def gq(N,mu=0.,shift=0.,scale=1.):
from spyctral.hermite.coeffs import recurrence_range
from spyctral.opoly1d.quad import gq as ogq
from spyctral.common.maps import physical_scaleshift as pss
[a_s,b_s] = recurrence_range(N,mu)
[x,w] = ogq(a_s,b_s)
pss(x,scale=scale,shift=shift)
w *= scale
return [x,w]
def gauss_quadrature(N, alpha=0.0, shift=0.0, scale=1.0):
"""
Returns the N-point Laguerre-Gauss(alpha) quadrature rule over the interval
(shift,inf). The quadrature rule is *not* normalized in the sense
that the affine parameters shift and scale are built into the new weight
function for which this quadrature rule is valid.
"""
from spyctral.laguerre.coeffs import recurrence_range
from spyctral.opoly1d.quad import gq as ogq
from spyctral.common.maps import physical_scaleshift as pss
[a, b] = recurrence_range(N, alpha)
temp = ogq(a, b)
pss(temp[0], scale=scale, shift=shift)
return temp
def gauss_quadrature(N,alpha=-1/2.,beta=-1/2.,shift=0.,scale=1.) :
# Returns the N-point Jacobi-Gauss(alpha,beta) quadrature rule over the interval
# (-scale,scale)+shift.
# The quadrature rule is *not* normalized in the sense that the affine parameters
# shift and scale are built into the new weight function for which this
# quadrature rule is valid.
from coeffs import recurrence_range
from spyctral.opoly1d.quad import gq as ogq
from spyctral import chebyshev
from spyctral.common.maps import physical_scaleshift as pss
tol = 1e-12;
if (abs(alpha+1/2.)<tol) & (abs(beta+1/2.)<tol) :
return chebyshev.quad.gq(N,shift=shift,scale=scale)
else :
[a,b] = recurrence_range(N,alpha,beta)
temp = ogq(a,b)
pss(temp[0],scale=scale,shift=shift)
return temp