from sympy.concrete.summations import Sum
from sympy.core.mod import Mod
from sympy.core.relational import (Equality, Unequality)
from sympy.core.symbol import Symbol
from sympy.functions.elementary.miscellaneous import sqrt
from sympy.functions.elementary.piecewise import Piecewise
from sympy.functions.special.gamma_functions import polygamma
from sympy.functions.special.error_functions import (Si, Ci)
from sympy.matrices.expressions.blockmatrix import BlockMatrix
from sympy.matrices.expressions.matexpr import MatrixSymbol
from sympy.matrices.expressions.special import Identity
from sympy.utilities.lambdify import lambdify

from sympy.abc import x, i, j, a, b, c, d
from sympy.core import Pow
from sympy.codegen.matrix_nodes import MatrixSolve
from sympy.codegen.numpy_nodes import logaddexp, logaddexp2
from sympy.codegen.cfunctions import log1p, expm1, hypot, log10, exp2, log2, Sqrt
from sympy.tensor.array import Array
from sympy.tensor.array.expressions.array_expressions import ArrayTensorProduct, ArrayAdd, \
    PermuteDims, ArrayDiagonal
from sympy.printing.numpy import NumPyPrinter, SciPyPrinter, _numpy_known_constants, \
    _numpy_known_functions, _scipy_known_constants, _scipy_known_functions
from sympy.tensor.array.expressions.from_matrix_to_array import convert_matrix_to_array

from sympy.testing.pytest import skip, raises
from sympy.external import import_module

np = import_module('numpy')

if np:
    deafult_float_info = np.finfo(np.array([]).dtype)
    NUMPY_DEFAULT_EPSILON = deafult_float_info.eps

def test_numpy_piecewise_regression():
    """
    NumPyPrinter needs to print Piecewise()'s choicelist as a list to avoid
    breaking compatibility with numpy 1.8. This is not necessary in numpy 1.9+.
    See gh-9747 and gh-9749 for details.
    """
    printer = NumPyPrinter()
    p = Piecewise((1, x < 0), (0, True))
    assert printer.doprint(p) == \
        'numpy.select([numpy.less(x, 0),True], [1,0], default=numpy.nan)'
    assert printer.module_imports == {'numpy': {'select', 'less', 'nan'}}

def test_numpy_logaddexp():
    lae = logaddexp(a, b)
    assert NumPyPrinter().doprint(lae) == 'numpy.logaddexp(a, b)'
    lae2 = logaddexp2(a, b)
    assert NumPyPrinter().doprint(lae2) == 'numpy.logaddexp2(a, b)'


def test_sum():
    if not np:
        skip("NumPy not installed")

    s = Sum(x ** i, (i, a, b))
    f = lambdify((a, b, x), s, 'numpy')

    a_, b_ = 0, 10
    x_ = np.linspace(-1, +1, 10)
    assert np.allclose(f(a_, b_, x_), sum(x_ ** i_ for i_ in range(a_, b_ + 1)))

    s = Sum(i * x, (i, a, b))
    f = lambdify((a, b, x), s, 'numpy')

    a_, b_ = 0, 10
    x_ = np.linspace(-1, +1, 10)
    assert np.allclose(f(a_, b_, x_), sum(i_ * x_ for i_ in range(a_, b_ + 1)))


def test_multiple_sums():
    if not np:
        skip("NumPy not installed")

    s = Sum((x + j) * i, (i, a, b), (j, c, d))
    f = lambdify((a, b, c, d, x), s, 'numpy')

    a_, b_ = 0, 10
    c_, d_ = 11, 21
    x_ = np.linspace(-1, +1, 10)
    assert np.allclose(f(a_, b_, c_, d_, x_),
                       sum((x_ + j_) * i_ for i_ in range(a_, b_ + 1) for j_ in range(c_, d_ + 1)))


def test_codegen_einsum():
    if not np:
        skip("NumPy not installed")

    M = MatrixSymbol("M", 2, 2)
    N = MatrixSymbol("N", 2, 2)

    cg = convert_matrix_to_array(M * N)
    f = lambdify((M, N), cg, 'numpy')

    ma = np.array([[1, 2], [3, 4]])
    mb = np.array([[1,-2], [-1, 3]])
    assert (f(ma, mb) == np.matmul(ma, mb)).all()


def test_codegen_extra():
    if not np:
        skip("NumPy not installed")

