1, 0]], [2])

    @pytest.mark.parametrize("coo_cls", [coo_matrix, coo_array])
    def test_vstack(self, coo_cls):
        A = coo_cls([[1,2],[3,4]])
        B = coo_cls([[5,6]])

        expected = array([[1, 2],
                          [3, 4],
                          [5, 6]])
        assert_equal(construct.vstack([A, B]).toarray(), expected)
        assert_equal(construct.vstack([A, B], dtype=np.float32).dtype,
                     np.float32)

        assert_equal(construct.vstack([A.todok(), B.todok()]).toarray(), expected)

        assert_equal(construct.vstack([A.tocsr(), B.tocsr()]).toarray(),
                     expected)
        result = construct.vstack([A.tocsr(), B.tocsr()],
                                  format="csr", dtype=np.float32)
        assert_equal(result.dtype, np.float32)
        assert_equal(result.indices.dtype, np.int32)
        assert_equal(result.indptr.dtype, np.int32)

        assert_equal(construct.vstack([A.tocsc(), B.tocsc()]).toarray(),
                     expected)
        result = construct.vstack([A.tocsc(), B.tocsc()],
                                  format="csc", dtype=np.float32)
        assert_equal(result.dtype, np.float32)
        assert_equal(result.indices.dtype, np.int32)
        assert_equal(result.indptr.dtype, np.int32)

    def test_vstack_maintain64bit_idx_dtype(self):
        # see gh-20389 v/hstack returns int32 idx_dtype with input int64 idx_dtype
        X = csr_array([[1, 0, 0], [0, 1, 0], [0, 1, 0]])
        X.indptr = X.indptr.astype(np.int64)
        X.indices = X.indices.astype(np.int64)
        assert construct.vstack([X, X]).indptr.dtype == np.int64
        assert construct.hstack([X, X]).indptr.dtype == np.int64

        X = csc_array([[1, 0, 0], [0, 1, 0], [0, 1, 0]])
        X.indptr = X.indptr.astype(np.int64)
        X.indices = X.indices.astype(np.int64)
        assert construct.vstack([X, X]).indptr.dtype == np.int64
        assert construct.hstack([X, X]).indptr.dtype == np.int64

        X = coo_array([[1, 0, 0], [0, 1, 0], [0, 1, 0]])
        X.coords = tuple(co.astype(np.int64) for co in X.coords)
        assert construct.vstack([X, X]).coords[0].dtype == np.int64
        assert construct.hstack([X, X]).coords[0].dtype == np.int64

    def test_vstack_matrix_or_array(self):
        A = [[1,2],[3,4]]
        B = [[5,6]]
        assert isinstance(construct.vstack([coo_array(A), coo_array(B)]), sparray)
        assert isinstance(construct.vstack([coo_array(A), coo_matrix(B)]), sparray)
        assert isinstance(construct.vstack([coo_matrix(A), coo_array(B)]), sparray)
        assert isinstance(construct.vstack([coo_matrix(A), coo_matrix(B)]), spmatrix)

    def test_vstack_1d_with_2d(self):
        # fixes gh-21064
        arr = csr_array([[1, 0, 0], [0, 1, 0]])
        arr1d = csr_array([1, 0, 0])
        arr1dcoo = coo_array([1, 0, 0])
        assert construct.vstack([arr, np.array([0, 0, 0])]).shape == (3, 3)
        assert construct.hstack([arr1d, np.array([[0]])]).shape == (1, 4)
        assert construct.hstack([arr1d, arr1d]).shape == (1, 6)
        assert construct.vstack([arr1d, arr1d]).shape == (2, 3)

        # check csr specialty stacking code like _stack_along_minor_axis
        assert construct.hstack([arr, arr]).shape == (2, 6)
        assert construct.hstack([arr1d, arr1d]).shape == (1, 6)

        assert construct.hstack([arr1d, arr1dcoo]).shape == (1, 6)
        assert construct.vstack([arr, arr1dcoo]).shape == (3, 3)
        assert construct.vstack([arr1d, arr1dcoo]).shape == (2, 3)

        with pytest.raises(ValueError, match="incompatible row dimensions"):
            construct.hstack([arr, np.array([0, 0])])
        with pytest.raises(ValueError, match="incompatible column dimensions"):
            construct.vstack([arr, np.array([0, 0])])

