Programs in Physics & Physical Chemistry
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|Manuscript Title: Program to calculate the least-squares estimates of the spherical harmonic expansion coefficients of equally angular gridded scalar field.|
|Authors: Z. Martinec|
|Program title: SPHAN|
|Catalogue identifier: ABTU_v1_0|
Distribution format: gz
|Journal reference: Comput. Phys. Commun. 64(1991)140|
|Programming language: Fortran.|
|Operating system: BS2000.|
|Keywords: General purpose, Fit, Associated Legendre function, Truncated spherical Harmonic expansion, Method of least squares Adjustment, Fast fourier transform Of mix-radix.|
Nature of problem:
There is a wide range of applications of spherical harmonic analysis of regularly spaced data in reduction of global data set to spherical harmonic coefficients.
The spherical harmonic coefficients of a scalar field are estimated by the method of least squares adjustment of data values measured on the globe in an equal angular grid. For such a regular grid the normal matrix is sparse, and thus the system of the normal equations can be reordered into a series of sub-systems according to the angular order m. The solution of each sub-system is sought by NAG subroutines FO4ABF based on Cholesky's decomposition. The fast Fourier transform of mix- radix is implemented in setting up the right-hand sides of the normal equations as well as in spherical harmonic synthesis at which series of spherical harmonic is summed.
For the number of the latitude circles NTH=90, the CPU-time is roughly 102 s for the cutoff degree JMAX=30, is about 260 s for JMAX=50, is about 522 s for JMAX=70, and is about 1100 s for JMAX=90.
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