from __future__ import division, print_function, absolute_import

import sys
import math
import numpy as np
from numpy import sqrt, cos, sin, arctan, exp, log, pi, Inf
from numpy.testing import (assert_, TestCase, run_module_suite, dec,
        assert_allclose, assert_array_less, assert_almost_equal)
from scipy.integrate import quad, dblquad, tplquad, nquad
from scipy.lib.six import xrange

try:
    import ctypes
    import ctypes.util
    _ctypes_missing = False
except ImportError:
    _ctypes_missing = True

try:
    import scipy.integrate._test_multivariate as clib_test
    _ctypes_multivariate_fail = False
except:
    _ctypes_multivariate_fail = True


def assert_quad(value_and_err, tabled_value, errTol=1.5e-8):
    value, err = value_and_err
    assert_allclose(value, tabled_value, atol=err, rtol=0)
    if errTol is not None:
        assert_array_less(err, errTol)


class TestCtypesQuad(TestCase):
    @dec.skipif(_ctypes_missing, msg="Ctypes library could not be found")
    def setUp(self):
        if sys.platform == 'win32':
            file = ctypes.util.find_msvcrt()
        elif sys.platform == 'darwin':
            file = 'libm.dylib'
        else:
            file = 'libm.so'
        self.lib = ctypes.CDLL(file)
        restype = ctypes.c_double
        argtypes = (ctypes.c_double,)
        for name in ['sin', 'cos', 'tan']:
            func = getattr(self.lib, name)
            func.restype = restype
            func.argtypes = argtypes

    @dec.skipif(_ctypes_missing, msg="Ctypes library could not be found")
    def test_typical(self):
        assert_quad(quad(self.lib.sin,0,5),quad(math.sin,0,5)[0])
        assert_quad(quad(self.lib.cos,0,5),quad(math.cos,0,5)[0])
        assert_quad(quad(self.lib.tan,0,1),quad(math.tan,0,1)[0])

    #@dec.skipif(_ctypes_missing, msg="Ctypes library could not be found")
    # This doesn't seem to always work.  Need a better way to figure out
    # whether the fast path is called.
    @dec.knownfailureif(True, msg="Unreliable test, see ticket 1684.")
    def test_improvement(self):
        import time
        start = time.time()
        for i in xrange(100):
            quad(self.lib.sin, 0, 100)
        fast = time.time() - start
        start = time.time()
        for i in xrange(100):
            quad(math.sin, 0, 100)
        slow = time.time() - start
        assert_(fast < 0.5*slow, (fast, slow))


class TestMultivariateCtypesQuad(TestCase):
    @dec.skipif(_ctypes_missing or _ctypes_multivariate_fail,
                msg="Compiled test functions not loaded")
    def setUp(self):
        self.lib = ctypes.CDLL(clib_test.__file__)
        restype = ctypes.c_double
        argtypes = (ctypes.c_int,ctypes.c_double)
        for name in ['_multivariate_typical','_multivariate_indefinite',
                     '_multivariate_sin']:
            func = getattr(self.lib, name)
            func.restype = restype
            func.argtypes = argtypes

    @dec.skipif(_ctypes_missing or _ctypes_multivariate_fail,
                msg="Compiled test functions not loaded")
    def test_typical(self):
        # 1) Typical function with two extra arguments:
        assert_quad(quad(self.lib._multivariate_typical,0,pi,(2,1.8)),
                    0.30614353532540296487)

    @dec.skipif(_ctypes_missing or _ctypes_multivariate_fail,
                msg="Compiled test functions not loaded")
    def test_indefinite(self):
        # 2) Infinite integration limits --- Euler's constant
        assert_quad(quad(self.lib._multivariate_indefinite,0,Inf),
                    0.577215664901532860606512)

    @dec.skipif(_ctypes_missing or _ctypes_multivariate_fail,
                msg="Compiled test functions not loaded")
    def test_threadsafety(self):
        # Ensure multivariate ctypes are threadsafe
        def threadsafety(y):
            return y + quad(self.lib._multivariate_sin, 0, 1)[0]
        assert_quad(quad(threadsafety, 0, 1), 0.9596976941318602)

