"""Test functions for the sparse.linalg.interface module
"""

from __future__ import division, print_function, absolute_import

from functools import partial
from itertools import product
import operator
import nose

from numpy.testing import TestCase, assert_, assert_equal, \
        assert_raises

import numpy as np
import scipy.sparse as sparse

from scipy.sparse.linalg import interface


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


class TestLinearOperator(TestCase):
    def setUp(self):
        self.A = np.array([[1,2,3],
                           [4,5,6]])
        self.B = np.array([[1,2],
                           [3,4],
                           [5,6]])
        self.C = np.array([[1,2],
                           [3,4]])

    def test_matvec(self):
        def get_matvecs(A):
            return [{
                        'shape': A.shape,
                        'matvec': lambda x: np.dot(A, x).reshape(A.shape[0]),
                        'rmatvec': lambda x: np.dot(A.T.conj(),
                                                    x).reshape(A.shape[1])
                    },
                    {
                        'shape': A.shape,
                        'matvec': lambda x: np.dot(A, x),
                        'rmatvec': lambda x: np.dot(A.T.conj(), x),
                        'matmat': lambda x: np.dot(A, x)
                    }]

        for matvecs in get_matvecs(self.A):
            A = interface.LinearOperator(**matvecs)

            assert_(A.args == ())

            assert_equal(A.matvec(np.array([1,2,3])), [14,32])
            assert_equal(A.matvec(np.array([[1],[2],[3]])), [[14],[32]])
            assert_equal(A * np.array([1,2,3]), [14,32])
            assert_equal(A * np.array([[1],[2],[3]]), [[14],[32]])
            assert_equal(A.dot(np.array([1,2,3])), [14,32])
            assert_equal(A.dot(np.array([[1],[2],[3]])), [[14],[32]])

            assert_equal(A.matvec(np.matrix([[1],[2],[3]])), [[14],[32]])
            assert_equal(A * np.matrix([[1],[2],[3]]), [[14],[32]])
            assert_equal(A.dot(np.matrix([[1],[2],[3]])), [[14],[32]])

            assert_equal((2*A)*[1,1,1], [12,30])
            assert_equal((2*A).rmatvec([1,1]), [10, 14, 18])
            assert_equal((2*A).H.matvec([1,1]), [10, 14, 18])
            assert_equal((2*A)*[[1],[1],[1]], [[12],[30]])
            assert_equal((2*A).matmat([[1],[1],[1]]), [[12],[30]])
            assert_equal((A*2)*[1,1,1], [12,30])
            assert_equal((A*2)*[[1],[1],[1]], [[12],[30]])
            assert_equal((2j*A)*[1,1,1], [12j,30j])
            assert_equal((A+A)*[1,1,1], [12, 30])
            assert_equal((A+A).rmatvec([1,1]), [10, 14, 18])
            assert_equal((A+A).H.matvec([1,1]), [10, 14, 18])
            assert_equal((A+A)*[[1],[1],[1]], [[12], [30]])
            assert_equal((A+A).matmat([[1],[1],[1]]), [[12], [30]])
            assert_equal((-A)*[1,1,1], [-6,-15])
            assert_equal((-A)*[[1],[1],[1]], [[-6],[-15]])
            assert_equal((A-A)*[1,1,1], [0,0])
            assert_equal((A-A)*[[1],[1],[1]], [[0],[0]])

            z = A+A
            assert_(len(z.args) == 2 and z.args[0] is A and z.args[1] is A)
            z = 2*A
            assert_(len(z.args) == 2 and z.args[0] is A and z.args[1] == 2)

            assert_(isinstance(A.matvec([1, 2, 3]), np.ndarray))
            assert_(isinstance(A.matvec(np.array([[1],[2],[3]])), np.ndarray))
            assert_(isinstance(A * np.array([1,2,3]), np.ndarray))
            assert_(isinstance(A * np.array([[1],[2],[3]]), np.ndarray))
            assert_(isinstance(A.dot(np.array([1,2,3])), np.ndarray))
            assert_(isinstance(A.dot(np.array([[1],[2],[3]])), np.ndarray))

            assert_(isinstance(A.matvec(np.matrix([[1],[2],[3]])), np.ndarray))
            assert_(isinstance(A * np.matrix([[1],[2],[3]]), np.ndarray))
            assert_(isinstance(A.dot(np.matrix([[1],[2],[3]])), np.ndarray))

