LSQ_G (Fortran)

Compute the data kernel matrix G that is used when computing spherical harmonic coefficients by least squares inversion.

Usage

call LSQ_G (g, lat, lon, nmax, lmax, norm, csphase, exitstatus)

Parameters

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

The data kernel matrix.

lat : input, real(dp), dimension (nmax)

The latitude in degrees of the data points.

lon : input, real(dp), dimension (nmax)

The longitude in degrees of the data pointss.

nmax : input, integer(int32)

The number of data points.

lmax : input, integer(int32)

The maximum spherical harmonic degree of the inversion.

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

1 (default) = Geodesy 4-pi normalized harmonics; 2 = Schmidt semi-normalized harmonics; 3 = unnormalized harmonics; 4 = orthonormal harmonics.

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

1 (default) = do not apply the Condon-Shortley phase factor to the associated Legendre functions; -1 = append the Condon-Shortley phase factor of (-1)^m 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

LSQ_G will compute the data kernel matrix G that is used when computing the spherical harmonic coefficients of an irregularly sampled function by least squares inversion, as used with SHExpandLSQ. The matrix G has dimension (nmax, (lmax+1)**2) where nmax is the number of data points and lmax is the maximum spherical harmonic degree of the expansion. Each element in a given row corresponds to the values of the spherical harmonic functions for a given latitude and longitude. The elements in each row are ordered by increasing degree, with all cosine terms for a given degree followed by all sin terms for the same degree (with increasing order).

The employed spherical harmonic normalization and Condon-Shortley phase convention can be set by the optional arguments norm and csphase; if not set, the default is to use geodesy 4-pi normalized harmonics that exclude the Condon-Shortley phase of (-1)^m.

See also

shexpandlsq, makegriddh, shexpanddh, makegriddhc, shexpanddhc, makegridglq, shexpandglq, makegridglqc, shexpandglqc, dgels(1)