#
# Authors: Travis Oliphant, Ed Schofield, Robert Cimrman, Nathan Bell, and others

""" Test functions for sparse matrices. Each class in the "Matrix class
based tests" section become subclasses of the classes in the "Generic
tests" section. This is done by the functions in the "Tailored base
class for generic tests" section.

"""

from __future__ import division, print_function, absolute_import

__usage__ = """
Build sparse:
  python setup.py build
Run tests if scipy is installed:
  python -c 'import scipy;scipy.sparse.test()'
Run tests if sparse is not installed:
  python tests/test_base.py
"""

import warnings
import operator
import contextlib

import numpy as np
from scipy._lib.six import xrange, zip as izip
from numpy import (arange, zeros, array, dot, matrix, asmatrix, asarray,
                   vstack, ndarray, transpose, diag, kron, inf, conjugate,
                   int8, ComplexWarning, power)

import random
from numpy.testing import (assert_raises, assert_equal, assert_array_equal,
        assert_array_almost_equal, assert_almost_equal, assert_,
        dec, run_module_suite, assert_allclose)

import scipy.linalg

import scipy.sparse as sparse
from scipy.sparse import (csc_matrix, csr_matrix, dok_matrix,
        coo_matrix, lil_matrix, dia_matrix, bsr_matrix,
        eye, isspmatrix, SparseEfficiencyWarning, issparse)
from scipy.sparse.sputils import supported_dtypes, isscalarlike, get_index_dtype
from scipy.sparse.linalg import splu, expm, inv

from scipy._lib._version import NumpyVersion
from scipy._lib.decorator import decorator

import nose
try:
    from nose.tools import assert_in
except ImportError:
    def assert_in(member, collection, msg=None):
        assert_(member in collection, msg=msg if msg is not None else "%r not found in %r" % (member, collection))


# Check for __numpy_ufunc__
class _UFuncCheck(object):
    def __array__(self):
        return np.array([1])

    def __numpy_ufunc__(self, *a, **kwargs):
        global HAS_NUMPY_UFUNC
        HAS_NUMPY_UFUNC = True

HAS_NUMPY_UFUNC = False
np.add(_UFuncCheck(), np.array([1]))


# Only test matmul operator (A @ B) when available (Python 3.5+)
TEST_MATMUL = hasattr(operator, 'matmul')


warnings.simplefilter('ignore', SparseEfficiencyWarning)
warnings.simplefilter('ignore', ComplexWarning)


def with_64bit_maxval_limit(maxval_limit=None, random=False, fixed_dtype=None,
                            downcast_maxval=None, assert_32bit=False):
    """
    Monkeypatch the maxval threshold at which scipy.sparse switches to
    64-bit index arrays, or make it (pseudo-)random.

    """
    if maxval_limit is None:
        maxval_limit = 10

    if assert_32bit:
        def new_get_index_dtype(arrays=(), maxval=None, check_contents=False):
            tp = get_index_dtype(arrays, maxval, check_contents)
            assert_equal(np.iinfo(tp).max, np.iinfo(np.int32).max)
            assert_(tp == np.int32 or tp == np.intc)
            return tp
    elif fixed_dtype is not None:
        def new_get_index_dtype(arrays=(), maxval=None, check_contents=False):
            return fixed_dtype
    elif random:
        counter = np.random.RandomState(seed=1234)

        def new_get_index_dtype(arrays=(), maxval=None, check_contents=False):
            return (np.int32, np.int64)[counter.randint(2)]
    else:
        def new_get_index_dtype(arrays=(), maxval=None, check_contents=False):
            dtype = np.int32
            if maxval is not None:
                if maxval > maxval_limit:
                    dtype = np.int64
            for arr in arrays:
                arr = np.asarray(arr)
                if arr.dtype > np.int32:
                    if check_contents:
                        if arr.size == 0:
                            # a bigger type not needed
                            continue
                        elif np.issubdtype(arr.dtype, np.integer):
                            maxval = arr.max()
                            minval = arr.min()
                            if minval >= -maxval_limit and maxval <= maxval_limit:
                                # a bigger type not needed
                                continue
                    dtype = np.int64
            return dtype

    if downcast_maxval is not None:
        def new_downcast_intp_index(arr):
            if arr.max() > downcast_maxval:
                raise AssertionError("downcast limited")
            return arr.astype(np.intp)

    @decorator
    def deco(func, *a, **kw):
        backup = []
        modules = [scipy.sparse.bsr, scipy.sparse.coo, scipy.sparse.csc,
                   scipy.sparse.csr, scipy.sparse.dia, scipy.sparse.dok,
                   scipy.sparse.lil, scipy.sparse.sputils,
                   scipy.sparse.compressed, scipy.sparse.construct]
        try:
            for mod in modules:
                backup.append((mod, 'get_index_dtype',
                               getattr(mod, 'get_index_dtype', None)))
                setattr(mod, 'get_index_dtype', new_get_index_dtype)
                if downcast_maxval is not None:
                    backup.append((mod, 'downcast_intp_index',
                                   getattr(mod, 'downcast_intp_index', None)))
                    setattr(mod, 'downcast_intp_index', new_downcast_intp_index)
            return func(*a, **kw)
        finally:
            for mod, name, oldfunc in backup:
                if oldfunc is not None:
                    setattr(mod, name, oldfunc)

    return deco


def todense(a):
    if isinstance(a, np.ndarray) or isscalarlike(a):
        return a
    return a.todense()


class BinopTester(object):
    # Custom type to test binary operations on sparse matrices.

    def __add__(self, mat):
        return "matrix on the right"

    def __mul__(self, mat):
        return "matrix on the right"

    def __sub__(self, mat):
        return "matrix on the right"

    def __radd__(self, mat):
        return "matrix on the left"

    def __rmul__(self, mat):
        return "matrix on the left"

    def __rsub__(self, mat):
        return "matrix on the left"

    def __matmul__(self, mat):
        return "matrix on the right"

    def __rmatmul__(self, mat):
        return "matrix on the left"


#------------------------------------------------------------------------------
# Generic tests
#------------------------------------------------------------------------------


# TODO check that spmatrix( ... , copy=X ) is respected
# TODO test prune
# TODO test has_sorted_indices
class _TestCommon:
    """test common functionality shared by all sparse formats"""
    math_dtypes = supported_dtypes

    def __init__(self):
        # Canonical data.
        self.dat = matrix([[1,0,0,2],[3,0,1,0],[0,2,0,0]],'d')
        self.datsp = self.spmatrix(self.dat)

        # Some sparse and dense matrices with data for every supported
        # dtype.
        # This set union is a workaround for numpy#6295, which means that
        # two np.int64 dtypes don't hash to the same value.
        self.checked_dtypes = set(supported_dtypes).union(self.math_dtypes)
        self.dat_dtypes = {}
        self.datsp_dtypes = {}
        for dtype in self.checked_dtypes:
            self.dat_dtypes[dtype] = self.dat.astype(dtype)
            self.datsp_dtypes[dtype] = self.spmatrix(self.dat.astype(dtype))

        # Check that the original data is equivalent to the
        # corresponding dat_dtypes & datsp_dtypes.
        assert_equal(self.dat, self.dat_dtypes[np.float64])
        assert_equal(self.datsp.todense(),
                     self.datsp_dtypes[np.float64].todense())

    def test_bool(self):
        def check(dtype):
            datsp = self.datsp_dtypes[dtype]

            assert_raises(ValueError, bool, datsp)
            assert_(self.spmatrix([1]))
            assert_(not self.spmatrix([0]))
        for dtype in self.checked_dtypes:
            fails = isinstance(self, TestDOK)
            msg = "Cannot create a rank <= 2 DOK matrix."
            yield dec.skipif(fails, msg)(check), dtype

    def test_bool_rollover(self):
        # bool's underlying dtype is 1 byte, check that it does not
        # rollover True -> False at 256.
        dat = np.matrix([[True, False]])
        datsp = self.spmatrix(dat)

        for _ in range(10):
            datsp = datsp + datsp
            dat = dat + dat
        assert_array_equal(dat, datsp.todense())

    def test_eq(self):
        def check(dtype):
            dat = self.dat_dtypes[dtype]
            datsp = self.datsp_dtypes[dtype]
            dat2 = dat.copy()
            dat2[:,0] = 0
            datsp2 = self.spmatrix(dat2)
            datbsr = bsr_matrix(dat)
            datcsr = csr_matrix(dat)
            datcsc = csc_matrix(dat)
            datlil = lil_matrix(dat)

            # sparse/sparse
            assert_array_equal(dat == dat2, (datsp == datsp2).todense())
            # mix sparse types
            assert_array_equal(dat == dat2, (datbsr == datsp2).todense())
            assert_array_equal(dat == dat2, (datcsr == datsp2).todense())
            assert_array_equal(dat == dat2, (datcsc == datsp2).todense())
            assert_array_equal(dat == dat2, (datlil == datsp2).todense())
            # sparse/dense
            assert_array_equal(dat == datsp2, datsp2 == dat)
            # sparse/scalar
            assert_array_equal(dat == 0, (datsp == 0).todense())
            assert_array_equal(dat == 1, (datsp == 1).todense())
            assert_array_equal(dat == np.nan, (datsp == np.nan).todense())

        msg = "Bool comparisons only implemented for BSR, CSC, and CSR."
        fails = not isinstance(self, (TestBSR, TestCSC, TestCSR))
        for dtype in self.checked_dtypes:
            with warnings.catch_warnings():
                warnings.simplefilter("ignore", category=np.ComplexWarning)
                warnings.simplefilter("ignore", category=SparseEfficiencyWarning)
                yield dec.skipif(fails, msg)(check), dtype

    def test_ne(self):
        def check(dtype):
            dat = self.dat_dtypes[dtype]
            datsp = self.datsp_dtypes[dtype]
            dat2 = dat.copy()
            dat2[:,0] = 0
            datsp2 = self.spmatrix(dat2)
            datbsr = bsr_matrix(dat)
            datcsc = csc_matrix(dat)
            datcsr = csr_matrix(dat)
            datlil = lil_matrix(dat)

            # sparse/sparse
            assert_array_equal(dat != dat2, (datsp != datsp2).todense())
            # mix sparse types
            assert_array_equal(dat != dat2, (datbsr != datsp2).todense())
            assert_array_equal(dat != dat2, (datcsc != datsp2).todense())
            assert_array_equal(dat != dat2, (datcsr != datsp2).todense())
            assert_array_equal(dat != dat2, (datlil != datsp2).todense())
            # sparse/dense
            assert_array_equal(dat != datsp2, datsp2 != dat)
            # sparse/scalar
            assert_array_equal(dat != 0, (datsp != 0).todense())
            assert_array_equal(dat != 1, (datsp != 1).todense())
            assert_array_equal(0 != dat, (0 != datsp).todense())
            assert_array_equal(1 != dat, (1 != datsp).todense())
            assert_array_equal(dat != np.nan, (datsp != np.nan).todense())

        msg = "Bool comparisons only implemented for BSR, CSC, and CSR."
        fails = not isinstance(self, (TestBSR, TestCSC, TestCSR))
        for dtype in self.checked_dtypes:
            with warnings.catch_warnings():
                warnings.simplefilter("ignore", category=np.ComplexWarning)
                warnings.simplefilter("ignore", category=SparseEfficiencyWarning)
                yield dec.skipif(fails, msg)(check), dtype

    def test_lt(self):
        def check(dtype):
            # data
            dat = self.dat_dtypes[dtype]
            datsp = self.datsp_dtypes[dtype]
            dat2 = dat.copy()
            dat2[:,0] = 0
            datsp2 = self.spmatrix(dat2)
            datcomplex = dat.astype(complex)
            datcomplex[:,0] = 1 + 1j
            datspcomplex = self.spmatrix(datcomplex)
            datbsr = bsr_matrix(dat)
            datcsc = csc_matrix(dat)
            datcsr = csr_matrix(dat)
            datlil = lil_matrix(dat)

            # sparse/sparse
            assert_array_equal(dat < dat2, (datsp < datsp2).todense())
            assert_array_equal(datcomplex < dat2, (datspcomplex < datsp2).todense())
            # mix sparse types
            assert_array_equal(dat < dat2, (datbsr < datsp2).todense())
            assert_array_equal(dat < dat2, (datcsc < datsp2).todense())
            assert_array_equal(dat < dat2, (datcsr < datsp2).todense())
            assert_array_equal(dat < dat2, (datlil < datsp2).todense())

            assert_array_equal(dat2 < dat, (datsp2 < datbsr).todense())
            assert_array_equal(dat2 < dat, (datsp2 < datcsc).todense())
            assert_array_equal(dat2 < dat, (datsp2 < datcsr).todense())
            assert_array_equal(dat2 < dat, (datsp2 < datlil).todense())
            # sparse/dense
            assert_array_equal(dat < dat2, datsp < dat2)
            assert_array_equal(datcomplex < dat2, datspcomplex < dat2)
            # sparse/scalar
            assert_array_equal((datsp < 2).todense(), dat < 2)
            assert_array_equal((datsp < 1).todense(), dat < 1)
            assert_array_equal((datsp < 0).todense(), dat < 0)
            assert_array_equal((datsp < -1).todense(), dat < -1)
            assert_array_equal((datsp < -2).todense(), dat < -2)
            with np.errstate(invalid='ignore'):
                assert_array_equal((datsp < np.nan).todense(), dat < np.nan)

            assert_array_equal((2 < datsp).todense(), 2 < dat)
            assert_array_equal((1 < datsp).todense(), 1 < dat)
            assert_array_equal((0 < datsp).todense(), 0 < dat)
            assert_array_equal((-1 < datsp).todense(), -1 < dat)
            assert_array_equal((-2 < datsp).todense(), -2 < dat)

            if NumpyVersion(np.__version__) >= '1.8.0':
                # data
                dat = self.dat_dtypes[dtype]
                datsp = self.datsp_dtypes[dtype]
                dat2 = dat.copy()
                dat2[:,0] = 0
                datsp2 = self.spmatrix(dat2)

                # dense rhs
                assert_array_equal(dat < datsp2, datsp < dat2)

        msg = "Bool comparisons only implemented for BSR, CSC, and CSR."
        fails = not isinstance(self, (TestBSR, TestCSC, TestCSR))
        for dtype in self.checked_dtypes:
            with warnings.catch_warnings():
                with np.errstate(invalid='ignore'):
                    warnings.simplefilter("ignore", category=np.ComplexWarning)
                    warnings.simplefilter("ignore", category=SparseEfficiencyWarning)
                    yield dec.skipif(fails, msg)(check), dtype

    def test_gt(self):
        def check(dtype):
            dat = self.dat_dtypes[dtype]
            datsp = self.datsp_dtypes[dtype]
            dat2 = dat.copy()
            dat2[:,0] = 0
            datsp2 = self.spmatrix(dat2)
            datcomplex = dat.astype(complex)
            datcomplex[:,0] = 1 + 1j
            datspcomplex = self.spmatrix(datcomplex)
            datbsr = bsr_matrix(dat)
            datcsc = csc_matrix(dat)
            datcsr = csr_matrix(dat)
            datlil = lil_matrix(dat)

            # sparse/sparse
            assert_array_equal(dat > dat2, (datsp > datsp2).todense())
            assert_array_equal(datcomplex > dat2, (datspcomplex > datsp2).todense())
            # mix sparse types
            assert_array_equal(dat > dat2, (datbsr > datsp2).todense())
            assert_array_equal(dat > dat2, (datcsc > datsp2).todense())
            assert_array_equal(dat > dat2, (datcsr > datsp2).todense())
            assert_array_equal(dat > dat2, (datlil > datsp2).todense())

            assert_array_equal(dat2 > dat, (datsp2 > datbsr).todense())
            assert_array_equal(dat2 > dat, (datsp2 > datcsc).todense())
            assert_array_equal(dat2 > dat, (datsp2 > datcsr).todense())
            assert_array_equal(dat2 > dat, (datsp2 > datlil).todense())
            # sparse/dense
            assert_array_equal(dat > dat2, datsp > dat2)
            assert_array_equal(datcomplex > dat2, datspcomplex > dat2)
            # sparse/scalar
            assert_array_equal((datsp > 2).todense(), dat > 2)
            assert_array_equal((datsp > 1).todense(), dat > 1)
            assert_array_equal((datsp > 0).todense(), dat > 0)
            assert_array_equal((datsp > -1).todense(), dat > -1)
            assert_array_equal((datsp > -2).todense(), dat > -2)
            with np.errstate(invalid='ignore'):
                assert_array_equal((datsp > np.nan).todense(), dat > np.nan)

            assert_array_equal((2 > datsp).todense(), 2 > dat)
            assert_array_equal((1 > datsp).todense(), 1 > dat)
            assert_array_equal((0 > datsp).todense(), 0 > dat)
            assert_array_equal((-1 > datsp).todense(), -1 > dat)
            assert_array_equal((-2 > datsp).todense(), -2 > dat)

            if NumpyVersion(np.__version__) >= '1.8.0':
                # data
                dat = self.dat_dtypes[dtype]
                datsp = self.datsp_dtypes[dtype]
                dat2 = dat.copy()
                dat2[:,0] = 0
                datsp2 = self.spmatrix(dat2)

                # dense rhs
                assert_array_equal(dat > datsp2, datsp > dat2)

        msg = "Bool comparisons only implemented for BSR, CSC, and CSR."
        fails = not isinstance(self, (TestBSR, TestCSC, TestCSR))
        for dtype in self.checked_dtypes:
            with warnings.catch_warnings():
                warnings.simplefilter("ignore", category=np.ComplexWarning)
                warnings.simplefilter("ignore", category=SparseEfficiencyWarning)
                yield dec.skipif(fails, msg)(check), dtype

    def test_le(self):
        def check(dtype):
            dat = self.dat_dtypes[dtype]
            datsp = self.datsp_dtypes[dtype]
            dat2 = dat.copy()
            dat2[:,0] = 0
            datsp2 = self.spmatrix(dat2)
            datcomplex = dat.astype(complex)
            datcomplex[:,0] = 1 + 1j
            datspcomplex = self.spmatrix(datcomplex)
            datbsr = bsr_matrix(dat)
            datcsc = csc_matrix(dat)
            datcsr = csr_matrix(dat)
            datlil = lil_matrix(dat)

            # sparse/sparse
            assert_array_equal(dat <= dat2, (datsp <= datsp2).todense())
            assert_array_equal(datcomplex <= dat2, (datspcomplex <= datsp2).todense())
            # mix sparse types
            assert_array_equal((datbsr <= datsp2).todense(), dat <= dat2)
            assert_array_equal((datcsc <= datsp2).todense(), dat <= dat2)
            assert_array_equal((datcsr <= datsp2).todense(), dat <= dat2)
            assert_array_equal((datlil <= datsp2).todense(), dat <= dat2)

            assert_array_equal((datsp2 <= datbsr).todense(), dat2 <= dat)
            assert_array_equal((datsp2 <= datcsc).todense(), dat2 <= dat)
            assert_array_equal((datsp2 <= datcsr).todense(), dat2 <= dat)
            assert_array_equal((datsp2 <= datlil).todense(), dat2 <= dat)
            # sparse/dense
            assert_array_equal(datsp <= dat2, dat <= dat2)
            assert_array_equal(datspcomplex <= dat2, datcomplex <= dat2)
            # sparse/scalar
            assert_array_equal((datsp <= 2).todense(), dat <= 2)
            assert_array_equal((datsp <= 1).todense(), dat <= 1)
            assert_array_equal((datsp <= -1).todense(), dat <= -1)
            assert_array_equal((datsp <= -2).todense(), dat <= -2)

            assert_array_equal((2 <= datsp).todense(), 2 <= dat)
            assert_array_equal((1 <= datsp).todense(), 1 <= dat)
            assert_array_equal((-1 <= datsp).todense(), -1 <= dat)
            assert_array_equal((-2 <= datsp).todense(), -2 <= dat)

            if NumpyVersion(np.__version__) >= '1.8.0':
                # data
                dat = self.dat_dtypes[dtype]
                datsp = self.datsp_dtypes[dtype]
                dat2 = dat.copy()
                dat2[:,0] = 0
                datsp2 = self.spmatrix(dat2)

                # dense rhs
                assert_array_equal(dat <= datsp2, datsp <= dat2)

        msg = "Bool comparisons only implemented for BSR, CSC, and CSR."
        fails = not isinstance(self, (TestBSR, TestCSC, TestCSR))
        for dtype in self.checked_dtypes:
            with warnings.catch_warnings():
                warnings.simplefilter("ignore", category=np.ComplexWarning)
                warnings.simplefilter("ignore", category=SparseEfficiencyWarning)
                yield dec.skipif(fails, msg)(check), dtype

    def test_ge(self):
        def check(dtype):
            dat = self.dat_dtypes[dtype]
            datsp = self.datsp_dtypes[dtype]
            dat2 = dat.copy()
            dat2[:,0] = 0
            datsp2 = self.spmatrix(dat2)
            datcomplex = dat.astype(complex)
            datcomplex[:,0] = 1 + 1j
            datspcomplex = self.spmatrix(datcomplex)
            datbsr = bsr_matrix(dat)
            datcsc = csc_matrix(dat)
            datcsr = csr_matrix(dat)
            datlil = lil_matrix(dat)

