import sys import math import numpy as np from numpy import sqrt, cos, sin, arctan, exp, log, pi from numpy.testing import (assert_, assert_allclose, assert_array_less, assert_almost_equal) import pytest from scipy.integrate import quad, dblquad, tplquad, nquad from scipy.special import erf, erfc from scipy._lib._ccallback import LowLevelCallable import ctypes import ctypes.util from scipy._lib._ccallback_c import sine_ctypes import scipy.integrate._test_multivariate as clib_test def assert_quad(value_and_err, tabled_value, error_tolerance=1.5e-8): value, err = value_and_err assert_allclose(value, tabled_value, atol=err, rtol=0) if error_tolerance is not None: assert_array_less(err, error_tolerance) def get_clib_test_routine(name, restype, *argtypes): ptr = getattr(clib_test, name) return ctypes.cast(ptr, ctypes.CFUNCTYPE(restype, *argtypes)) class TestCtypesQuad: def setup_method(self): if sys.platform == 'win32': files = ['api-ms-win-crt-math-l1-1-0.dll'] elif sys.platform == 'darwin': files = ['libm.dylib'] else: files = ['libm.so', 'libm.so.6'] for file in files: try: self.lib = ctypes.CDLL(file) break except OSError: pass else: # This test doesn't work on some Linux platforms (Fedora for # example) that put an ld script in libm.so - see gh-5370 pytest.skip("Ctypes can't import libm.so") 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 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]) def test_ctypes_sine(self): quad(LowLevelCallable(sine_ctypes), 0, 1) def test_ctypes_variants(self): sin_0 = get_clib_test_routine('_sin_0', ctypes.c_double, ctypes.c_double, ctypes.c_void_p) sin_1 = get_clib_test_routine('_sin_1', ctypes.c_double, ctypes.c_int, ctypes.POINTER(ctypes.c_double), ctypes.c_void_p) sin_2 = get_clib_test_routine('_sin_2', ctypes.c_double, ctypes.c_double) sin_3 = get_clib_test_routine('_sin_3', ctypes.c_double, ctypes.c_int, ctypes.POINTER(ctypes.c_double)) sin_4 = get_clib_test_routine('_sin_3', ctypes.c_double, ctypes.c_int, ctypes.c_double) all_sigs = [sin_0, sin_1, sin_2, sin_3, sin_4] legacy_sigs = [sin_2, sin_4] legacy_only_sigs = [sin_4] # LowLevelCallables work for new signatures for j, func in enumerate(all_sigs): callback = LowLevelCallable(func) if func in legacy_only_sigs: pytest.raises(ValueError, quad, callback, 0, pi) else: assert_allclose(quad(callback, 0, pi)[0], 2.0) # Plain ctypes items work only for legacy signatures for j, func in enumerate(legacy_sigs): if func in legacy_sigs: assert_allclose(quad(func, 0, pi)[0], 2.0) else: pytest.raises(ValueError, quad, func, 0, pi) class TestMultivariateCtypesQuad: def setup_method(self): restype = ctypes.c_double argtypes = (ctypes.c_int, ctypes.c_double) for name in ['_multivariate_typical', '_multivariate_indefinite', '_multivariate_sin']: func = get_clib_test_routine(name, restype, *argtypes) setattr(self, name, func) def test_typical(self): # 1) Typical function with two extra arguments: assert_quad(quad(self._multivariate_typical, 0, pi, (2, 1.8)), 0.30614353532540296487) def test_indefinite(self): # 2) Infinite integration limits --- Euler's constant assert_quad(quad(self._multivariate_indefinite, 0, np.inf), 0.577215664901532860606512) def test_threadsafety(self): # Ensure multivariate ctypes are threadsafe def threadsafety(y): return y + quad(self._multivariate_sin, 0, 1)[0] assert_quad(quad(threadsafety, 0, 1), 0.9596976941318602) class TestQuad: 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, np.inf), 0.577215664901532860606512) def test_singular(self): # 3) Singular points in region of integration. def myfunc(x): if 0 < x < 2.5: return sin(x) elif 2.5 <= 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, np.