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CGESDD(l)) CGESDD(l)NAMECGESDD - compute the singular value decomposition (SVD) of a complex M-by-N matrix A, optionally computing the left and/or right singular vectors, by using divide-and-conquer methodSYNOPSISSUBROUTINE CGESDD( JOBZ, M, N, A, LDA, S, U, LDU, VT, LDVT, WORK, LWORK, RWORK, IWORK, INFO ) CHARACTER JOBZ INTEGER INFO, LDA, LDU, LDVT, LWORK, M, N INTEGER IWORK( * ) REAL RWORK( * ), S( * ) COMPLEX A( LDA, * ), U( LDU, * ), VT( LDVT, * ), WORK( * )PURPOSECGESDD computes the singular value decomposition (SVD) of a complex M-by-N matrix A, optionally computing the left and/or right singular vectors, by using divide-and-conquer method. The SVD is written A = U * SIGMA * conjugate-transpose(V) where SIGMA is an M-by-N matrix which is zero except for its min(m,n) diagonal elements, U is an M-by-M unitary matrix, and V is an N-by-N unitary matrix. The diagonal elements of SIGMA 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 VT = V**H, not V. The divide and conquer algorithm makes very mild assumptions about floating point arith- metic. It will work on machines with a guard digit in add/subtract, or on those binary machines without guard digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. It could conceivably fail on hexadecimal or decimal machines without guard digits, but we know of none.ARGUMENTSJOBZ (input) CHARACTER*1 Specifies options for computing all or part of the matrix U: = 'A': all M columns of U and all N rows of V**H are returned in the arrays U and VT; = 'S': the first min(M,N) columns of U and the first min(M,N) rows of V**H are returned in the arrays U and VT; = 'O': If M >= N, the first N columns of U are overwritten on the array A and all rows of V**H are returned in the array VT; otherwise, all columns of U are returned in the array U and the first M rows of V**H are overwritten in the array VT; = 'N': no columns of U or rows of V**H are computed. M (input) INTEGER The number of rows of the input matrix A. M >= 0. N (input) INTEGER The number of columns of the input matrix A. N >= 0. A (input/output) COMPLEX array, dimension (LDA,N) On entry, the M-by-N matrix A. On exit, if JOBZ = 'O', A is overwritten with the first N columns of U (the left singular vectors, stored columnwise) if M >= N; A is overwritten with the first M rows of V**H (the right singular vectors, stored rowwise) otherwise. if JOBZ .ne. 'O', the contents of A are destroyed. LDA (input) INTEGER The leading dimension of the array A. LDA >= max(1,M). S (output) REAL array, dimension (min(M,N)) The singular values of A, sorted so that S(i) >= S(i+1). U (output) COMPLEX array, dimension (LDU,UCOL) UCOL = M if JOBZ = 'A' or JOBZ = 'O' and M < N; UCOL = min(M,N) if JOBZ = 'S'. If JOBZ = 'A' or JOBZ = 'O' and M < N, U contains the M-by-M unitary matrix U; if JOBZ = 'S', U contains the first min(M,N) columns of U (the left singular vectors, stored columnwise); if JOBZ = 'O' and M >= N, or JOBZ = 'N', U is not referenced. LDU (input) INTEGER The leading dimension of the array U. LDU >= 1; if JOBZ = 'S' or 'A' or JOBZ = 'O' and M < N, LDU >= M. VT (output) COMPLEX array, dimension (LDVT,N) If JOBZ = 'A' or JOBZ = 'O' and M >= N, VT contains the N-by-N unitary matrix V**H; if JOBZ = 'S', VT contains the first min(M,N) rows of V**H (the right singu- lar vectors, stored rowwise); if JOBZ = 'O' and M < N, or JOBZ = 'N', VT is not referenced. LDVT (input) INTEGER The leading dimension of the array VT. LDVT >= 1; if JOBZ = 'A' or JOBZ = 'O' and M >= N, LDVT >= N; if JOBZ = 'S', LDVT >= min(M,N). WORK (workspace/output) COMPLEX array, dimension (LWORK) On exit, if INFO = 0, WORK(1) returns the optimal LWORK. LWORK (input) INTEGER The dimension of the array WORK. LWORK >= 1. if JOBZ = 'N', LWORK >= 2*min(M,N)+max(M,N). if JOBZ = 'O', LWORK >= 2*min(M,N)*min(M,N)+2*min(M,N)+max(M,N). if JOBZ = 'S' or 'A', LWORK >= min(M,N)*min(M,N)+2*min(M,N)+max(M,N). For good performance, LWORK should gener- ally be larger. If LWORK < 0 but other input arguments are legal, WORK(1) returns the optimal LWORK. RWORK (workspace) REAL array, dimension (LRWORK) If JOBZ = 'N', LRWORK >= 7*min(M,N). Otherwise, LRWORK >= 5*min(M,N)*min(M,N) + 5*min(M,N) IWORK (workspace) INTEGER array, dimension (8*min(M,N)) INFO (output) INTEGER = 0: successful exit. < 0: if INFO =, the i-th argument had an illegal value. > 0: The updating process of SBDSDC did not converge.-iFURTHER DETAILSBased on contributions by Ming Gu and Huan Ren, Computer Science Division, University of California at Berkeley, USALAPACK version 3.015 June 2000 CGESDD(l)

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