    M = MatrixSymbol("M", 2, 2)
    N = MatrixSymbol("N", 2, 2)
    P = MatrixSymbol("P", 2, 2)
    Q = MatrixSymbol("Q", 2, 2)
    ma = np.array([[1, 2], [3, 4]])
    mb = np.array([[1,-2], [-1, 3]])
    mc = np.array([[2, 0], [1, 2]])
    md = np.array([[1,-1], [4, 7]])

    cg = ArrayTensorProduct(M, N)
    f = lambdify((M, N), cg, 'numpy')
    assert (f(ma, mb) == np.einsum(ma, [0, 1], mb, [2, 3])).all()

    cg = ArrayAdd(M, N)
    f = lambdify((M, N), cg, 'numpy')
    assert (f(ma, mb) == ma+mb).all()

    cg = ArrayAdd(M, N, P)
    f = lambdify((M, N, P), cg, 'numpy')
    assert (f(ma, mb, mc) == ma+mb+mc).all()

    cg = ArrayAdd(M, N, P, Q)
    f = lambdify((M, N, P, Q), cg, 'numpy')
    assert (f(ma, mb, mc, md) == ma+mb+mc+md).all()

    cg = PermuteDims(M, [1, 0])
    f = lambdify((M,), cg, 'numpy')
    assert (f(ma) == ma.T).all()

    cg = PermuteDims(ArrayTensorProduct(M, N), [1, 2, 3, 0])
    f = lambdify((M, N), cg, 'numpy')
    assert (f(ma, mb) == np.transpose(np.einsum(ma, [0, 1], mb, [2, 3]), (1, 2, 3, 0))).all()

    cg = ArrayDiagonal(ArrayTensorProduct(M, N), (1, 2))
    f = lambdify((M, N), cg, 'numpy')
    assert (f(ma, mb) == np.diagonal(np.einsum(ma, [0, 1], mb, [2, 3]), axis1=1, axis2=2)).all()


def test_relational():
    if not np:
        skip("NumPy not installed")

    e = Equality(x, 1)

    f = lambdify((x,), e)
    x_ = np.array([0, 1, 2])
    assert np.array_equal(f(x_), [False, True, False])

    e = Unequality(x, 1)

    f = lambdify((x,), e)
    x_ = np.array([0, 1, 2])
    assert np.array_equal(f(x_), [True, False, True])

    e = (x < 1)

    f = lambdify((x,), e)
    x_ = np.array([0, 1, 2])
    assert np.array_equal(f(x_), [True, False, False])

    e = (x <= 1)

    f = lambdify((x,), e)
    x_ = np.array([0, 1, 2])
    assert np.array_equal(f(x_), [True, True, False])

    e = (x > 1)

    f = lambdify((x,), e)
    x_ = np.array([0, 1, 2])
    assert np.array_equal(f(x_), [False, False, True])

    e = (x >= 1)

    f = lambdify((x,), e)
    x_ = np.array([0, 1, 2])
    assert np.array_equal(f(x_), [False, True, True])


def test_mod():
    if not np:
        skip("NumPy not installed")

    e = Mod(a, b)
    f = lambdify((a, b), e)

    a_ = np.array([0, 1, 2, 3])
    b_ = 2
    assert np.array_equal(f(a_, b_), [0, 1, 0, 1])

    a_ = np.array([0, 1, 2, 3])
    b_ = np.array([2, 2, 2, 2])
    assert np.array_equal(f(a_, b_), [0, 1, 0, 1])

    a_ = np.array([2, 3, 4, 5])
    b_ = np.array([2, 3, 4, 5])
    assert np.array_equal(f(a_, b_), [0, 0, 0, 0])


def test_pow():
    if not np:
        skip('NumPy not installed')

    expr = Pow(2, -1, evaluate=False)
    f = lambdify([], expr, 'numpy')
    assert f() == 0.5


def test_expm1():
    if not np:
        skip("NumPy not installed")

    f = lambdify((a,), expm1(a), 'numpy')
    assert abs(f(1e-10) - 1e-10 - 5e-21) <= 1e-10 * NUMPY_DEFAULT_EPSILON


def test_log1p():
    if not np:
        skip("NumPy not installed")

    f = lambdify((a,), log1p(a), 'numpy')
    assert abs(f(1e-99) - 1e-99) <= 1e-99 * NUMPY_DEFAULT_EPSILON

def test_hypot():
    if not np:
        skip("NumPy not installed")
    assert abs(lambdify((a, b), hypot(a, b), 'numpy')(3, 4) - 5) <= NUMPY_DEFAULT_EPSILON

def test_log10():
    if not np:
        skip("NumPy not installed")
    assert abs(lambdify((a,), log10(a), 'numpy')(100) - 2) <= NUMPY_DEFAULT_EPSILON