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, -np.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, error_tolerance=1.9e-8) def test_b_less_than_a(self): def f(x, p, q): return p * np.exp(-q*x) val_1, err_1 = quad(f, 0, np.inf, args=(2, 3)) val_2, err_2 = quad(f, np.inf, 0, args=(2, 3)) assert_allclose(val_1, -val_2, atol=max(err_1, err_2)) def test_b_less_than_a_2(self): def f(x, s): return np.exp(-x**2 / 2 / s) / np.sqrt(2.*s) val_1, err_1 = quad(f, -np.inf, np.inf, args=(2,)) val_2, err_2 = quad(f, np.inf, -np.inf, args=(2,)) assert_allclose(val_1, -val_2, atol=max(err_1, err_2)) def test_b_less_than_a_3(self): def f(x): return 1.0 val_1, err_1 = quad(f, 0, 1, weight='alg', wvar=(0, 0)) val_2, err_2 = quad(f, 1, 0, weight='alg', wvar=(0, 0)) assert_allclose(val_1, -val_2, atol=max(err_1, err_2)) def test_b_less_than_a_full_output(self): def f(x): return 1.0 res_1 = quad(f, 0, 1, weight='alg', wvar=(0, 0), full_output=True) res_2 = quad(f, 1, 0, weight='alg', wvar=(0, 0), full_output=True) err = max(res_1[1], res_2[1]) assert_allclose(res_1[0], -res_2[0], atol=err) 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_double_integral2(self): def func(x0, x1, t0, t1): return x0 + x1 + t0 + t1 def g(x): return x def h(x): return 2 * x args = 1, 2 assert_quad(dblquad(func, 1, 2, g, h, args=args),35./6 + 9*.5) def test_double_integral3(self): def func(x0, x1): return x0 + x1 + 1 + 2 assert_quad(dblquad(func, 1, 2, 1, 2),6.) @pytest.mark.parametrize( "x_lower, x_upper, y_lower, y_upper, expected", [ # Multiple integration of a function in n = 2 variables: f(x, y, z) # over domain D = [-inf, 0] for all n. (-np.inf, 0, -np.inf, 0, np.pi / 4), # Multiple integration of a function in n = 2 variables: f(x, y, z) # over domain D = [-inf, -1] for each n (one at a time). (-np.inf, -1, -np.inf, 0, np.pi / 4 * erfc(1)), (-np.inf, 0, -np.inf, -1, np.pi / 4 * erfc(1)), # Multiple integration of a function in n = 2 variables: f(x, y, z) # over domain D = [-inf, -1] for all n. (-np.inf, -1, -np.inf, -1, np.pi / 4 * (erfc(1) ** 2)), # Multiple integration of a function in n = 2 variables: f(x, y, z) # over domain D = [-inf, 1] for each n (one at a time). (-np.inf, 1, -np.inf, 0, np.pi / 4 * (erf(1) + 1)), (-np.inf, 0, -np.inf, 1, np.pi / 4 * (erf(1) + 1)), # Multiple integration of a function in n = 2 variables: f(x, y, z) # over domain D = [-inf, 1] for all n. (-np.inf, 1, -np.inf, 1, np.pi / 4 * ((erf(1) + 1) ** 2)), # Multiple integration of a function in n = 2 variables: f(x, y, z) # over domain Dx = [-inf, -1] and Dy = [-inf, 1]. (-np.inf, -1, -np.inf, 1, np.pi / 4 * ((erf(1) + 1) * erfc(1))), # Multiple integration of a function in n = 2 variables: f(x, y, z) # over domain Dx = [-inf, 1] and Dy = [-inf, -1]. (-np.inf, 1, -np.inf, -1, np.pi / 4 * ((erf(1) + 1) * erfc(1))), # Multiple integration of a function in n = 2 variables: f(x, y, z) # over domain D = [0, inf] for all n. (0, np.inf, 0, np.inf, np.pi / 4), # Multiple integration of a function in n = 2 variables: f(x, y, z) # over domain D = [1, inf] for each n (one at a time). (1, np.inf, 0, np.inf, np.pi / 4 * erfc(1)), (0, np.inf, 1, np.inf, np.pi / 4 * erfc(1)), # Multiple integration of a function