    @pytest.mark.parametrize("coo_cls", [coo_matrix, coo_array])
    def test_hstack(self, coo_cls):
        A = coo_cls([[1,2],[3,4]])
        B = coo_cls([[5],[6]])

        expected = array([[1, 2, 5],
                          [3, 4, 6]])
        assert_equal(construct.hstack([A, B]).toarray(), expected)
        assert_equal(construct.hstack([A, B], dtype=np.float32).dtype,
                     np.float32)

        assert_equal(construct.hstack([A.todok(), B.todok()]).toarray(), expected)

        assert_equal(construct.hstack([A.tocsc(), B.tocsc()]).toarray(),
                     expected)
        assert_equal(construct.hstack([A.tocsc(), B.tocsc()],
                                      dtype=np.float32).dtype,
                     np.float32)
        assert_equal(construct.hstack([A.tocsr(), B.tocsr()]).toarray(),
                     expected)
        assert_equal(construct.hstack([A.tocsr(), B.tocsr()],
                                      dtype=np.float32).dtype,
                     np.float32)

    def test_hstack_matrix_or_array(self):
        A = [[1,2],[3,4]]
        B = [[5],[6]]
        assert isinstance(construct.hstack([coo_array(A), coo_array(B)]), sparray)
        assert isinstance(construct.hstack([coo_array(A), coo_matrix(B)]), sparray)
        assert isinstance(construct.hstack([coo_matrix(A), coo_array(B)]), sparray)
        assert isinstance(construct.hstack([coo_matrix(A), coo_matrix(B)]), spmatrix)

    @pytest.mark.parametrize("block_array", (construct.bmat, construct.block_array))
    def test_block_creation(self, block_array):

        A = coo_array([[1, 2], [3, 4]])
        B = coo_array([[5],[6]])
        C = coo_array([[7]])
        D = coo_array((0, 0))

        expected = array([[1, 2, 5],
                          [3, 4, 6],
                          [0, 0, 7]])
        assert_equal(block_array([[A, B], [None, C]]).toarray(), expected)
        E = csr_array((1, 2), dtype=np.int32)
        assert_equal(block_array([[A.tocsr(), B.tocsr()],
                                  [E, C.tocsr()]]).toarray(),
                     expected)
        assert_equal(block_array([[A.tocsc(), B.tocsc()],
                                  [E.tocsc(), C.tocsc()]]).toarray(),
                     expected)

        expected = array([[1, 2, 0],
                          [3, 4, 0],
                          [0, 0, 7]])
        assert_equal(block_array([[A, None], [None, C]]).toarray(), expected)
        assert_equal(block_array([[A.tocsr(), E.T.tocsr()],
                                  [E, C.tocsr()]]).toarray(),
                     expected)
        assert_equal(block_array([[A.tocsc(), E.T.tocsc()],
                                  [E.tocsc(), C.tocsc()]]).toarray(),
                     expected)

        Z = csr_array((1, 1), dtype=np.int32)
        expected = array([[0, 5],
                          [0, 6],
                          [7, 0]])
        assert_equal(block_array([[None, B], [C, None]]).toarray(), expected)
        assert_equal(block_array([[E.T.tocsr(), B.tocsr()],
                                  [C.tocsr(), Z]]).toarray(),
                     expected)
        assert_equal(block_array([[E.T.tocsc(), B.tocsc()],
                                  [C.tocsc(), Z.tocsc()]]).toarray(),
                     expected)

        expected = np.empty((0, 0))
        assert_equal(block_array([[None, None]]).toarray(), expected)
        assert_equal(block_array([[None, D], [D, None]]).toarray(),
                     expected)

        # test bug reported in gh-5976
        expected = array([[7]])
        assert_equal(block_array([[None, D], [C, None]]).toarray(),
                     expected)

