plschmidt_d1.3

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.TH "plschmidt_d1" "1" "2021-02-15" "Fortran 95" "SHTOOLS 4.11"
.hy
.SH PlSchmidt_d1
.PP
Compute all the Schmidt-normalized Legendre polynomials and first
derivatives.
.SH Usage
.PP
call PlSchmidt_d1 (\f[V]p\f[R], \f[V]dp\f[R], \f[V]lmax\f[R],
\f[V]z\f[R], \f[V]exitstatus\f[R])
.SH Parameters
.TP
\f[V]p\f[R] : output, real(dp), dimension (\f[V]lmax\f[R]+1)
An array of Schmidt-normalized Legendre polynomials up to degree
\f[V]lmax\f[R].
Degree \f[V]l\f[R] corresponds to array index \f[V]l+1\f[R].
.TP
\f[V]dp\f[R] : output, real(dp), dimension (\f[V]lmax\f[R]+1)
An array of the first derivatives of the Schmidt-normalized Legendre
polynomials up to degree \f[V]lmax\f[R].
Degree \f[V]l\f[R] corresponds to array index \f[V]l+1\f[R].
.TP
\f[V]lmax\f[R] : input, integer(int32)
The maximum degree of the Legendre polynomials to be computed.
.TP
\f[V]z\f[R] : input, real(dp)
The argument of the Legendre polynomial.
.TP
\f[V]exitstatus\f[R] : 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.
.SH Description
.PP
\f[V]PlSchmidt_d1\f[R] will calculate all of the Schmidt-normalized
Legendre polynomials and first derivatives up to degree \f[V]lmax\f[R]
for a given argument.
These are calculated using a standard three-term recursion formula, and
the integral of the Schmidt-normalized Legendre polynomials over the
interval [-1, 1] is \f[V]2/(2l+1)\f[R].
Note that the derivative of the Legendre polynomials is calculated with
respect to its arguement \f[V]z\f[R], and not latitude or colatitude.
If \f[V]z=cos(theta)\f[R], where \f[V]theta\f[R] is the colatitude, then
it is only necessary to multiply \f[V]dp\f[R] by \f[V]-sin(theta)\f[R]
to obtain the derivative with respect to \f[V]theta\f[R].
.SH See also
.PP
plbar, plbar_d1, plmbar, plmbar_d1, plon, plon_d1, plmon, plmon_d1,
plschmidt, plmschmidt, plmschmidt_d1, plegendre, plegendre_d1,
plegendrea, plegendrea_d1