            assert_(isinstance(2*A, interface._ScaledLinearOperator))
            assert_(isinstance(2j*A, interface._ScaledLinearOperator))
            assert_(isinstance(A+A, interface._SumLinearOperator))
            assert_(isinstance(-A, interface._ScaledLinearOperator))
            assert_(isinstance(A-A, interface._SumLinearOperator))

            assert_((2j*A).dtype == np.complex_)

            assert_raises(ValueError, A.matvec, np.array([1,2]))
            assert_raises(ValueError, A.matvec, np.array([1,2,3,4]))
            assert_raises(ValueError, A.matvec, np.array([[1],[2]]))
            assert_raises(ValueError, A.matvec, np.array([[1],[2],[3],[4]]))

            assert_raises(ValueError, lambda: A*A)
            assert_raises(ValueError, lambda: A**2)

        for matvecsA, matvecsB in product(get_matvecs(self.A),
                                          get_matvecs(self.B)):
            A = interface.LinearOperator(**matvecsA)
            B = interface.LinearOperator(**matvecsB)

            assert_equal((A*B)*[1,1], [50,113])
            assert_equal((A*B)*[[1],[1]], [[50],[113]])
            assert_equal((A*B).matmat([[1],[1]]), [[50],[113]])

            assert_equal((A*B).rmatvec([1,1]), [71,92])
            assert_equal((A*B).H.matvec([1,1]), [71,92])

            assert_(isinstance(A*B, interface._ProductLinearOperator))

            assert_raises(ValueError, lambda: A+B)
            assert_raises(ValueError, lambda: A**2)

            z = A*B
            assert_(len(z.args) == 2 and z.args[0] is A and z.args[1] is B)

        for matvecsC in get_matvecs(self.C):
            C = interface.LinearOperator(**matvecsC)

            assert_equal((C**2)*[1,1], [17,37])
            assert_equal((C**2).rmatvec([1,1]), [22,32])
            assert_equal((C**2).H.matvec([1,1]), [22,32])
            assert_equal((C**2).matmat([[1],[1]]), [[17],[37]])

            assert_(isinstance(C**2, interface._PowerLinearOperator))

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

        D = {'shape': self.A.shape,
             'matvec': lambda x: np.dot(self.A, x).reshape(self.A.shape[0]),
             'rmatvec': lambda x: np.dot(self.A.T.conj(),
                                         x).reshape(self.A.shape[1]),
             'matmat': lambda x: np.dot(self.A, x)}
        A = interface.LinearOperator(**D)
        B = np.array([[1, 2, 3],
                      [4, 5, 6],
                      [7, 8, 9]])
        b = B[0]

        assert_equal(operator.matmul(A, b), A * b)
        assert_equal(operator.matmul(A, B), A * B)
        assert_raises(ValueError, operator.matmul, A, 2)
        assert_raises(ValueError, operator.matmul, 2, A)


class TestAsLinearOperator(TestCase):
    def setUp(self):
        self.cases = []

        def make_cases(dtype):
            self.cases.append(np.matrix([[1,2,3],[4,5,6]], dtype=dtype))
            self.cases.append(np.array([[1,2,3],[4,5,6]], dtype=dtype))
            self.cases.append(sparse.csr_matrix([[1,2,3],[4,5,6]], dtype=dtype))

            # Test default implementations of _adjoint and _rmatvec, which
            # refer to each other.
            def mv(x, dtype):
                y = np.array([1 * x[0] + 2 * x[1] + 3 * x[2],
                              4 * x[0] + 5 * x[1] + 6 * x[2]], dtype=dtype)
                if len(x.shape) == 2:
                    y = y.reshape(-1, 1)
                return y

            def rmv(x, dtype):
                return np.array([1 * x[0] + 4 * x[1],
                                 2 * x[0] + 5 * x[1],
                                 3 * x[0] + 6 * x[1]], dtype=dtype)

            class BaseMatlike(interface.LinearOperator):
                def __init__(self, dtype):
                    self.dtype = np.dtype(dtype)
                    self.shape = (2,3)

                def _matvec(self, x):
                    return mv(x, self.dtype)

