def tst_gauss_hermite_engine():
# test with known values
ghe = sm.gauss_hermite_engine(4)
x_ams_55 = [0.524647623275290, 1.650680123885785]
w_ams_55 = [0.8049140900055 , 0.08131283544725]
wexs_ams_55 = [1.0599644828950 , 1.2402258176958]
x_this = ghe.x()[0:2]
w_this = ghe.w()[0:2]
for x,xx in zip( x_this, x_ams_55):
assert approx_equal( x, xx, eps=1e-8 )
for w,ww in zip( w_this, w_ams_55):
assert approx_equal( w, ww, eps=1e-8 )
# test a large order set of number
for n in range(2,29):
ghe = sm.gauss_hermite_engine(n)
x_this = ghe.x()
step = 0.5/math.sqrt(n*1.0)
for ix in range( x_this.size() ):
f = ghe.f( x_this[ix] )[0]
assert approx_equal(f,0,eps=1e-5)
# check the uniqueness of each point
for jj in range( x_this.size() ):
if jj != ix:
assert ( math.fabs(x_this[ix]-x_this[jj]) >= step )
def tst_gauss_hermite_engine():
# test with known values
ghe = sm.gauss_hermite_engine(4)
x_ams_55 = [0.524647623275290, 1.650680123885785]
w_ams_55 = [0.8049140900055, 0.08131283544725]
wexs_ams_55 = [1.0599644828950, 1.2402258176958]
x_this = ghe.x()[0:2]
w_this = ghe.w()[0:2]
for x, xx in zip(x_this, x_ams_55):
assert approx_equal(x, xx, eps=1e-8)
for w, ww in zip(w_this, w_ams_55):
assert approx_equal(w, ww, eps=1e-8)
# test a large order set of number
for n in range(2, 29):
ghe = sm.gauss_hermite_engine(n)
x_this = ghe.x()
step = 0.5 / math.sqrt(n * 1.0)
for ix in range(x_this.size()):
f = ghe.f(x_this[ix])[0]
assert approx_equal(f, 0, eps=1e-5)
# check the uniqueness of each point
for jj in range(x_this.size()):
if jj != ix:
assert (math.fabs(x_this[ix] - x_this[jj]) >= step)
def examples():
# an illustration of Hermite Gauss quadrature
# we will try to integrate
# Exp[-x^2-x] {x,-inf, inf}
# The true answer is Exp[0.25] Sqrt[Pi]
#
f_theory = math.exp(0.25)*math.sqrt( math.pi )
for ii in xrange(6,10):
ghq = sm.gauss_hermite_engine(ii)
w = ghq.w()
x = ghq.x()
f = flex.sum( (flex.exp( -x ))*w )
assert approx_equal(f,f_theory, eps=1e-5)
# an example of Gauss-Legendre integration
# we integrate exp(-x) between -1 and 1
f_theory = math.exp(1) - math.exp(-1)
for ii in xrange(5,90):
glq = sm.gauss_legendre_engine(ii)
w = glq.w()
x = glq.x()
f = flex.sum( (flex.exp( -x ))*w )
def examples():
# an illustration of Hermite Gauss quadrature
# we will try to integrate
# Exp[-x^2-x] {x,-inf, inf}
# The true answer is Exp[0.25] Sqrt[Pi]
#
f_theory = math.exp(0.25) * math.sqrt(math.pi)
for ii in xrange(6, 10):
ghq = sm.gauss_hermite_engine(ii)
w = ghq.w()
x = ghq.x()
f = flex.sum((flex.exp(-x)) * w)
assert approx_equal(f, f_theory, eps=1e-5)
# an example of Gauss-Legendre integration
# we integrate exp(-x) between -1 and 1
f_theory = math.exp(1) - math.exp(-1)
for ii in xrange(5, 90):
glq = sm.gauss_legendre_engine(ii)
w = glq.w()
x = glq.x()
f = flex.sum((flex.exp(-x)) * w)