def test_exp2():
    if not np:
        skip("NumPy not installed")
    assert abs(lambdify((a,), exp2(a), 'numpy')(5) - 32) <= NUMPY_DEFAULT_EPSILON


def test_log2():
    if not np:
        skip("NumPy not installed")
    assert abs(lambdify((a,), log2(a), 'numpy')(256) - 8) <= NUMPY_DEFAULT_EPSILON


def test_Sqrt():
    if not np:
        skip("NumPy not installed")
    assert abs(lambdify((a,), Sqrt(a), 'numpy')(4) - 2) <= NUMPY_DEFAULT_EPSILON


def test_sqrt():
    if not np:
        skip("NumPy not installed")
    assert abs(lambdify((a,), sqrt(a), 'numpy')(4) - 2) <= NUMPY_DEFAULT_EPSILON


def test_matsolve():
    if not np:
        skip("NumPy not installed")

    M = MatrixSymbol("M", 3, 3)
    x = MatrixSymbol("x", 3, 1)

    expr = M**(-1) * x + x
    matsolve_expr = MatrixSolve(M, x) + x

    f = lambdify((M, x), expr)
    f_matsolve = lambdify((M, x), matsolve_expr)

    m0 = np.array([[1, 2, 3], [3, 2, 5], [5, 6, 7]])
    assert np.linalg.matrix_rank(m0) == 3

    x0 = np.array([3, 4, 5])

    assert np.allclose(f_matsolve(m0, x0), f(m0, x0))


def test_16857():
    if not np:
        skip("NumPy not installed")

    a_1 = MatrixSymbol('a_1', 10, 3)
    a_2 = MatrixSymbol('a_2', 10, 3)
    a_3 = MatrixSymbol('a_3', 10, 3)
    a_4 = MatrixSymbol('a_4', 10, 3)
    A = BlockMatrix([[a_1, a_2], [a_3, a_4]])
    assert A.shape == (20, 6)

    printer = NumPyPrinter()
    assert printer.doprint(A) == 'numpy.block([[a_1, a_2], [a_3, a_4]])'


def test_issue_17006():
    if not np:
        skip("NumPy not installed")

    M = MatrixSymbol("M", 2, 2)

    f = lambdify(M, M + Identity(2))
    ma = np.array([[1, 2], [3, 4]])
    mr = np.array([[2, 2], [3, 5]])

    assert (f(ma) == mr).all()

    from sympy.core.symbol import symbols
    n = symbols('n', integer=True)
    N = MatrixSymbol("M", n, n)
    raises(NotImplementedError, lambda: lambdify(N, N + Identity(n)))

def test_numpy_array():
    assert NumPyPrinter().doprint(Array(((1, 2), (3, 5)))) == 'numpy.array([[1, 2], [3, 5]])'
    assert NumPyPrinter().doprint(Array((1, 2))) == 'numpy.array((1, 2))'

def test_numpy_known_funcs_consts():
    assert _numpy_known_constants['NaN'] == 'numpy.nan'
    assert _numpy_known_constants['EulerGamma'] == 'numpy.euler_gamma'

    assert _numpy_known_functions['acos'] == 'numpy.arccos'
    assert _numpy_known_functions['log'] == 'numpy.log'

def test_scipy_known_funcs_consts():
    assert _scipy_known_constants['GoldenRatio'] == 'scipy.constants.golden_ratio'
    assert _scipy_known_constants['Pi'] == 'scipy.constants.pi'

    assert _scipy_known_functions['erf'] == 'scipy.special.erf'
    assert _scipy_known_functions['factorial'] == 'scipy.special.factorial'

def test_numpy_print_methods():
    prntr = NumPyPrinter()
    assert hasattr(prntr, '_print_acos')
    assert hasattr(prntr, '_print_log')

def test_scipy_print_methods():
    prntr = SciPyPrinter()
    assert hasattr(prntr, '_print_acos')
    assert hasattr(prntr, '_print_log')
    assert hasattr(prntr, '_print_erf')
    assert hasattr(prntr, '_print_factorial')
    assert hasattr(prntr, '_print_chebyshevt')
    k = Symbol('k', integer=True, nonnegative=True)
    x = Symbol('x', real=True)
    assert prntr.doprint(polygamma(k, x)) == "scipy.special.polygamma(k, x)"
    assert prntr.doprint(Si(x)) == "scipy.special.sici(x)[0]"
    assert prntr.doprint(Ci(x)) == "scipy.special.sici(x)[1]"