from sympy.utilities.pytest import XFAIL, raises
from sympy import (
    symbols, lambdify, sqrt, sin, cos, pi, atan, Rational, Float,
    Matrix, Lambda, exp, Integral, oo, I, Abs, Function)
from sympy.printing.lambdarepr import LambdaPrinter
from sympy import mpmath
from sympy.utilities.lambdify import implemented_function
from sympy.utilities.pytest import skip
from sympy.utilities.decorator import conserve_mpmath_dps
from sympy.external import import_module
import math
import sympy

MutableDenseMatrix = Matrix

numpy = import_module('numpy', min_python_version=(2, 6))

x, y, z = symbols('x,y,z')

#================== Test different arguments =======================


def test_no_args():
    f = lambdify([], 1)
    raises(TypeError, lambda: f(-1))
    assert f() == 1


def test_single_arg():
    f = lambdify(x, 2*x)
    assert f(1) == 2


def test_list_args():
    f = lambdify([x, y], x + y)
    assert f(1, 2) == 3


def test_str_args():
    f = lambdify('x,y,z', 'z,y,x')
    assert f(3, 2, 1) == (1, 2, 3)
    assert f(1.0, 2.0, 3.0) == (3.0, 2.0, 1.0)
    # make sure correct number of args required
    raises(TypeError, lambda: f(0))


def test_own_namespace():
    myfunc = lambda x: 1
    f = lambdify(x, sin(x), {"sin": myfunc})
    assert f(0.1) == 1
    assert f(100) == 1


def test_own_module():
    f = lambdify(x, sin(x), math)
    assert f(0) == 0.0
    f = lambdify(x, sympy.ceiling(x), math)
    raises(NameError, lambda: f(4.5))


def test_bad_args():
    # no vargs given
    raises(TypeError, lambda: lambdify(1))
    # same with vector exprs
    raises(TypeError, lambda: lambdify([1, 2]))


def test_atoms():
    # Non-Symbol atoms should not be pulled out from the expression namespace
    f = lambdify(x, pi + x, {"pi": 3.14})
    assert f(0) == 3.14
    f = lambdify(x, I + x, {"I": 1j})
    assert f(1) == 1 + 1j

#================== Test different modules =========================

# high precision output of sin(0.2*pi) is used to detect if precision is lost unwanted


@conserve_mpmath_dps
def test_sympy_lambda():
    mpmath.mp.dps = 50
    sin02 = mpmath.mpf("0.19866933079506121545941262711838975037020672954020")
    f = lambdify(x, sin(x), "sympy")
    assert f(x) == sin(x)
    prec = 1e-15
    assert -prec < f(Rational(1, 5)).evalf() - Float(str(sin02)) < prec
    # arctan is in numpy module and should not be available
    raises(NameError, lambda: lambdify(x, arctan(x), "sympy"))


@conserve_mpmath_dps
def test_math_lambda():
    mpmath.mp.dps = 50
    sin02 = mpmath.mpf("0.19866933079506121545941262711838975037020672954020")
    f = lambdify(x, sin(x), "math")
    prec = 1e-15
    assert -prec < f(0.2) - sin02 < prec
    raises(ValueError, lambda: f(x))
           # if this succeeds, it can't be a python math function


@conserve_mpmath_dps
def test_mpmath_lambda():
    mpmath.mp.dps = 50
    sin02 = mpmath.mpf("0.19866933079506121545941262711838975037020672954020")
    f = lambdify(x, sin(x), "mpmath")
    prec = 1e-49  # mpmath precision is around 50 decimal places
    assert -prec < f(mpmath.mpf("0.2")) - sin02 < prec
    raises(TypeError, lambda: f(x))
           # if this succeeds, it can't be a mpmath function


@conserve_mpmath_dps
@XFAIL
def test_number_precision():
    mpmath.mp.dps = 50
    sin02 = mpmath.mpf("0.19866933079506121545941262711838975037020672954020")
    f = lambdify(x, sin02, "mpmath")
    prec = 1e-49  # mpmath precision is around 50 decimal places
    assert -prec < f(0) - sin02 < prec

#================== Test Translations ==============================
# We can only check if all translated functions are valid. It has to be checked
# by hand if they are complete.


def test_math_transl():
    from sympy.utilities.lambdify import MATH_TRANSLATIONS
    for sym, mat in MATH_TRANSLATIONS.iteritems():
        assert sym in sympy.__dict__
        assert mat in math.__dict__


def test_mpmath_transl():
    from sympy.utilities.lambdify import MPMATH_TRANSLATIONS
    for sym, mat in MPMATH_TRANSLATIONS.iteritems():
        assert sym in sympy.__dict__ or sym == 'Matrix'
        assert mat in mpmath.__dict__


def test_numpy_transl():
    if not numpy:
        skip("numpy not installed or Python too old.")