            # sparse/sparse
            assert_array_equal(dat >= dat2, (datsp >= datsp2).todense())
            assert_array_equal(datcomplex >= dat2, (datspcomplex >= datsp2).todense())
            # mix sparse types
            # mix sparse types
            assert_array_equal((datbsr >= datsp2).todense(), dat >= dat2)
            assert_array_equal((datcsc >= datsp2).todense(), dat >= dat2)
            assert_array_equal((datcsr >= datsp2).todense(), dat >= dat2)
            assert_array_equal((datlil >= datsp2).todense(), dat >= dat2)

            assert_array_equal((datsp2 >= datbsr).todense(), dat2 >= dat)
            assert_array_equal((datsp2 >= datcsc).todense(), dat2 >= dat)
            assert_array_equal((datsp2 >= datcsr).todense(), dat2 >= dat)
            assert_array_equal((datsp2 >= datlil).todense(), dat2 >= dat)
            # sparse/dense
            assert_array_equal(datsp >= dat2, dat >= dat2)
            assert_array_equal(datspcomplex >= dat2, datcomplex >= dat2)
            # sparse/scalar
            assert_array_equal((datsp >= 2).todense(), dat >= 2)
            assert_array_equal((datsp >= 1).todense(), dat >= 1)
            assert_array_equal((datsp >= -1).todense(), dat >= -1)
            assert_array_equal((datsp >= -2).todense(), dat >= -2)

            assert_array_equal((2 >= datsp).todense(), 2 >= dat)
            assert_array_equal((1 >= datsp).todense(), 1 >= dat)
            assert_array_equal((-1 >= datsp).todense(), -1 >= dat)
            assert_array_equal((-2 >= datsp).todense(), -2 >= dat)

            if NumpyVersion(np.__version__) >= '1.8.0':
                # dense data
                dat = self.dat_dtypes[dtype]
                datsp = self.datsp_dtypes[dtype]
                dat2 = dat.copy()
                dat2[:,0] = 0
                datsp2 = self.spmatrix(dat2)

                # dense rhs
                assert_array_equal(dat >= datsp2, datsp >= dat2)

        msg = "Bool comparisons only implemented for BSR, CSC, and CSR."
        fails = not isinstance(self, (TestBSR, TestCSC, TestCSR))
        for dtype in self.checked_dtypes:
            with warnings.catch_warnings():
                warnings.simplefilter("ignore", category=np.ComplexWarning)
                warnings.simplefilter("ignore", category=SparseEfficiencyWarning)
                yield dec.skipif(fails, msg)(check), dtype

    def test_empty(self):
        # create empty matrices
        assert_equal(self.spmatrix((3,3)).todense(), np.zeros((3,3)))
        assert_equal(self.spmatrix((3,3)).nnz, 0)
        assert_equal(self.spmatrix((3,3)).count_nonzero(), 0)

    def test_count_nonzero(self):
        expected = np.count_nonzero(self.datsp.toarray())
        assert_equal(self.datsp.count_nonzero(), expected)
        assert_equal(self.datsp.T.count_nonzero(), expected)

    def test_invalid_shapes(self):
        assert_raises(ValueError, self.spmatrix, (-1,3))
        assert_raises(ValueError, self.spmatrix, (3,-1))
        assert_raises(ValueError, self.spmatrix, (-1,-1))

    def test_repr(self):
        repr(self.datsp)

    def test_str(self):
        str(self.datsp)

    def test_empty_arithmetic(self):
        # Test manipulating empty matrices. Fails in SciPy SVN <= r1768
        shape = (5, 5)
        for mytype in [np.dtype('int32'), np.dtype('float32'),
                np.dtype('float64'), np.dtype('complex64'),
                np.dtype('complex128')]:
            a = self.spmatrix(shape, dtype=mytype)
            b = a + a
            c = 2 * a
            d = a * a.tocsc()
            e = a * a.tocsr()
            f = a * a.tocoo()
            for m in [a,b,c,d,e,f]:
                assert_equal(m.A, a.A*a.A)
                # These fail in all revisions <= r1768:
                assert_equal(m.dtype,mytype)
                assert_equal(m.A.dtype,mytype)

    def test_abs(self):
        A = matrix([[-1, 0, 17],[0, -5, 0],[1, -4, 0],[0,0,0]],'d')
        assert_equal(abs(A),abs(self.spmatrix(A)).todense())
        
    def test_elementwise_power(self):
        A = matrix([[-4, -3, -2],[-1, 0, 1],[2, 3, 4]], 'd')        
        assert_equal(np.power(A, 2), self.spmatrix(A).power(2).todense())
                
        #it's element-wise power function, input has to be a scalar
        assert_raises(NotImplementedError, self.spmatrix(A).power, A)       

    def test_neg(self):
        A = matrix([[-1, 0, 17],[0, -5, 0],[1, -4, 0],[0,0,0]],'d')
        assert_equal(-A,(-self.spmatrix(A)).todense())

    def test_real(self):
        D = matrix([[1 + 3j, 2 - 4j]])
        A = self.spmatrix(D)
        assert_equal(A.real.todense(),D.real)

    def test_imag(self):
        D = matrix([[1 + 3j, 2 - 4j]])
        A = self.spmatrix(D)
        assert_equal(A.imag.todense(),D.imag)

    def test_diagonal(self):
        # Does the matrix's .diagonal() method work?
        mats = []
        mats.append([[1,0,2]])
        mats.append([[1],[0],[2]])
        mats.append([[0,1],[0,2],[0,3]])
        mats.append([[0,0,1],[0,0,2],[0,3,0]])

        mats.append(kron(mats[0],[[1,2]]))
        mats.append(kron(mats[0],[[1],[2]]))
        mats.append(kron(mats[1],[[1,2],[3,4]]))
        mats.append(kron(mats[2],[[1,2],[3,4]]))
        mats.append(kron(mats[3],[[1,2],[3,4]]))
        mats.append(kron(mats[3],[[1,2,3,4]]))

        for m in mats:
            assert_equal(self.spmatrix(m).diagonal(),diag(m))

        # Test all-zero matrix.
        assert_equal(self.spmatrix((40, 16130)).diagonal(), np.zeros(40))

    @dec.slow
    def test_setdiag(self):
        def dense_setdiag(a, v, k):
            v = np.asarray(v)
            if k >= 0:
                n = min(a.shape[0], a.shape[1] - k)
                if v.ndim != 0:
                    n = min(n, len(v))
                    v = v[:n]
                i = np.arange(0, n)
                j = np.arange(k, k + n)
                a[i,j] = v
            elif k < 0:
                dense_setdiag(a.T, v, -k)
                return

        def check_setdiag(a, b, k):
            # Check setting diagonal using a scalar, a vector of
            # correct length, and too short or too long vectors
            for r in [-1, len(np.diag(a, k)), 2, 30]:
                if r < 0:
                    v = int(np.random.randint(1, 20, size=1))
                else:
                    v = np.random.randint(1, 20, size=r)

                dense_setdiag(a, v, k)
                b.setdiag(v, k)

                # check that dense_setdiag worked
                d = np.diag(a, k)
                if np.asarray(v).ndim == 0:
                    assert_array_equal(d, v, err_msg=msg + " %d" % (r,))
                else:
                    n = min(len(d), len(v))
                    assert_array_equal(d[:n], v[:n], err_msg=msg + " %d" % (r,))
                # check that sparse setdiag worked
                assert_array_equal(b.A, a, err_msg=msg + " %d" % (r,))

        # comprehensive test
        np.random.seed(1234)
        for dtype in [np.int8, np.float64]:
            for m in [0, 1, 3, 10]:
                for n in [0, 1, 3, 10]:
                    for k in range(-m+1, n-1):
                        msg = repr((dtype, m, n, k))
                        a = np.zeros((m, n), dtype=dtype)
                        b = self.spmatrix((m, n), dtype=dtype)

                        check_setdiag(a, b, k)

                        # check overwriting etc
                        for k2 in np.random.randint(-m+1, n-1, size=12):
                            check_setdiag(a, b, k2)

        # simpler test case
        m = self.spmatrix(np.eye(3))
        values = [3, 2, 1]
        assert_raises(ValueError, m.setdiag, values, k=4)
        m.setdiag(values)
        assert_array_equal(m.diagonal(), values)
        m.setdiag(values, k=1)
        assert_array_equal(m.A, np.array([[3, 3, 0],
                                          [0, 2, 2],
                                          [0, 0, 1]]))
        m.setdiag(values, k=-2)
        assert_array_equal(m.A, np.array([[3, 3, 0],
                                          [0, 2, 2],
                                          [3, 0, 1]]))
        m.setdiag((9,), k=2)
        assert_array_equal(m.A[0,2], 9)
        m.setdiag((9,), k=-2)
        assert_array_equal(m.A[2,0], 9)

    def test_nonzero(self):
        A = array([[1, 0, 1],[0, 1, 1],[0, 0, 1]])
        Asp = self.spmatrix(A)

        A_nz = set([tuple(ij) for ij in transpose(A.nonzero())])
        Asp_nz = set([tuple(ij) for ij in transpose(Asp.nonzero())])

        assert_equal(A_nz, Asp_nz)

    def test_numpy_nonzero(self):
        # See gh-5987
        A = array([[1, 0, 1], [0, 1, 1], [0, 0, 1]])
        Asp = self.spmatrix(A)

        A_nz = set([tuple(ij) for ij in transpose(np.nonzero(A))])
        Asp_nz = set([tuple(ij) for ij in transpose(np.nonzero(Asp))])

        assert_equal(A_nz, Asp_nz)

    def test_getrow(self):
        assert_array_equal(self.datsp.getrow(1).todense(), self.dat[1,:])
        assert_array_equal(self.datsp.getrow(-1).todense(), self.dat[-1,:])

    def test_getcol(self):
        assert_array_equal(self.datsp.getcol(1).todense(), self.dat[:,1])
        assert_array_equal(self.datsp.getcol(-1).todense(), self.dat[:,-1])

    def test_sum(self):
        np.random.seed(1234)
        dat_1 = np.matrix([[0, 1, 2],
                           [3, -4, 5],
                           [-6, 7, 9]])
        dat_2 = np.random.rand(5, 5)
        dat_3 = np.array([[]])
        dat_4 = np.zeros((40, 40))
        dat_5 = sparse.rand(5, 5, density=1e-2).A
        matrices = [dat_1, dat_2, dat_3, dat_4, dat_5]

        def check(dtype, j):
            dat = np.matrix(matrices[j], dtype=dtype)
            datsp = self.spmatrix(dat, dtype=dtype)
            with np.errstate(over='ignore'):
                assert_array_almost_equal(dat.sum(), datsp.sum())
                assert_equal(dat.sum().dtype, datsp.sum().dtype)
                assert_(np.isscalar(datsp.sum(axis=None)))
                assert_array_almost_equal(dat.sum(axis=None),
                                          datsp.sum(axis=None))
                assert_equal(dat.sum(axis=None).dtype,
                             datsp.sum(axis=None).dtype)
                assert_array_almost_equal(dat.sum(axis=0), datsp.sum(axis=0))
                assert_equal(dat.sum(axis=0).dtype, datsp.sum(axis=0).dtype)
                assert_array_almost_equal(dat.sum(axis=1), datsp.sum(axis=1))
                assert_equal(dat.sum(axis=1).dtype, datsp.sum(axis=1).dtype)
                assert_array_almost_equal(dat.sum(axis=-2), datsp.sum(axis=-2))
                assert_equal(dat.sum(axis=-2).dtype, datsp.sum(axis=-2).dtype)
                assert_array_almost_equal(dat.sum(axis=-1), datsp.sum(axis=-1))
                assert_equal(dat.sum(axis=-1).dtype, datsp.sum(axis=-1).dtype)

        for dtype in self.checked_dtypes:
            for j in range(len(matrices)):
                yield check, dtype, j

    def test_sum_invalid_params(self):
        out = np.asmatrix(np.zeros((1, 3)))
        dat = np.matrix([[0, 1, 2],
                         [3, -4, 5],
                         [-6, 7, 9]])
        datsp = self.spmatrix(dat)

        assert_raises(ValueError, datsp.sum, axis=3)
        assert_raises(TypeError, datsp.sum, axis=(0, 1))
        assert_raises(TypeError, datsp.sum, axis=1.5)
        assert_raises(ValueError, datsp.sum, axis=1, out=out)

    def test_sum_dtype(self):
        dat = np.matrix([[0, 1, 2],
                         [3, -4, 5],
                         [-6, 7, 9]])
        datsp = self.spmatrix(dat)

        def check(dtype):
            dat_mean = dat.mean(dtype=dtype)
            datsp_mean = datsp.mean(dtype=dtype)

            assert_array_almost_equal(dat_mean, datsp_mean)
            assert_equal(dat_mean.dtype, datsp_mean.dtype)

        for dtype in self.checked_dtypes:
            yield check, dtype

    def test_sum_out(self):
        dat = np.matrix([[0, 1, 2],
                         [3, -4, 5],
                         [-6, 7, 9]])
        datsp = self.spmatrix(dat)

        dat_out = np.matrix(0)
        datsp_out = np.matrix(0)

        dat.sum(out=dat_out)
        datsp.sum(out=datsp_out)
        assert_array_almost_equal(dat_out, datsp_out)

        dat_out = np.asmatrix(np.zeros((3, 1)))
        datsp_out = np.asmatrix(np.zeros((3, 1)))

        dat.sum(axis=1, out=dat_out)
        datsp.sum(axis=1, out=datsp_out)
        assert_array_almost_equal(dat_out, datsp_out)

    def test_numpy_sum(self):
        # See gh-5987
        dat = np.matrix([[0, 1, 2],
                         [3, -4, 5],
                         [-6, 7, 9]])
        datsp = self.spmatrix(dat)

        dat_mean = np.sum(dat)
        datsp_mean = np.sum(datsp)

        assert_array_almost_equal(dat_mean, datsp_mean)
        assert_equal(dat_mean.dtype, datsp_mean.dtype)

    def test_mean(self):
        def check(dtype):
            dat = np.matrix([[0, 1, 2],
                            [3, -4, 5],
                            [-6, 7, 9]], dtype=dtype)
            datsp = self.spmatrix(dat, dtype=dtype)

            assert_array_almost_equal(dat.mean(), datsp.mean())
            assert_equal(dat.mean().dtype, datsp.mean().dtype)
            assert_(np.isscalar(datsp.mean(axis=None)))
            assert_array_almost_equal(dat.mean(axis=None), datsp.mean(axis=None))
            assert_equal(dat.mean(axis=None).dtype, datsp.mean(axis=None).dtype)
            assert_array_almost_equal(dat.mean(axis=0), datsp.mean(axis=0))
            assert_equal(dat.mean(axis=0).dtype, datsp.mean(axis=0).dtype)
            assert_array_almost_equal(dat.mean(axis=1), datsp.mean(axis=1))
            assert_equal(dat.mean(axis=1).dtype, datsp.mean(axis=1).dtype)
            assert_array_almost_equal(dat.mean(axis=-2), datsp.mean(axis=-2))
            assert_equal(dat.mean(axis=-2).dtype, datsp.mean(axis=-2).dtype)
            assert_array_almost_equal(dat.mean(axis=-1), datsp.mean(axis=-1))
            assert_equal(dat.mean(axis=-1).dtype, datsp.mean(axis=-1).dtype)

        for dtype in self.checked_dtypes:
            yield check, dtype

    def test_mean_invalid_params(self):
        out = np.asmatrix(np.zeros((1, 3)))
        dat = np.matrix([[0, 1, 2],
                         [3, -4, 5],
                         [-6, 7, 9]])
        datsp = self.spmatrix(dat)

        assert_raises(ValueError, datsp.mean, axis=3)
        assert_raises(TypeError, datsp.mean, axis=(0, 1))
        assert_raises(TypeError, datsp.mean, axis=1.5)
        assert_raises(ValueError, datsp.mean, axis=1, out=out)

    def test_mean_dtype(self):
        dat = np.matrix([[0, 1, 2],
                         [3, -4, 5],
                         [-6, 7, 9]])
        datsp = self.spmatrix(dat)

        def check(dtype):
            dat_mean = dat.mean(dtype=dtype)
            datsp_mean = datsp.mean(dtype=dtype)

            assert_array_almost_equal(dat_mean, datsp_mean)
            assert_equal(dat_mean.dtype, datsp_mean.dtype)

        for dtype in self.checked_dtypes:
            yield check, dtype

    def test_mean_out(self):
        dat = np.matrix([[0, 1, 2],
                         [3, -4, 5],
                         [-6, 7, 9]])
        datsp = self.spmatrix(dat)

        dat_out = np.matrix(0)
        datsp_out = np.matrix(0)

        dat.mean(out=dat_out)
        datsp.mean(out=datsp_out)
        assert_array_almost_equal(dat_out, datsp_out)

        dat_out = np.asmatrix(np.zeros((3, 1)))
        datsp_out = np.asmatrix(np.zeros((3, 1)))

        dat.mean(axis=1, out=dat_out)
        datsp.mean(axis=1, out=datsp_out)
        assert_array_almost_equal(dat_out, datsp_out)

    def test_numpy_mean(self):
        # See gh-5987
        dat = np.matrix([[0, 1, 2],
                         [3, -4, 5],
                         [-6, 7, 9]])
        datsp = self.spmatrix(dat)

        dat_mean = np.mean(dat)
        datsp_mean = np.mean(datsp)

        assert_array_almost_equal(dat_mean, datsp_mean)
        assert_equal(dat_mean.dtype, datsp_mean.dtype)

    def test_expm(self):
        with warnings.catch_warnings():
            warnings.simplefilter("ignore", category=SparseEfficiencyWarning)

            M = array([[1, 0, 2], [0, 0, 3], [-4, 5, 6]], float)
            sM = self.spmatrix(M, shape=(3,3), dtype=float)
            Mexp = scipy.linalg.expm(M)
            sMexp = expm(sM).todense()
            assert_array_almost_equal((sMexp - Mexp), zeros((3, 3)))

            N = array([[3., 0., 1.], [0., 2., 0.], [0., 0., 0.]])
            sN = self.spmatrix(N, shape=(3,3), dtype=float)
            Nexp = scipy.linalg.expm(N)
            sNexp = expm(sN).todense()
            assert_array_almost_equal((sNexp - Nexp), zeros((3, 3)))

    def test_inv(self):
        def check(dtype):
            M = array([[1, 0, 2], [0, 0, 3], [-4, 5, 6]], dtype)
            sM = self.spmatrix(M, shape=(3,3), dtype=dtype)
            sMinv = inv(sM)
            assert_array_almost_equal(sMinv.dot(sM).todense(), np.eye(3))
        for dtype in [float]:
            with warnings.catch_warnings():
                warnings.simplefilter("ignore", category=SparseEfficiencyWarning)
                yield check, dtype

    def test_from_array(self):
        A = array([[1,0,0],[2,3,4],[0,5,0],[0,0,0]])
        assert_array_equal(self.spmatrix(A).toarray(), A)

        A = array([[1.0 + 3j, 0, 0],
                   [0, 2.0 + 5, 0],
                   [0, 0, 0]])
        assert_array_equal(self.spmatrix(A).toarray(), A)
        with warnings.catch_warnings():
            warnings.simplefilter("ignore", category=np.ComplexWarning)
            assert_array_equal(self.spmatrix(A, dtype='int16').toarray(), A.astype('int16'))

    def test_from_matrix(self):
        A = matrix([[1,0,0],[2,3,4],[0,5,0],[0,0,0]])
        assert_array_equal(self.spmatrix(A).todense(), A)

        A = matrix([[1.0 + 3j, 0, 0],
                    [0, 2.0 + 5, 0],
                    [0, 0, 0]])
        assert_array_equal(self.spmatrix(A).toarray(), A)
        with warnings.catch_warnings():
            warnings.simplefilter("ignore", category=np.ComplexWarning)
            assert_array_equal(self.spmatrix(A, dtype='int16').toarray(), A.astype('int16'))

    def test_from_list(self):
        A = [[1,0,0],[2,3,4],[0,5,0],[0,0,0]]
        assert_array_equal(self.spmatrix(A).todense(), A)

        A = [[1.0 + 3j, 0, 0],
             [0, 2.0 + 5, 0],
             [0, 0, 0]]
        assert_array_equal(self.spmatrix(A).toarray(), array(A))
        with warnings.catch_warnings():
            warnings.simplefilter("ignore", category=np.ComplexWarning)
            assert_array_equal(self.spmatrix(A, dtype='int16').todense(), array(A).astype('int16'))

    def test_from_sparse(self):
        D = array([[1,0,0],[2,3,4],[0,5,0],[0,0,0]])
        S = csr_matrix(D)
        assert_array_equal(self.spmatrix(S).toarray(), D)
        S = self.spmatrix(D)
        assert_array_equal(self.spmatrix(S).toarray(), D)

        with warnings.catch_warnings():
            warnings.simplefilter("ignore", category=np.ComplexWarning)
            D = array([[1.0 + 3j, 0, 0],
                       [0, 2.0 + 5, 0],
                       [0, 0, 0]])
            S = csr_matrix(D)
            assert_array_equal(self.spmatrix(S).toarray(), D)
            assert_array_equal(self.spmatrix(S, dtype='int16').toarray(), D.astype('int16'))
            S = self.spmatrix(D)
            assert_array_equal(self.spmatrix(S).toarray(), D)
            assert_array_equal(self.spmatrix(S, dtype='int16').toarray(), D.astype('int16'))

