library.sum Submodule

Module Summary

Interfaces for the NAG Mark 27.1 sum Chapter.

sum - Summation of Series

This module is concerned with the following tasks:

  1. calculating the discrete Fourier transform of a sequence of real or complex data values;

  2. calculating the discrete convolution or the discrete correlation of two sequences of real or complex data values using discrete Fourier transforms;

  3. calculating the inverse Laplace transform of a user-supplied function;

  4. calculating the fast Gauss transform approximation to the discrete Gauss transform;

  5. direct summation of orthogonal series;

  6. acceleration of convergence of a sequence of real values.

See Also

naginterfaces.library.examples.sum :

This subpackage contains examples for the sum module. See also the Examples subsection.

Functionality Index

Acceleration of convergence: accelerate()

Convolution or Correlation

complex vectors: convcorr_complex()

real vectors

time-saving: convcorr_real()

Discrete Fourier Transform


complex sequence

complex storage: fft_complex_multid()

real storage: fft_complex_multid_sep()

multiple half - and quarter-wave transforms

Fourier cosine transforms

Fourier cosine transforms, simple use: fft_cosine()

Fourier sine transforms

Fourier sine transforms, simple use: fft_sine()

quarter-wave cosine transforms

quarter-wave cosine transforms, simple use: fft_qtrcosine()

quarter-wave sine transforms

quarter-wave sine transforms, simple use: fft_qtrsine()


multiple transforms

complex sequence

complex storage, contiguous sequence elements: fft_complex_1d_multi_col()

complex storage by rows: fft_complex_1d_multi_row()

Hermitian/real sequence

complex storage, contiguous sequence elements: fft_realherm_1d_multi_col()

complex storage, strided sequence elements: fft_realherm_1d_multi_row()


complex sequence

single transforms

complex sequence


complex storage: fft_complex_1d()

real storage: fft_complex_1d_sep()

Hermitian/real sequence


complex storage: fft_realherm_1d()

Hermitian sequence


real sequence


real storage: fft_real_1d_rfmt()


complex sequence

complex storage: fft_complex_3d()

real storage: fft_complex_3d_sep()

Hermitian/real sequence

complex-to-real: fft_hermitian_3d()

real-to-complex: fft_real_3d()


complex sequence

complex storage: fft_complex_2d()

Hermitian/real sequence

complex-to-real: fft_hermitian_2d()

real-to-complex: fft_real_2d()

Fast Gauss Transform: fast_gauss()

Inverse Laplace Transform

Crump’s method: invlaplace_crump()

Weeks’ method

compute coefficients of solution: invlaplace_weeks()

evaluate solution: invlaplace_weeks_eval()

Summation of Chebyshev series: chebyshev()

For full information please refer to the NAG Library document



Example for naginterfaces.library.sum.convcorr_real().

Circular convolution or correlation of two real vectors.

>>> main()
naginterfaces.library.sum.convcorr_real Python Example Results.
Circular convolution of two real vectors.
(2.000000, 2.000000, 2.000000, 2.000000, 2.000000).