def dgen1(**kwargs):
from spyctral.laguerre.eval import laguerre_function
from spyctral.laguerre.weights import sqrt_weight
[x,w] = pgq(**kwargs)
ps = laguerre_function(x,range(2*N),alpha=alpha,scale=scale,shift=shift)
ps[:,0] = 0
ps = (ps.T*sqrt_weight(x,alpha=alpha,scale=scale,shift=shift)).T
return [w,ps]
def laguerre_function(x,n,alpha=0.,scale=1.,shift=0.):
"""
Evaluates the L^2-orthonormalized Laguerre functions: i.e. the Laguerre
polynomials with the weight function multiplicatively distributed to the
polynomials.
"""
from spyctral.laguerre.weights import sqrt_weight
lpolys = laguerre_polynomial(x=x,n=n,alpha=alpha,scale=scale,shift=shift)
w = sqrt_weight(x=x,alpha=alpha,shift=shift,scale=scale)
return (lpolys.T*w).T
def laguerre_function_derivative(x,n,alpha=0.,scale=1.,shift=0.):
"""
Evaluates the derivative of the L^2-orthonormalized Laguerre functions: i.e.
the Laguerre polynomials with the weight function multiplicatively
distributed to the polynomials.
"""
from spyctral.laguerre.weights import sqrt_weight, dsqrt_weight
w = sqrt_weight(x=x,alpha=alpha,shift=shift,scale=scale)
dw = dsqrt_weight(x=x,alpha=alpha,shift=shift,scale=scale)
ps = laguerre_polynomial(x=x,n=n,alpha=alpha,scale=scale,shift=shift)
dps = laguerre_polynomial(x=x,n=n,d=1,alpha=alpha,scale=scale,shift=shift)
# Yay product rule
return (w*dps.T + dw*ps.T).T