    # def test_array(self):
    #    """test array(A) where A is in sparse format"""
    #    assert_equal( array(self.datsp), self.dat )

    def test_todense(self):
        # Check C-contiguous (default).
        chk = self.datsp.todense()
        assert_array_equal(chk, self.dat)
        assert_(chk.flags.c_contiguous)
        assert_(not chk.flags.f_contiguous)
        # Check C-contiguous (with arg).
        chk = self.datsp.todense(order='C')
        assert_array_equal(chk, self.dat)
        assert_(chk.flags.c_contiguous)
        assert_(not chk.flags.f_contiguous)
        # Check F-contiguous (with arg).
        chk = self.datsp.todense(order='F')
        assert_array_equal(chk, self.dat)
        assert_(not chk.flags.c_contiguous)
        assert_(chk.flags.f_contiguous)
        # Check with out argument (array).
        out = np.zeros(self.datsp.shape, dtype=self.datsp.dtype)
        chk = self.datsp.todense(out=out)
        assert_array_equal(self.dat, out)
        assert_array_equal(self.dat, chk)
        assert_(chk.base is out)
        # Check with out array (matrix).
        out = np.asmatrix(np.zeros(self.datsp.shape, dtype=self.datsp.dtype))
        chk = self.datsp.todense(out=out)
        assert_array_equal(self.dat, out)
        assert_array_equal(self.dat, chk)
        assert_(chk is out)
        a = matrix([1.,2.,3.])
        dense_dot_dense = a * self.dat
        check = a * self.datsp.todense()
        assert_array_equal(dense_dot_dense, check)
        b = matrix([1.,2.,3.,4.]).T
        dense_dot_dense = self.dat * b
        check2 = self.datsp.todense() * b
        assert_array_equal(dense_dot_dense, check2)
        # Check bool data works.
        spbool = self.spmatrix(self.dat, dtype=bool)
        matbool = self.dat.astype(bool)
        assert_array_equal(spbool.todense(), matbool)

    def test_toarray(self):
        # Check C-contiguous (default).
        dat = asarray(self.dat)
        chk = self.datsp.toarray()
        assert_array_equal(chk, dat)
        assert_(chk.flags.c_contiguous)
        assert_(not chk.flags.f_contiguous)
        # Check C-contiguous (with arg).
        chk = self.datsp.toarray(order='C')
        assert_array_equal(chk, dat)
        assert_(chk.flags.c_contiguous)
        assert_(not chk.flags.f_contiguous)
        # Check F-contiguous (with arg).
        chk = self.datsp.toarray(order='F')
        assert_array_equal(chk, dat)
        assert_(not chk.flags.c_contiguous)
        assert_(chk.flags.f_contiguous)
        # Check with output arg.
        out = np.zeros(self.datsp.shape, dtype=self.datsp.dtype)
        self.datsp.toarray(out=out)
        assert_array_equal(chk, dat)
        # Check that things are fine when we don't initialize with zeros.
        out[...] = 1.
        self.datsp.toarray(out=out)
        assert_array_equal(chk, dat)
        a = array([1.,2.,3.])
        dense_dot_dense = dot(a, dat)
        check = dot(a, self.datsp.toarray())
        assert_array_equal(dense_dot_dense, check)
        b = array([1.,2.,3.,4.])
        dense_dot_dense = dot(dat, b)
        check2 = dot(self.datsp.toarray(), b)
        assert_array_equal(dense_dot_dense, check2)
        # Check bool data works.
        spbool = self.spmatrix(self.dat, dtype=bool)
        arrbool = dat.astype(bool)
        assert_array_equal(spbool.toarray(), arrbool)

    def test_astype(self):
        D = array([[2.0 + 3j, 0, 0],
                   [0, 4.0 + 5j, 0],
                   [0, 0, 0]])
        S = self.spmatrix(D)

        with warnings.catch_warnings():
            warnings.simplefilter("ignore", category=np.ComplexWarning)

            for x in supported_dtypes:
                assert_equal(S.astype(x).dtype, D.astype(x).dtype)  # correct type
                assert_equal(S.astype(x).toarray(), D.astype(x))        # correct values
                assert_equal(S.astype(x).format, S.format)           # format preserved

    def test_asfptype(self):
        A = self.spmatrix(arange(6,dtype='int32').reshape(2,3))

        assert_equal(A.dtype, np.dtype('int32'))
        assert_equal(A.asfptype().dtype, np.dtype('float64'))
        assert_equal(A.asfptype().format, A.format)
        assert_equal(A.astype('int16').asfptype().dtype, np.dtype('float32'))
        assert_equal(A.astype('complex128').asfptype().dtype, np.dtype('complex128'))

        B = A.asfptype()
        C = B.asfptype()
        assert_(B is C)

    def test_mul_scalar(self):
        def check(dtype):
            dat = self.dat_dtypes[dtype]
            datsp = self.datsp_dtypes[dtype]

            assert_array_equal(dat*2,(datsp*2).todense())
            assert_array_equal(dat*17.3,(datsp*17.3).todense())

        for dtype in self.math_dtypes:
            yield check, dtype

    def test_rmul_scalar(self):
        def check(dtype):
            dat = self.dat_dtypes[dtype]
            datsp = self.datsp_dtypes[dtype]

            assert_array_equal(2*dat,(2*datsp).todense())
            assert_array_equal(17.3*dat,(17.3*datsp).todense())

        for dtype in self.math_dtypes:
            yield check, dtype

    def test_add(self):
        def check(dtype):
            dat = self.dat_dtypes[dtype]
            datsp = self.datsp_dtypes[dtype]

            a = dat.copy()
            a[0,2] = 2.0
            b = datsp
            c = b + a
            assert_array_equal(c, b.todense() + a)

            c = b + b.tocsr()
            assert_array_equal(c.todense(),
                               b.todense() + b.todense())

        for dtype in self.math_dtypes:
            yield check, dtype

    def test_radd(self):
        def check(dtype):
            dat = self.dat_dtypes[dtype]
            datsp = self.datsp_dtypes[dtype]

            a = dat.copy()
            a[0,2] = 2.0
            b = datsp
            c = a + b
            assert_array_equal(c, a + b.todense())

        for dtype in self.math_dtypes:
            yield check, dtype

    def test_sub(self):
        def check(dtype):
            dat = self.dat_dtypes[dtype]
            datsp = self.datsp_dtypes[dtype]

            assert_array_equal((datsp - datsp).todense(),[[0,0,0,0],[0,0,0,0],[0,0,0,0]])
            assert_array_equal((datsp - 0).todense(), dat)

            A = self.spmatrix(matrix([[1,0,0,4],[-1,0,0,0],[0,8,0,-5]],'d'))
            assert_array_equal((datsp - A).todense(),dat - A.todense())
            assert_array_equal((A - datsp).todense(),A.todense() - dat)

        for dtype in self.math_dtypes:
            yield check, dtype

    def test_rsub(self):
        def check(dtype):
            dat = self.dat_dtypes[dtype]
            datsp = self.datsp_dtypes[dtype]

            assert_array_equal((dat - datsp),[[0,0,0,0],[0,0,0,0],[0,0,0,0]])
            assert_array_equal((datsp - dat),[[0,0,0,0],[0,0,0,0],[0,0,0,0]])
            assert_array_equal((0 - datsp).todense(), -dat)

            A = self.spmatrix(matrix([[1,0,0,4],[-1,0,0,0],[0,8,0,-5]],'d'))
            assert_array_equal((dat - A),dat - A.todense())
            assert_array_equal((A - dat),A.todense() - dat)
            assert_array_equal(A.todense() - datsp,A.todense() - dat)
            assert_array_equal(datsp - A.todense(),dat - A.todense())

        for dtype in self.math_dtypes:
            if dtype == np.dtype('bool'):
                # boolean array subtraction deprecated in 1.9.0
                continue

            yield check, dtype

    def test_add0(self):
        def check(dtype):
            dat = self.dat_dtypes[dtype]
            datsp = self.datsp_dtypes[dtype]

            # Adding 0 to a sparse matrix
            assert_array_equal((datsp + 0).todense(), dat)
            # use sum (which takes 0 as a starting value)
            sumS = sum([k * datsp for k in range(1, 3)])
            sumD = sum([k * dat for k in range(1, 3)])
            assert_almost_equal(sumS.todense(), sumD)

        for dtype in self.math_dtypes:
            yield check, dtype

    def test_elementwise_multiply(self):
        # real/real
        A = array([[4,0,9],[2,-3,5]])
        B = array([[0,7,0],[0,-4,0]])
        Asp = self.spmatrix(A)
        Bsp = self.spmatrix(B)
        assert_almost_equal(Asp.multiply(Bsp).todense(), A*B)  # sparse/sparse
        assert_almost_equal(Asp.multiply(B).todense(), A*B)  # sparse/dense

        # complex/complex
        C = array([[1-2j,0+5j,-1+0j],[4-3j,-3+6j,5]])
        D = array([[5+2j,7-3j,-2+1j],[0-1j,-4+2j,9]])
        Csp = self.spmatrix(C)
        Dsp = self.spmatrix(D)
        assert_almost_equal(Csp.multiply(Dsp).todense(), C*D)  # sparse/sparse
        assert_almost_equal(Csp.multiply(D).todense(), C*D)  # sparse/dense

        # real/complex
        assert_almost_equal(Asp.multiply(Dsp).todense(), A*D)  # sparse/sparse
        assert_almost_equal(Asp.multiply(D).todense(), A*D)  # sparse/dense

    def test_elementwise_multiply_broadcast(self):
        A = array([4])
        B = array([[-9]])
        C = array([1,-1,0])
        D = array([[7,9,-9]])
        E = array([[3],[2],[1]])
        F = array([[8,6,3],[-4,3,2],[6,6,6]])
        G = [1, 2, 3]
        H = np.ones((3, 4))
        J = H.T
        K = array([[0]])

        # Rank 1 arrays can't be cast as spmatrices (A and C) so leave
        # them out.
        Bsp = self.spmatrix(B)
        Dsp = self.spmatrix(D)
        Esp = self.spmatrix(E)
        Fsp = self.spmatrix(F)
        Hsp = self.spmatrix(H)
        Hspp = self.spmatrix(H[0,None])
        Jsp = self.spmatrix(J)
        Jspp = self.spmatrix(J[:,0,None])
        Ksp = self.spmatrix(K)

        matrices = [A, B, C, D, E, F, G, H, J, K]
        spmatrices = [Bsp, Dsp, Esp, Fsp, Hsp, Hspp, Jsp, Jspp, Ksp]

        # sparse/sparse
        for i in spmatrices:
            for j in spmatrices:
                try:
                    dense_mult = np.multiply(i.todense(), j.todense())
                except ValueError:
                    assert_raises(ValueError, i.multiply, j)
                    continue
                sp_mult = i.multiply(j)
                if isspmatrix(sp_mult):
                    assert_almost_equal(sp_mult.todense(), dense_mult)
                else:
                    assert_almost_equal(sp_mult, dense_mult)

        # sparse/dense
        for i in spmatrices:
            for j in matrices:
                try:
                    dense_mult = np.multiply(i.todense(), j)
                except ValueError:
                    assert_raises(ValueError, i.multiply, j)
                    continue
                sp_mult = i.multiply(j)
                if isspmatrix(sp_mult):
                    assert_almost_equal(sp_mult.todense(), dense_mult)
                else:
                    assert_almost_equal(sp_mult, dense_mult)

    def test_elementwise_divide(self):
        expected = [[1,np.nan,np.nan,1],[1,np.nan,1,np.nan],[np.nan,1,np.nan,np.nan]]
        assert_array_equal(todense(self.datsp / self.datsp),expected)

        denom = self.spmatrix(matrix([[1,0,0,4],[-1,0,0,0],[0,8,0,-5]],'d'))
        res = matrix([[1,np.nan,np.nan,0.5],[-3,np.nan,inf,np.nan],[np.nan,0.25,np.nan,np.nan]],'d')
        assert_array_equal(todense(self.datsp / denom),res)

        # complex
        A = array([[1-2j,0+5j,-1+0j],[4-3j,-3+6j,5]])
        B = array([[5+2j,7-3j,-2+1j],[0-1j,-4+2j,9]])
        Asp = self.spmatrix(A)
        Bsp = self.spmatrix(B)
        assert_almost_equal(todense(Asp / Bsp), A/B)

        # integer
        A = array([[1,2,3],[-3,2,1]])
        B = array([[0,1,2],[0,-2,3]])
        Asp = self.spmatrix(A)
        Bsp = self.spmatrix(B)
        with np.errstate(divide='ignore'):
            assert_array_equal(todense(Asp / Bsp), A / B)

    def test_pow(self):
        A = matrix([[1,0,2,0],[0,3,4,0],[0,5,0,0],[0,6,7,8]])
        B = self.spmatrix(A)

        for exponent in [0,1,2,3]:
            assert_array_equal((B**exponent).todense(),A**exponent)

        # invalid exponents
        for exponent in [-1, 2.2, 1 + 3j]:
            assert_raises(Exception, B.__pow__, exponent)

        # nonsquare matrix
        B = self.spmatrix(A[:3,:])
        assert_raises(Exception, B.__pow__, 1)

    def test_rmatvec(self):
        M = self.spmatrix(matrix([[3,0,0],[0,1,0],[2,0,3.0],[2,3,0]]))
        assert_array_almost_equal([1,2,3,4]*M, dot([1,2,3,4], M.toarray()))
        row = matrix([[1,2,3,4]])
        assert_array_almost_equal(row*M, row*M.todense())

    def test_small_multiplication(self):
        # test that A*x works for x with shape () (1,) (1,1) and (1,0)
        A = self.spmatrix([[1],[2],[3]])

        assert_(isspmatrix(A * array(1)))
        assert_equal((A * array(1)).todense(), [[1],[2],[3]])
        assert_equal(A * array([1]), array([1,2,3]))
        assert_equal(A * array([[1]]), array([[1],[2],[3]]))
        assert_equal(A * np.ones((1,0)), np.ones((3,0)))

    def test_binop_custom_type(self):
        # Non-regression test: previously, binary operations would raise
        # NotImplementedError instead of returning NotImplemented
        # (https://docs.python.org/library/constants.html#NotImplemented)
        # so overloading Custom + matrix etc. didn't work.
        A = self.spmatrix([[1], [2], [3]])
        B = BinopTester()
        assert_equal(A + B, "matrix on the left")
        assert_equal(A - B, "matrix on the left")
        assert_equal(A * B, "matrix on the left")
        assert_equal(B + A, "matrix on the right")
        assert_equal(B - A, "matrix on the right")
        assert_equal(B * A, "matrix on the right")

        if TEST_MATMUL:
            assert_equal(eval('A @ B'), "matrix on the left")
            assert_equal(eval('B @ A'), "matrix on the right")

    def test_matmul(self):
        if not TEST_MATMUL:
            raise nose.SkipTest("matmul is only tested in Python 3.5+")

        M = self.spmatrix(matrix([[3,0,0],[0,1,0],[2,0,3.0],[2,3,0]]))
        B = self.spmatrix(matrix([[0,1],[1,0],[0,2]],'d'))
        col = matrix([1,2,3]).T

        # check matrix-vector
        assert_array_almost_equal(operator.matmul(M, col),
                                  M.todense() * col)

        # check matrix-matrix
        assert_array_almost_equal(operator.matmul(M, B).todense(),
                                  (M * B).todense())
        assert_array_almost_equal(operator.matmul(M.todense(), B),
                                  (M * B).todense())
        assert_array_almost_equal(operator.matmul(M, B.todense()),
                                  (M * B).todense())

        # check error on matrix-scalar
        assert_raises(ValueError, operator.matmul, M, 1)
        assert_raises(ValueError, operator.matmul, 1, M)

    def test_matvec(self):
        M = self.spmatrix(matrix([[3,0,0],[0,1,0],[2,0,3.0],[2,3,0]]))
        col = matrix([1,2,3]).T
        assert_array_almost_equal(M * col, M.todense() * col)

        # check result dimensions (ticket #514)
        assert_equal((M * array([1,2,3])).shape,(4,))
        assert_equal((M * array([[1],[2],[3]])).shape,(4,1))
        assert_equal((M * matrix([[1],[2],[3]])).shape,(4,1))

        # check result type
        assert_(isinstance(M * array([1,2,3]), ndarray))
        assert_(isinstance(M * matrix([1,2,3]).T, matrix))

        # ensure exception is raised for improper dimensions
        bad_vecs = [array([1,2]), array([1,2,3,4]), array([[1],[2]]),
                    matrix([1,2,3]), matrix([[1],[2]])]
        for x in bad_vecs:
            assert_raises(ValueError, M.__mul__, x)

        # Should this be supported or not?!
        # flat = array([1,2,3])
        # assert_array_almost_equal(M*flat, M.todense()*flat)
        # Currently numpy dense matrices promote the result to a 1x3 matrix,
        # whereas sparse matrices leave the result as a rank-1 array.  Which
        # is preferable?

        # Note: the following command does not work.  Both NumPy matrices
        # and spmatrices should raise exceptions!
        # assert_array_almost_equal(M*[1,2,3], M.todense()*[1,2,3])

        # The current relationship between sparse matrix products and array
        # products is as follows:
        assert_array_almost_equal(M*array([1,2,3]), dot(M.A,[1,2,3]))
        assert_array_almost_equal(M*[[1],[2],[3]], asmatrix(dot(M.A,[1,2,3])).T)
        # Note that the result of M * x is dense if x has a singleton dimension.

        # Currently M.matvec(asarray(col)) is rank-1, whereas M.matvec(col)
        # is rank-2.  Is this desirable?

    def test_matmat_sparse(self):
        a = matrix([[3,0,0],[0,1,0],[2,0,3.0],[2,3,0]])
        a2 = array([[3,0,0],[0,1,0],[2,0,3.0],[2,3,0]])
        b = matrix([[0,1],[1,0],[0,2]],'d')
        asp = self.spmatrix(a)
        bsp = self.spmatrix(b)
        assert_array_almost_equal((asp*bsp).todense(), a*b)
        assert_array_almost_equal(asp*b, a*b)
        assert_array_almost_equal(a*bsp, a*b)
        assert_array_almost_equal(a2*bsp, a*b)

        # Now try performing cross-type multplication:
        csp = bsp.tocsc()
        c = b
        assert_array_almost_equal((asp*csp).todense(), a*c)
        assert_array_almost_equal(asp*c, a*c)

        assert_array_almost_equal(a*csp, a*c)
        assert_array_almost_equal(a2*csp, a*c)
        csp = bsp.tocsr()
        assert_array_almost_equal((asp*csp).todense(), a*c)
        assert_array_almost_equal(asp*c, a*c)

        assert_array_almost_equal(a*csp, a*c)
        assert_array_almost_equal(a2*csp, a*c)
        csp = bsp.tocoo()
        assert_array_almost_equal((asp*csp).todense(), a*c)
        assert_array_almost_equal(asp*c, a*c)

        assert_array_almost_equal(a*csp, a*c)
        assert_array_almost_equal(a2*csp, a*c)

        # Test provided by Andy Fraser, 2006-03-26
        L = 30
        frac = .3
        random.seed(0)  # make runs repeatable
        A = zeros((L,2))
        for i in xrange(L):
            for j in xrange(2):
                r = random.random()
                if r < frac:
                    A[i,j] = r/frac

        A = self.spmatrix(A)
        B = A*A.T
        assert_array_almost_equal(B.todense(), A.todense() * A.T.todense())
        assert_array_almost_equal(B.todense(), A.todense() * A.todense().T)

        # check dimension mismatch  2x2 times 3x2
        A = self.spmatrix([[1,2],[3,4]])
        B = self.spmatrix([[1,2],[3,4],[5,6]])
        assert_raises(ValueError, A.__mul__, B)

    def test_matmat_dense(self):
        a = matrix([[3,0,0],[0,1,0],[2,0,3.0],[2,3,0]])
        asp = self.spmatrix(a)

        # check both array and matrix types
        bs = [array([[1,2],[3,4],[5,6]]), matrix([[1,2],[3,4],[5,6]])]

        for b in bs:
            result = asp*b
            assert_(isinstance(result, type(b)))
            assert_equal(result.shape, (4,2))
            assert_equal(result, dot(a,b))

    def test_sparse_format_conversions(self):
        A = sparse.kron([[1,0,2],[0,3,4],[5,0,0]], [[1,2],[0,3]])
        D = A.todense()
        A = self.spmatrix(A)

        for format in ['bsr','coo','csc','csr','dia','dok','lil']:
            a = A.asformat(format)
            assert_equal(a.format,format)
            assert_array_equal(a.todense(), D)

            b = self.spmatrix(D+3j).asformat(format)
            assert_equal(b.format,format)
            assert_array_equal(b.todense(), D+3j)

            c = eval(format + '_matrix')(A)
            assert_equal(c.format,format)
            assert_array_equal(c.todense(), D)

    def test_tobsr(self):
        x = array([[1,0,2,0],[0,0,0,0],[0,0,4,5]])
        y = array([[0,1,2],[3,0,5]])
        A = kron(x,y)
        Asp = self.spmatrix(A)
        for format in ['bsr']:
            fn = getattr(Asp, 'to' + format)

            for X in [1, 2, 3, 6]:
                for Y in [1, 2, 3, 4, 6, 12]:
                    assert_equal(fn(blocksize=(X,Y)).todense(), A)

    def test_transpose(self):
        dat_1 = self.dat
        dat_2 = np.array([[]])
        matrices = [dat_1, dat_2]

        def check(dtype, j):
            dat = np.matrix(matrices[j], dtype=dtype)
            datsp = self.spmatrix(dat)

            a = datsp.transpose()
            b = dat.transpose()

            assert_array_equal(a.todense(), b)
            assert_array_equal(a.transpose().todense(), dat)
            assert_equal(a.dtype, b.dtype)

        # See gh-5987
        empty = self.spmatrix((3, 4))
        assert_array_equal(np.transpose(empty).todense(),
                           np.transpose(zeros((3, 4))))
        assert_array_equal(empty.T.todense(), zeros((4, 3)))
        assert_raises(ValueError, empty.transpose, axes=0)

        for dtype in self.checked_dtypes:
            for j in range(len(matrices)):
                yield check, dtype, j

    def test_add_dense(self):
        def check(dtype):
            dat = self.dat_dtypes[dtype]
            datsp = self.datsp_dtypes[dtype]

            # adding a dense matrix to a sparse matrix
            sum1 = dat + datsp
            assert_array_equal(sum1, dat + dat)
            sum2 = datsp + dat
            assert_array_equal(sum2, dat + dat)

        for dtype in self.math_dtypes:
            yield check, dtype

    def test_sub_dense(self):
        # subtracting a dense matrix to/from a sparse matrix
        def check(dtype):
            dat = self.dat_dtypes[dtype]
            datsp = self.datsp_dtypes[dtype]

