WZgesvd WZgesvd2 WZggsvd3 WZggsvd32

WZgesvd2() Function WZgesvd2 ( Jobu As  String, JobVt As  String, M As  Long, N As  Long, A As  Variant  ) Singular value decomposition (SVD) of a complex matrix (complex numbers in pairs of cells) Purpose WZgesvd2 computes the singular value decomposition (SVD) of a complex M x N matrix A, optionally computing the left and/or right singular vectors. The SVD is written A = U * Σ * V^H 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 unitary matrix, and V is an N x N unitary 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^H, not V. To represent complex numbers, a real part and an imaginary part are stored in a pair of adjacent cells (a real part in a left cell, and an imaginary part in a right cell). The computed results are stored in the same way. 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 2M+1 (Jobu = "A", Jobvt = "N") Column 1 Columns 2 to 2M+1 Rows 1 to M Singular values (in descending order) (Rows 1 to min(M, N)) Left unitary matrix U Row M+1 Return code 0 N+1 x 2N+1 (Jobu = "N", Jobvt = "A") Column 1 Columns 2 to 2N+1 Rows 1 to N Singular values (in descending order) (Rows 1 to min(M, N)) Transpose of right unitary matrix V (V^H) Row N+1 Return code 0 max(M,N)+1 x 2M+2N+1 (Jobu = "A", Jobvt = "A") Column 1 Columns 2 to 2M+1 Columns 2M+2 to 2M+2N+1 Rows 1 to max(M,N) Singular values (in descending order) (Rows 1 to min(M, N)) Left unitary matrix U (Rows 1 to M) Transpose of right unitary matrix V (V^H) (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 unitary matrix U. = "A": Compute left unitary matrix U. [in] Jobvt = "N": Do not compute transpose of right unitary matrix V (V^H). = "A": Compute transpose of right unitary matrix V (V^H). [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 2N) M x N complex matrix A. Reference LAPACK Example Compute singular values and left and right singular vectors of matrix A, where ( 0.20-0.11i -0.93-0.32i 0.81+0.37i ) A = ( -0.80-0.92i -0.29+0.86i 0.64+0.51i ) ( 0.71+0.59i -0.15+0.19i 0.20+0.94i )