def tst_gauss_legendre_engine():
for n in range(2,95):
gle = sm.gauss_legendre_engine(n)
x_this = gle.x()
step=1e-5 # check AMS pg 919. nodes for n=96 are allways more then stpe away from each other
for ix in range( x_this.size() ):
f = gle.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_legendre_engine():
for n in range(2, 95):
gle = sm.gauss_legendre_engine(n)
x_this = gle.x()
step = 1e-5 # check AMS pg 919. nodes for n=96 are allways more then stpe away from each other
for ix in range(x_this.size()):
f = gle.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)