            # Behavior is different for bool.
            if dat.dtype == bool:
                sum1 = dat - datsp
                assert_array_equal(sum1, dat - dat)
                sum2 = datsp - dat
                assert_array_equal(sum2, dat - dat)
            else:
                # Manually add to avoid upcasting from scalar
                # multiplication.
                sum1 = (dat + dat + dat) - datsp
                assert_array_equal(sum1, dat + dat)
                sum2 = (datsp + datsp + datsp) - dat
                assert_array_equal(sum2, dat + dat)

        for dtype in self.math_dtypes:
            if (dtype == np.dtype('bool')) and (
                    NumpyVersion(np.__version__) >= '1.9.0.dev'):
                # boolean array subtraction deprecated in 1.9.0
                continue

            yield check, dtype

    def test_maximum_minimum(self):
        A_dense = np.array([[1, 0, 3], [0, 4, 5], [0, 0, 0]])
        B_dense = np.array([[1, 1, 2], [0, 3, 6], [1, -1, 0]])

        A_dense_cpx = np.array([[1, 0, 3], [0, 4+2j, 5], [0, 1j, -1j]])

        def check(dtype, dtype2, btype):
            if np.issubdtype(dtype, np.complexfloating):
                A = self.spmatrix(A_dense_cpx.astype(dtype))
            else:
                A = self.spmatrix(A_dense.astype(dtype))
            if btype == 'scalar':
                B = dtype2.type(1)
            elif btype == 'scalar2':
                B = dtype2.type(-1)
            elif btype == 'dense':
                B = B_dense.astype(dtype2)
            elif btype == 'sparse':
                B = self.spmatrix(B_dense.astype(dtype2))
            else:
                raise ValueError()

            max_s = A.maximum(B)
            max_d = np.maximum(todense(A), todense(B))
            assert_array_equal(todense(max_s), max_d)
            assert_equal(max_s.dtype, max_d.dtype)

            min_s = A.minimum(B)
            min_d = np.minimum(todense(A), todense(B))
            assert_array_equal(todense(min_s), min_d)
            assert_equal(min_s.dtype, min_d.dtype)

        for dtype in self.math_dtypes:
            for dtype2 in [np.int8, np.float_, np.complex_]:
                for btype in ['scalar', 'scalar2', 'dense', 'sparse']:
                    yield check, np.dtype(dtype), np.dtype(dtype2), btype

    def test_copy(self):
        # Check whether the copy=True and copy=False keywords work
        A = self.datsp

        # check that copy preserves format
        assert_equal(A.copy().format, A.format)
        assert_equal(A.__class__(A,copy=True).format, A.format)
        assert_equal(A.__class__(A,copy=False).format, A.format)

        assert_equal(A.copy().todense(), A.todense())
        assert_equal(A.__class__(A,copy=True).todense(), A.todense())
        assert_equal(A.__class__(A,copy=False).todense(), A.todense())

        # check that XXX_matrix.toXXX() works
        toself = getattr(A,'to' + A.format)
        assert_equal(toself().format, A.format)
        assert_equal(toself(copy=True).format, A.format)
        assert_equal(toself(copy=False).format, A.format)

        assert_equal(toself().todense(), A.todense())
        assert_equal(toself(copy=True).todense(), A.todense())
        assert_equal(toself(copy=False).todense(), A.todense())

        # check whether the data is copied?
        # TODO: deal with non-indexable types somehow
        B = A.copy()
        try:
            B[0,0] += 1
            assert_(B[0,0] != A[0,0])
        except NotImplementedError:
            # not all sparse matrices can be indexed
            pass
        except TypeError:
            # not all sparse matrices can be indexed
            pass

    # test that __iter__ is compatible with NumPy matrix
    def test_iterator(self):
        B = np.matrix(np.arange(50).reshape(5, 10))
        A = self.spmatrix(B)

        for x, y in zip(A, B):
            assert_equal(x.todense(), y)

    def test_size_zero_matrix_arithmetic(self):
        # Test basic matrix arithmatic with shapes like (0,0), (10,0),
        # (0, 3), etc.
        mat = np.matrix([])
        a = mat.reshape((0, 0))
        b = mat.reshape((0, 1))
        c = mat.reshape((0, 5))
        d = mat.reshape((1, 0))
        e = mat.reshape((5, 0))
        f = np.matrix(np.ones([5, 5]))

        asp = self.spmatrix(a)
        bsp = self.spmatrix(b)
        csp = self.spmatrix(c)
        dsp = self.spmatrix(d)
        esp = self.spmatrix(e)
        fsp = self.spmatrix(f)

        # matrix product.
        assert_array_equal(asp.dot(asp).A, np.dot(a, a).A)
        assert_array_equal(bsp.dot(dsp).A, np.dot(b, d).A)
        assert_array_equal(dsp.dot(bsp).A, np.dot(d, b).A)
        assert_array_equal(csp.dot(esp).A, np.dot(c, e).A)
        assert_array_equal(csp.dot(fsp).A, np.dot(c, f).A)
        assert_array_equal(esp.dot(csp).A, np.dot(e, c).A)
        assert_array_equal(dsp.dot(csp).A, np.dot(d, c).A)
        assert_array_equal(fsp.dot(esp).A, np.dot(f, e).A)

        # bad matrix products
        assert_raises(ValueError, dsp.dot, e)
        assert_raises(ValueError, asp.dot, d)

        # elemente-wise multiplication
        assert_array_equal(asp.multiply(asp).A, np.multiply(a, a).A)
        assert_array_equal(bsp.multiply(bsp).A, np.multiply(b, b).A)
        assert_array_equal(dsp.multiply(dsp).A, np.multiply(d, d).A)

        assert_array_equal(asp.multiply(a).A, np.multiply(a, a).A)
        assert_array_equal(bsp.multiply(b).A, np.multiply(b, b).A)
        assert_array_equal(dsp.multiply(d).A, np.multiply(d, d).A)

        assert_array_equal(asp.multiply(6).A, np.multiply(a, 6).A)
        assert_array_equal(bsp.multiply(6).A, np.multiply(b, 6).A)
        assert_array_equal(dsp.multiply(6).A, np.multiply(d, 6).A)

        # bad element-wise multiplication
        assert_raises(ValueError, asp.multiply, c)
        assert_raises(ValueError, esp.multiply, c)

        # Addition
        assert_array_equal(asp.__add__(asp).A, a.__add__(a).A)
        assert_array_equal(bsp.__add__(bsp).A, b.__add__(b).A)
        assert_array_equal(dsp.__add__(dsp).A, d.__add__(d).A)

        # bad addition
        assert_raises(ValueError, asp.__add__, dsp)
        assert_raises(ValueError, bsp.__add__, asp)

    def test_size_zero_conversions(self):
        mat = np.matrix([])
        a = mat.reshape((0, 0))
        b = mat.reshape((0, 5))
        c = mat.reshape((5, 0))

        for m in [a, b, c]:
            spm = self.spmatrix(m)
            assert_array_equal(spm.tocoo().A, m)
            assert_array_equal(spm.tocsr().A, m)
            assert_array_equal(spm.tocsc().A, m)
            assert_array_equal(spm.tolil().A, m)
            assert_array_equal(spm.todok().A, m)
            assert_array_equal(spm.tobsr().A, m)

    def test_unary_ufunc_overrides(self):
        def check(name):
            if not HAS_NUMPY_UFUNC:
                if name == "sign":
                    raise nose.SkipTest("sign conflicts with comparison op "
                                        "support on Numpy without __numpy_ufunc__")
                if self.spmatrix in (dok_matrix, lil_matrix):
                    raise nose.SkipTest("Unary ops not implemented for dok/lil "
                                        "with Numpy without __numpy_ufunc__")
            ufunc = getattr(np, name)

            X = self.spmatrix(np.arange(20).reshape(4, 5) / 20.)
            X0 = ufunc(X.toarray())

            X2 = ufunc(X)
            assert_array_equal(X2.toarray(), X0)

            if HAS_NUMPY_UFUNC:
                # the out argument doesn't work on Numpy without __numpy_ufunc__
                out = np.zeros_like(X0)
                X3 = ufunc(X, out=out)
                assert_(X3 is out)
                assert_array_equal(todense(X3), ufunc(todense(X)))

                out = csc_matrix(out.shape, dtype=out.dtype)
                out[:,1] = 999
                X4 = ufunc(X, out=out)
                assert_(X4 is out)
                assert_array_equal(todense(X4), ufunc(todense(X)))

        for name in ["sin", "tan", "arcsin", "arctan", "sinh", "tanh",
                     "arcsinh", "arctanh", "rint", "sign", "expm1", "log1p",
                     "deg2rad", "rad2deg", "floor", "ceil", "trunc", "sqrt",
                     "abs"]:
            yield check, name

    def test_binary_ufunc_overrides(self):
        # data
        a = np.array([[1, 2, 3],
                      [4, 5, 0],
                      [7, 8, 9]])
        b = np.array([[9, 8, 7],
                      [6, 0, 0],
                      [3, 2, 1]])
        c = 1.0
        d = 1 + 2j
        e = 5

        asp = self.spmatrix(a)
        bsp = self.spmatrix(b)

        a_items = dict(dense=a, scalar=c, cplx_scalar=d, int_scalar=e, sparse=asp)
        b_items = dict(dense=b, scalar=c, cplx_scalar=d, int_scalar=e, sparse=bsp)

        @dec.skipif(not HAS_NUMPY_UFUNC, "feature requires Numpy with __numpy_ufunc__")
        def check(i, j, dtype):
            ax = a_items[i]
            bx = b_items[j]

            if issparse(ax):
                ax = ax.astype(dtype)
            if issparse(bx):
                bx = bx.astype(dtype)

            a = todense(ax)
            b = todense(bx)

            def check_one(ufunc, allclose=False):
                # without out argument
                expected = ufunc(a, b)
                got = ufunc(ax, bx)
                if allclose:
                    assert_allclose(todense(got), expected,
                                    rtol=5e-15, atol=0)
                else:
                    assert_array_equal(todense(got), expected)

                # with out argument
                out = np.zeros(got.shape, dtype=got.dtype)
                out.fill(np.nan)
                got = ufunc(ax, bx, out=out)
                assert_(got is out)
                if allclose:
                    assert_allclose(todense(got), expected,
                                    rtol=5e-15, atol=0)
                else:
                    assert_array_equal(todense(got), expected)

                out = csr_matrix(got.shape, dtype=out.dtype)
                out[0,:] = 999
                got = ufunc(ax, bx, out=out)
                assert_(got is out)
                if allclose:
                    assert_allclose(todense(got), expected,
                                    rtol=5e-15, atol=0)
                else:
                    assert_array_equal(todense(got), expected)

            # -- associative

            # multiply
            check_one(np.multiply)

            # add
            if isscalarlike(ax) or isscalarlike(bx):
                try:
                    check_one(np.add)
                except NotImplementedError:
                    # Not implemented for all spmatrix types
                    pass
            else:
                check_one(np.add)

            # maximum
            check_one(np.maximum)

            # minimum
            check_one(np.minimum)

            # -- non-associative

            # dot
            check_one(np.dot)

            # subtract
            if isscalarlike(ax) or isscalarlike(bx):
                try:
                    check_one(np.subtract)
                except NotImplementedError:
                    # Not implemented for all spmatrix types
                    pass
            else:
                check_one(np.subtract)

            # divide
            with np.errstate(divide='ignore', invalid='ignore'):
                if isscalarlike(bx):
                    # Rounding error may be different, as the sparse implementation
                    # computes a/b -> a * (1/b) if b is a scalar
                    check_one(np.divide, allclose=True)
                else:
                    check_one(np.divide)

                # true_divide
                if isscalarlike(bx):
                    check_one(np.true_divide, allclose=True)
                else:
                    check_one(np.true_divide)

        for i in a_items.keys():
            for j in b_items.keys():
                for dtype in [np.int_, np.float_, np.complex_]:
                    if i == 'sparse' or j == 'sparse':
                        yield check, i, j, dtype

    @dec.skipif(not HAS_NUMPY_UFUNC, "feature requires Numpy with __numpy_ufunc__")
    def test_ufunc_object_array(self):
        # This tests compatibility with previous Numpy object array
        # ufunc behavior. See gh-3345.
        a = self.spmatrix([[1, 2]])
        b = self.spmatrix([[3], [4]])
        c = self.spmatrix([[5], [6]])

        # Should distribute the operation across the object array
        d = np.multiply(a, np.array([[b], [c]]))
        assert_(d.dtype == np.object_)
        assert_(d.shape == (2, 1))
        assert_allclose(d[0,0].A, (a*b).A)
        assert_allclose(d[1,0].A, (a*c).A)

        # Lists also get cast to object arrays
        d = np.multiply(a, [[b], [c]])
        assert_(d.dtype == np.object_)
        assert_(d.shape == (2, 1))
        assert_allclose(d[0,0].A, (a*b).A)
        assert_allclose(d[1,0].A, (a*c).A)

        # This returned NotImplemented in Numpy < 1.9; do it properly now
        d = np.multiply(np.array([[b], [c]]), a)
        assert_(d.dtype == np.object_)
        assert_(d.shape == (2, 1))
        assert_allclose(d[0,0].A, (b*a).A)
        assert_allclose(d[1,0].A, (c*a).A)

        d = np.subtract(np.array(b, dtype=object), c)
        assert_(isinstance(d, sparse.spmatrix))
        assert_allclose(d.A, (b - c).A)


class _TestInplaceArithmetic:
    def test_inplace_dense(self):
        a = np.ones((3, 4))
        b = self.spmatrix(a)

        with warnings.catch_warnings():
            if not HAS_NUMPY_UFUNC:
                warnings.simplefilter("ignore", DeprecationWarning)

            x = a.copy()
            y = a.copy()
            x += a
            y += b
            assert_array_equal(x, y)

            x = a.copy()
            y = a.copy()
            x -= a
            y -= b
            assert_array_equal(x, y)

            # This is matrix product, from __rmul__
            assert_raises(ValueError, operator.imul, x, b)
            x = a.copy()
            y = a.copy()
            x = x.dot(a.T)
            y *= b.T
            assert_array_equal(x, y)

            # Matrix (non-elementwise) floor division is not defined
            assert_raises(TypeError, operator.ifloordiv, x, b)

    def test_imul_scalar(self):
        def check(dtype):
            dat = self.dat_dtypes[dtype]
            datsp = self.datsp_dtypes[dtype]

            # Avoid implicit casting.
            if np.can_cast(type(2), dtype, casting='same_kind'):
                a = datsp.copy()
                a *= 2
                b = dat.copy()
                b *= 2
                assert_array_equal(b, a.todense())

            if np.can_cast(type(17.3), dtype, casting='same_kind'):
                a = datsp.copy()
                a *= 17.3
                b = dat.copy()
                b *= 17.3
                assert_array_equal(b, a.todense())

        for dtype in self.math_dtypes:
            yield check, dtype

    def test_idiv_scalar(self):
        def check(dtype):
            dat = self.dat_dtypes[dtype]
            datsp = self.datsp_dtypes[dtype]

            if np.can_cast(type(2), dtype, casting='same_kind'):
                a = datsp.copy()
                a /= 2
                b = dat.copy()
                b /= 2
                assert_array_equal(b, a.todense())

            if np.can_cast(type(17.3), dtype, casting='same_kind'):
                a = datsp.copy()
                a /= 17.3
                b = dat.copy()
                b /= 17.3
                assert_array_equal(b, a.todense())

        for dtype in self.math_dtypes:
            # /= should only be used with float dtypes to avoid implicit
            # casting.
            if not np.can_cast(dtype, np.int_):
                yield check, dtype

    def test_inplace_success(self):
        # Inplace ops should work even if a specialized version is not
        # implemented, falling back to x = x <op> y
        a = self.spmatrix(np.eye(5))
        b = self.spmatrix(np.eye(5))
        bp = self.spmatrix(np.eye(5))

        b += a
        bp = bp + a
        assert_allclose(b.A, bp.A)

        b *= a
        bp = bp * a
        assert_allclose(b.A, bp.A)

        b -= a
        bp = bp - a
        assert_allclose(b.A, bp.A)

        assert_raises(TypeError, operator.ifloordiv, a, b)


class _TestGetSet:
    def test_getelement(self):
        def check(dtype):
            with warnings.catch_warnings():
                warnings.simplefilter("ignore", category=SparseEfficiencyWarning)
                D = array([[1,0,0],
                           [4,3,0],
                           [0,2,0],
                           [0,0,0]], dtype=dtype)
                A = self.spmatrix(D)

                M,N = D.shape

                for i in range(-M, M):
                    for j in range(-N, N):
                        assert_equal(A[i,j], D[i,j])

                for ij in [(0,3),(-1,3),(4,0),(4,3),(4,-1), (1, 2, 3)]:
                    assert_raises((IndexError, TypeError), A.__getitem__, ij)

        for dtype in supported_dtypes:
            yield check, np.dtype(dtype)

    def test_setelement(self):
        def check(dtype):
            with warnings.catch_warnings():
                warnings.simplefilter("ignore", category=SparseEfficiencyWarning)
                A = self.spmatrix((3,4), dtype=dtype)
                A[0, 0] = dtype.type(0)  # bug 870
                A[1, 2] = dtype.type(4.0)
                A[0, 1] = dtype.type(3)
                A[2, 0] = dtype.type(2.0)
                A[0,-1] = dtype.type(8)
                A[-1,-2] = dtype.type(7)
                A[0, 1] = dtype.type(5)

                if dtype != np.bool_:
                    assert_array_equal(A.todense(),[[0,5,0,8],[0,0,4,0],[2,0,7,0]])

                for ij in [(0,4),(-1,4),(3,0),(3,4),(3,-1)]:
                    assert_raises(IndexError, A.__setitem__, ij, 123.0)

                for v in [[1,2,3], array([1,2,3])]:
                    assert_raises(ValueError, A.__setitem__, (0,0), v)

                if (not np.issubdtype(dtype, np.complexfloating) and
                        dtype != np.bool_):
                    for v in [3j]:
                        assert_raises(TypeError, A.__setitem__, (0,0), v)

        for dtype in supported_dtypes:
            yield check, np.dtype(dtype)

    def test_negative_index_assignment(self):
        # Regression test for github issue 4428.

        def check(dtype):
            A = self.spmatrix((3, 10), dtype=dtype)
            A[0, -4] = 1
            assert_equal(A[0, -4], 1)

        for dtype in self.math_dtypes:
            yield check, np.dtype(dtype)

    def test_scalar_assign_2(self):
        n, m = (5, 10)

        def _test_set(i, j, nitems):
            msg = "%r ; %r ; %r" % (i, j, nitems)
            A = self.spmatrix((n, m))
            A[i, j] = 1
            assert_almost_equal(A.sum(), nitems, err_msg=msg)
            assert_almost_equal(A[i, j], 1, err_msg=msg)

        # [i,j]
        for i, j in [(2, 3), (-1, 8), (-1, -2), (array(-1), -2), (-1, array(-2)),
                     (array(-1), array(-2))]:
            with warnings.catch_warnings():
                warnings.simplefilter("ignore", category=SparseEfficiencyWarning)
                _test_set(i, j, 1)

    def test_index_scalar_assign(self):
        with warnings.catch_warnings():
            warnings.simplefilter("ignore", category=SparseEfficiencyWarning)
            A = self.spmatrix((5, 5))
            B = np.zeros((5, 5))
            for C in [A, B]:
                C[0,1] = 1
                C[3,0] = 4
                C[3,0] = 9
            assert_array_equal(A.toarray(), B)


class _TestSolve:
    def test_solve(self):
        # Test whether the lu_solve command segfaults, as reported by Nils
        # Wagner for a 64-bit machine, 02 March 2005 (EJS)
        n = 20
        np.random.seed(0)  # make tests repeatable
        A = zeros((n,n), dtype=complex)
        x = np.random.rand(n)
        y = np.random.rand(n-1)+1j*np.random.rand(n-1)
        r = np.random.rand(n)
        for i in range(len(x)):
            A[i,i] = x[i]
        for i in range(len(y)):
            A[i,i+1] = y[i]
            A[i+1,i] = conjugate(y[i])
        A = self.spmatrix(A)
        x = splu(A).solve(r)
        assert_almost_equal(A*x,r)


class _TestSlicing:
    def test_dtype_preservation(self):
        assert_equal(self.spmatrix((1,10), dtype=np.int16)[0,1:5].dtype, np.int16)
        assert_equal(self.spmatrix((1,10), dtype=np.int32)[0,1:5].dtype, np.int32)
        assert_equal(self.spmatrix((1,10), dtype=np.float32)[0,1:5].dtype, np.float32)
        assert_equal(self.spmatrix((1,10), dtype=np.float64)[0,1:5].dtype, np.float64)

    def test_get_horiz_slice(self):
        B = asmatrix(arange(50.).reshape(5,10))
        A = self.spmatrix(B)
        assert_array_equal(B[1,:], A[1,:].todense())
        assert_array_equal(B[1,2:5], A[1,2:5].todense())

        C = matrix([[1, 2, 1], [4, 0, 6], [0, 0, 0], [0, 0, 1]])
        D = self.spmatrix(C)
        assert_array_equal(C[1, 1:3], D[1, 1:3].todense())

        # Now test slicing when a row contains only zeros
        E = matrix([[1, 2, 1], [4, 0, 0], [0, 0, 0], [0, 0, 1]])
        F = self.spmatrix(E)
        assert_array_equal(E[1, 1:3], F[1, 1:3].todense())
        assert_array_equal(E[2, -2:], F[2, -2:].A)

        # The following should raise exceptions:
        assert_raises(IndexError, A.__getitem__, (slice(None), 11))
        assert_raises(IndexError, A.__getitem__, (6, slice(3, 7)))

    def test_get_vert_slice(self):
        B = asmatrix(arange(50.).reshape(5,10))
        A = self.spmatrix(B)
        assert_array_equal(B[2:5,0], A[2:5,0].todense())
        assert_array_equal(B[:,1], A[:,1].todense())

