def test_l_roots():
weightf = orth.laguerre(5).weight_func
verify_gauss_quad(orth.l_roots, orth.eval_laguerre, weightf, 0., np.inf, 5)
verify_gauss_quad(orth.l_roots,
orth.eval_laguerre,
weightf,
0.,
np.inf,
25,
atol=1e-13)
verify_gauss_quad(orth.l_roots,
orth.eval_laguerre,
weightf,
0.,
np.inf,
100,
atol=1e-12)
x, w = orth.l_roots(5, False)
y, v, m = orth.l_roots(5, True)
assert_allclose(x, y, 1e-14, 1e-14)
assert_allclose(w, v, 1e-14, 1e-14)
muI, muI_err = integrate.quad(weightf, 0, np.inf)
assert_allclose(m, muI, rtol=muI_err)
assert_raises(ValueError, orth.l_roots, 0)
assert_raises(ValueError, orth.l_roots, 3.3)
def test_l_roots():
verify_gauss_quad(orth.l_roots, orth.eval_laguerre, 5)
verify_gauss_quad(orth.l_roots, orth.eval_laguerre, 25, atol=1e-13)
verify_gauss_quad(orth.l_roots, orth.eval_laguerre, 100, atol=1e-12)
x, w = orth.l_roots(5, False)
y, v, m = orth.l_roots(5, True)
assert_allclose(x, y, 1e-14, 1e-14)
assert_allclose(w, v, 1e-14, 1e-14)
assert_raises(ValueError, orth.l_roots, 0)
assert_raises(ValueError, orth.l_roots, 3.3)
def test_l_roots():
verify_gauss_quad(orth.l_roots, orth.eval_laguerre, 5)
verify_gauss_quad(orth.l_roots, orth.eval_laguerre, 25, atol=1e-13)
verify_gauss_quad(orth.l_roots, orth.eval_laguerre, 100, atol=1e-12)
x, w = orth.l_roots(5, False)
y, v, m = orth.l_roots(5, True)
assert_allclose(x, y, 1e-14, 1e-14)
assert_allclose(w, v, 1e-14, 1e-14)
assert_raises(ValueError, orth.l_roots, 0)
assert_raises(ValueError, orth.l_roots, 3.3)
def test_l_roots():
weightf = orth.laguerre(5).weight_func
verify_gauss_quad(orth.l_roots, orth.eval_laguerre, weightf, 0.0, np.inf, 5)
verify_gauss_quad(orth.l_roots, orth.eval_laguerre, weightf, 0.0, np.inf, 25, atol=1e-13)
verify_gauss_quad(orth.l_roots, orth.eval_laguerre, weightf, 0.0, np.inf, 100, atol=1e-12)
x, w = orth.l_roots(5, False)
y, v, m = orth.l_roots(5, True)
assert_allclose(x, y, 1e-14, 1e-14)
assert_allclose(w, v, 1e-14, 1e-14)
muI, muI_err = integrate.quad(weightf, 0, np.inf)
assert_allclose(m, muI, rtol=muI_err)
assert_raises(ValueError, orth.l_roots, 0)
assert_raises(ValueError, orth.l_roots, 3.3)
c = 299792458
M = 10**6
beta = 1.0 / (20.0 * M)
hbar = 6.58211928 * (10**(-16)) # eV
########################################
########################################
####### Problem 2 - first Part #########
########################################
########################################
xGridCount = 50
constant = 8.0 * pi * ((1.0 / beta)**3) / ((2 * pi * c * hbar)**3)
[laguerre_roots, laguerre_weights] = scipy_orth.l_roots(xGridCount, 0)
IntegralSum = 0.0
for i in range(0, xGridCount):
IntegralSum = IntegralSum + laguerre_weights[i] * (
laguerre_roots[i]**2 * exp(laguerre_roots[i]) /
(exp(laguerre_roots[i]) + 1.0))
else:
print "The Integral is (gaussian-laguerre method) : ", IntegralSum
##################################################
# Checking the integral answer by another method #
##################################################
xGridCount = 10000
c = 299792458 M = 10**6 beta = 1.0/(20.0*M) hbar = 6.58211928*(10**(-16)) # eV ######################################## ######################################## ####### Problem 2 - first Part ######### ######################################## ######################################## xGridCount = 50; constant = 8.0*pi*((1.0/beta)**3) / ((2*pi*c*hbar)**3) [laguerre_roots,laguerre_weights] = scipy_orth.l_roots(xGridCount,0) IntegralSum = 0.0; for i in range(0, xGridCount): IntegralSum = IntegralSum + laguerre_weights[i]*(laguerre_roots[i]**2 * exp(laguerre_roots[i]) / (exp(laguerre_roots[i]) + 1.0)); else: print "The Integral is (gaussian-laguerre method) : ", IntegralSum ################################################## # Checking the integral answer by another method # ################################################## xGridCount = 10000; IntegralSum = 0.0;