Library fourpack

Library FOURPACK was developed for

1. Implementing fast spherical harmonics transform, direct and inverse, as well as computation of a function with a given set of spherical harmonics at a point with a given longitude and latitude. Fast computation of the derivatives over longitudinal and latitudinal directions is also supported. For dimensions less than 2700 algorithm of Holmes and Featherstone (2002) is used. For dimensions higher than 2700 the algebra of X-number introduced by Fukushima (2012) is used on order to avoid numerical catastrophe at the polar regions related to the insufficient range of double precision numbers. Spherical harmonics transform of degree/order as high as 65536 is supported, although in practice it is limited by the amount of available RAM. The algorithm complexity is O³.

   The following spherical harmonics transform routines are implemented

   • direct spherical harmonics transform of a function defined on a regular longitude/latitude grid according to Driscoll and Healy (1994) sampling theorem.
   • inverse spherical harmonics transform that generates result on a regular longitude/latitude grid.
   • inverse vector spherical harmonics transform that generates result on a regular longitude/latitude grid. It generates the function and its partial derivatives over longitude and latitude.
   • value of the inverse spherical harmonics transform at a given longitude and latitude.
   • value of the vector inverse spherical harmonics transform at a given longitude and latitude that includes the function and its partial derivatives over longitude and latitude.

2. Providing a convenient interface to fast Fourier transform (FFT). Although the FFT algorithm can be implemented in less than 50 lines, the highly optimized version of FFT may have more than 100 000 lines of code and a rather complicated interface. The optimized routines usually runs one order of magnitude faster, so using them brings tangible benefits.

   The following FFT routines are implemented:

   • complex forward and backward FFT, 1D and 2D;
   • real to complex forward 1D FFT;
   • complex to real backward 1D FFT.

   Program for automatic generation so-called plan for FFT optimization is implemented.

3. Implementing a digital linear filter in frequency domain. A filter of this kind involves three operations: forward FFT, multiplication the spectrum by a bandpass function, backward FFT.

Download

Dependencies

• Library petools (gfortran,gcc,atlas,readline);
• Library FFTW;
• (Optionally) Intel Math Kernel Library   (not free).

Documentation

1. Fourpack library Installation instruction
2. Fourpack library User guide.
3. Fourpack library Timing test.

Credit

Acknowledgment

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This web page was prepared by Leonid Petrov ()
Last update: 2020.11.11_12:54:39