        C = matrix([[1, 2, 1], [4, 0, 6], [0, 0, 0], [0, 0, 1]])
        D = self.spmatrix(C)
        assert_array_equal(C[1:3, 1], D[1:3, 1].todense())
        assert_array_equal(C[:, 2], D[:, 2].todense())

        # Now test slicing when a column contains only zeros
        E = matrix([[1, 0, 1], [4, 0, 0], [0, 0, 0], [0, 0, 1]])
        F = self.spmatrix(E)
        assert_array_equal(E[:, 1], F[:, 1].todense())
        assert_array_equal(E[-2:, 2], F[-2:, 2].todense())

        # The following should raise exceptions:
        assert_raises(IndexError, A.__getitem__, (slice(None), 11))
        assert_raises(IndexError, A.__getitem__, (6, slice(3, 7)))

    def test_get_slices(self):
        B = asmatrix(arange(50.).reshape(5,10))
        A = self.spmatrix(B)
        assert_array_equal(A[2:5,0:3].todense(), B[2:5,0:3])
        assert_array_equal(A[1:,:-1].todense(), B[1:,:-1])
        assert_array_equal(A[:-1,1:].todense(), B[:-1,1:])

        # Now test slicing when a column contains only zeros
        E = matrix([[1, 0, 1], [4, 0, 0], [0, 0, 0], [0, 0, 1]])
        F = self.spmatrix(E)
        assert_array_equal(E[1:2, 1:2], F[1:2, 1:2].todense())
        assert_array_equal(E[:, 1:], F[:, 1:].todense())

    def test_non_unit_stride_2d_indexing(self):
        # Regression test -- used to silently ignore the stride.
        v0 = np.random.rand(50, 50)
        try:
            v = self.spmatrix(v0)[0:25:2, 2:30:3]
        except ValueError:
            # if unsupported
            raise nose.SkipTest("feature not implemented")

        assert_array_equal(v.todense(),
                           v0[0:25:2, 2:30:3])

    def test_slicing_2(self):
        B = asmatrix(arange(50).reshape(5,10))
        A = self.spmatrix(B)

        # [i,j]
        assert_equal(A[2,3], B[2,3])
        assert_equal(A[-1,8], B[-1,8])
        assert_equal(A[-1,-2],B[-1,-2])
        assert_equal(A[array(-1),-2],B[-1,-2])
        assert_equal(A[-1,array(-2)],B[-1,-2])
        assert_equal(A[array(-1),array(-2)],B[-1,-2])

        # [i,1:2]
        assert_equal(A[2,:].todense(), B[2,:])
        assert_equal(A[2,5:-2].todense(),B[2,5:-2])
        assert_equal(A[array(2),5:-2].todense(),B[2,5:-2])

        # [1:2,j]
        assert_equal(A[:,2].todense(), B[:,2])
        assert_equal(A[3:4,9].todense(), B[3:4,9])
        assert_equal(A[1:4,-5].todense(),B[1:4,-5])
        assert_equal(A[2:-1,3].todense(),B[2:-1,3])
        assert_equal(A[2:-1,array(3)].todense(),B[2:-1,3])

        # [1:2,1:2]
        assert_equal(A[1:2,1:2].todense(),B[1:2,1:2])
        assert_equal(A[4:,3:].todense(), B[4:,3:])
        assert_equal(A[:4,:5].todense(), B[:4,:5])
        assert_equal(A[2:-1,:5].todense(),B[2:-1,:5])

        # [i]
        assert_equal(A[1,:].todense(), B[1,:])
        assert_equal(A[-2,:].todense(),B[-2,:])
        assert_equal(A[array(-2),:].todense(),B[-2,:])

        # [1:2]
        assert_equal(A[1:4].todense(), B[1:4])
        assert_equal(A[1:-2].todense(),B[1:-2])

        # Check bug reported by Robert Cimrman:
        # http://thread.gmane.org/gmane.comp.python.scientific.devel/7986
        s = slice(int8(2),int8(4),None)
        assert_equal(A[s,:].todense(), B[2:4,:])
        assert_equal(A[:,s].todense(), B[:,2:4])

    def test_slicing_3(self):
        B = asmatrix(arange(50).reshape(5,10))
        A = self.spmatrix(B)

        s_ = np.s_
        slices = [s_[:2], s_[1:2], s_[3:], s_[3::2],
                  s_[8:3:-1], s_[4::-2], s_[:5:-1],
                  0, 1, s_[:], s_[1:5], -1, -2, -5,
                  array(-1), np.int8(-3)]

        def check_1(a):
            x = A[a]
            y = B[a]
            if y.shape == ():
                assert_equal(x, y, repr(a))
            else:
                if x.size == 0 and y.size == 0:
                    pass
                else:
                    assert_array_equal(x.todense(), y, repr(a))

        for j, a in enumerate(slices):
            yield check_1, a

        def check_2(a, b):
            # Indexing np.matrix with 0-d arrays seems to be broken,
            # as they seem not to be treated as scalars.
            # https://github.com/numpy/numpy/issues/3110
            if isinstance(a, np.ndarray):
                ai = int(a)
            else:
                ai = a
            if isinstance(b, np.ndarray):
                bi = int(b)
            else:
                bi = b

            x = A[a, b]
            y = B[ai, bi]

            if y.shape == ():
                assert_equal(x, y, repr((a, b)))
            else:
                if x.size == 0 and y.size == 0:
                    pass
                else:
                    assert_array_equal(x.todense(), y, repr((a, b)))

        for i, a in enumerate(slices):
            for j, b in enumerate(slices):
                yield check_2, a, b

    def test_ellipsis_slicing(self):
        b = asmatrix(arange(50).reshape(5,10))
        a = self.spmatrix(b)

        assert_array_equal(a[...].A, b[...].A)
        assert_array_equal(a[...,].A, b[...,].A)

        assert_array_equal(a[1, ...].A, b[1, ...].A)
        assert_array_equal(a[..., 1].A, b[..., 1].A)
        assert_array_equal(a[1:, ...].A, b[1:, ...].A)
        assert_array_equal(a[..., 1:].A, b[..., 1:].A)

        assert_array_equal(a[1:, 1, ...].A, b[1:, 1, ...].A)
        assert_array_equal(a[1, ..., 1:].A, b[1, ..., 1:].A)
        # These return ints
        assert_equal(a[1, 1, ...], b[1, 1, ...])
        assert_equal(a[1, ..., 1], b[1, ..., 1])

    @dec.skipif(NumpyVersion(np.__version__) >= '1.9.0.dev')
    def test_multiple_ellipsis_slicing(self):
        b = asmatrix(arange(50).reshape(5,10))
        a = self.spmatrix(b)

        assert_array_equal(a[..., ...].A, b[..., ...].A)
        assert_array_equal(a[..., ..., ...].A, b[..., ..., ...].A)
        assert_array_equal(a[1, ..., ...].A, b[1, ..., ...].A)
        assert_array_equal(a[1:, ..., ...].A, b[1:, ..., ...].A)
        assert_array_equal(a[..., ..., 1:].A, b[..., ..., 1:].A)

        # Bug in NumPy's slicing
        assert_array_equal(a[..., ..., 1].A, b[..., ..., 1].A.reshape((5,1)))


class _TestSlicingAssign:
    def test_slice_scalar_assign(self):
        with warnings.catch_warnings():
            warnings.simplefilter("ignore", category=SparseEfficiencyWarning)
            A = self.spmatrix((5, 5))
            B = np.zeros((5, 5))
            for C in [A, B]:
                C[0:1,1] = 1
                C[3:0,0] = 4
                C[3:4,0] = 9
                C[0,4:] = 1
                C[3::-1,4:] = 9
            assert_array_equal(A.toarray(), B)

    def test_slice_assign_2(self):
        n, m = (5, 10)

        def _test_set(i, j):
            msg = "i=%r; j=%r" % (i, j)
            A = self.spmatrix((n, m))
            A[i, j] = 1
            B = np.zeros((n, m))
            B[i, j] = 1
            assert_array_almost_equal(A.todense(), B, err_msg=msg)
        # [i,1:2]
        for i, j in [(2, slice(3)), (2, slice(None, 10, 4)), (2, slice(5, -2)),
                     (array(2), slice(5, -2))]:
            with warnings.catch_warnings():
                warnings.simplefilter("ignore", category=SparseEfficiencyWarning)
                _test_set(i, j)

    def test_self_self_assignment(self):
        # Tests whether a row of one lil_matrix can be assigned to
        # another.
        with warnings.catch_warnings():
            warnings.simplefilter("ignore", category=SparseEfficiencyWarning)
            B = self.spmatrix((4,3))
            B[0,0] = 2
            B[1,2] = 7
            B[2,1] = 3
            B[3,0] = 10

            A = B / 10
            B[0,:] = A[0,:]
            assert_array_equal(A[0,:].A, B[0,:].A)
            assert_equal(A.nnz, B.nnz)

            A = B / 10
            B[:,:] = A[:1,:1]
            assert_array_equal(np.zeros((4,3)) + A[0,0], B.A)

            A = B / 10
            B[:-1,0] = A[0,:].T
            assert_array_equal(A[0,:].A.T, B[:-1,0].A)

    def test_slice_assignment(self):
        with warnings.catch_warnings():
            warnings.simplefilter("ignore", category=SparseEfficiencyWarning)
            B = self.spmatrix((4,3))
            B[0,0] = 5
            B[1,2] = 3
            B[2,1] = 7

            expected = array([[10,0,0],
                              [0,0,6],
                              [0,14,0],
                              [0,0,0]])

            B[:,:] = B+B
            assert_array_equal(B.todense(),expected)

            block = [[1,0],[0,4]]
            B[:2,:2] = csc_matrix(array(block))
            assert_array_equal(B.todense()[:2,:2],block)

    def test_sparsity_modifying_assignment(self):
        with warnings.catch_warnings():
            warnings.simplefilter("ignore", category=SparseEfficiencyWarning)
            B = self.spmatrix((4,3))
            B[0,0] = 5
            B[1,2] = 3
            B[2,1] = 7
            B[3,0] = 10

            expected = array([[1,0,0],[0,1,0],[0,0,1],[10,0,0]])
            B[:3] = csr_matrix(np.eye(3))
            assert_array_equal(B.toarray(), expected)

    def test_set_slice(self):
        with warnings.catch_warnings():
            warnings.simplefilter("ignore", category=SparseEfficiencyWarning)
            A = self.spmatrix((5,10))
            B = matrix(zeros((5,10), float))

            s_ = np.s_
            slices = [s_[:2], s_[1:2], s_[3:], s_[3::2],
                      s_[8:3:-1], s_[4::-2], s_[:5:-1],
                      0, 1, s_[:], s_[1:5], -1, -2, -5,
                      array(-1), np.int8(-3)]

            for j, a in enumerate(slices):
                A[a] = j
                B[a] = j
                assert_array_equal(A.todense(), B, repr(a))

            for i, a in enumerate(slices):
                for j, b in enumerate(slices):
                    A[a,b] = 10*i + 1000*(j+1)
                    B[a,b] = 10*i + 1000*(j+1)
                    assert_array_equal(A.todense(), B, repr((a, b)))

            A[0, 1:10:2] = xrange(1,10,2)
            B[0, 1:10:2] = xrange(1,10,2)
            assert_array_equal(A.todense(), B)
            A[1:5:2,0] = np.array(range(1,5,2))[:,None]
            B[1:5:2,0] = np.array(range(1,5,2))[:,None]
            assert_array_equal(A.todense(), B)

            # The next commands should raise exceptions
            assert_raises(ValueError, A.__setitem__, (0, 0), list(range(100)))
            assert_raises(ValueError, A.__setitem__, (0, 0), arange(100))
            assert_raises(ValueError, A.__setitem__, (0, slice(None)),
                          list(range(100)))
            assert_raises(ValueError, A.__setitem__, (slice(None), 1),
                          list(range(100)))
            assert_raises(ValueError, A.__setitem__, (slice(None), 1), A.copy())
            assert_raises(ValueError, A.__setitem__,
                          ([[1, 2, 3], [0, 3, 4]], [1, 2, 3]), [1, 2, 3, 4])
            assert_raises(ValueError, A.__setitem__,
                          ([[1, 2, 3], [0, 3, 4], [4, 1, 3]],
                           [[1, 2, 4], [0, 1, 3]]), [2, 3, 4])


class _TestFancyIndexing:
    """Tests fancy indexing features.  The tests for any matrix formats
    that implement these features should derive from this class.
    """

    def test_bad_index(self):
        A = self.spmatrix(np.zeros([5, 5]))
        assert_raises((IndexError, ValueError, TypeError), A.__getitem__, "foo")
        assert_raises((IndexError, ValueError, TypeError), A.__getitem__, (2, "foo"))
        assert_raises((IndexError, ValueError), A.__getitem__,
                      ([1, 2, 3], [1, 2, 3, 4]))

    def test_fancy_indexing(self):
        B = asmatrix(arange(50).reshape(5,10))
        A = self.spmatrix(B)

        # [i]
        assert_equal(A[[1,3]].todense(), B[[1,3]])

        # [i,[1,2]]
        assert_equal(A[3,[1,3]].todense(), B[3,[1,3]])
        assert_equal(A[-1,[2,-5]].todense(),B[-1,[2,-5]])
        assert_equal(A[array(-1),[2,-5]].todense(),B[-1,[2,-5]])
        assert_equal(A[-1,array([2,-5])].todense(),B[-1,[2,-5]])
        assert_equal(A[array(-1),array([2,-5])].todense(),B[-1,[2,-5]])

        # [1:2,[1,2]]
        assert_equal(A[:,[2,8,3,-1]].todense(),B[:,[2,8,3,-1]])
        assert_equal(A[3:4,[9]].todense(), B[3:4,[9]])
        assert_equal(A[1:4,[-1,-5]].todense(), B[1:4,[-1,-5]])
        assert_equal(A[1:4,array([-1,-5])].todense(), B[1:4,[-1,-5]])

        # [[1,2],j]
        assert_equal(A[[1,3],3].todense(), B[[1,3],3])
        assert_equal(A[[2,-5],-4].todense(), B[[2,-5],-4])
        assert_equal(A[array([2,-5]),-4].todense(), B[[2,-5],-4])
        assert_equal(A[[2,-5],array(-4)].todense(), B[[2,-5],-4])
        assert_equal(A[array([2,-5]),array(-4)].todense(), B[[2,-5],-4])

        # [[1,2],1:2]
        assert_equal(A[[1,3],:].todense(), B[[1,3],:])
        assert_equal(A[[2,-5],8:-1].todense(),B[[2,-5],8:-1])
        assert_equal(A[array([2,-5]),8:-1].todense(),B[[2,-5],8:-1])

        # [[1,2],[1,2]]
        assert_equal(todense(A[[1,3],[2,4]]), B[[1,3],[2,4]])
        assert_equal(todense(A[[-1,-3],[2,-4]]), B[[-1,-3],[2,-4]])
        assert_equal(todense(A[array([-1,-3]),[2,-4]]), B[[-1,-3],[2,-4]])
        assert_equal(todense(A[[-1,-3],array([2,-4])]), B[[-1,-3],[2,-4]])
        assert_equal(todense(A[array([-1,-3]),array([2,-4])]), B[[-1,-3],[2,-4]])

        # [[[1],[2]],[1,2]]
        assert_equal(A[[[1],[3]],[2,4]].todense(), B[[[1],[3]],[2,4]])
        assert_equal(A[[[-1],[-3],[-2]],[2,-4]].todense(),B[[[-1],[-3],[-2]],[2,-4]])
        assert_equal(A[array([[-1],[-3],[-2]]),[2,-4]].todense(),B[[[-1],[-3],[-2]],[2,-4]])
        assert_equal(A[[[-1],[-3],[-2]],array([2,-4])].todense(),B[[[-1],[-3],[-2]],[2,-4]])
        assert_equal(A[array([[-1],[-3],[-2]]),array([2,-4])].todense(),B[[[-1],[-3],[-2]],[2,-4]])

        # [[1,2]]
        assert_equal(A[[1,3]].todense(), B[[1,3]])
        assert_equal(A[[-1,-3]].todense(),B[[-1,-3]])
        assert_equal(A[array([-1,-3])].todense(),B[[-1,-3]])

        # [[1,2],:][:,[1,2]]
        assert_equal(A[[1,3],:][:,[2,4]].todense(), B[[1,3],:][:,[2,4]])
        assert_equal(A[[-1,-3],:][:,[2,-4]].todense(), B[[-1,-3],:][:,[2,-4]])
        assert_equal(A[array([-1,-3]),:][:,array([2,-4])].todense(), B[[-1,-3],:][:,[2,-4]])

        # [:,[1,2]][[1,2],:]
        assert_equal(A[:,[1,3]][[2,4],:].todense(), B[:,[1,3]][[2,4],:])
        assert_equal(A[:,[-1,-3]][[2,-4],:].todense(), B[:,[-1,-3]][[2,-4],:])
        assert_equal(A[:,array([-1,-3])][array([2,-4]),:].todense(), B[:,[-1,-3]][[2,-4],:])

        # Check bug reported by Robert Cimrman:
        # http://thread.gmane.org/gmane.comp.python.scientific.devel/7986
        s = slice(int8(2),int8(4),None)
        assert_equal(A[s,:].todense(), B[2:4,:])
        assert_equal(A[:,s].todense(), B[:,2:4])

    def test_fancy_indexing_randomized(self):
        np.random.seed(1234)  # make runs repeatable

        NUM_SAMPLES = 50
        M = 6
        N = 4

        D = np.asmatrix(np.random.rand(M,N))
        D = np.multiply(D, D > 0.5)

        I = np.random.randint(-M + 1, M, size=NUM_SAMPLES)
        J = np.random.randint(-N + 1, N, size=NUM_SAMPLES)

        S = self.spmatrix(D)

        SIJ = S[I,J]
        if isspmatrix(SIJ):
            SIJ = SIJ.todense()
        assert_equal(SIJ, D[I,J])

        I_bad = I + M
        J_bad = J - N

        assert_raises(IndexError, S.__getitem__, (I_bad,J))
        assert_raises(IndexError, S.__getitem__, (I,J_bad))

    def test_fancy_indexing_boolean(self):
        np.random.seed(1234)  # make runs repeatable

        B = asmatrix(arange(50).reshape(5,10))
        A = self.spmatrix(B)

        I = np.array(np.random.randint(0, 2, size=5), dtype=bool)
        J = np.array(np.random.randint(0, 2, size=10), dtype=bool)
        X = np.array(np.random.randint(0, 2, size=(5, 10)), dtype=bool)

        assert_equal(todense(A[I]), B[I])
        assert_equal(todense(A[:,J]), B[:, J])
        assert_equal(todense(A[X]), B[X])
        assert_equal(todense(A[B > 9]), B[B > 9])

        I = np.array([True, False, True, True, False])
        J = np.array([False, True, True, False, True,
                      False, False, False, False, False])

        assert_equal(todense(A[I, J]), B[I, J])

        Z1 = np.zeros((6, 11), dtype=bool)
        Z2 = np.zeros((6, 11), dtype=bool)
        Z2[0,-1] = True
        Z3 = np.zeros((6, 11), dtype=bool)
        Z3[-1,0] = True

        assert_equal(A[Z1], np.array([]))
        assert_raises(IndexError, A.__getitem__, Z2)
        assert_raises(IndexError, A.__getitem__, Z3)
        assert_raises((IndexError, ValueError), A.__getitem__, (X, 1))

    def test_fancy_indexing_sparse_boolean(self):
        np.random.seed(1234)  # make runs repeatable

        B = asmatrix(arange(50).reshape(5,10))
        A = self.spmatrix(B)

        X = np.array(np.random.randint(0, 2, size=(5, 10)), dtype=bool)

        Xsp = csr_matrix(X)

        assert_equal(todense(A[Xsp]), B[X])
        assert_equal(todense(A[A > 9]), B[B > 9])

        Z = np.array(np.random.randint(0, 2, size=(5, 11)), dtype=bool)
        Y = np.array(np.random.randint(0, 2, size=(6, 10)), dtype=bool)

        Zsp = csr_matrix(Z)
        Ysp = csr_matrix(Y)

        assert_raises(IndexError, A.__getitem__, Zsp)
        assert_raises(IndexError, A.__getitem__, Ysp)
        assert_raises((IndexError, ValueError), A.__getitem__, (Xsp, 1))

    def test_fancy_indexing_regression_3087(self):
        mat = self.spmatrix(array([[1, 0, 0], [0,1,0], [1,0,0]]))
        desired_cols = np.ravel(mat.sum(0)) > 0
        assert_equal(mat[:, desired_cols].A, [[1, 0], [0, 1], [1, 0]])

    def test_fancy_indexing_seq_assign(self):
        mat = self.spmatrix(array([[1, 0], [0, 1]]))
        assert_raises(ValueError, mat.__setitem__, (0, 0), np.array([1,2]))

    def test_fancy_indexing_empty(self):
        B = asmatrix(arange(50).reshape(5,10))
        B[1,:] = 0
        B[:,2] = 0
        B[3,6] = 0
        A = self.spmatrix(B)

        K = np.array([False, False, False, False, False])
        assert_equal(todense(A[K]), B[K])
        K = np.array([], dtype=int)
        assert_equal(todense(A[K]), B[K])
        assert_equal(todense(A[K,K]), B[K,K])
        J = np.array([0, 1, 2, 3, 4], dtype=int)[:,None]
        assert_equal(todense(A[K,J]), B[K,J])
        assert_equal(todense(A[J,K]), B[J,K])