            class HasRmatvec(BaseMatlike):
                def _rmatvec(self,x):
                    return rmv(x, self.dtype)

            class HasAdjoint(BaseMatlike):
                def _adjoint(self):
                    shape = self.shape[1], self.shape[0]
                    matvec = partial(rmv, dtype=self.dtype)
                    rmatvec = partial(mv, dtype=self.dtype)
                    return interface.LinearOperator(matvec=matvec,
                                                    rmatvec=rmatvec,
                                                    dtype=self.dtype,
                                                    shape=shape)

            self.cases.append(HasRmatvec(dtype))
            self.cases.append(HasAdjoint(dtype))

        make_cases('int32')
        make_cases('float32')
        make_cases('float64')

    def test_basic(self):

        for M in self.cases:
            A = interface.aslinearoperator(M)
            M,N = A.shape

            assert_equal(A.matvec(np.array([1,2,3])), [14,32])
            assert_equal(A.matvec(np.array([[1],[2],[3]])), [[14],[32]])

            assert_equal(A * np.array([1,2,3]), [14,32])
            assert_equal(A * np.array([[1],[2],[3]]), [[14],[32]])

            assert_equal(A.rmatvec(np.array([1,2])), [9,12,15])
            assert_equal(A.rmatvec(np.array([[1],[2]])), [[9],[12],[15]])
            assert_equal(A.H.matvec(np.array([1,2])), [9,12,15])
            assert_equal(A.H.matvec(np.array([[1],[2]])), [[9],[12],[15]])

            assert_equal(
                    A.matmat(np.array([[1,4],[2,5],[3,6]])),
                    [[14,32],[32,77]])

            assert_equal(A * np.array([[1,4],[2,5],[3,6]]), [[14,32],[32,77]])

            if hasattr(M,'dtype'):
                assert_equal(A.dtype, M.dtype)

    def test_dot(self):

        for M in self.cases:
            A = interface.aslinearoperator(M)
            M,N = A.shape

            assert_equal(A.dot(np.array([1,2,3])), [14,32])
            assert_equal(A.dot(np.array([[1],[2],[3]])), [[14],[32]])

            assert_equal(
                    A.dot(np.array([[1,4],[2,5],[3,6]])),
                    [[14,32],[32,77]])


def test_repr():
    A = interface.LinearOperator(shape=(1, 1), matvec=lambda x: 1)
    repr_A = repr(A)
    assert_('unspecified dtype' not in repr_A, repr_A)


def test_identity():
    ident = interface.IdentityOperator((3, 3))
    assert_equal(ident * [1, 2, 3], [1, 2, 3])
    assert_equal(ident.dot(np.arange(9).reshape(3, 3)).ravel(), np.arange(9))

    assert_raises(ValueError, ident.matvec, [1, 2, 3, 4])


def test_attributes():
    A = interface.aslinearoperator(np.arange(16).reshape(4, 4))

    def always_four_ones(x):
        x = np.asarray(x)
        assert_(x.shape == (3,) or x.shape == (3, 1))
        return np.ones(4)

    B = interface.LinearOperator(shape=(4, 3), matvec=always_four_ones)

    for op in [A, B, A * B, A.H, A + A, B + B, A ** 4]:
        assert_(hasattr(op, "dtype"))
        assert_(hasattr(op, "shape"))
        assert_(hasattr(op, "_matvec"))


def test_inheritance():
    class Empty(interface.LinearOperator):
        pass

    assert_raises(TypeError, Empty)

    class Identity(interface.LinearOperator):
        def __init__(self, n):
            super(Identity, self).__init__(dtype=None, shape=(n, n))

        def _matvec(self, x):
            return x

    id3 = Identity(3)
    assert_equal(id3.matvec([1, 2, 3]), [1, 2, 3])
    assert_raises(NotImplementedError, id3.rmatvec, [4, 5, 6])

    class MatmatOnly(interface.LinearOperator):
        def __init__(self, A):
            super(MatmatOnly, self).__init__(A.dtype, A.shape)
            self.A = A

        def _matmat(self, x):
            return self.A.dot(x)

    mm = MatmatOnly(np.random.randn(5, 3))
    assert_equal(mm.matvec(np.random.randn(3)).shape, (5,))
