# This testfile tests SymPy <-> NumPy compatibility

# Don't test any SymPy features here. Just pure interaction with NumPy.
# Always write regular SymPy tests for anything, that can be tested in pure
# Python (without numpy). Here we test everything, that a user may need when
# using SymPy with NumPy

from __future__ import division

from sympy.external import import_module

numpy = import_module('numpy')
if numpy:
    array, matrix, ndarray = numpy.array, numpy.matrix, numpy.ndarray
else:
    #bin/test will not execute any tests now
    disabled = True


from sympy import (Rational, Symbol, list2numpy, matrix2numpy, sin, Float,
        Matrix, lambdify, symarray, symbols, Integer)
import sympy

import mpmath
from sympy.abc import x, y, z
from sympy.utilities.decorator import conserve_mpmath_dps


# first, systematically check, that all operations are implemented and don't
# raise an exception


def test_systematic_basic():
    def s(sympy_object, numpy_array):
        x = sympy_object + numpy_array
        x = numpy_array + sympy_object
        x = sympy_object - numpy_array
        x = numpy_array - sympy_object
        x = sympy_object * numpy_array
        x = numpy_array * sympy_object
        x = sympy_object / numpy_array
        x = numpy_array / sympy_object
        x = sympy_object ** numpy_array
        x = numpy_array ** sympy_object
    x = Symbol("x")
    y = Symbol("y")
    sympy_objs = [
        Rational(2, 3),
        Float("1.3"),
        x,
        y,
        pow(x, y)*y,
        Integer(5),
        Float(5.5),
    ]
    numpy_objs = [
        array([1]),
        array([3, 8, -1]),
        array([x, x**2, Rational(5)]),
        array([x/y*sin(y), 5, Rational(5)]),
    ]
    for x in sympy_objs:
        for y in numpy_objs:
            s(x, y)


# now some random tests, that test particular problems and that also
# check that the results of the operations are correct

def test_basics():
    one = Rational(1)
    zero = Rational(0)
    assert array(1) == array(one)
    assert array([one]) == array([one])
    assert array([x]) == array([x])
    assert array(x) == array(Symbol("x"))
    assert array(one + x) == array(1 + x)

    X = array([one, zero, zero])
    assert (X == array([one, zero, zero])).all()
    assert (X == array([one, 0, 0])).all()


def test_arrays():
    one = Rational(1)
    zero = Rational(0)
    X = array([one, zero, zero])
    Y = one*X
    X = array([Symbol("a") + Rational(1, 2)])
    Y = X + X
    assert Y == array([1 + 2*Symbol("a")])
    Y = Y + 1
    assert Y == array([2 + 2*Symbol("a")])
    Y = X - X
    assert Y == array([0])


def test_conversion1():
    a = list2numpy([x**2, x])
    #looks like an array?
    assert isinstance(a, ndarray)
    assert a[0] == x**2
    assert a[1] == x
    assert len(a) == 2
    #yes, it's the array


def test_conversion2():
    a = 2*list2numpy([x**2, x])
    b = list2numpy([2*x**2, 2*x])
    assert (a == b).all()

    one = Rational(1)
    zero = Rational(0)
    X = list2numpy([one, zero, zero])
    Y = one*X
    X = list2numpy([Symbol("a") + Rational(1, 2)])
    Y = X + X
    assert Y == array([1 + 2*Symbol("a")])
    Y = Y + 1
    assert Y == array([2 + 2*Symbol("a")])
    Y = X - X
    assert Y == array([0])


def test_list2numpy():
    assert (array([x**2, x]) == list2numpy([x**2, x])).all()


def test_Matrix1():
    m = Matrix([[x, x**2], [5, 2/x]])
    assert (array(m.subs(x, 2)) == array([[2, 4], [5, 1]])).all()
    m = Matrix([[sin(x), x**2], [5, 2/x]])
    assert (array(m.subs(x, 2)) == array([[sin(2), 4], [5, 1]])).all()