@contextlib.contextmanager
def check_remains_sorted(X):
    """Checks that sorted indices property is retained through an operation
    """
    if not hasattr(X, 'has_sorted_indices') or not X.has_sorted_indices:
        yield
        return
    yield
    indices = X.indices.copy()
    X.has_sorted_indices = False
    X.sort_indices()
    assert_array_equal(indices, X.indices,
                       'Expected sorted indices, found unsorted')


class _TestFancyIndexingAssign:
    def test_bad_index_assign(self):
        with warnings.catch_warnings():
            warnings.simplefilter("ignore", category=SparseEfficiencyWarning)
            A = self.spmatrix(np.zeros([5, 5]))
            assert_raises((IndexError, ValueError, TypeError), A.__setitem__, "foo", 2)
            assert_raises((IndexError, ValueError, TypeError), A.__setitem__, (2, "foo"), 5)

    def test_fancy_indexing_set(self):
        n, m = (5, 10)

        def _test_set_slice(i, j):
            A = self.spmatrix((n, m))
            with check_remains_sorted(A):
                A[i, j] = 1
            B = asmatrix(np.zeros((n, m)))
            B[i, j] = 1
            assert_array_almost_equal(A.todense(), B)
        # [1:2,1:2]
        with warnings.catch_warnings():
            warnings.simplefilter("ignore", category=SparseEfficiencyWarning)
            for i, j in [((2, 3, 4), slice(None, 10, 4)),
                         (np.arange(3), slice(5, -2)),
                         (slice(2, 5), slice(5, -2))]:
                _test_set_slice(i, j)
            for i, j in [(np.arange(3), np.arange(3)), ((0, 3, 4), (1, 2, 4))]:
                _test_set_slice(i, j)

    def test_fancy_assignment_dtypes(self):
        def check(dtype):
            A = self.spmatrix((5, 5), dtype=dtype)
            A[[0,1],[0,1]] = dtype.type(1)
            assert_equal(A.sum(), dtype.type(1)*2)
            A[0:2,0:2] = dtype.type(1.0)
            assert_equal(A.sum(), dtype.type(1)*4)
            A[2,2] = dtype.type(1.0)
            assert_equal(A.sum(), dtype.type(1)*4 + dtype.type(1))

        for dtype in supported_dtypes:
            yield check, np.dtype(dtype)

    def test_sequence_assignment(self):
        with warnings.catch_warnings():
            warnings.simplefilter("ignore", category=SparseEfficiencyWarning)
            A = self.spmatrix((4,3))
            B = self.spmatrix(eye(3,4))

            i0 = [0,1,2]
            i1 = (0,1,2)
            i2 = array(i0)

            with check_remains_sorted(A):
                A[0,i0] = B[i0,0].T
                A[1,i1] = B[i1,1].T
                A[2,i2] = B[i2,2].T
            assert_array_equal(A.todense(),B.T.todense())

            # column slice
            A = self.spmatrix((2,3))
            with check_remains_sorted(A):
                A[1,1:3] = [10,20]
            assert_array_equal(A.todense(), [[0,0,0],[0,10,20]])

            # row slice
            A = self.spmatrix((3,2))
            with check_remains_sorted(A):
                A[1:3,1] = [[10],[20]]
            assert_array_equal(A.todense(), [[0,0],[0,10],[0,20]])

            # both slices
            A = self.spmatrix((3,3))
            B = asmatrix(np.zeros((3,3)))
            with check_remains_sorted(A):
                for C in [A, B]:
                    C[[0,1,2], [0,1,2]] = [4,5,6]
            assert_array_equal(A.toarray(), B)

            # both slices (2)
            A = self.spmatrix((4, 3))
            with check_remains_sorted(A):
                A[(1, 2, 3), (0, 1, 2)] = [1, 2, 3]
            assert_almost_equal(A.sum(), 6)
            B = asmatrix(np.zeros((4, 3)))
            B[(1, 2, 3), (0, 1, 2)] = [1, 2, 3]
            assert_array_equal(A.todense(), B)

    def test_fancy_assign_empty(self):
        B = asmatrix(arange(50).reshape(5,10))
        B[1,:] = 0
        B[:,2] = 0
        B[3,6] = 0
        A = self.spmatrix(B)

        K = np.array([False, False, False, False, False])
        A[K] = 42
        assert_equal(todense(A), B)

        K = np.array([], dtype=int)
        A[K] = 42
        assert_equal(todense(A), B)
        A[K,K] = 42
        assert_equal(todense(A), B)

        J = np.array([0, 1, 2, 3, 4], dtype=int)[:,None]
        A[K,J] = 42
        assert_equal(todense(A), B)
        A[J,K] = 42
        assert_equal(todense(A), B)


class _TestFancyMultidim:
    def test_fancy_indexing_ndarray(self):
        sets = [
            (np.array([[1], [2], [3]]), np.array([3, 4, 2])),
            (np.array([[1], [2], [3]]), np.array([[3, 4, 2]])),
            (np.array([[1, 2, 3]]), np.array([[3], [4], [2]])),
            (np.array([1, 2, 3]), np.array([[3], [4], [2]])),
            (np.array([[1, 2, 3], [3, 4, 2]]),
             np.array([[5, 6, 3], [2, 3, 1]]))
            ]
        # These inputs generate 3-D outputs
        #    (np.array([[[1], [2], [3]], [[3], [4], [2]]]),
        #     np.array([[[5], [6], [3]], [[2], [3], [1]]])),

        for I, J in sets:
            np.random.seed(1234)
            D = np.asmatrix(np.random.rand(5, 7))
            S = self.spmatrix(D)

            SIJ = S[I,J]
            if isspmatrix(SIJ):
                SIJ = SIJ.todense()
            assert_equal(SIJ, D[I,J])

            I_bad = I + 5
            J_bad = J + 7

            assert_raises(IndexError, S.__getitem__, (I_bad,J))
            assert_raises(IndexError, S.__getitem__, (I,J_bad))

            # This would generate 3-D arrays -- not supported
            assert_raises(IndexError, S.__getitem__, ([I, I], slice(None)))
            assert_raises(IndexError, S.__getitem__, (slice(None), [J, J]))


class _TestFancyMultidimAssign:
    def test_fancy_assign_ndarray(self):
        np.random.seed(1234)

        D = np.asmatrix(np.random.rand(5, 7))
        S = self.spmatrix(D)
        X = np.random.rand(2, 3)

        I = np.array([[1, 2, 3], [3, 4, 2]])
        J = np.array([[5, 6, 3], [2, 3, 1]])

        with check_remains_sorted(S):
            S[I,J] = X
        D[I,J] = X
        assert_equal(S.todense(), D)

        I_bad = I + 5
        J_bad = J + 7

        C = [1, 2, 3]

        with check_remains_sorted(S):
            S[I,J] = C
        D[I,J] = C
        assert_equal(S.todense(), D)

        with check_remains_sorted(S):
            S[I,J] = 3
        D[I,J] = 3
        assert_equal(S.todense(), D)

        assert_raises(IndexError, S.__setitem__, (I_bad,J), C)
        assert_raises(IndexError, S.__setitem__, (I,J_bad), C)

    def test_fancy_indexing_multidim_set(self):
        n, m = (5, 10)

        def _test_set_slice(i, j):
            A = self.spmatrix((n, m))
            with check_remains_sorted(A):
                A[i, j] = 1
            B = asmatrix(np.zeros((n, m)))
            B[i, j] = 1
            assert_array_almost_equal(A.todense(), B)
        # [[[1, 2], [1, 2]], [1, 2]]
        with warnings.catch_warnings():
            warnings.simplefilter("ignore", category=SparseEfficiencyWarning)
            for i, j in [(np.array([[1, 2], [1, 3]]), [1, 3]),
                            (np.array([0, 4]), [[0, 3], [1, 2]]),
                            ([[1, 2, 3], [0, 2, 4]], [[0, 4, 3], [4, 1, 2]])]:
                _test_set_slice(i, j)

    def test_fancy_assign_list(self):
        np.random.seed(1234)

        D = np.asmatrix(np.random.rand(5, 7))
        S = self.spmatrix(D)
        X = np.random.rand(2, 3)

        I = [[1, 2, 3], [3, 4, 2]]
        J = [[5, 6, 3], [2, 3, 1]]

        S[I,J] = X
        D[I,J] = X
        assert_equal(S.todense(), D)

        I_bad = [[ii + 5 for ii in i] for i in I]
        J_bad = [[jj + 7 for jj in j] for j in J]
        C = [1, 2, 3]

        S[I,J] = C
        D[I,J] = C
        assert_equal(S.todense(), D)

        S[I,J] = 3
        D[I,J] = 3
        assert_equal(S.todense(), D)

        assert_raises(IndexError, S.__setitem__, (I_bad,J), C)
        assert_raises(IndexError, S.__setitem__, (I,J_bad), C)

    def test_fancy_assign_slice(self):
        np.random.seed(1234)

        D = np.asmatrix(np.random.rand(5, 7))
        S = self.spmatrix(D)

        I = [[1, 2, 3], [3, 4, 2]]
        J = [[5, 6, 3], [2, 3, 1]]

        I_bad = [[ii + 5 for ii in i] for i in I]
        J_bad = [[jj + 7 for jj in j] for j in J]

        C = [1, 2, 3, 4, 5, 6, 7]
        assert_raises(IndexError, S.__setitem__, (I_bad, slice(None)), C)
        assert_raises(IndexError, S.__setitem__, (slice(None), J_bad), C)


class _TestArithmetic:
    """
    Test real/complex arithmetic
    """
    def __arith_init(self):
        # these can be represented exactly in FP (so arithmetic should be exact)
        self.__A = matrix([[-1.5, 6.5, 0, 2.25, 0, 0],
                         [3.125, -7.875, 0.625, 0, 0, 0],
                         [0, 0, -0.125, 1.0, 0, 0],
                         [0, 0, 8.375, 0, 0, 0]],'float64')
        self.__B = matrix([[0.375, 0, 0, 0, -5, 2.5],
                         [14.25, -3.75, 0, 0, -0.125, 0],
                         [0, 7.25, 0, 0, 0, 0],
                         [18.5, -0.0625, 0, 0, 0, 0]],'complex128')
        self.__B.imag = matrix([[1.25, 0, 0, 0, 6, -3.875],
                              [2.25, 4.125, 0, 0, 0, 2.75],
                              [0, 4.125, 0, 0, 0, 0],
                              [-0.0625, 0, 0, 0, 0, 0]],'float64')

        # fractions are all x/16ths
        assert_array_equal((self.__A*16).astype('int32'),16*self.__A)
        assert_array_equal((self.__B.real*16).astype('int32'),16*self.__B.real)
        assert_array_equal((self.__B.imag*16).astype('int32'),16*self.__B.imag)

        self.__Asp = self.spmatrix(self.__A)
        self.__Bsp = self.spmatrix(self.__B)

    def test_add_sub(self):
        self.__arith_init()

        # basic tests
        assert_array_equal((self.__Asp+self.__Bsp).todense(),self.__A+self.__B)

        # check conversions
        for x in supported_dtypes:
            A = self.__A.astype(x)
            Asp = self.spmatrix(A)
            for y in supported_dtypes:
                if not np.issubdtype(y, np.complexfloating):
                    B = self.__B.real.astype(y)
                else:
                    B = self.__B.astype(y)
                Bsp = self.spmatrix(B)

                # addition
                D1 = A + B
                S1 = Asp + Bsp

                assert_equal(S1.dtype,D1.dtype)
                assert_array_equal(S1.todense(),D1)
                assert_array_equal(Asp + B,D1)          # check sparse + dense
                assert_array_equal(A + Bsp,D1)          # check dense + sparse

                # subtraction
                if (np.dtype('bool') in [x, y]) and (
                        NumpyVersion(np.__version__) >= '1.9.0.dev'):
                    # boolean array subtraction deprecated in 1.9.0
                    continue

                D1 = A - B
                S1 = Asp - Bsp

                assert_equal(S1.dtype,D1.dtype)
                assert_array_equal(S1.todense(),D1)
                assert_array_equal(Asp - B,D1)          # check sparse - dense
                assert_array_equal(A - Bsp,D1)          # check dense - sparse

    def test_mu(self):
        self.__arith_init()

        # basic tests
        assert_array_equal((self.__Asp*self.__Bsp.T).todense(),self.__A*self.__B.T)

        for x in supported_dtypes:
            A = self.__A.astype(x)
            Asp = self.spmatrix(A)
            for y in supported_dtypes:
                if np.issubdtype(y, np.complexfloating):
                    B = self.__B.astype(y)
                else:
                    B = self.__B.real.astype(y)
                Bsp = self.spmatrix(B)

                D1 = A * B.T
                S1 = Asp * Bsp.T

                assert_allclose(S1.todense(), D1,
                                atol=1e-14*abs(D1).max())
                assert_equal(S1.dtype,D1.dtype)


class _TestMinMax(object):
    def test_minmax(self):
        for dtype in [np.float32, np.float64, np.int32, np.int64, np.complex128]:
            D = np.arange(20, dtype=dtype).reshape(5,4)

            X = self.spmatrix(D)
            assert_equal(X.min(), 0)
            assert_equal(X.max(), 19)
            assert_equal(X.min().dtype, dtype)
            assert_equal(X.max().dtype, dtype)

            D *= -1
            X = self.spmatrix(D)
            assert_equal(X.min(), -19)
            assert_equal(X.max(), 0)

            D += 5
            X = self.spmatrix(D)
            assert_equal(X.min(), -14)
            assert_equal(X.max(), 5)

        # try a fully dense matrix
        X = self.spmatrix(np.arange(1, 10).reshape(3, 3))
        assert_equal(X.min(), 1)
        assert_equal(X.min().dtype, X.dtype)

        X = -X
        assert_equal(X.max(), -1)

        # and a fully sparse matrix
        Z = self.spmatrix(np.zeros(1))
        assert_equal(Z.min(), 0)
        assert_equal(Z.max(), 0)
        assert_equal(Z.max().dtype, Z.dtype)

        # another test
        D = np.arange(20, dtype=float).reshape(5,4)
        D[0:2, :] = 0
        X = self.spmatrix(D)
        assert_equal(X.min(), 0)
        assert_equal(X.max(), 19)

        # zero-size matrices
        for D in [np.zeros((0, 0)), np.zeros((0, 10)), np.zeros((10, 0))]:
            X = self.spmatrix(D)
            assert_raises(ValueError, X.min)
            assert_raises(ValueError, X.max)

    def test_minmax_axis(self):
        D = np.matrix(np.arange(50).reshape(5,10))
        # completely empty rows, leaving some completely full:
        D[1, :] = 0
        # empty at end for reduceat:
        D[:, 9] = 0
        # partial rows/cols:
        D[3, 3] = 0
        # entries on either side of 0:
        D[2, 2] = -1
        X = self.spmatrix(D)

        axes = [-2, -1, 0, 1]
        for axis in axes:
            assert_array_equal(X.max(axis=axis).A, D.max(axis=axis).A)
            assert_array_equal(X.min(axis=axis).A, D.min(axis=axis).A)

        # full matrix
        D = np.matrix(np.arange(1, 51).reshape(10, 5))
        X = self.spmatrix(D)
        for axis in axes:
            assert_array_equal(X.max(axis=axis).A, D.max(axis=axis).A)
            assert_array_equal(X.min(axis=axis).A, D.min(axis=axis).A)

        # empty matrix
        D = np.matrix(np.zeros((10, 5)))
        X = self.spmatrix(D)
        for axis in axes:
            assert_array_equal(X.max(axis=axis).A, D.max(axis=axis).A)
            assert_array_equal(X.min(axis=axis).A, D.min(axis=axis).A)

        axes_even = [0, -2]
        axes_odd = [1, -1]

        # zero-size matrices
        D = np.zeros((0, 10))
        X = self.spmatrix(D)
        for axis in axes_even:
            assert_raises(ValueError, X.min, axis=axis)
            assert_raises(ValueError, X.max, axis=axis)
        for axis in axes_odd:
            assert_array_equal(np.zeros((0, 1)), X.min(axis=axis).A)
            assert_array_equal(np.zeros((0, 1)), X.max(axis=axis).A)

        D = np.zeros((10, 0))
        X = self.spmatrix(D)
        for axis in axes_odd:
            assert_raises(ValueError, X.min, axis=axis)
            assert_raises(ValueError, X.max, axis=axis)
        for axis in axes_even:
            assert_array_equal(np.zeros((1, 0)), X.min(axis=axis).A)
            assert_array_equal(np.zeros((1, 0)), X.max(axis=axis).A)

    def test_minmax_invalid_params(self):
        dat = np.matrix([[0, 1, 2],
                         [3, -4, 5],
                         [-6, 7, 9]])
        datsp = self.spmatrix(dat)

        for fname in ('min', 'max'):
            func = getattr(datsp, fname)
            assert_raises(ValueError, func, axis=3)
            assert_raises(TypeError, func, axis=(0, 1))
            assert_raises(TypeError, func, axis=1.5)
            assert_raises(ValueError, func, axis=1, out=1)

    def test_numpy_minmax(self):
        # See gh-5987
        # xref gh-7460 in 'numpy'
        from scipy.sparse import data

        dat = np.matrix([[0, 1, 2],
                         [3, -4, 5],
                         [-6, 7, 9]])
        datsp = self.spmatrix(dat)

        # We are only testing sparse matrices who have
        # implemented 'min' and 'max' because they are
        # the ones with the compatibility issues with
        # the 'numpy' implementation.
        if isinstance(datsp, data._minmax_mixin):
            assert_array_equal(np.min(datsp), np.min(dat))
            assert_array_equal(np.max(datsp), np.max(dat))


class _TestGetNnzAxis(object):
    def test_getnnz_axis(self):
        dat = np.matrix([[0, 2],
                        [3, 5],
                        [-6, 9]])
        bool_dat = dat.astype(bool).A
        datsp = self.spmatrix(dat)

        accepted_return_dtypes = (np.int32, np.int64)

        assert_array_equal(bool_dat.sum(axis=None), datsp.getnnz(axis=None))
        assert_array_equal(bool_dat.sum(), datsp.getnnz())
        assert_array_equal(bool_dat.sum(axis=0), datsp.getnnz(axis=0))
        assert_in(datsp.getnnz(axis=0).dtype, accepted_return_dtypes)
        assert_array_equal(bool_dat.sum(axis=1), datsp.getnnz(axis=1))
        assert_in(datsp.getnnz(axis=1).dtype, accepted_return_dtypes)
        assert_array_equal(bool_dat.sum(axis=-2), datsp.getnnz(axis=-2))
        assert_in(datsp.getnnz(axis=-2).dtype, accepted_return_dtypes)
        assert_array_equal(bool_dat.sum(axis=-1), datsp.getnnz(axis=-1))
        assert_in(datsp.getnnz(axis=-1).dtype, accepted_return_dtypes)

        assert_raises(ValueError, datsp.getnnz, axis=2)


#------------------------------------------------------------------------------
# Tailored base class for generic tests
#------------------------------------------------------------------------------

def _possibly_unimplemented(cls, require=True):
    """
    Construct a class that either runs tests as usual (require=True),
    or each method raises SkipTest if it encounters a common error.
    """
    if require:
        return cls
    else:
        def wrap(fc):
            def wrapper(*a, **kw):
                try:
                    return fc(*a, **kw)
                except (NotImplementedError, TypeError, ValueError,
                        IndexError, AttributeError):
                    raise nose.SkipTest("feature not implemented")

            wrapper.__name__ = fc.__name__
            return wrapper

        new_dict = dict(cls.__dict__)
        for name, func in cls.__dict__.items():
            if name.startswith('test_'):
                new_dict[name] = wrap(func)
        return type(cls.__name__ + "NotImplemented",
                    cls.__bases__,
                    new_dict)


def sparse_test_class(getset=True, slicing=True, slicing_assign=True,
                      fancy_indexing=True, fancy_assign=True,
                      fancy_multidim_indexing=True, fancy_multidim_assign=True,
                      minmax=True, nnz_axis=True):
    """
    Construct a base class, optionally converting some of the tests in
    the suite to check that the feature is not implemented.
    """
    bases = (_TestCommon,
             _possibly_unimplemented(_TestGetSet, getset),
             _TestSolve,
             _TestInplaceArithmetic,
             _TestArithmetic,
             _possibly_unimplemented(_TestSlicing, slicing),
             _possibly_unimplemented(_TestSlicingAssign, slicing_assign),
             _possibly_unimplemented(_TestFancyIndexing, fancy_indexing),
             _possibly_unimplemented(_TestFancyIndexingAssign,
                                     fancy_assign),
             _possibly_unimplemented(_TestFancyMultidim,
                                     fancy_indexing and fancy_multidim_indexing),
             _possibly_unimplemented(_TestFancyMultidimAssign,
                                     fancy_multidim_assign and fancy_assign),
             _possibly_unimplemented(_TestMinMax, minmax),
             _possibly_unimplemented(_TestGetNnzAxis, nnz_axis))

    # check that test names do not clash
    names = {}
    for cls in bases:
        for name in cls.__dict__:
            if not name.startswith('test_'):
                continue
            old_cls = names.get(name)
            if old_cls is not None:
                raise ValueError("Test class %s overloads test %s defined in %s" % (
                    cls.__name__, name, old_cls.__name__))
            names[name] = cls

    return type("TestBase", bases, {})


