def lpmn(m,n,z):
"""Associated Legendre functions of the first kind, Pmn(z) and its
derivative, Pmn'(z) of order m and degree n. Returns two
arrays of size (m+1,n+1) containing Pmn(z) and Pmn'(z) for
all orders from 0..m and degrees from 0..n.
z can be complex.
"""
if not isscalar(m) or (abs(m)>n):
raise ValueError, "m must be <= n."
if not isscalar(n) or (n<0):
raise ValueError, "n must be a non-negative integer."
if not isscalar(z):
raise ValueError, "z must be scalar."
if (m < 0):
mp = -m
mf,nf = mgrid[0:mp+1,0:n+1]
sv = errprint(0)
fixarr = where(mf>nf,0.0,(-1)**mf * gamma(nf-mf+1) / gamma(nf+mf+1))
sv = errprint(sv)
else:
mp = m
if iscomplex(z):
p,pd = specfun.clpmn(mp,n,real(z),imag(z))
else:
p,pd = specfun.lpmn(mp,n,z)
if (m < 0):
p = p * fixarr
pd = pd * fixarr
return p,pd
def lpmn(m, n, z):
"""Associated Legendre functions of the first kind, Pmn(z) and its
derivative, Pmn'(z) of order m and degree n. Returns two
arrays of size (m+1,n+1) containing Pmn(z) and Pmn'(z) for
all orders from 0..m and degrees from 0..n.
z can be complex.
"""
if not isscalar(m) or (abs(m) > n):
raise ValueError, "m must be <= n."
if not isscalar(n) or (n < 0):
raise ValueError, "n must be a non-negative integer."
if not isscalar(z):
raise ValueError, "z must be scalar."
if (m < 0):
mp = -m
mf, nf = mgrid[0:mp + 1, 0:n + 1]
sv = errprint(0)
fixarr = where(mf > nf, 0.0,
(-1)**mf * gamma(nf - mf + 1) / gamma(nf + mf + 1))
sv = errprint(sv)
else:
mp = m
if iscomplex(z):
p, pd = specfun.clpmn(mp, n, real(z), imag(z))
else:
p, pd = specfun.lpmn(mp, n, z)
if (m < 0):
p = p * fixarr
pd = pd * fixarr
return p, pd
def lpmn(m, n, z):
"""Associated Legendre functions of the first kind, Pmn(z) and its
derivative, Pmn'(z) of order m and degree n. Returns two
arrays of size (m+1,n+1) containing Pmn(z) and Pmn'(z) for
all orders from 0..m and degrees from 0..n.
z can be complex.
Parameters
----------
m : int
|m| <= n; the order of the Legendre function
n : int
where `n` >= 0; the degree of the Legendre function. Often
called ``l`` (lower case L) in descriptions of the associated
Legendre function
z : float or complex
input value
Returns
-------
Pmn_z : (m+1, n+1) array
Values for all orders 0..m and degrees 0..n
Pmn_d_z : (m+1, n+1) array
Derivatives for all orders 0..m and degrees 0..n
"""
if not isscalar(m) or (abs(m) > n):
raise ValueError, "m must be <= n."
if not isscalar(n) or (n < 0):
raise ValueError, "n must be a non-negative integer."
if not isscalar(z):
raise ValueError, "z must be scalar."
if (m < 0):
mp = -m
mf, nf = mgrid[0:mp + 1, 0:n + 1]
sv = errprint(0)
fixarr = where(mf > nf, 0.0,
(-1)**mf * gamma(nf - mf + 1) / gamma(nf + mf + 1))
sv = errprint(sv)
else:
mp = m
if iscomplex(z):
p, pd = specfun.clpmn(mp, n, real(z), imag(z))
else:
p, pd = specfun.lpmn(mp, n, z)
if (m < 0):
p = p * fixarr
pd = pd * fixarr
return p, pd
def lpmn(m,n,z):
"""Associated Legendre functions of the first kind, Pmn(z) and its
derivative, Pmn'(z) of order m and degree n. Returns two
arrays of size (m+1,n+1) containing Pmn(z) and Pmn'(z) for
all orders from 0..m and degrees from 0..n.
z can be complex.
Parameters
----------
m : int
|m| <= n; the order of the Legendre function
n : int
where `n` >= 0; the degree of the Legendre function. Often
called ``l`` (lower case L) in descriptions of the associated
Legendre function
z : float or complex
input value
Returns
-------
Pmn_z : (m+1, n+1) array
Values for all orders 0..m and degrees 0..n
Pmn_d_z : (m+1, n+1) array
Derivatives for all orders 0..m and degrees 0..n
"""
if not isscalar(m) or (abs(m)>n):
raise ValueError("m must be <= n.")
if not isscalar(n) or (n<0):
raise ValueError("n must be a non-negative integer.")
if not isscalar(z):
raise ValueError("z must be scalar.")
if (m < 0):
mp = -m
mf,nf = mgrid[0:mp+1,0:n+1]
sv = errprint(0)
fixarr = where(mf>nf,0.0,(-1)**mf * gamma(nf-mf+1) / gamma(nf+mf+1))
sv = errprint(sv)
else:
mp = m
if iscomplex(z):
p,pd = specfun.clpmn(mp,n,real(z),imag(z))
else:
p,pd = specfun.lpmn(mp,n,z)
if (m < 0):
p = p * fixarr
pd = pd * fixarr
return p,pd