def test_nu_varying_gamma_mod(s, nu, N, h): ht = HankelTransform(nu=nu, N=N, h=h) ans = ht.integrate(lambda x: x ** (nu - 2 * s + 1) * gammainc_(s, x ** 2), False, False) anl = 0.5 ** (2 * s - nu - 1) * gammaincc_(1 - s + nu, 0.25) print("Numerical Result: ", ans, " (required %s)" % anl) assert np.isclose(ans, anl, rtol=1e-3)
def test_nu_varying_powerlaw(s, nu, N, h): ht = HankelTransform(nu=nu, N=N, h=h) ans = ht.integrate(lambda x: x**(s + 1), False, False) anl = 2**(s + 1) * gamma(0.5 * (2 + nu + s)) / gamma(0.5 * (nu - s)) print("Numerical Result: ", ans, " (required %s)" % anl) assert np.isclose(ans, anl, rtol=1e-3)
def test_nu0_x4(): """ Result on wikipedia """ ht = HankelTransform(nu=0, N=150, h=10 ** -1.5) ans = ht.integrate(lambda x: x ** 4, False, False) print("Numerical Result: ", ans, " (required 9)") assert np.isclose(ans, 9, rtol=1e-3)
def test_nu0_x4(): """ Result on wikipedia """ ht = HankelTransform(nu=0, N=150, h=10**-1.5) ans = ht.integrate(lambda x: x**4, False, False) print("Numerical Result: ", ans, " (required 9)") assert np.isclose(ans, 9, rtol=1e-3)
def test_nu_varying_powerlaw(s, nu, N, h): ht = HankelTransform(nu=nu, N=N, h=h) ans = ht.integrate(lambda x: x ** (s + 1), False, False) anl = 2 ** (s + 1) * gamma(0.5 * (2 + nu + s)) / gamma(0.5 * (nu - s)) print("Numerical Result: ", ans, " (required %s)" % anl) assert np.isclose(ans, anl, rtol=1e-3)
def test_nu_varying_gamma_mod(s, nu, N, h): ht = HankelTransform(nu=nu, N=N, h=h) ans = ht.integrate(lambda x: x**(nu - 2 * s + 1) * gammainc_(s, x**2), False, False) anl = 0.5**(2 * s - nu - 1) * gammaincc_(1 - s + nu, 0.25) print("Numerical Result: ", ans, " (required %s)" % anl) assert np.isclose(ans, anl, rtol=1e-3)
def test_nu0_f_gauss(): """ Result on wikipedia """ z = 2 ht = HankelTransform(nu=0, N=50, h=0.01) ans = ht.integrate(lambda x: x * np.exp(-0.5 * z**2 * x**2), False, False) anl = 1.0 / z**2 * np.exp(-0.5 / z**2) print("Numerical Result: ", ans, " (required %s)" % anl) assert np.isclose(ans, anl, rtol=1e-3)
def test_nu0_f_gauss(): """ Result on wikipedia """ z = 2 ht = HankelTransform(nu=0, N=50, h=0.01) ans = ht.integrate(lambda x: x * np.exp(-0.5 * z ** 2 * x ** 2), False, False) anl = 1. / z ** 2 * np.exp(-0.5 / z ** 2) print("Numerical Result: ", ans, " (required %s)" % anl) assert np.isclose(ans, anl, rtol=1e-3)
def test_nu0_f_x2(): """ Test f(x) = x^2, nu=0 Result on wikipedia """ ht = HankelTransform(nu=0, N=100, h=10 ** -1.5) ans = ht.integrate(lambda x: x ** 2, False, False) print("Numerical Result: ", ans, " (required -1)") assert np.isclose(ans, -1, rtol=1e-3)
def test_nu0_f_x_on_x2(): """ Test f(x) = x/(x**2 + 1), nu=0 This test is done in the Ogata (2005) paper, section 5" """ ht = HankelTransform(nu=0, N=50, h=10 ** -1.5) ans = ht.integrate(lambda x: x / (x ** 2 + 1), False, False) print("Numerical Result: ", ans, " (required %s)" % k0(1)) assert np.isclose(ans, k0(1), rtol=1e-3)
def test_nu0_f_unity(): """ Test f(x) = 1, nu=0 This test is done in the Ogata (2005) paper, section 5" """ ht = HankelTransform(nu=0, N=50, h=0.1) ans = ht.integrate(lambda x: 1, False, False) print("Numerical Result: ", ans, " (required %s)" % 1) assert np.isclose(ans, 1, rtol=1e-3)
