PLegendreA_d1 (Fortran)

Compute all the unnormalized associated Legendre functions and first derivatives.

Usage

call PLegendreA_d1 (p, dp, lmax, z, csphase, exitstatus)

Parameters

p : output, real(dp), dimension ((lmax+1)*(lmax+2)/2)

An array of unnormalized associated Legendre functions up to degree lmax. The index corresponds to l*(l+1)/2+m+1, which can be calculated by a call to PlmIndex.

dp : output, real(dp), dimension ((lmax+1)*(lmax+2)/2)

An array of the first derivatives of the unnormalized associated Legendre functions up to degree lmax. The index corresponds to l*(l+1)/2+m+1, which can be calculated by a call to PlmIndex.

lmax : input, integer(int32)

The maximum degree of the associated Legendre functions to be computed.

z : input, real(dp)

The argument of the associated Legendre functions.

csphase : input, optional, integer(int32), default = 1

If 1 (default), the Condon-Shortley phase will be excluded. If -1, the Condon-Shortley phase of (-1)^m will be appended to the associated Legendre functions.

exitstatus : output, optional, integer(int32)

If present, instead of executing a STOP when an error is encountered, the variable exitstatus will be returned describing the error. 0 = No errors; 1 = Improper dimensions of input array; 2 = Improper bounds for input variable; 3 = Error allocating memory; 4 = File IO error.

Description

PLegendreA_d1 will calculate all of the unnormalized associated Legendre functions and first derivatives up to degree lmax for a given argument. These are calculated using a standard three-term recursion formula and hence will overflow for moderate values of l and m. The index of the array corresponding to a given degree l and angular order m corresponds to l*(l+1)/2+m+1, which can be calculated by a call to PlmIndex. The integral of the associated Legendre functions over the interval [-1, 1] is 2*(l+m)!/(l-m)!/(2l+1). The default is to exclude the Condon-Shortley phase, but this can be modified by setting the optional argument csphase to -1. Note that the derivative of the Legendre polynomials is calculated with respect to its arguement z, and not latitude or colatitude. If z=cos(theta), where theta is the colatitude, then it is only necessary to multiply dp by -sin(theta) to obtain the derivative with respect to theta.

See also

plbar, plbar_d1, plmbar, plmbar_d1, plon, plon_d1, plmon, `plmon_d1](plmon_d1.html), plschmidt, plschmidt_d1, plmschmidt, plmschmidt_d1, plegendre, plegendre_d1, plegendrea, plmindex