def test_Matrix2():
    m = Matrix([[x, x**2], [5, 2/x]])
    assert (matrix(m.subs(x, 2)) == matrix([[2, 4], [5, 1]])).all()
    m = Matrix([[sin(x), x**2], [5, 2/x]])
    assert (matrix(m.subs(x, 2)) == matrix([[sin(2), 4], [5, 1]])).all()


def test_Matrix3():
    a = array([[2, 4], [5, 1]])
    assert Matrix(a) == Matrix([[2, 4], [5, 1]])
    assert Matrix(a) != Matrix([[2, 4], [5, 2]])
    a = array([[sin(2), 4], [5, 1]])
    assert Matrix(a) == Matrix([[sin(2), 4], [5, 1]])
    assert Matrix(a) != Matrix([[sin(0), 4], [5, 1]])


def test_Matrix4():
    a = matrix([[2, 4], [5, 1]])
    assert Matrix(a) == Matrix([[2, 4], [5, 1]])
    assert Matrix(a) != Matrix([[2, 4], [5, 2]])
    a = matrix([[sin(2), 4], [5, 1]])
    assert Matrix(a) == Matrix([[sin(2), 4], [5, 1]])
    assert Matrix(a) != Matrix([[sin(0), 4], [5, 1]])


def test_Matrix_sum():
    M = Matrix([[1, 2, 3], [x, y, x], [2*y, -50, z*x]])
    m = matrix([[2, 3, 4], [x, 5, 6], [x, y, z**2]])
    assert M + m == Matrix([[3, 5, 7], [2*x, y + 5, x + 6], [2*y + x, y - 50, z*x + z**2]])
    assert m + M == Matrix([[3, 5, 7], [2*x, y + 5, x + 6], [2*y + x, y - 50, z*x + z**2]])
    assert M + m == M.add(m)


def test_Matrix_mul():
    M = Matrix([[1, 2, 3], [x, y, x]])
    m = matrix([[2, 4], [x, 6], [x, z**2]])
    assert M*m == Matrix([
        [         2 + 5*x,        16 + 3*z**2],
        [2*x + x*y + x**2, 4*x + 6*y + x*z**2],
    ])

    assert m*M == Matrix([
        [   2 + 4*x,      4 + 4*y,      6 + 4*x],
        [       7*x,    2*x + 6*y,          9*x],
        [x + x*z**2, 2*x + y*z**2, 3*x + x*z**2],
    ])
    a = array([2])
    assert a[0] * M == 2 * M
    assert M * a[0] == 2 * M


def test_Matrix_array():
    class matarray(object):
        def __array__(self):
            from numpy import array
            return array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
    matarr = matarray()
    assert Matrix(matarr) == Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]])


def test_matrix2numpy():
    a = matrix2numpy(Matrix([[1, x**2], [3*sin(x), 0]]))
    assert isinstance(a, ndarray)
    assert a.shape == (2, 2)
    assert a[0, 0] == 1
    assert a[0, 1] == x**2
    assert a[1, 0] == 3*sin(x)
    assert a[1, 1] == 0


def test_matrix2numpy_conversion():
    a = Matrix([[1, 2, sin(x)], [x**2, x, Rational(1, 2)]])
    b = array([[1, 2, sin(x)], [x**2, x, Rational(1, 2)]])
    assert (matrix2numpy(a) == b).all()
    assert matrix2numpy(a).dtype == numpy.dtype('object')

    c = matrix2numpy(Matrix([[1, 2], [10, 20]]), dtype='int8')
    d = matrix2numpy(Matrix([[1, 2], [10, 20]]), dtype='float64')
    assert c.dtype == numpy.dtype('int8')
    assert d.dtype == numpy.dtype('float64')


def test_issue_3728():
    assert (Rational(1, 2)*array([2*x, 0]) == array([x, 0])).all()
    assert (Rational(1, 2) + array(
        [2*x, 0]) == array([2*x + Rational(1, 2), Rational(1, 2)])).all()
    assert (Float("0.5")*array([2*x, 0]) == array([Float("1.0")*x, 0])).all()
    assert (Float("0.5") + array(
        [2*x, 0]) == array([2*x + Float("0.5"), Float("0.5")])).all()