#------------------------------------------------------------------------------
# Matrix class based tests
#------------------------------------------------------------------------------

class TestCSR(sparse_test_class()):
    spmatrix = csr_matrix
    math_dtypes = [np.bool_, np.int_, np.float_, np.complex_]

    def test_constructor1(self):
        b = matrix([[0,4,0],
                   [3,0,0],
                   [0,2,0]],'d')
        bsp = csr_matrix(b)
        assert_array_almost_equal(bsp.data,[4,3,2])
        assert_array_equal(bsp.indices,[1,0,1])
        assert_array_equal(bsp.indptr,[0,1,2,3])
        assert_equal(bsp.getnnz(),3)
        assert_equal(bsp.getformat(),'csr')
        assert_array_equal(bsp.todense(),b)

    def test_constructor2(self):
        b = zeros((6,6),'d')
        b[3,4] = 5
        bsp = csr_matrix(b)
        assert_array_almost_equal(bsp.data,[5])
        assert_array_equal(bsp.indices,[4])
        assert_array_equal(bsp.indptr,[0,0,0,0,1,1,1])
        assert_array_almost_equal(bsp.todense(),b)

    def test_constructor3(self):
        b = matrix([[1,0],
                   [0,2],
                   [3,0]],'d')
        bsp = csr_matrix(b)
        assert_array_almost_equal(bsp.data,[1,2,3])
        assert_array_equal(bsp.indices,[0,1,0])
        assert_array_equal(bsp.indptr,[0,1,2,3])
        assert_array_almost_equal(bsp.todense(),b)

### currently disabled
##    def test_constructor4(self):
##        """try using int64 indices"""
##        data = arange( 6 ) + 1
##        col = array( [1, 2, 1, 0, 0, 2], dtype='int64' )
##        ptr = array( [0, 2, 4, 6], dtype='int64' )
##
##        a = csr_matrix( (data, col, ptr), shape = (3,3) )
##
##        b = matrix([[0,1,2],
##                    [4,3,0],
##                    [5,0,6]],'d')
##
##        assert_equal(a.indptr.dtype,numpy.dtype('int64'))
##        assert_equal(a.indices.dtype,numpy.dtype('int64'))
##        assert_array_equal(a.todense(),b)

    def test_constructor4(self):
        # using (data, ij) format
        row = array([2, 3, 1, 3, 0, 1, 3, 0, 2, 1, 2])
        col = array([0, 1, 0, 0, 1, 1, 2, 2, 2, 2, 1])
        data = array([6., 10., 3., 9., 1., 4.,
                              11., 2., 8., 5., 7.])

        ij = vstack((row,col))
        csr = csr_matrix((data,ij),(4,3))
        assert_array_equal(arange(12).reshape(4,3),csr.todense())

    def test_constructor5(self):
        # infer dimensions from arrays
        indptr = array([0,1,3,3])
        indices = array([0,5,1,2])
        data = array([1,2,3,4])
        csr = csr_matrix((data, indices, indptr))
        assert_array_equal(csr.shape,(3,6))

    def test_constructor6(self):
        # infer dimensions and dtype from lists
        indptr = [0, 1, 3, 3]
        indices = [0, 5, 1, 2]
        data = [1, 2, 3, 4]
        csr = csr_matrix((data, indices, indptr))
        assert_array_equal(csr.shape, (3,6))
        assert_(np.issubdtype(csr.dtype, int))

    def test_sort_indices(self):
        data = arange(5)
        indices = array([7, 2, 1, 5, 4])
        indptr = array([0, 3, 5])
        asp = csr_matrix((data, indices, indptr), shape=(2,10))
        bsp = asp.copy()
        asp.sort_indices()
        assert_array_equal(asp.indices,[1, 2, 7, 4, 5])
        assert_array_equal(asp.todense(),bsp.todense())

    def test_eliminate_zeros(self):
        data = array([1, 0, 0, 0, 2, 0, 3, 0])
        indices = array([1, 2, 3, 4, 5, 6, 7, 8])
        indptr = array([0, 3, 8])
        asp = csr_matrix((data, indices, indptr), shape=(2,10))
        bsp = asp.copy()
        asp.eliminate_zeros()
        assert_array_equal(asp.nnz, 3)
        assert_array_equal(asp.data,[1, 2, 3])
        assert_array_equal(asp.todense(),bsp.todense())

    def test_ufuncs(self):
        X = csr_matrix(np.arange(20).reshape(4, 5) / 20.)
        for f in ["sin", "tan", "arcsin", "arctan", "sinh", "tanh",
                  "arcsinh", "arctanh", "rint", "sign", "expm1", "log1p",
                  "deg2rad", "rad2deg", "floor", "ceil", "trunc", "sqrt"]:
            assert_equal(hasattr(csr_matrix, f), True)
            X2 = getattr(X, f)()
            assert_equal(X.shape, X2.shape)
            assert_array_equal(X.indices, X2.indices)
            assert_array_equal(X.indptr, X2.indptr)
            assert_array_equal(X2.toarray(), getattr(np, f)(X.toarray()))

    def test_unsorted_arithmetic(self):
        data = arange(5)
        indices = array([7, 2, 1, 5, 4])
        indptr = array([0, 3, 5])
        asp = csr_matrix((data, indices, indptr), shape=(2,10))
        data = arange(6)
        indices = array([8, 1, 5, 7, 2, 4])
        indptr = array([0, 2, 6])
        bsp = csr_matrix((data, indices, indptr), shape=(2,10))
        assert_equal((asp + bsp).todense(), asp.todense() + bsp.todense())

    def test_fancy_indexing_broadcast(self):
        # broadcasting indexing mode is supported
        I = np.array([[1], [2], [3]])
        J = np.array([3, 4, 2])

        np.random.seed(1234)
        D = np.asmatrix(np.random.rand(5, 7))
        S = self.spmatrix(D)

        SIJ = S[I,J]
        if isspmatrix(SIJ):
            SIJ = SIJ.todense()
        assert_equal(SIJ, D[I,J])

    def test_has_sorted_indices(self):
        "Ensure has_sorted_indices memoizes sorted state for sort_indices"
        sorted_inds = np.array([0, 1])
        unsorted_inds = np.array([1, 0])
        data = np.array([1, 1])
        indptr = np.array([0, 2])
        M = csr_matrix((data, sorted_inds, indptr)).copy()
        assert_equal(True, M.has_sorted_indices)

        M = csr_matrix((data, unsorted_inds, indptr)).copy()
        assert_equal(False, M.has_sorted_indices)

        # set by sorting
        M.sort_indices()
        assert_equal(True, M.has_sorted_indices)
        assert_array_equal(M.indices, sorted_inds)

        M = csr_matrix((data, unsorted_inds, indptr)).copy()
        # set manually (although underlyingly unsorted)
        M.has_sorted_indices = True
        assert_equal(True, M.has_sorted_indices)
        assert_array_equal(M.indices, unsorted_inds)

        # ensure sort bypassed when has_sorted_indices == True
        M.sort_indices()
        assert_array_equal(M.indices, unsorted_inds)

    def test_has_canonical_format(self):
        "Ensure has_canonical_format memoizes state for sum_duplicates"

        M = csr_matrix((np.array([2]), np.array([0]), np.array([0, 1])))
        assert_equal(True, M.has_canonical_format)

        indices = np.array([0, 0])  # contains duplicate
        data = np.array([1, 1])
        indptr = np.array([0, 2])

        M = csr_matrix((data, indices, indptr)).copy()
        assert_equal(False, M.has_canonical_format)

        # set by deduplicating
        M.sum_duplicates()
        assert_equal(True, M.has_canonical_format)
        assert_equal(1, len(M.indices))

        M = csr_matrix((data, indices, indptr)).copy()
        # set manually (although underlyingly duplicated)
        M.has_canonical_format = True
        assert_equal(True, M.has_canonical_format)
        assert_equal(2, len(M.indices))  # unaffected content

        # ensure deduplication bypassed when has_canonical_format == True
        M.sum_duplicates()
        assert_equal(2, len(M.indices))  # unaffected content

    def test_scalar_idx_dtype(self):
        # Check that index dtype takes into account all parameters
        # passed to sparsetools, including the scalar ones
        indptr = np.zeros(2, dtype=np.int32)
        indices = np.zeros(0, dtype=np.int32)
        vals = np.zeros(0)
        a = csr_matrix((vals, indices, indptr), shape=(1, 2**31-1))
        b = csr_matrix((vals, indices, indptr), shape=(1, 2**31))
        ij = np.zeros((2, 0), dtype=np.int32)
        c = csr_matrix((vals, ij), shape=(1, 2**31-1))
        d = csr_matrix((vals, ij), shape=(1, 2**31))
        e = csr_matrix((1, 2**31-1))
        f = csr_matrix((1, 2**31))
        assert_equal(a.indptr.dtype, np.int32)
        assert_equal(b.indptr.dtype, np.int64)
        assert_equal(c.indptr.dtype, np.int32)
        assert_equal(d.indptr.dtype, np.int64)
        assert_equal(e.indptr.dtype, np.int32)
        assert_equal(f.indptr.dtype, np.int64)

        # These shouldn't fail
        for x in [a, b, c, d, e, f]:
            x + x


class TestCSC(sparse_test_class()):
    spmatrix = csc_matrix
    math_dtypes = [np.bool_, np.int_, np.float_, np.complex_]

    def test_constructor1(self):
        b = matrix([[1,0,0,0],[0,0,1,0],[0,2,0,3]],'d')
        bsp = csc_matrix(b)
        assert_array_almost_equal(bsp.data,[1,2,1,3])
        assert_array_equal(bsp.indices,[0,2,1,2])
        assert_array_equal(bsp.indptr,[0,1,2,3,4])
        assert_equal(bsp.getnnz(),4)
        assert_equal(bsp.shape,b.shape)
        assert_equal(bsp.getformat(),'csc')

    def test_constructor2(self):
        b = zeros((6,6),'d')
        b[2,4] = 5
        bsp = csc_matrix(b)
        assert_array_almost_equal(bsp.data,[5])
        assert_array_equal(bsp.indices,[2])
        assert_array_equal(bsp.indptr,[0,0,0,0,0,1,1])

    def test_constructor3(self):
        b = matrix([[1,0],[0,0],[0,2]],'d')
        bsp = csc_matrix(b)
        assert_array_almost_equal(bsp.data,[1,2])
        assert_array_equal(bsp.indices,[0,2])
        assert_array_equal(bsp.indptr,[0,1,2])

    def test_constructor4(self):
        # using (data, ij) format
        row = array([2, 3, 1, 3, 0, 1, 3, 0, 2, 1, 2])
        col = array([0, 1, 0, 0, 1, 1, 2, 2, 2, 2, 1])
        data = array([6., 10., 3., 9., 1., 4.,
                              11., 2., 8., 5., 7.])

        ij = vstack((row,col))
        csc = csc_matrix((data,ij),(4,3))
        assert_array_equal(arange(12).reshape(4,3),csc.todense())

    def test_constructor5(self):
        # infer dimensions from arrays
        indptr = array([0,1,3,3])
        indices = array([0,5,1,2])
        data = array([1,2,3,4])
        csc = csc_matrix((data, indices, indptr))
        assert_array_equal(csc.shape,(6,3))

    def test_constructor6(self):
        # infer dimensions and dtype from lists
        indptr = [0, 1, 3, 3]
        indices = [0, 5, 1, 2]
        data = [1, 2, 3, 4]
        csc = csc_matrix((data, indices, indptr))
        assert_array_equal(csc.shape,(6,3))
        assert_(np.issubdtype(csc.dtype, int))

    def test_eliminate_zeros(self):
        data = array([1, 0, 0, 0, 2, 0, 3, 0])
        indices = array([1, 2, 3, 4, 5, 6, 7, 8])
        indptr = array([0, 3, 8])
        asp = csc_matrix((data, indices, indptr), shape=(10,2))
        bsp = asp.copy()
        asp.eliminate_zeros()
        assert_array_equal(asp.nnz, 3)
        assert_array_equal(asp.data,[1, 2, 3])
        assert_array_equal(asp.todense(),bsp.todense())

    def test_sort_indices(self):
        data = arange(5)
        row = array([7, 2, 1, 5, 4])
        ptr = [0, 3, 5]
        asp = csc_matrix((data, row, ptr), shape=(10,2))
        bsp = asp.copy()
        asp.sort_indices()
        assert_array_equal(asp.indices,[1, 2, 7, 4, 5])
        assert_array_equal(asp.todense(),bsp.todense())

    def test_ufuncs(self):
        X = csc_matrix(np.arange(21).reshape(7, 3) / 21.)
        for f in ["sin", "tan", "arcsin", "arctan", "sinh", "tanh",
                  "arcsinh", "arctanh", "rint", "sign", "expm1", "log1p",
                  "deg2rad", "rad2deg", "floor", "ceil", "trunc", "sqrt"]:
            assert_equal(hasattr(csr_matrix, f), True)
            X2 = getattr(X, f)()
            assert_equal(X.shape, X2.shape)
            assert_array_equal(X.indices, X2.indices)
            assert_array_equal(X.indptr, X2.indptr)
            assert_array_equal(X2.toarray(), getattr(np, f)(X.toarray()))

    def test_unsorted_arithmetic(self):
        data = arange(5)
        indices = array([7, 2, 1, 5, 4])
        indptr = array([0, 3, 5])
        asp = csc_matrix((data, indices, indptr), shape=(10,2))
        data = arange(6)
        indices = array([8, 1, 5, 7, 2, 4])
        indptr = array([0, 2, 6])
        bsp = csc_matrix((data, indices, indptr), shape=(10,2))
        assert_equal((asp + bsp).todense(), asp.todense() + bsp.todense())

    def test_fancy_indexing_broadcast(self):
        # broadcasting indexing mode is supported
        I = np.array([[1], [2], [3]])
        J = np.array([3, 4, 2])

        np.random.seed(1234)
        D = np.asmatrix(np.random.rand(5, 7))
        S = self.spmatrix(D)

        SIJ = S[I,J]
        if isspmatrix(SIJ):
            SIJ = SIJ.todense()
        assert_equal(SIJ, D[I,J])

    def test_scalar_idx_dtype(self):
        # Check that index dtype takes into account all parameters
        # passed to sparsetools, including the scalar ones
        indptr = np.zeros(2, dtype=np.int32)
        indices = np.zeros(0, dtype=np.int32)
        vals = np.zeros(0)
        a = csc_matrix((vals, indices, indptr), shape=(2**31-1, 1))
        b = csc_matrix((vals, indices, indptr), shape=(2**31, 1))
        ij = np.zeros((2, 0), dtype=np.int32)
        c = csc_matrix((vals, ij), shape=(2**31-1, 1))
        d = csc_matrix((vals, ij), shape=(2**31, 1))
        e = csr_matrix((1, 2**31-1))
        f = csr_matrix((1, 2**31))
        assert_equal(a.indptr.dtype, np.int32)
        assert_equal(b.indptr.dtype, np.int64)
        assert_equal(c.indptr.dtype, np.int32)
        assert_equal(d.indptr.dtype, np.int64)
        assert_equal(e.indptr.dtype, np.int32)
        assert_equal(f.indptr.dtype, np.int64)

        # These shouldn't fail
        for x in [a, b, c, d, e, f]:
            x + x


class TestDOK(sparse_test_class(minmax=False, nnz_axis=False)):
    spmatrix = dok_matrix
    math_dtypes = [np.int_, np.float_, np.complex_]

    def test_mult(self):
        A = dok_matrix((10,10))
        A[0,3] = 10
        A[5,6] = 20
        D = A*A.T
        E = A*A.H
        assert_array_equal(D.A, E.A)

    def test_add_nonzero(self):
        with warnings.catch_warnings():
            warnings.simplefilter("ignore", category=SparseEfficiencyWarning)
            A = self.spmatrix((3,2))
            A[0,1] = -10
            A[2,0] = 20
            A = A + 10
            B = matrix([[10, 0], [10, 10], [30, 10]])
            assert_array_equal(A.todense(), B)

            A = A + 1j
            B = B + 1j
            assert_array_equal(A.todense(), B)

    def test_dok_divide_scalar(self):
        A = self.spmatrix((3,2))
        A[0,1] = -10
        A[2,0] = 20

        assert_array_equal((A/1j).todense(), A.todense()/1j)
        assert_array_equal((A/9).todense(), A.todense()/9)

    def test_convert(self):
        # Test provided by Andrew Straw.  Fails in SciPy <= r1477.
        (m, n) = (6, 7)
        a = dok_matrix((m, n))

        # set a few elements, but none in the last column
        a[2,1] = 1
        a[0,2] = 2
        a[3,1] = 3
        a[1,5] = 4
        a[4,3] = 5
        a[4,2] = 6

        # assert that the last column is all zeros
        assert_array_equal(a.toarray()[:,n-1], zeros(m,))

        # make sure it still works for CSC format
        csc = a.tocsc()
        assert_array_equal(csc.toarray()[:,n-1], zeros(m,))

        # now test CSR
        (m, n) = (n, m)
        b = a.transpose()
        assert_equal(b.shape, (m, n))
        # assert that the last row is all zeros
        assert_array_equal(b.toarray()[m-1,:], zeros(n,))

        # make sure it still works for CSR format
        csr = b.tocsr()
        assert_array_equal(csr.toarray()[m-1,:], zeros(n,))

    def test_ctor(self):
        # Empty ctor
        assert_raises(TypeError, dok_matrix)

        # Dense ctor
        b = matrix([[1,0,0,0],[0,0,1,0],[0,2,0,3]],'d')
        A = dok_matrix(b)
        assert_equal(b.dtype, A.dtype)
        assert_equal(A.todense(), b)

        # Sparse ctor
        c = csr_matrix(b)
        assert_equal(A.todense(), c.todense())

        data = [[0, 1, 2], [3, 0, 0]]
        d = dok_matrix(data, dtype=np.float32)
        assert_equal(d.dtype, np.float32)
        da = d.toarray()
        assert_equal(da.dtype, np.float32)
        assert_array_equal(da, data)

    def test_resize(self):
        # A couple basic tests of the resize() method.
        #
        # resize(shape) resizes the array in-place.
        a = dok_matrix((5,5))
        a[:,0] = 1
        a.resize((2,2))
        expected1 = array([[1,0],[1,0]])
        assert_array_equal(a.todense(), expected1)
        a.resize((3,2))
        expected2 = array([[1,0],[1,0],[0,0]])
        assert_array_equal(a.todense(), expected2)

    def test_ticket1160(self):
        # Regression test for ticket #1160.
        a = dok_matrix((3,3))
        a[0,0] = 0
        # This assert would fail, because the above assignment would
        # incorrectly call __set_item__ even though the value was 0.
        assert_((0,0) not in a.keys(), "Unexpected entry (0,0) in keys")

        # Slice assignments were also affected.
        b = dok_matrix((3,3))
        b[:,0] = 0
        assert_(len(b.keys()) == 0, "Unexpected entries in keys")


class TestLIL(sparse_test_class(minmax=False)):
    spmatrix = lil_matrix
    math_dtypes = [np.int_, np.float_, np.complex_]

    def test_dot(self):
        A = matrix(zeros((10,10)))
        A[0,3] = 10
        A[5,6] = 20

        B = lil_matrix((10,10))
        B[0,3] = 10
        B[5,6] = 20
        assert_array_equal(A * A.T, (B * B.T).todense())
        assert_array_equal(A * A.H, (B * B.H).todense())

    def test_scalar_mul(self):
        x = lil_matrix((3,3))
        x[0,0] = 2

        x = x*2
        assert_equal(x[0,0],4)

        x = x*0
        assert_equal(x[0,0],0)

    def test_reshape(self):
        x = lil_matrix((4, 3))
        x[0, 0] = 1
        x[2, 1] = 3
        x[3, 2] = 5
        x[0, 2] = 7

        for s in [(12, 1), (1, 12)]:
            assert_array_equal(x.reshape(s).todense(),
                               x.todense().reshape(s))

            # LIL matrices are read/written in row-major order
            assert_array_equal(x.reshape(s, order='C').todense(),
                               x.todense().reshape(s, order='C'))

            # See gh-5987
            assert_array_equal(np.reshape(x, s).todense(),
                               np.reshape(x.todense(), s))

        assert_raises(TypeError, x.reshape, 2)
        assert_raises(ValueError, x.reshape, (1, 5, 3))
        assert_raises(ValueError, x.reshape, (1, 5))
        assert_raises(ValueError, x.reshape, (6, 2), order=2)
        assert_raises(ValueError, x.reshape, (6, 2), order='A')

    def test_inplace_ops(self):
        A = lil_matrix([[0,2,3],[4,0,6]])
        B = lil_matrix([[0,1,0],[0,2,3]])

        data = {'add': (B,A + B),
                'sub': (B,A - B),
                'mul': (3,A * 3)}

        for op,(other,expected) in data.items():
            result = A.copy()
            getattr(result, '__i%s__' % op)(other)

            assert_array_equal(result.todense(), expected.todense())

        # Ticket 1604.
        A = lil_matrix((1,3), dtype=np.dtype('float64'))
        B = array([0.1,0.1,0.1])
        A[0,:] += B
        assert_array_equal(A[0,:].toarray().squeeze(), B)

    def test_lil_iteration(self):
        row_data = [[1,2,3],[4,5,6]]
        B = lil_matrix(array(row_data))
        for r,row in enumerate(B):
            assert_array_equal(row.todense(),array(row_data[r],ndmin=2))

    def test_lil_from_csr(self):
        # Tests whether a lil_matrix can be constructed from a
        # csr_matrix.
        B = lil_matrix((10,10))
        B[0,3] = 10
        B[5,6] = 20
        B[8,3] = 30
        B[3,8] = 40
        B[8,9] = 50
        C = B.tocsr()
        D = lil_matrix(C)
        assert_array_equal(C.A, D.A)

    def test_fancy_indexing_lil(self):
        M = asmatrix(arange(25).reshape(5,5))
        A = lil_matrix(M)

        assert_equal(A[array([1,2,3]),2:3].todense(), M[array([1,2,3]),2:3])

    def test_point_wise_multiply(self):
        l = lil_matrix((4,3))
        l[0,0] = 1
        l[1,1] = 2
        l[2,2] = 3
        l[3,1] = 4

        m = lil_matrix((4,3))
        m[0,0] = 1
        m[0,1] = 2
        m[2,2] = 3
        m[3,1] = 4
        m[3,2] = 4

        assert_array_equal(l.multiply(m).todense(),
                           m.multiply(l).todense())

        assert_array_equal(l.multiply(m).todense(),
                           [[1,0,0],
                            [0,0,0],
                            [0,0,9],
                            [0,16,0]])

    def test_lil_multiply_removal(self):
        # Ticket #1427.
        a = lil_matrix(np.ones((3,3)))
        a *= 2.
        a[0, :] = 0


class TestCOO(sparse_test_class(getset=False,
                                slicing=False, slicing_assign=False,
                                fancy_indexing=False, fancy_assign=False)):
    spmatrix = coo_matrix
    math_dtypes = [np.int_, np.float_, np.complex_]

    def test_constructor1(self):
        # unsorted triplet format
        row = array([2, 3, 1, 3, 0, 1, 3, 0, 2, 1, 2])
        col = array([0, 1, 0, 0, 1, 1, 2, 2, 2, 2, 1])
        data = array([6., 10., 3., 9., 1., 4.,
                              11., 2., 8., 5., 7.])