    @dec.skipif(_ctypes_missing or _ctypes_multivariate_fail,
                msg="Compiled test functions not loaded")
    def test_improvement(self):
        def myfunc(x):           # Euler's constant integrand
            return -exp(-x)*log(x)
        import time
        start = time.time()
        for i in xrange(20):
            quad(self.lib._multivariate_indefinite, 0, 100)
        fast = time.time() - start
        start = time.time()
        for i in xrange(20):
            quad(myfunc, 0, 100)
        slow = time.time() - start
        # 2+ times faster speeds generated by nontrivial ctypes
        # function (single variable)
        assert_(fast < 0.5*slow, (fast, slow))


class TestQuad(TestCase):
    def test_typical(self):
        # 1) Typical function with two extra arguments:
        def myfunc(x,n,z):       # Bessel function integrand
            return cos(n*x-z*sin(x))/pi
        assert_quad(quad(myfunc,0,pi,(2,1.8)), 0.30614353532540296487)

    def test_indefinite(self):
        # 2) Infinite integration limits --- Euler's constant
        def myfunc(x):           # Euler's constant integrand
            return -exp(-x)*log(x)
        assert_quad(quad(myfunc,0,Inf), 0.577215664901532860606512)

    def test_singular(self):
        # 3) Singular points in region of integration.
        def myfunc(x):
            if x > 0 and x < 2.5:
                return sin(x)
            elif x >= 2.5 and x <= 5.0:
                return exp(-x)
            else:
                return 0.0

        assert_quad(quad(myfunc,0,10,points=[2.5,5.0]),
                    1 - cos(2.5) + exp(-2.5) - exp(-5.0))

    def test_sine_weighted_finite(self):
        # 4) Sine weighted integral (finite limits)
        def myfunc(x,a):
            return exp(a*(x-1))

        ome = 2.0**3.4
        assert_quad(quad(myfunc,0,1,args=20,weight='sin',wvar=ome),
                    (20*sin(ome)-ome*cos(ome)+ome*exp(-20))/(20**2 + ome**2))

    def test_sine_weighted_infinite(self):
        # 5) Sine weighted integral (infinite limits)
        def myfunc(x,a):
            return exp(-x*a)

        a = 4.0
        ome = 3.0
        assert_quad(quad(myfunc,0,Inf,args=a,weight='sin',wvar=ome),
                    ome/(a**2 + ome**2))

    def test_cosine_weighted_infinite(self):
        # 6) Cosine weighted integral (negative infinite limits)
        def myfunc(x,a):
            return exp(x*a)

        a = 2.5
        ome = 2.3
        assert_quad(quad(myfunc,-Inf,0,args=a,weight='cos',wvar=ome),
                    a/(a**2 + ome**2))

    def test_algebraic_log_weight(self):
        # 6) Algebraic-logarithmic weight.
        def myfunc(x,a):
            return 1/(1+x+2**(-a))

        a = 1.5
        assert_quad(quad(myfunc,-1,1,args=a,weight='alg',wvar=(-0.5,-0.5)),
                    pi/sqrt((1+2**(-a))**2 - 1))

    def test_cauchypv_weight(self):
        # 7) Cauchy prinicpal value weighting w(x) = 1/(x-c)
        def myfunc(x,a):
            return 2.0**(-a)/((x-1)**2+4.0**(-a))

        a = 0.4
        tabledValue = (2.0**(-0.4)*log(1.5)-2.0**(-1.4)*log((4.0**(-a)+16)/(4.0**(-a)+1))
                     - arctan(2.0**(a+2)) - arctan(2.0**a))/(4.0**(-a) + 1)
        assert_quad(quad(myfunc,0,5,args=0.4,weight='cauchy',wvar=2.0),
                    tabledValue, errTol=1.9e-8)

    def test_double_integral(self):
        # 8) Double Integral test
        def simpfunc(y,x):       # Note order of arguments.
            return x+y

        a, b = 1.0, 2.0
        assert_quad(dblquad(simpfunc,a,b,lambda x: x, lambda x: 2*x),
                    5/6.0 * (b**3.0-a**3.0))

    def test_triple_integral(self):
        # 9) Triple Integral test
        def simpfunc(z,y,x):      # Note order of arguments.
            return x+y+z

        a, b = 1.0, 2.0
        assert_quad(tplquad(simpfunc,a,b,
                            lambda x: x, lambda x: 2*x,
                            lambda x,y: x-y, lambda x,y: x+y),
                    8/3.0 * (b**4.0 - a**4.0))


class TestNQuad(TestCase):
    def test_fixed_limits(self):
        def func1(x0, x1, x2, x3):
            return x0**2 + x1*x2 - x3**3 + np.sin(x0) + (1 if
                        (x0 - 0.2*x3 - 0.5 - 0.25*x1 > 0) else 0)