in n = 2 variables: f(x, y, z) # over domain D = [1, inf] for all n. (1, np.inf, 1, np.inf, np.pi / 4 * (erfc(1) ** 2)), # Multiple integration of a function in n = 2 variables: f(x, y, z) # over domain D = [-1, inf] for each n (one at a time). (-1, np.inf, 0, np.inf, np.pi / 4 * (erf(1) + 1)), (0, np.inf, -1, np.inf, np.pi / 4 * (erf(1) + 1)), # Multiple integration of a function in n = 2 variables: f(x, y, z) # over domain D = [-1, inf] for all n. (-1, np.inf, -1, np.inf, np.pi / 4 * ((erf(1) + 1) ** 2)), # Multiple integration of a function in n = 2 variables: f(x, y, z) # over domain Dx = [-1, inf] and Dy = [1, inf]. (-1, np.inf, 1, np.inf, np.pi / 4 * ((erf(1) + 1) * erfc(1))), # Multiple integration of a function in n = 2 variables: f(x, y, z) # over domain Dx = [1, inf] and Dy = [-1, inf]. (1, np.inf, -1, np.inf, np.pi / 4 * ((erf(1) + 1) * erfc(1))), # Multiple integration of a function in n = 2 variables: f(x, y, z) # over domain D = [-inf, inf] for all n. (-np.inf, np.inf, -np.inf, np.inf, np.pi) ] ) def test_double_integral_improper( self, x_lower, x_upper, y_lower, y_upper, expected ): # The Gaussian Integral. def f(x, y): return np.exp(-x ** 2 - y ** 2) assert_quad( dblquad(f, x_lower, x_upper, y_lower, y_upper), expected, error_tolerance=3e-8 ) def test_triple_integral(self): # 9) Triple Integral test def simpfunc(z, y, x, t): # Note order of arguments. return (x+y+z)*t 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, (2.,)), 2*8/3.0 * (b**4.0 - a**4.0)) @pytest.mark.parametrize( "x_lower, x_upper, y_lower, y_upper, z_lower, z_upper, expected", [ # Multiple integration of a function in n = 3 variables: f(x, y, z) # over domain D = [-inf, 0] for all n. (-np.inf, 0, -np.inf, 0, -np.inf, 0, (np.pi ** (3 / 2)) / 8), # Multiple integration of a function in n = 3 variables: f(x, y, z) # over domain D = [-inf, -1] for each n (one at a time). (-np.inf, -1, -np.inf, 0, -np.inf, 0, (np.pi ** (3 / 2)) / 8 * erfc(1)), (-np.inf, 0, -np.inf, -1, -np.inf, 0, (np.pi ** (3 / 2)) / 8 * erfc(1)), (-np.inf, 0, -np.inf, 0, -np.inf, -1, (np.pi ** (3 / 2)) / 8 * erfc(1)), # Multiple integration of a function in n = 3 variables: f(x, y, z) # over domain D = [-inf, -1] for each n (two at a time). (-np.inf, -1, -np.inf, -1, -np.inf, 0, (np.pi ** (3 / 2)) / 8 * (erfc(1) ** 2)), (-np.inf, -1, -np.inf, 0, -np.inf, -1, (np.pi ** (3 / 2)) / 8 * (erfc(1) ** 2)), (-np.inf, 0, -np.inf, -1, -np.inf, -1, (np.pi ** (3 / 2)) / 8 * (erfc(1) ** 2)), # Multiple integration of a function in n = 3 variables: f(x, y, z) # over domain D = [-inf, -1] for all n. (-np.inf, -1, -np.inf, -1, -np.inf, -1, (np.pi ** (3 / 2)) / 8 * (erfc(1) ** 3)), # Multiple integration of a function in n = 3 variables: f(x, y, z) # over domain Dx = [-inf, -1] and Dy = Dz = [-inf, 1]. (-np.inf, -1, -np.inf, 1, -np.inf, 1, (np.pi ** (3 / 2)) / 8 * (((erf(1) + 1) ** 2) * erfc(1))), # Multiple integration of a function in n = 3 variables: f(x, y, z) # over domain Dx = Dy = [-inf, -1] and Dz = [-inf, 1]. (-np.inf, -1, -np.inf, -1, -np.inf, 1, (np.pi ** (3 / 2)) / 8 * ((erf(1) + 1) * (erfc(1) ** 2))), # Multiple integration of a function in n = 3 variables: f(x, y, z) # over domain Dx = Dz = [-inf, -1] and Dy = [-inf, 1]. (-np.inf, -1, -np.inf, 1, -np.inf, -1, (np.pi ** (3 / 2)) / 8 * ((erf(1) + 1) * (erfc(1) ** 2))), # Multiple integration of a function in n = 3 variables: f(x, y, z) # over domain Dx = [-inf, 1] and Dy = Dz = [-inf, -1]. (-np.inf, 1, -np.inf, -1, -np.inf, -1, (np.pi ** (3 / 2)) / 8 * ((erf(1) + 1) * (erfc(1) ** 2))), # Multiple integration of a function in n = 3 variables: f(x, y, z) # over domain Dx = Dy = [-inf, 1] and Dz = [-inf, -1]. (-np.inf, 1, -np.inf, 1, -np.inf, -1, (np.pi ** (3 / 2)) / 8 * (((erf(1) + 1) ** 2) * erfc(1))), # Multiple integration of a function in n = 3 variables: f(x, y, z) # over domain Dx = Dz = [-inf, 1] and Dy = [-inf, -1]. (-np.inf, 1, -np.inf, -1, -np.inf, 1, (np.pi ** (3 / 2)) / 8 * (((erf(1) + 1) ** 2) * erfc(1))), # Multiple integration of a function in n = 3 variables: f(x, y, z) # over domain D = [-inf, 1] for each n (one at a time). (-np.inf, 1, -np.inf, 0, -np.inf, 0, (np.pi ** (3 / 2)) / 8 * (erf(1) + 1)), (-np.inf, 0, -np.inf, 1, -np.inf, 0, (np.pi ** (3 / 2)) / 8 * (erf(1) + 1)), (-np.inf, 0, -np.inf, 0, -np.inf, 1, (np.pi ** (3 / 2)) / 8 * (erf(1) + 1)), # Multiple integration of a function in n = 3 variables: f(x, y, z) # over domain D = [-inf, 1] for each n (two at a time). (-np.inf, 1, -np.inf, 1, -np.inf, 0, (np.pi ** (3 / 2)) / 8 * ((erf(1) + 1) ** 2)), (-np.inf, 1, -np.inf, 0, -np.inf, 1, (np.pi ** (3 / 2)) / 8 * ((erf(1) + 1) ** 2)), (-np.inf, 0, -np.inf, 1, -np.inf, 1, (np.pi ** (3 / 2)) / 8 * ((erf(1) + 1) ** 2)), # Multiple integration of a function in n = 3 variables: f(x, y, z) # over domain D = [-inf, 1] for all n. (-np.inf, 1, -np.inf, 1, -np.inf, 1, (np.pi ** (3 / 2)) / 8 * ((erf(1) + 1) ** 3)), # Multiple integration of a function in n = 3 variables: f(x, y, z) # over domain D = [0, inf] for all n. (0, np.inf, 0, np.inf, 0, np.inf, (np.pi ** (3 / 2)) / 8), # Multiple integration of a function in n = 3 variables: f(x, y, z) # over domain D = [1, inf] for each n (one at a time). (1, np.inf, 0, np.inf, 0, np.inf, (np.pi ** (3 / 2)) / 8 * erfc(1)), (0, np.inf, 1, np.inf, 0, np.inf, (np.pi ** (3 / 2)) / 8 * erfc(1)), (0, np.inf, 0, np.inf, 1, np.inf, (np.pi ** (3 / 2)) / 8 * erfc(1)), # Multiple integration of a function in n = 3 variables: f(x, y, z) # over domain D = [1, inf] for each n (two at a time). (1, np.inf, 1, np.inf, 0, np.inf, (np.pi ** (3 / 2)) / 8 * (erfc(1) ** 2)), (1, np.inf, 0, np.inf, 1, np.inf, (np.pi ** (3 / 2)) / 8 * (erfc(1) ** 2)), (0, np.inf, 1, np.inf, 1, np.inf, (np.pi ** (3 / 2)) / 8 * (erfc(1) ** 2)), # Multiple integration of a function in n = 3 variables: f(x, y, z) # over domain D = [1, inf] for all n. (1, np.inf, 1, np.inf, 1, np.inf, (np.pi ** (3 / 2)) / 8 * (erfc(1) ** 3)), # Multiple integration of a function in n = 3 variables: f(x, y, z) # over domain D = [-1, inf] for each n (one at a time). (-1, np.inf, 0, np.inf, 0, np.inf, (np.pi ** (3 / 2)) / 8 * (erf(1) + 1)), (0, np.inf, -1, np.inf, 0, np.inf, (np.pi ** (3 / 2)) / 8 * (erf(1) + 1)), (0, np.inf, 0, np.inf, -1, np.inf, (np.pi ** (3 / 2)) / 8 * (erf(1) + 1)), # Multiple integration of a function in n = 3 variables: f(x, y, z) # over domain D = [-1, inf] for each n (two at a time). (-1, np.inf, -1, np.inf, 0, np.inf, (np.pi ** (3 / 2)) / 8 * ((erf(1) + 1) ** 2)), (-1, np.inf, 0, np.inf, -1, np.inf, (np.pi ** (3 / 2)) / 8 * ((erf(1) + 1) ** 2)), (0, np.inf, -1, np.inf, -1, np.inf, (np.pi ** (3 / 2)) / 8 * ((erf(1) + 1) ** 2)), # Multiple integration of a function in n = 3 variables: f(x, y, z) # over domain D = [-1, inf] for all n. (-1, np.inf, -1, np.inf, -1, np.inf, (np.pi ** (3 / 2)) / 8 * ((erf(1) + 1) ** 3)), # Multiple integration of a function in