def test_nu0_f_unity(): """ Test f(x) = 1, nu=0 This test is done in the Ogata (2005) paper, section 5" """ ht = HankelTransform(nu=0, N=50, h=0.1) ans = ht.integrate(lambda x: 1, False, False) print("Numerical Result: ", ans, " (required %s)" % 1) assert np.isclose(ans, 1, rtol=1e-3)
def test_nu0_f_x_on_x2(): """ Test f(x) = x/(x**2 + 1), nu=0 This test is done in the Ogata (2005) paper, section 5" """ ht = HankelTransform(nu=0, N=50, h=10**-1.5) ans = ht.integrate(lambda x: x / (x**2 + 1), False, False) print("Numerical Result: ", ans, " (required %s)" % k0(1)) assert np.isclose(ans, k0(1), rtol=1e-3)
def test_nu0_f_x2(): """ Test f(x) = x^2, nu=0 Result on wikipedia """ ht = HankelTransform(nu=0, N=100, h=10**-1.5) ans = ht.integrate(lambda x: x**2, False, False) print("Numerical Result: ", ans, " (required -1)") assert np.isclose(ans, -1, rtol=1e-3)
def test_nu0_x_on_sqrt_x2_pz2(): """ Result on wikipedia """ # Note that the number required is highly dependent on z .... smaller z is harder. ht = HankelTransform(nu=0, N=50, h=10**-1.3) z = 1 ans = ht.integrate(lambda x: x / np.sqrt(x**2 + z**2), False, False) anl = np.exp(-z) print("Numerical Result: ", ans, " (required %s)" % anl) assert np.isclose(ans, anl, rtol=1e-3)
def test_nu0_1_on_sqrt_x(): """ Result on wikipedia """ # NOTE: this is REALLY finnicky!! (check devel/) ht = HankelTransform(nu=0, N=160, h=10**-3.5) ans = ht.integrate(lambda x: 1.0 / np.sqrt(x), False, False) m = -1.5 anl = 2**(m + 1) * gamma(m / 2 + 1) / gamma(-m / 2) print("Numerical Result: ", ans, " (required %s)" % anl) assert np.isclose(ans, anl, rtol=1e-3)
def test_nu0_1_on_sqrt_x(): """ Result on wikipedia """ # NOTE: this is REALLY finnicky!! (check devel/) ht = HankelTransform(nu=0, N=160, h=10 ** -3.5) ans = ht.integrate(lambda x: 1. / np.sqrt(x), False, False) m = -1.5 anl = 2 ** (m + 1) * gamma(m / 2 + 1) / gamma(-m / 2) print("Numerical Result: ", ans, " (required %s)" % anl) assert np.isclose(ans, anl, rtol=1e-3)
def test_nu0_x_on_sqrt_x2_pz2(): """ Result on wikipedia """ # Note that the number required is highly dependent on z .... smaller z is harder. ht = HankelTransform(nu=0, N=50, h=10 ** -1.3) z = 1 ans = ht.integrate(lambda x: x / np.sqrt(x ** 2 + z ** 2), False, False) anl = np.exp(-z) print("Numerical Result: ", ans, " (required %s)" % anl) assert np.isclose(ans, anl, rtol=1e-3)
def test_equivalence_of_integrate_and_transform(): ht = HankelTransform(N=50) intg = ht.integrate(lambda x: 1, False) tr = ht.transform(lambda x: 1.0 / x, ret_err=False) assert intg == tr
def test_ret_err_and_cumsum(): ht = HankelTransform(N=50) res, err, cumsum = ht.integrate(lambda x: 1.0 / x, True, True)
def test_ret_cumsum(): ht = HankelTransform(N=50) res, cumsum = ht.integrate(lambda x: 1.0 / x, False, True)
def test_ret_err(): ht = HankelTransform(N=50) res, err = ht.integrate(lambda x: 1.0 / x, True)
def test_equivalence_of_integrate_and_transform(): ht = HankelTransform(N=50) int = ht.integrate(lambda x: 1, False) tr = ht.transform(lambda x: 1. / x, ret_err=False) assert int == tr
def test_ret_err_and_cumsum(): ht = HankelTransform(N=50) res, err, cumsum = ht.integrate(lambda x: 1. / x, True, True)
def test_ret_cumsum(): ht = HankelTransform(N=50) res, cumsum = ht.integrate(lambda x: 1. / x, False, True)
def test_ret_err(): ht = HankelTransform(N=50) res, err = ht.integrate(lambda x: 1. / x, True)