        coo = coo_matrix((data,(row,col)),(4,3))

        assert_array_equal(arange(12).reshape(4,3),coo.todense())

    def test_constructor2(self):
        # unsorted triplet format with duplicates (which are summed)
        row = array([0,1,2,2,2,2,0,0,2,2])
        col = array([0,2,0,2,1,1,1,0,0,2])
        data = array([2,9,-4,5,7,0,-1,2,1,-5])
        coo = coo_matrix((data,(row,col)),(3,3))

        mat = matrix([[4,-1,0],[0,0,9],[-3,7,0]])

        assert_array_equal(mat,coo.todense())

    def test_constructor3(self):
        # empty matrix
        coo = coo_matrix((4,3))

        assert_array_equal(coo.shape,(4,3))
        assert_array_equal(coo.row,[])
        assert_array_equal(coo.col,[])
        assert_array_equal(coo.data,[])
        assert_array_equal(coo.todense(),zeros((4,3)))

    def test_constructor4(self):
        # from dense matrix
        mat = array([[0,1,0,0],
                     [7,0,3,0],
                     [0,4,0,0]])
        coo = coo_matrix(mat)
        assert_array_equal(coo.todense(),mat)

        # upgrade rank 1 arrays to row matrix
        mat = array([0,1,0,0])
        coo = coo_matrix(mat)
        assert_array_equal(coo.todense(),mat.reshape(1,-1))

    @dec.knownfailureif(True, 'COO does not have a __getitem__')
    def test_iterator(self):
        pass

    def test_todia_all_zeros(self):
        zeros = [[0, 0]]
        dia = coo_matrix(zeros).todia()
        assert_array_equal(dia.A, zeros)

    def test_sum_duplicates(self):
        coo = coo_matrix((4,3))
        coo.sum_duplicates()
        coo = coo_matrix(([1,2], ([1,0], [1,0])))
        coo.sum_duplicates()
        assert_array_equal(coo.A, [[2,0],[0,1]])
        coo = coo_matrix(([1,2], ([1,1], [1,1])))
        coo.sum_duplicates()
        assert_array_equal(coo.A, [[0,0],[0,3]])
        assert_array_equal(coo.row, [1])
        assert_array_equal(coo.col, [1])
        assert_array_equal(coo.data, [3])

    def test_todok_duplicates(self):
        coo = coo_matrix(([1,1,1,1], ([0,2,2,0], [0,1,1,0])))
        dok = coo.todok()
        assert_array_equal(dok.A, coo.A)

    def test_eliminate_zeros(self):
        data = array([1, 0, 0, 0, 2, 0, 3, 0])
        row = array([0, 0, 0, 1, 1, 1, 1, 1])
        col = array([1, 2, 3, 4, 5, 6, 7, 8])
        asp = coo_matrix((data, (row, col)), shape=(2,10))
        bsp = asp.copy()
        asp.eliminate_zeros()
        assert_((asp.data != 0).all())
        assert_array_equal(asp.A, bsp.A)


class TestDIA(sparse_test_class(getset=False, slicing=False, slicing_assign=False,
                                fancy_indexing=False, fancy_assign=False,
                                minmax=False, nnz_axis=False)):
    spmatrix = dia_matrix
    math_dtypes = [np.int_, np.float_, np.complex_]

    def test_constructor1(self):
        D = matrix([[1, 0, 3, 0],
                    [1, 2, 0, 4],
                    [0, 2, 3, 0],
                    [0, 0, 3, 4]])
        data = np.array([[1,2,3,4]]).repeat(3,axis=0)
        offsets = np.array([0,-1,2])
        assert_equal(dia_matrix((data,offsets), shape=(4,4)).todense(), D)

    @dec.knownfailureif(True, 'DIA does not have a __getitem__')
    def test_iterator(self):
        pass

    @with_64bit_maxval_limit(3)
    def test_setdiag_dtype(self):
        m = dia_matrix(np.eye(3))
        assert_equal(m.offsets.dtype, np.int32)
        m.setdiag((3,), k=2)
        assert_equal(m.offsets.dtype, np.int32)

        m = dia_matrix(np.eye(4))
        assert_equal(m.offsets.dtype, np.int64)
        m.setdiag((3,), k=3)
        assert_equal(m.offsets.dtype, np.int64)

    @dec.skipif(True, 'DIA stores extra zeros')
    def test_getnnz_axis(self):
        pass


class TestBSR(sparse_test_class(getset=False,
                                slicing=False, slicing_assign=False,
                                fancy_indexing=False, fancy_assign=False,
                                nnz_axis=False)):
    spmatrix = bsr_matrix
    math_dtypes = [np.int_, np.float_, np.complex_]

    def test_constructor1(self):
        # check native BSR format constructor
        indptr = array([0,2,2,4])
        indices = array([0,2,2,3])
        data = zeros((4,2,3))

        data[0] = array([[0, 1, 2],
                         [3, 0, 5]])
        data[1] = array([[0, 2, 4],
                         [6, 0, 10]])
        data[2] = array([[0, 4, 8],
                         [12, 0, 20]])
        data[3] = array([[0, 5, 10],
                         [15, 0, 25]])

        A = kron([[1,0,2,0],[0,0,0,0],[0,0,4,5]], [[0,1,2],[3,0,5]])
        Asp = bsr_matrix((data,indices,indptr),shape=(6,12))
        assert_equal(Asp.todense(),A)

        # infer shape from arrays
        Asp = bsr_matrix((data,indices,indptr))
        assert_equal(Asp.todense(),A)

    def test_constructor2(self):
        # construct from dense

        # test zero mats
        for shape in [(1,1), (5,1), (1,10), (10,4), (3,7), (2,1)]:
            A = zeros(shape)
            assert_equal(bsr_matrix(A).todense(),A)
        A = zeros((4,6))
        assert_equal(bsr_matrix(A,blocksize=(2,2)).todense(),A)
        assert_equal(bsr_matrix(A,blocksize=(2,3)).todense(),A)

        A = kron([[1,0,2,0],[0,0,0,0],[0,0,4,5]], [[0,1,2],[3,0,5]])
        assert_equal(bsr_matrix(A).todense(),A)
        assert_equal(bsr_matrix(A,shape=(6,12)).todense(),A)
        assert_equal(bsr_matrix(A,blocksize=(1,1)).todense(),A)
        assert_equal(bsr_matrix(A,blocksize=(2,3)).todense(),A)
        assert_equal(bsr_matrix(A,blocksize=(2,6)).todense(),A)
        assert_equal(bsr_matrix(A,blocksize=(2,12)).todense(),A)
        assert_equal(bsr_matrix(A,blocksize=(3,12)).todense(),A)
        assert_equal(bsr_matrix(A,blocksize=(6,12)).todense(),A)

        A = kron([[1,0,2,0],[0,1,0,0],[0,0,0,0]], [[0,1,2],[3,0,5]])
        assert_equal(bsr_matrix(A,blocksize=(2,3)).todense(),A)

    def test_constructor3(self):
        # construct from coo-like (data,(row,col)) format
        arg = ([1,2,3], ([0,1,1], [0,0,1]))
        A = array([[1,0],[2,3]])
        assert_equal(bsr_matrix(arg, blocksize=(2,2)).todense(), A)

    def test_constructor4(self):
        # regression test for gh-6292: bsr_matrix((data, indices, indptr)) was
        #  trying to compare an int to a None
        n = 8
        data = np.ones((n, n, 1), dtype=np.int8)
        indptr = np.array([0, n], dtype=np.int32)
        indices = np.arange(n, dtype=np.int32)
        bsr_matrix((data, indices, indptr), blocksize=(n, 1), copy=False)

    def test_eliminate_zeros(self):
        data = kron([1, 0, 0, 0, 2, 0, 3, 0], [[1,1],[1,1]]).T
        data = data.reshape(-1,2,2)
        indices = array([1, 2, 3, 4, 5, 6, 7, 8])
        indptr = array([0, 3, 8])
        asp = bsr_matrix((data, indices, indptr), shape=(4,20))
        bsp = asp.copy()
        asp.eliminate_zeros()
        assert_array_equal(asp.nnz, 3*4)
        assert_array_equal(asp.todense(),bsp.todense())

    def test_bsr_matvec(self):
        A = bsr_matrix(arange(2*3*4*5).reshape(2*4,3*5), blocksize=(4,5))
        x = arange(A.shape[1]).reshape(-1,1)
        assert_equal(A*x, A.todense()*x)
        assert_equal(A.matvec(x), A.todense()*x)

    def test_bsr_matvecs(self):
        A = bsr_matrix(arange(2*3*4*5).reshape(2*4,3*5), blocksize=(4,5))
        x = arange(A.shape[1]*6).reshape(-1,6)
        assert_equal(A*x, A.todense()*x)
        assert_equal(A.matmat(x), A.todense()*x)

    @dec.knownfailureif(True, 'BSR does not have a __getitem__')
    def test_iterator(self):
        pass

    @dec.knownfailureif(True, 'BSR does not have a __setitem__')
    def test_setdiag(self):
        pass

    def test_scalar_idx_dtype(self):
        # Check that index dtype takes into account all parameters
        # passed to sparsetools, including the scalar ones
        indptr = np.zeros(2, dtype=np.int32)
        indices = np.zeros(0, dtype=np.int32)
        vals = np.zeros((0, 1, 1))
        a = bsr_matrix((vals, indices, indptr), shape=(1, 2**31-1))
        b = bsr_matrix((vals, indices, indptr), shape=(1, 2**31))
        c = bsr_matrix((1, 2**31-1))
        d = bsr_matrix((1, 2**31))
        assert_equal(a.indptr.dtype, np.int32)
        assert_equal(b.indptr.dtype, np.int64)
        assert_equal(c.indptr.dtype, np.int32)
        assert_equal(d.indptr.dtype, np.int64)

        try:
            vals2 = np.zeros((0, 1, 2**31-1))
            vals3 = np.zeros((0, 1, 2**31))
            e = bsr_matrix((vals2, indices, indptr), shape=(1, 2**31-1))
            f = bsr_matrix((vals3, indices, indptr), shape=(1, 2**31))
            assert_equal(e.indptr.dtype, np.int32)
            assert_equal(f.indptr.dtype, np.int64)
        except (MemoryError, ValueError):
            # May fail on 32-bit Python
            e = 0
            f = 0

        # These shouldn't fail
        for x in [a, b, c, d, e, f]:
            x + x


#------------------------------------------------------------------------------
# Tests for non-canonical representations (with duplicates, unsorted indices)
#------------------------------------------------------------------------------

def _same_sum_duplicate(data, *inds, **kwargs):
    """Duplicates entries to produce the same matrix"""
    indptr = kwargs.pop('indptr', None)
    if np.issubdtype(data.dtype, np.bool_) or \
       np.issubdtype(data.dtype, np.unsignedinteger):
        if indptr is None:
            return (data,) + inds
        else:
            return (data,) + inds + (indptr,)

    zeros_pos = (data == 0).nonzero()

    # duplicate data
    data = data.repeat(2, axis=0)
    data[::2] -= 1
    data[1::2] = 1

    # don't spoil all explicit zeros
    if zeros_pos[0].size > 0:
        pos = tuple(p[0] for p in zeros_pos)
        pos1 = (2*pos[0],) + pos[1:]
        pos2 = (2*pos[0]+1,) + pos[1:]
        data[pos1] = 0
        data[pos2] = 0

    inds = tuple(indices.repeat(2) for indices in inds)

    if indptr is None:
        return (data,) + inds
    else:
        return (data,) + inds + (indptr * 2,)


class _NonCanonicalMixin(object):
    def spmatrix(self, D, **kwargs):
        """Replace D with a non-canonical equivalent: containing
        duplicate elements and explicit zeros"""
        construct = super(_NonCanonicalMixin, self).spmatrix
        M = construct(D, **kwargs)

        zero_pos = (M.A == 0).nonzero()
        has_zeros = (zero_pos[0].size > 0)
        if has_zeros:
            k = zero_pos[0].size//2
            M = self._insert_explicit_zero(M,
                                           zero_pos[0][k],
                                           zero_pos[1][k])

        arg1 = self._arg1_for_noncanonical(M)
        if 'shape' not in kwargs:
            kwargs['shape'] = M.shape
        NC = construct(arg1, **kwargs)

        # check that result is valid
        if NC.dtype in [np.float32, np.complex64]:
            # For single-precision floats, the differences between M and NC
            # that are introduced by the extra operations involved in the
            # construction of NC necessitate a more lenient tolerance level
            # than the default.
            rtol = 1e-05
        else:
            rtol = 1e-07
        assert_allclose(NC.A, M.A, rtol=rtol)

        # check that at least one explicit zero
        if has_zeros:
            assert_((NC.data == 0).any())

        return NC

    @dec.skipif(True, 'bool(matrix) counts explicit zeros')
    def test_bool(self):
        pass

    @dec.skipif(True, 'getnnz-axis counts explicit zeros')
    def test_getnnz_axis(self):
        pass

    @dec.skipif(True, 'nnz counts explicit zeros')
    def test_empty(self):
        pass

    @dec.knownfailureif(True, 'unary ufunc overrides broken with non-canonical matrix')
    def test_unary_ufunc_overrides(self):
        pass


class _NonCanonicalCompressedMixin(_NonCanonicalMixin):
    def _arg1_for_noncanonical(self, M):
        """Return non-canonical constructor arg1 equivalent to M"""
        data, indices, indptr = _same_sum_duplicate(M.data, M.indices,
                                                    indptr=M.indptr)
        # unsorted
        for start, stop in izip(indptr, indptr[1:]):
            indices[start:stop] = indices[start:stop][::-1].copy()
            data[start:stop] = data[start:stop][::-1].copy()
        return data, indices, indptr

    def _insert_explicit_zero(self, M, i, j):
        M[i,j] = 0
        return M


class _NonCanonicalCSMixin(_NonCanonicalCompressedMixin):
    @dec.knownfailureif(True, 'inverse broken with non-canonical matrix')
    def test_inv(self):
        pass

    @dec.knownfailureif(True, 'solve broken with non-canonical matrix')
    def test_solve(self):
        pass


class TestCSRNonCanonical(_NonCanonicalCSMixin, TestCSR):
    pass


class TestCSCNonCanonical(_NonCanonicalCSMixin, TestCSC):
    pass


class TestBSRNonCanonical(_NonCanonicalCompressedMixin, TestBSR):
    def _insert_explicit_zero(self, M, i, j):
        x = M.tocsr()
        x[i,j] = 0
        return x.tobsr(blocksize=M.blocksize)

    @dec.knownfailureif(True, 'diagonal broken with non-canonical BSR')
    def test_diagonal(self):
        pass

    @dec.knownfailureif(True, 'expm broken with non-canonical BSR')
    def test_expm(self):
        pass


class TestCOONonCanonical(_NonCanonicalMixin, TestCOO):
    def _arg1_for_noncanonical(self, M):
        """Return non-canonical constructor arg1 equivalent to M"""
        data, row, col = _same_sum_duplicate(M.data, M.row, M.col)
        return data, (row, col)

    def _insert_explicit_zero(self, M, i, j):
        M.data = np.r_[M.data.dtype.type(0), M.data]
        M.row = np.r_[M.row.dtype.type(i), M.row]
        M.col = np.r_[M.col.dtype.type(j), M.col]
        return M

    def test_setdiag_noncanonical(self):
        m = self.spmatrix(np.eye(3))
        m.sum_duplicates()
        m.setdiag([3, 2], k=1)
        m.sum_duplicates()
        assert_(np.all(np.diff(m.col) >= 0))


class Test64Bit(object):

    TEST_CLASSES = [TestBSR, TestCOO, TestCSC, TestCSR, TestDIA,
                    # lil/dok->other conversion operations have get_index_dtype
                    TestDOK, TestLIL
                    ]

    MAT_CLASSES = [bsr_matrix, coo_matrix, csc_matrix, csr_matrix, dia_matrix]

    # The following features are missing, so skip the tests:
    SKIP_TESTS = {
        'test_expm': 'expm for 64-bit indices not available',
        'test_solve': 'linsolve for 64-bit indices not available',
        'test_scalar_idx_dtype': 'test implemented in base class',
    }

    def _create_some_matrix(self, mat_cls, m, n):
        return mat_cls(np.random.rand(m, n))

    def _compare_index_dtype(self, m, dtype):
        dtype = np.dtype(dtype)
        if isinstance(m, csc_matrix) or isinstance(m, csr_matrix) \
               or isinstance(m, bsr_matrix):
            return (m.indices.dtype == dtype) and (m.indptr.dtype == dtype)
        elif isinstance(m, coo_matrix):
            return (m.row.dtype == dtype) and (m.col.dtype == dtype)
        elif isinstance(m, dia_matrix):
            return (m.offsets.dtype == dtype)
        else:
            raise ValueError("matrix %r has no integer indices" % (m,))

    def test_decorator_maxval_limit(self):
        # Test that the with_64bit_maxval_limit decorator works

        @with_64bit_maxval_limit(maxval_limit=10)
        def check(mat_cls):
            m = mat_cls(np.random.rand(10, 1))
            assert_(self._compare_index_dtype(m, np.int32))
            m = mat_cls(np.random.rand(11, 1))
            assert_(self._compare_index_dtype(m, np.int64))

        for mat_cls in self.MAT_CLASSES:
            yield check, mat_cls

    def test_decorator_maxval_random(self):
        # Test that the with_64bit_maxval_limit decorator works (2)

        @with_64bit_maxval_limit(random=True)
        def check(mat_cls):
            seen_32 = False
            seen_64 = False
            for k in range(100):
                m = self._create_some_matrix(mat_cls, 9, 9)
                seen_32 = seen_32 or self._compare_index_dtype(m, np.int32)
                seen_64 = seen_64 or self._compare_index_dtype(m, np.int64)
                if seen_32 and seen_64:
                    break
            else:
                raise AssertionError("both 32 and 64 bit indices not seen")

        for mat_cls in self.MAT_CLASSES:
            yield check, mat_cls

    def _check_resiliency(self, **kw):
        # Resiliency test, to check that sparse matrices deal reasonably
        # with varying index data types.

        skip = kw.pop('skip', ())

        @with_64bit_maxval_limit(**kw)
        def check(cls, method_name):
            instance = cls()
            if hasattr(instance, 'setup'):
                instance.setup()
            try:
                getattr(instance, method_name)()
            finally:
                if hasattr(instance, 'teardown'):
                    instance.teardown()

        for cls in self.TEST_CLASSES:
            for method_name in dir(cls):
                method = getattr(cls, method_name)
                if (method_name.startswith('test_') and
                        not getattr(method, 'slow', False) and
                        (cls.__name__ + '.' + method_name) not in skip):
                    msg = self.SKIP_TESTS.get(method_name)
                    yield dec.skipif(msg, msg)(check), cls, method_name

    def test_resiliency_limit_10(self):
        for t in self._check_resiliency(maxval_limit=10):
            yield t

    def test_resiliency_random(self):
        # bsr_matrix.eliminate_zeros relies on csr_matrix constructor
        # not making copies of index arrays --- this is not
        # necessarily true when we pick the index data type randomly
        skip = ['TestBSR.test_eliminate_zeros']

        for t in self._check_resiliency(random=True, skip=skip):
            yield t

    def test_resiliency_all_32(self):
        for t in self._check_resiliency(fixed_dtype=np.int32):
            yield t

    def test_resiliency_all_64(self):
        for t in self._check_resiliency(fixed_dtype=np.int64):
            yield t

    def test_no_64(self):
        for t in self._check_resiliency(assert_32bit=True):
            yield t

    def test_downcast_intp(self):
        # Check that bincount and ufunc.reduceat intp downcasts are
        # dealt with. The point here is to trigger points in the code
        # that can fail on 32-bit systems when using 64-bit indices,
        # due to use of functions that only work with intp-size
        # indices.

        @with_64bit_maxval_limit(fixed_dtype=np.int64,
                                 downcast_maxval=1)
        def check_limited():
            # These involve indices larger than `downcast_maxval`
            a = csc_matrix([[1, 2], [3, 4], [5, 6]])
            assert_raises(AssertionError, a.getnnz, axis=1)
            assert_raises(AssertionError, a.sum, axis=0)

            a = csr_matrix([[1, 2, 3], [3, 4, 6]])
            assert_raises(AssertionError, a.getnnz, axis=0)

            a = coo_matrix([[1, 2, 3], [3, 4, 5]])
            assert_raises(AssertionError, a.getnnz, axis=0)

        @with_64bit_maxval_limit(fixed_dtype=np.int64)
        def check_unlimited():
            # These involve indices larger than `downcast_maxval`
            a = csc_matrix([[1, 2], [3, 4], [5, 6]])
            a.getnnz(axis=1)
            a.sum(axis=0)

            a = csr_matrix([[1, 2, 3], [3, 4, 6]])
            a.getnnz(axis=0)

            a = coo_matrix([[1, 2, 3], [3, 4, 5]])
            a.getnnz(axis=0)

        check_limited()
        check_unlimited()


if __name__ == "__main__":
    run_module_suite()
