The cvxopt.fftw module is an interface to the FFTW library and contains routines for discrete Fourier, cosine, and sine transforms. This module is optional, and only installed when the FFTW library is made available during the CVXOPT installation.
Replaces the columns of a dense complex matrix with their discrete
Fourier transforms: if X has rows,
Replaces the columns of a dense complex matrix with their inverse
discrete Fourier transforms: if X has rows,
The module also includes a discrete N-dimensional Fourier transform. The input matrix is interpreted as an N-dimensional matrix stored in column-major order. The discrete N-dimensional Fourier transform computes the corresponding one-dimensional transform along each dimension. For example, the two-dimensional transform applies a one-dimensional transform to all the columns of the matrix, followed by a one-dimensional transform to all the rows of the matrix.
Replaces the columns of a dense real matrix with their discrete
cosine transforms. The second argument, an integer between 1 and 4,
denotes the type of transform (DCT-I, DCT-II, DCT-III, DCT-IV).
The DCT-I transform requires that the row dimension of X is at
least 2. These transforms are defined as follows (for a matrix with
rows).
The module also includes a discrete N-dimensional cosine transform. The input matrix is interpreted as an N-dimensional matrix stored in column-major order. The discrete N-dimensional cosine transform computes the corresponding one-dimensional transform along each dimension. For example, the two-dimensional transform applies a one-dimensional transform to all the rows of the matrix, followed by a one-dimensional transform to all the columns of the matrix.
Replaces the columns of a dense real matrix with their discrete
sine transforms. The second argument, an integer between 1 and 4,
denotes the type of transform (DST-I, DST-II, DST-III, DST-IV).
These transforms are defined as follows (for a matrix with
rows).
The module also includes a discrete N-dimensional sine transform. The input matrix is interpreted as an N-dimensional matrix stored in column-major order. The discrete N-dimensional sine transform computes the corresponding one-dimensional transform along each dimension. For example, the two-dimensional transform applies a one-dimensional transform to all the rows of the matrix, followed by a one-dimensional transform to all the columns of the matrix.