        # test failure cases
        with assert_raises(ValueError) as excinfo:
            block_array([[A], [B]])
        excinfo.match(r'Got blocks\[1,0\]\.shape\[1\] == 1, expected 2')

        with assert_raises(ValueError) as excinfo:
            block_array([[A.tocsr()], [B.tocsr()]])
        excinfo.match(r'incompatible dimensions for axis 1')

        with assert_raises(ValueError) as excinfo:
            block_array([[A.tocsc()], [B.tocsc()]])
        excinfo.match(r'Mismatching dimensions along axis 1: ({1, 2}|{2, 1})')

        with assert_raises(ValueError) as excinfo:
            block_array([[A, C]])
        excinfo.match(r'Got blocks\[0,1\]\.shape\[0\] == 1, expected 2')

        with assert_raises(ValueError) as excinfo:
            block_array([[A.tocsr(), C.tocsr()]])
        excinfo.match(r'Mismatching dimensions along axis 0: ({1, 2}|{2, 1})')

        with assert_raises(ValueError) as excinfo:
            block_array([[A.tocsc(), C.tocsc()]])
        excinfo.match(r'incompatible dimensions for axis 0')

    def test_block_return_type(self):
        block = construct.block_array

        # csr format ensures we hit _compressed_sparse_stack
        # shape of F,G ensure we hit _stack_along_minor_axis
        # list version ensure we hit the path with neither helper function
        Fl, Gl = [[1, 2],[3, 4]], [[7], [5]]
        Fm, Gm = csr_matrix(Fl), csr_matrix(Gl)
        assert isinstance(block([[None, Fl], [Gl, None]], format="csr"), sparray)
        assert isinstance(block([[None, Fm], [Gm, None]], format="csr"), sparray)
        assert isinstance(block([[Fm, Gm]], format="csr"), sparray)

    def test_bmat_return_type(self):
        """This can be removed after sparse matrix is removed"""
        bmat = construct.bmat
        # check return type. if any input _is_array output array, else matrix
        Fl, Gl = [[1, 2],[3, 4]], [[7], [5]]
        Fm, Gm = csr_matrix(Fl), csr_matrix(Gl)
        Fa, Ga = csr_array(Fl), csr_array(Gl)
        assert isinstance(bmat([[Fa, Ga]], format="csr"), sparray)
        assert isinstance(bmat([[Fm, Gm]], format="csr"), spmatrix)
        assert isinstance(bmat([[None, Fa], [Ga, None]], format="csr"), sparray)
        assert isinstance(bmat([[None, Fm], [Ga, None]], format="csr"), sparray)
        assert isinstance(bmat([[None, Fm], [Gm, None]], format="csr"), spmatrix)
        assert isinstance(bmat([[None, Fl], [Gl, None]], format="csr"), spmatrix)

        # type returned by _compressed_sparse_stack (all csr)
        assert isinstance(bmat([[Ga, Ga]], format="csr"), sparray)
        assert isinstance(bmat([[Gm, Ga]], format="csr"), sparray)
        assert isinstance(bmat([[Ga, Gm]], format="csr"), sparray)
        assert isinstance(bmat([[Gm, Gm]], format="csr"), spmatrix)
        # shape is 2x2 so no _stack_along_minor_axis
        assert isinstance(bmat([[Fa, Fm]], format="csr"), sparray)
        assert isinstance(bmat([[Fm, Fm]], format="csr"), spmatrix)

        # type returned by _compressed_sparse_stack (all csc)
        assert isinstance(bmat([[Gm.tocsc(), Ga.tocsc()]], format="csc"), sparray)
        assert isinstance(bmat([[Gm.tocsc(), Gm.tocsc()]], format="csc"), spmatrix)
        # shape is 2x2 so no _stack_along_minor_axis
        assert isinstance(bmat([[Fa.tocsc(), Fm.tocsc()]], format="csr"), sparray)
        assert isinstance(bmat([[Fm.tocsc(), Fm.tocsc()]], format="csr"), spmatrix)

        # type returned when mixed input
        assert isinstance(bmat([[Gl, Ga]], format="csr"), sparray)
        assert isinstance(bmat([[Gm.tocsc(), Ga]], format="csr"), sparray)
        assert isinstance(bmat([[Gm.tocsc(), Gm]], format="csr"), spmatrix)
        assert isinstance(bmat([[Gm, Gm]], format="csc"), spmatrix)