n = 3 variables: f(x, y, z) # over domain Dx = [1, inf] and Dy = Dz = [-1, inf]. (1, np.inf, -1, np.inf, -1, np.inf, (np.pi ** (3 / 2)) / 8 * (((erf(1) + 1) ** 2) * erfc(1))), # Multiple integration of a function in n = 3 variables: f(x, y, z) # over domain Dx = Dy = [1, inf] and Dz = [-1, inf]. (1, np.inf, 1, np.inf, -1, np.inf, (np.pi ** (3 / 2)) / 8 * ((erf(1) + 1) * (erfc(1) ** 2))), # Multiple integration of a function in n = 3 variables: f(x, y, z) # over domain Dx = Dz = [1, inf] and Dy = [-1, inf]. (1, np.inf, -1, np.inf, 1, np.inf, (np.pi ** (3 / 2)) / 8 * ((erf(1) + 1) * (erfc(1) ** 2))), # Multiple integration of a function in n = 3 variables: f(x, y, z) # over domain Dx = [-1, inf] and Dy = Dz = [1, inf]. (-1, np.inf, 1, np.inf, 1, np.inf, (np.pi ** (3 / 2)) / 8 * ((erf(1) + 1) * (erfc(1) ** 2))), # Multiple integration of a function in n = 3 variables: f(x, y, z) # over domain Dx = Dy = [-1, inf] and Dz = [1, inf]. (-1, np.inf, -1, np.inf, 1, np.inf, (np.pi ** (3 / 2)) / 8 * (((erf(1) + 1) ** 2) * erfc(1))), # Multiple integration of a function in n = 3 variables: f(x, y, z) # over domain Dx = Dz = [-1, inf] and Dy = [1, inf]. (-1, np.inf, 1, np.inf, -1, np.inf, (np.pi ** (3 / 2)) / 8 * (((erf(1) + 1) ** 2) * erfc(1))), # Multiple integration of a function in n = 3 variables: f(x, y, z) # over domain D = [-inf, inf] for all n. (-np.inf, np.inf, -np.inf, np.inf, -np.inf, np.inf, np.pi ** (3 / 2)), ], ) def test_triple_integral_improper( self, x_lower, x_upper, y_lower, y_upper, z_lower, z_upper, expected ): # The Gaussian Integral. def f(x, y, z): return np.exp(-x ** 2 - y ** 2 - z ** 2) assert_quad( tplquad(f, x_lower, x_upper, y_lower, y_upper, z_lower, z_upper), expected, error_tolerance=6e-8 ) def test_complex(self): def tfunc(x): return np.exp(1j*x) assert np.allclose( quad(tfunc, 0, np.pi/2, complex_func=True)[0], 1+1j) # We consider a divergent case in order to force quadpack # to return an error message. The output is compared # against what is returned by explicit integration # of the parts. kwargs = {'a': 0, 'b': np.inf, 'full_output': True, 'weight': 'cos', 'wvar': 1} res_c = quad(tfunc, complex_func=True, **kwargs) res_r = quad(lambda x: np.real(np.exp(1j*x)), complex_func=False, **kwargs) res_i = quad(lambda x: np.imag(np.exp(1j*x)), complex_func=False, **kwargs) np.testing.assert_equal(res_c[0], res_r[0] + 1j*res_i[0]) np.testing.assert_equal(res_c[1], res_r[1] + 1j*res_i[1]) assert len(res_c[2]['real']) == len(res_r[2:]) == 3 assert res_c[2]['real'][2] == res_r[4] assert res_c[2]['real'][1] == res_r[3] assert res_c[2]['real'][0]['lst'] == res_r[2]['lst'] assert len(res_c[2]['imag']) == len(res_i[2:]) == 1 assert res_c[2]['imag'][0]['lst'] == res_i[2]['lst'] class TestNQuad: def test_fixed_limits(self): def func1(x0, x1, x2, x3): val = (x0**2 + x1*x2 - x3**3 + np.sin(x0) + (1 if (x0 - 0.2*x3 - 0.5 - 0.25*x1 > 0) else 0)) return val 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, {}, {}, {}], full_output=True) assert_quad(res[:-1], 1.5267454070738635) assert_(res[-1]['neval'] > 0 and res[-1]['neval'] < 4e5) def test_variable_limits(self): scale = .1 def func2(x0, x1, x2, x3, t0, t1): val = (x0*x1*x3**2 + np.sin(x2) + 1 + (1 if x0 + t1*x1 - t0 > 0 else 0)) return val 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) def test_dict_as_opts(self): try: nquad(lambda x, y: x * y, [[0, 1], [0, 1]], opts={'epsrel': 0.0001}) except TypeError: assert False