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Manuscript Title: Fast sine/cosine transform for periodic functions with reflection
symmetry. | ||

Authors: A. Besprozvannaya, D.J. Tannor | ||

Program title: ROFT/REFT/COFT/CEFT | ||

Catalogue identifier: ABTX_v1_0Distribution format: gz | ||

Journal reference: Comput. Phys. Commun. 63(1991)569 | ||

Programming language: Fortran. | ||

Computer: STELLAR GS2000. | ||

Operating system: STELLIX. | ||

Keywords: General purpose, Fourier, Sine/cosine fast Transform, Periodic function, Real/complex, Odd/even symmetry, Inverse transform. | ||

Classification: 4.6. | ||

Nature of problem:In many physical applications one is interested in obtaining a Fourier transform of a function having a particular reflection symmetry using only half of the grid points, thus saving both computation time and space without any loss of information. | ||

Solution method:The algorithm is based on fast sine/cosine transforms with some modifications which make it applicable to a wider class of real and complex functions. | ||

Restrictions:The number of grid points should be a power of two in odd case and a power of two plus one in even case. We strongly recommend all the data to be double precision to achieve sufficient accuracy in the computations. | ||

Running time:It depends greatly on the computer type, the compiler optimization and the efficiency of the FFT routine used. For example, to perform 10**5 forward/inverse transform operations with an even data array of 33 elements using a highly-optimized Stellar FFT library, it took about 40 s for real and 80 s for complex double precision data. |

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