    @pytest.mark.slow
    @pytest.mark.thread_unsafe
    @pytest.mark.xfail_on_32bit("Can't create large array for test")
    def test_concatenate_int32_overflow(self):
        """ test for indptr overflow when concatenating matrices """
        check_free_memory(30000)

        n = 33000
        A = csr_array(np.ones((n, n), dtype=bool))
        B = A.copy()
        C = construct._compressed_sparse_stack((A, B), axis=0,
                                               return_spmatrix=False)

        assert_(np.all(np.equal(np.diff(C.indptr), n)))
        assert_equal(C.indices.dtype, np.int64)
        assert_equal(C.indptr.dtype, np.int64)

    def test_block_diag_basic(self):
        """ basic test for block_diag """
        A = coo_array([[1,2],[3,4]])
        B = coo_array([[5],[6]])
        C = coo_array([[7]])

        expected = array([[1, 2, 0, 0],
                          [3, 4, 0, 0],
                          [0, 0, 5, 0],
                          [0, 0, 6, 0],
                          [0, 0, 0, 7]])

        ABC = construct.block_diag((A, B, C))
        assert_equal(ABC.toarray(), expected)
        assert ABC.coords[0].dtype == np.int32

    def test_block_diag_idx_dtype(self):
        X = coo_array([[1, 0, 0], [0, 1, 0], [0, 1, 0]])
        X.coords = tuple(co.astype(np.int64) for co in X.coords)
        assert construct.block_diag([X, X]).coords[0].dtype == np.int64

    def test_block_diag_scalar_1d_args(self):
        """ block_diag with scalar and 1d arguments """
        # one 1d matrix and a scalar
        assert_array_equal(construct.block_diag([[2,3], 4]).toarray(),
                           [[2, 3, 0], [0, 0, 4]])
        # 1d sparse arrays
        A = coo_array([1,0,3])
        B = coo_array([0,4])
        assert_array_equal(construct.block_diag([A, B]).toarray(),
                           [[1, 0, 3, 0, 0], [0, 0, 0, 0, 4]])

    def test_block_diag_1(self):
        """ block_diag with one matrix """
        assert_equal(construct.block_diag([[1, 0]]).toarray(),
                     array([[1, 0]]))
        assert_equal(construct.block_diag([[[1, 0]]]).toarray(),
                     array([[1, 0]]))
        assert_equal(construct.block_diag([[[1], [0]]]).toarray(),
                     array([[1], [0]]))
        # just on scalar
        assert_equal(construct.block_diag([1]).toarray(),
                     array([[1]]))

    def test_block_diag_sparse_arrays(self):
        """ block_diag with sparse arrays """

        A = coo_array([[1, 2, 3]], shape=(1, 3))
        B = coo_array([[4, 5]], shape=(1, 2))
        assert_equal(construct.block_diag([A, B]).toarray(),
                     array([[1, 2, 3, 0, 0], [0, 0, 0, 4, 5]]))

        A = coo_array([[1], [2], [3]], shape=(3, 1))
        B = coo_array([[4], [5]], shape=(2, 1))
        assert_equal(construct.block_diag([A, B]).toarray(),
                     array([[1, 0], [2, 0], [3, 0], [0, 4], [0, 5]]))

    def test_block_diag_return_type(self):
        A, B = coo_array([[1, 2, 3]]), coo_matrix([[2, 3, 4]])
        assert isinstance(construct.block_diag([A, A]), sparray)
        assert isinstance(construct.block_diag([A, B]), sparray)
        assert isinstance(construct.block_diag([B, A]), sparray)
        assert isinstance(construct.block_diag([B, B]), spmatrix)

    def test_random_sampling(self):
        # Simple sanity checks for sparse random sampling.
        for f in sprand, _sprandn:
            for t in [np.float32, np.float64, np.longdouble,
                      np.int32, np.int64, np.complex64, np.complex128]:
                x = f(5, 10, density=0.1, dtype=t)
                assert_equal(x.dtype, t)
                assert_equal(x.shape, (5, 10))
                assert_equal(x.nnz, 5)

            x1 = f(5, 10, density=0.1, rng=4321)
            assert_equal(x1.dtype, np.float64)

            x2 = f(5, 10, density=0.1, rng=np.random.default_rng(4321))

            assert_array_equal(x1.data, x2.data)
            assert_array_equal(x1.row, x2.row)
            assert_array_equal(x1.col, x2.col)

            for density in [0.0, 0.1, 0.5, 1.0]:
                x = f(5, 10, density=density)
                assert_equal(x.nnz, int(density * np.prod(x.shape)))

            for fmt in ['coo', 'csc', 'csr', 'lil']:
                x = f(5, 10, format=fmt)
                assert_equal(x.format, fmt)

            assert_raises(ValueError, lambda: f(5, 10, 1.1))
            assert_raises(ValueError, lambda: f(5, 10, -0.1))