@conserve_mpmath_dps
def test_lambdify():
    mpmath.mp.dps = 16
    sin02 = mpmath.mpf("0.198669330795061215459412627")
    f = lambdify(x, sin(x), "numpy")
    prec = 1e-15
    assert -prec < f(0.2) - sin02 < prec
    try:
        f(x)  # if this succeeds, it can't be a numpy function
        assert False
    except AttributeError:
        pass


def test_lambdify_matrix():
    f = lambdify(x, Matrix([[x, 2*x], [1, 2]]), [{'ImmutableMatrix': numpy.array}, "numpy"])
    assert (f(1) == array([[1, 2], [1, 2]])).all()


def test_lambdify_matrix_multi_input():
    M = sympy.Matrix([[x**2, x*y, x*z],
                      [y*x, y**2, y*z],
                      [z*x, z*y, z**2]])
    f = lambdify((x, y, z), M, [{'ImmutableMatrix': numpy.array}, "numpy"])

    xh, yh, zh = 1.0, 2.0, 3.0
    expected = array([[xh**2, xh*yh, xh*zh],
                      [yh*xh, yh**2, yh*zh],
                      [zh*xh, zh*yh, zh**2]])
    actual = f(xh, yh, zh)
    assert numpy.allclose(actual, expected)


def test_lambdify_matrix_vec_input():
    X = sympy.DeferredVector('X')
    M = Matrix([
        [X[0]**2, X[0]*X[1], X[0]*X[2]],
        [X[1]*X[0], X[1]**2, X[1]*X[2]],
        [X[2]*X[0], X[2]*X[1], X[2]**2]])
    f = lambdify(X, M, [{'ImmutableMatrix': numpy.array}, "numpy"])

    Xh = array([1.0, 2.0, 3.0])
    expected = array([[Xh[0]**2, Xh[0]*Xh[1], Xh[0]*Xh[2]],
                      [Xh[1]*Xh[0], Xh[1]**2, Xh[1]*Xh[2]],
                      [Xh[2]*Xh[0], Xh[2]*Xh[1], Xh[2]**2]])
    actual = f(Xh)
    assert numpy.allclose(actual, expected)


def test_lambdify_transl():
    from sympy.utilities.lambdify import NUMPY_TRANSLATIONS
    for sym, mat in NUMPY_TRANSLATIONS.items():
        assert sym in sympy.__dict__
        assert mat in numpy.__dict__


def test_symarray():
    """Test creation of numpy arrays of sympy symbols."""

    import numpy as np
    import numpy.testing as npt

    syms = symbols('_0,_1,_2')
    s1 = symarray("", 3)
    s2 = symarray("", 3)
    npt.assert_array_equal(s1, np.array(syms, dtype=object))
    assert s1[0] == s2[0]

    a = symarray('a', 3)
    b = symarray('b', 3)
    assert not(a[0] == b[0])

    asyms = symbols('a_0,a_1,a_2')
    npt.assert_array_equal(a, np.array(asyms, dtype=object))

    # Multidimensional checks
    a2d = symarray('a', (2, 3))
    assert a2d.shape == (2, 3)
    a00, a12 = symbols('a_0_0,a_1_2')
    assert a2d[0, 0] == a00
    assert a2d[1, 2] == a12

    a3d = symarray('a', (2, 3, 2))
    assert a3d.shape == (2, 3, 2)
    a000, a120, a121 = symbols('a_0_0_0,a_1_2_0,a_1_2_1')
    assert a3d[0, 0, 0] == a000
    assert a3d[1, 2, 0] == a120
    assert a3d[1, 2, 1] == a121


def test_vectorize():
    assert (numpy.vectorize(
        sin)([1, 2, 3]) == numpy.array([sin(1), sin(2), sin(3)])).all()