        def opts_basic(*args):
            return {'points': [0.2*args[2] + 0.5 + 0.25*args[0]]}

        res = nquad(func1, [[0,1], [-1,1], [.13,.8], [-.15,1]],
                    opts=[opts_basic, {}, {}, {}])
        assert_quad(res, 1.5267454070738635)

    def test_variable_limits(self):
        scale = .1

        def func2(x0, x1, x2, x3, t0, t1):
            return x0*x1*x3**2 + np.sin(x2) + 1 + (1 if x0 + t1*x1 - t0 > 0 else 0)

        def lim0(x1, x2, x3, t0, t1):
            return [scale * (x1**2 + x2 + np.cos(x3)*t0*t1 + 1) - 1,
                    scale * (x1**2 + x2 + np.cos(x3)*t0*t1 + 1) + 1]

        def lim1(x2, x3, t0, t1):
            return [scale * (t0*x2 + t1*x3) - 1,
                    scale * (t0*x2 + t1*x3) + 1]

        def lim2(x3, t0, t1):
            return [scale * (x3 + t0**2*t1**3) - 1,
                    scale * (x3 + t0**2*t1**3) + 1]

        def lim3(t0, t1):
            return [scale * (t0 + t1) - 1, scale * (t0 + t1) + 1]

        def opts0(x1, x2, x3, t0, t1):
            return {'points':[t0 - t1*x1]}

        def opts1(x2, x3, t0, t1):
            return {}

        def opts2(x3, t0, t1):
            return {}

        def opts3(t0, t1):
            return {}

        res = nquad(func2, [lim0, lim1, lim2, lim3], args=(0,0),
                    opts=[opts0, opts1, opts2, opts3])
        assert_quad(res, 25.066666666666663)

    def test_square_separate_ranges_and_opts(self):
        def f(y, x):
            return 1.0

        assert_quad(nquad(f, [[-1, 1], [-1, 1]], opts=[{}, {}]), 4.0)

    def test_square_aliased_ranges_and_opts(self):
        def f(y, x):
            return 1.0

        r = [-1, 1]
        opt = {}
        assert_quad(nquad(f, [r, r], opts=[opt, opt]), 4.0)

    def test_square_separate_fn_ranges_and_opts(self):
        def f(y, x):
            return 1.0

        def fn_range0(*args):
            return (-1, 1)

        def fn_range1(*args):
            return (-1, 1)

        def fn_opt0(*args):
            return {}

        def fn_opt1(*args):
            return {}

        ranges = [fn_range0, fn_range1]
        opts = [fn_opt0, fn_opt1]
        assert_quad(nquad(f, ranges, opts=opts), 4.0)

    def test_square_aliased_fn_ranges_and_opts(self):
        def f(y, x):
            return 1.0

        def fn_range(*args):
            return (-1, 1)

        def fn_opt(*args):
            return {}

        ranges = [fn_range, fn_range]
        opts = [fn_opt, fn_opt]
        assert_quad(nquad(f, ranges, opts=opts), 4.0)

    def test_matching_quad(self):
        def func(x):
            return x**2 + 1

        res, reserr = quad(func, 0, 4)
        res2, reserr2 = nquad(func, ranges=[[0, 4]])
        assert_almost_equal(res, res2)
        assert_almost_equal(reserr, reserr2)

    def test_matching_dblquad(self):
        def func2d(x0, x1):
            return x0**2 + x1**3 - x0 * x1 + 1

        res, reserr = dblquad(func2d, -2, 2, lambda x:-3, lambda x:3)
        res2, reserr2 = nquad(func2d, [[-3, 3], (-2, 2)])
        assert_almost_equal(res, res2)
        assert_almost_equal(reserr, reserr2)

    def test_matching_tplquad(self):
        def func3d(x0, x1, x2, c0, c1):
            return x0**2 + c0 * x1**3 - x0 * x1 + 1 + c1 * np.sin(x2)

        res = tplquad(func3d, -1, 2, lambda x: -2, lambda x: 2,
                      lambda x, y: -np.pi, lambda x, y: np.pi,
                      args=(2, 3))
        res2 = nquad(func3d, [[-np.pi, np.pi], [-2, 2], (-1, 2)], args=(2, 3))
        assert_almost_equal(res, res2)


if __name__ == "__main__":
    run_module_suite()