    @pytest.mark.parametrize("rng", [None, 4321, np.random.default_rng(4321)])
    def test_rand(self, rng):
        # Simple distributional checks for sparse.rand.
        x = sprand(10, 20, density=0.5, dtype=np.float64, rng=rng)
        assert_(np.all(np.less_equal(0, x.data)))
        assert_(np.all(np.less_equal(x.data, 1)))

    @pytest.mark.parametrize("rng", [None, 4321, np.random.default_rng(4321)])
    def test_randn(self, rng):
        # Simple distributional checks for sparse.randn.
        # Statistically, some of these should be negative
        # and some should be greater than 1.
        x = _sprandn(10, 20, density=0.5, dtype=np.float64, rng=rng)
        assert_(np.any(np.less(x.data, 0)))
        assert_(np.any(np.less(1, x.data)))
        x = _sprandn_array(10, 20, density=0.5, dtype=np.float64, rng=rng)
        assert_(np.any(np.less(x.data, 0)))
        assert_(np.any(np.less(1, x.data)))

    def test_random_accept_str_dtype(self):
        # anything that np.dtype can convert to a dtype should be accepted
        # for the dtype
        construct.random(10, 10, dtype='d')
        construct.random_array((10, 10), dtype='d')
        construct.random_array((10, 10, 10), dtype='d')
        construct.random_array((10, 10, 10, 10, 10), dtype='d')

    def test_random_array_maintains_array_shape(self):
        # preserve use of old random_state during SPEC 7 transition
        arr = construct.random_array((0, 4), density=0.3, dtype=int, random_state=0)
        assert arr.shape == (0, 4)

        arr = construct.random_array((10, 10, 10), density=0.3, dtype=int, rng=0)
        assert arr.shape == (10, 10, 10)

        arr = construct.random_array((10, 10, 10, 10, 10), density=0.3, dtype=int,
                                     rng=0)
        assert arr.shape == (10, 10, 10, 10, 10)

    def test_random_array_idx_dtype(self):
        A = construct.random_array((10, 10))
        assert A.coords[0].dtype == np.int32

    def test_random_sparse_matrix_returns_correct_number_of_non_zero_elements(self):
        # A 10 x 10 matrix, with density of 12.65%, should have 13 nonzero elements.
        # 10 x 10 x 0.1265 = 12.65, which should be rounded up to 13, not 12.
        sparse_matrix = construct.random(10, 10, density=0.1265)
        assert_equal(sparse_matrix.count_nonzero(),13)
        # check random_array
        sparse_array = construct.random_array((10, 10), density=0.1265)
        assert_equal(sparse_array.count_nonzero(),13)
        assert isinstance(sparse_array, sparray)
        # check big size
        shape = (2**33, 2**33)
        sparse_array = construct.random_array(shape, density=2.7105e-17)
        assert_equal(sparse_array.count_nonzero(),2000)

        # for n-D
        # check random_array
        sparse_array = construct.random_array((10, 10, 10, 10), density=0.12658)
        assert_equal(sparse_array.count_nonzero(),1266)
        assert isinstance(sparse_array, sparray)
        # check big size
        shape = (2**33, 2**33, 2**33)
        sparse_array = construct.random_array(shape, density=2.7105e-28)
        assert_equal(sparse_array.count_nonzero(),172)


def test_diags_array():
    """Tests of diags_array that do not rely on diags wrapper."""
    diag = np.arange(1, 5)

    assert_array_equal(construct.diags_array(diag).toarray(), np.diag(diag))

    assert_array_equal(
        construct.diags_array(diag, offsets=2).toarray(), np.diag(diag, k=2)
    )

    assert_array_equal(
        construct.diags_array(diag, offsets=2, shape=(4, 4)).toarray(),
        np.diag(diag, k=2)[:4, :4]
    )

    # Offset outside bounds when shape specified
    with pytest.raises(ValueError, match=".*out of bounds"):
        construct.diags(np.arange(1, 5), 5, shape=(4, 4))