    from sympy.utilities.lambdify import NUMPY_TRANSLATIONS
    for sym, nump in NUMPY_TRANSLATIONS.iteritems():
        assert sym in sympy.__dict__
        assert nump in numpy.__dict__


def test_numpy_translation_abs():
    if not numpy:
        skip("numpy not installed or Python too old.")

    f = lambdify(x, Abs(x), "numpy")
    assert f(-1) == 1
    assert f(1) == 1

#================== Test some functions ============================


def test_exponentiation():
    f = lambdify(x, x**2)
    assert f(-1) == 1
    assert f(0) == 0
    assert f(1) == 1
    assert f(-2) == 4
    assert f(2) == 4
    assert f(2.5) == 6.25


def test_sqrt():
    f = lambdify(x, sqrt(x))
    assert f(0) == 0.0
    assert f(1) == 1.0
    assert f(4) == 2.0
    assert abs(f(2) - 1.414) < 0.001
    assert f(6.25) == 2.5


def test_trig():
    f = lambdify([x], [cos(x), sin(x)])
    d = f(pi)
    prec = 1e-11
    assert -prec < d[0] + 1 < prec
    assert -prec < d[1] < prec
    d = f(3.14159)
    prec = 1e-5
    assert -prec < d[0] + 1 < prec
    assert -prec < d[1] < prec

#================== Test vectors ===================================


def test_vector_simple():
    f = lambdify((x, y, z), (z, y, x))
    assert f(3, 2, 1) == (1, 2, 3)
    assert f(1.0, 2.0, 3.0) == (3.0, 2.0, 1.0)
    # make sure correct number of args required
    raises(TypeError, lambda: f(0))


def test_vector_discontinuous():
    f = lambdify(x, (-1/x, 1/x))
    raises(ZeroDivisionError, lambda: f(0))
    assert f(1) == (-1.0, 1.0)
    assert f(2) == (-0.5, 0.5)
    assert f(-2) == (0.5, -0.5)


def test_trig_symbolic():
    f = lambdify([x], [cos(x), sin(x)])
    d = f(pi)
    assert abs(d[0] + 1) < 0.0001
    assert abs(d[1] - 0) < 0.0001


def test_trig_float():
    f = lambdify([x], [cos(x), sin(x)])
    d = f(3.14159)
    assert abs(d[0] + 1) < 0.0001
    assert abs(d[1] - 0) < 0.0001


def test_docs():
    f = lambdify(x, x**2)
    assert f(2) == 4
    f = lambdify([x, y, z], [z, y, x])
    assert f(1, 2, 3) == [3, 2, 1]
    f = lambdify(x, sqrt(x))
    assert f(4) == 2.0
    f = lambdify((x, y), sin(x*y)**2)
    assert f(0, 5) == 0


def test_math():
    f = lambdify((x, y), sin(x), modules="math")
    assert f(0, 5) == 0


def test_sin():
    f = lambdify(x, sin(x)**2)
    assert isinstance(f(2), float)
    f = lambdify(x, sin(x)**2, modules="math")
    assert isinstance(f(2), float)


def test_matrix():
    A = Matrix([[x, x*y], [sin(z) + 4, x**z]])
    sol = Matrix([[1, 2], [sin(3) + 4, 1]])
    f = lambdify((x, y, z), A, modules="sympy")
    assert f(1, 2, 3) == sol
    f = lambdify((x, y, z), (A, [A]), modules="sympy")
    assert f(1, 2, 3) == (sol, [sol])
    J = Matrix((x, x + y)).jacobian((x, y))
    v = Matrix((x, y))
    sol = Matrix([[1, 0], [1, 1]])
    assert lambdify(v, J, modules='sympy')(1, 2) == sol
    assert lambdify(v.T, J, modules='sympy')(1, 2) == sol


def test_integral():
    f = Lambda(x, exp(-x**2))
    l = lambdify(x, Integral(f(x), (x, -oo, oo)), modules="sympy")
    assert l(x) == Integral(exp(-x**2), (x, -oo, oo))

