WDgesvd WDggsvd3

WDgesvd() Function WDgesvd ( Jobu As  String, JobVt As  String, M As  Long, N As  Long, A As  Variant  ) Singular value decomposition (SVD) Purpose WDgesvd computes the singular value decomposition (SVD) of a real M x N matrix A, optionally computing the left and/or right singular vectors. The SVD is written A = U * Σ * V^T where Σ is an M x N matrix which is zero except for its min(M, N) diagonal elements, U is an M x M orthogonal matrix, and V is an N x N orthogonal matrix. The diagonal elements of Σ are the singular values of A. They are real and non-negative, and are returned in descending order. The first min(M, N) columns of U and V are the left and right singular vectors of A. Note that the routine returns V^T, not V. Returns min(M, N)+1 x 1 (Jobu = "N", Jobvt = "N") Column 1 Rows 1 to min(M, N) Singular values (in descending order) Row min(M, N)+1 Return code M+1 x M+1 (Jobu = "A", Jobvt = "N") Column 1 Columns 2 to M+1 Rows 1 to M Singular values (in descending order) (Rows 1 to min(M, N)) Left orthogonal matrix U Row M+1 Return code 0 N+1 x N+1 (Jobu = "N", Jobvt = "A") Column 1 Columns 2 to N+1 Rows 1 to N Singular values (in descending order) (Rows 1 to min(M, N)) Transpose of right orthogonal matrix V (V^T) Row N+1 Return code 0 max(M,N)+1 x M+N+1 (Jobu = "A", Jobvt = "A") Column 1 Columns 2 to M+1 Columns M+2 to M+N+1 Rows 1 to max(M,N) Singular values (in descending order) (Rows 1 to min(M, N)) Left orthogonal matrix U (Rows 1 to M) Transpose of right orthogonal matrix V (V^T) (Rows 1 to N) Row max(M,N)+1 Return code 0 0 Return code. = 0: Successful exit. = i > 0: i super-diagonals of an intermediate bidiagonal form did not converge to zero. Parameters [in] Jobu = "N": Do not compute left orthogonal matrix U. = "A": Compute left orthogonal matrix U. [in] Jobvt = "N": Do not compute transpose of right orthogonal matrix V (V^T). = "A": Compute transpose of right orthogonal matrix V (V^T). [in] M Number of rows of the input matrix A. (M >= 1) [in] N Number of columns of the input matrix A. (N >= 1) [in] A (M x N) M x N matrix A. Reference LAPACK Example Compute singular values and left and right singular vectors of matrix A, where ( 1 6 11 ) ( 2 7 12 ) A = ( 3 8 13 ) ( 4 9 14 ) ( 5 10 15 )