dct(X[, type=2])
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 n rows).
![k n∑- 2
DCT -I: X [k,:] := X [0,:]+ (- 1)X [n - 1,:]+ 2 X[j,:]cos(πjk∕(n - 1)), k = 0,...,n - 1.
j=1
n∑-1
DCT -II: X [k,:] := 2 X [j,:]cos(π(j + 1∕2)k∕n), k = 0,...,n - 1.
j=0
n∑-1
DCT -III: X [k,:] := X [0,:]+ 2 X [j,:]cos(πj(k + 1∕2)∕n), k = 0,...,n - 1.
j=1
n∑-1
DCT -IV: X [k,:] := 2 X [j,:]cos(π(j + 1∕2)(k + 1∕2)∕n), k = 0,...,n- 1.
j=0](cvxopt96x.png)
idct(X[, type=2])
Replaces the columns of a dense real matrix with the inverses of the discrete cosine transforms defined above.
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.
dctn(X[, dims=X.size[, type=2]])
Replaces a dense real matrix with its N-dimensional discrete cosine transform. The dimensions of the N-dimensional matrix are given by the N-tuple dim. The two-dimensional transform is computed as dctn(X, X.size).
idctn(X[, dims=X.size[, type=2]])
Replaces a dense real N-dimensional matrix with its inverse N-dimensional discrete cosine transform. The dimensions of the matrix are given by the tuple dim. The two-dimensional inverse transform is computed as idctn(X, X.size).