#================== Test symbolic ==================================


def test_sym_single_arg():
    f = lambdify(x, x * y)
    assert f(z) == z * y


def test_sym_list_args():
    f = lambdify([x, y], x + y + z)
    assert f(1, 2) == 3 + z


def test_sym_integral():
    f = Lambda(x, exp(-x**2))
    l = lambdify(x, Integral(f(x), (x, -oo, oo)), modules="sympy")
    assert l(y).doit() == sqrt(pi)


def test_namespace_order():
    # lambdify had a bug, such that module dictionaries or cached module
    # dictionaries would pull earlier namespaces into themselves.
    # Because the module dictionaries form the namespace of the
    # generated lambda, this meant that the behavior of a previously
    # generated lambda function could change as a result of later calls
    # to lambdify.
    n1 = {'f': lambda x: 'first f'}
    n2 = {'f': lambda x: 'second f',
          'g': lambda x: 'function g'}
    f = sympy.Function('f')
    g = sympy.Function('g')
    if1 = lambdify(x, f(x), modules=(n1, "sympy"))
    assert if1(1) == 'first f'
    if2 = lambdify(x, g(x), modules=(n2, "sympy"))
    # previously gave 'second f'
    assert if1(1) == 'first f'


def test_imps():
    # Here we check if the default returned functions are anonymous - in
    # the sense that we can have more than one function with the same name
    f = implemented_function('f', lambda x: 2*x)
    g = implemented_function('f', lambda x: math.sqrt(x))
    l1 = lambdify(x, f(x))
    l2 = lambdify(x, g(x))
    assert str(f(x)) == str(g(x))
    assert l1(3) == 6
    assert l2(3) == math.sqrt(3)
    # check that we can pass in a Function as input
    func = sympy.Function('myfunc')
    assert not hasattr(func, '_imp_')
    my_f = implemented_function(func, lambda x: 2*x)
    assert hasattr(func, '_imp_')
    # Error for functions with same name and different implementation
    f2 = implemented_function("f", lambda x: x + 101)
    raises(ValueError, lambda: lambdify(x, f(f2(x))))


def test_imps_wrong_args():
    raises(ValueError, lambda: implemented_function(sin, lambda x: x))


def test_lambdify_imps():
    # Test lambdify with implemented functions
    # first test basic (sympy) lambdify
    f = sympy.cos
    assert lambdify(x, f(x))(0) == 1
    assert lambdify(x, 1 + f(x))(0) == 2
    assert lambdify((x, y), y + f(x))(0, 1) == 2
    # make an implemented function and test
    f = implemented_function("f", lambda x: x + 100)
    assert lambdify(x, f(x))(0) == 100
    assert lambdify(x, 1 + f(x))(0) == 101
    assert lambdify((x, y), y + f(x))(0, 1) == 101
    # Can also handle tuples, lists, dicts as expressions
    lam = lambdify(x, (f(x), x))
    assert lam(3) == (103, 3)
    lam = lambdify(x, [f(x), x])
    assert lam(3) == [103, 3]
    lam = lambdify(x, [f(x), (f(x), x)])
    assert lam(3) == [103, (103, 3)]
    lam = lambdify(x, {f(x): x})
    assert lam(3) == {103: 3}
    lam = lambdify(x, {f(x): x})
    assert lam(3) == {103: 3}
    lam = lambdify(x, {x: f(x)})
    assert lam(3) == {3: 103}
    # Check that imp preferred to other namespaces by default
    d = {'f': lambda x: x + 99}
    lam = lambdify(x, f(x), d)
    assert lam(3) == 103
    # Unless flag passed
    lam = lambdify(x, f(x), d, use_imps=False)
    assert lam(3) == 102

def test_dummification():
    t = symbols('t')
    F = Function('F')
    G = Function('G')
    some_expr = 2 * F(t)**2 / G(t)
    lam = lambdify((F(t), G(t)), some_expr)
    assert lam(3, 9) == 2
    lam = lambdify(sin(t), 2 * sin(t)**2)
    assert lam(F(t)) == 2 * F(t)**2
    raises(SyntaxError, lambda: lambdify(F(t) * G(t), F(t) * G(t) + 5))
    raises(SyntaxError, lambda: lambdify(2 * F(t), 2 * F(t) + 5))
    raises(SyntaxError, lambda: lambdify(2 * F(t), 4 * F(t) + 5))


#================== Test special printers ==========================


def test_special_printers():
    class IntervalPrinter(LambdaPrinter):
        """Use ``lambda`` printer but print numbers as ``mpi`` intervals. """

        def _print_Integer(self, expr):
            return "mpi('%s')" % super(IntervalPrinter, self)._print_Integer(expr)

        def _print_Rational(self, expr):
            return "mpi('%s')" % super(IntervalPrinter, self)._print_Rational(expr)

    def intervalrepr(expr):
        return IntervalPrinter().doprint(expr)

    expr = sympy.sqrt(sympy.sqrt(2) + sympy.sqrt(3)) + sympy.S(1)/2

    func0 = lambdify((), expr, modules="mpmath", printer=intervalrepr)
    func1 = lambdify((), expr, modules="mpmath", printer=IntervalPrinter)
    func2 = lambdify((), expr, modules="mpmath", printer=IntervalPrinter())

    mpi = type(mpmath.mpi(1, 2))

    assert isinstance(func0(), mpi)
    assert isinstance(func1(), mpi)
    assert isinstance(func2(), mpi)
