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PlSchmidt (Fortran) |
spherical harmonics software package, spherical harmonic transform, legendre functions, multitaper spectral analysis, fortran, Python, gravity, magnetic field |
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Compute all the Schmidt-normalized Legendre polynomials.
call PlSchmidt (p, lmax, z, exitstatus)
p : output, real(dp), dimension (lmax+1)
: An array of Schmidt-normalized Legendre polynomials up to degree lmax. Degree l corresponds to array index l+1.
lmax : input, integer
: The maximum degree of the Legendre polynomials to be computed.
z : input, real(dp)
: The argument of the Legendre polynomial.
exitstatus : output, optional, integer
: 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.
PlSchmidt will calculate all of the Schmidt-normalized Legendre polynomials up to degree lmax for a given argument. These are calculated using a standard three-term recursion formula. The integral of the Schmidt-normalized Legendre polynomials over the interval [-1, 1] is 2/(2l+1).
plbar, plbar_d1, plmbar, plmbar_d1, plon, plon_d1, plmon, plmon_d1, plschmidt, plschmidt_d1, plmschmidt_d1, plegendre, plegendre_d1, plegendrea, plegendrea_d1