.TH "dgesdd.f" 3 "Wed Oct 15 2014" "Version 3.4.2" "LAPACK" \" -*- nroff -*- .ad l .nh .SH NAME dgesdd.f \- .SH SYNOPSIS .br .PP .SS "Functions/Subroutines" .in +1c .ti -1c .RI "subroutine \fBdgesdd\fP (JOBZ, M, N, A, LDA, S, U, LDU, VT, LDVT, WORK, LWORK, IWORK, INFO)" .br .RI "\fI\fBDGESDD\fP \fP" .in -1c .SH "Function/Subroutine Documentation" .PP .SS "subroutine dgesdd (characterJOBZ, integerM, integerN, double precision, dimension( lda, * )A, integerLDA, double precision, dimension( * )S, double precision, dimension( ldu, * )U, integerLDU, double precision, dimension( ldvt, * )VT, integerLDVT, double precision, dimension( * )WORK, integerLWORK, integer, dimension( * )IWORK, integerINFO)" .PP \fBDGESDD\fP .PP \fBPurpose: \fP .RS 4 .PP .nf DGESDD computes the singular value decomposition (SVD) of a real M-by-N matrix A, optionally computing the left and right singular vectors. If singular vectors are desired, it uses a divide-and-conquer algorithm. The SVD is written A = U * SIGMA * 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 orthogonal matrix, and V is an N-by-N orthogonal 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**T, not V. The divide and conquer algorithm makes very mild assumptions about floating point arithmetic. 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. .fi .PP .RE .PP \fBParameters:\fP .RS 4 \fIJOBZ\fP .PP .nf JOBZ is 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**T 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**T 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**T are returned in the array VT; otherwise, all columns of U are returned in the array U and the first M rows of V**T are overwritten in the array A; = 'N': no columns of U or rows of V**T are computed. .fi .PP .br \fIM\fP .PP .nf M is INTEGER The number of rows of the input matrix A. M >= 0. .fi .PP .br \fIN\fP .PP .nf N is INTEGER The number of columns of the input matrix A. N >= 0. .fi .PP .br \fIA\fP .PP .nf A is DOUBLE PRECISION 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**T (the right singular vectors, stored rowwise) otherwise. if JOBZ .ne. 'O', the contents of A are destroyed. .fi .PP .br \fILDA\fP .PP .nf LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M). .fi .PP .br \fIS\fP .PP .nf S is DOUBLE PRECISION array, dimension (min(M,N)) The singular values of A, sorted so that S(i) >= S(i+1). .fi .PP .br \fIU\fP .PP .nf U is DOUBLE PRECISION 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 orthogonal 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. .fi .PP .br \fILDU\fP .PP .nf LDU is INTEGER The leading dimension of the array U. LDU >= 1; if JOBZ = 'S' or 'A' or JOBZ = 'O' and M < N, LDU >= M. .fi .PP .br \fIVT\fP .PP .nf VT is DOUBLE PRECISION array, dimension (LDVT,N) If JOBZ = 'A' or JOBZ = 'O' and M >= N, VT contains the N-by-N orthogonal matrix V**T; if JOBZ = 'S', VT contains the first min(M,N) rows of V**T (the right singular vectors, stored rowwise); if JOBZ = 'O' and M < N, or JOBZ = 'N', VT is not referenced. .fi .PP .br \fILDVT\fP .PP .nf LDVT is 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). .fi .PP .br \fIWORK\fP .PP .nf WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK; .fi .PP .br \fILWORK\fP .PP .nf LWORK is INTEGER The dimension of the array WORK. LWORK >= 1. If JOBZ = 'N', LWORK >= 3*min(M,N) + max(max(M,N),7*min(M,N)). If JOBZ = 'O', LWORK >= 3*min(M,N) + max(max(M,N),5*min(M,N)*min(M,N)+4*min(M,N)). If JOBZ = 'S' or 'A' LWORK >= min(M,N)*(6+4*min(M,N))+max(M,N) For good performance, LWORK should generally be larger. If LWORK = -1 but other input arguments are legal, WORK(1) returns the optimal LWORK. .fi .PP .br \fIIWORK\fP .PP .nf IWORK is INTEGER array, dimension (8*min(M,N)) .fi .PP .br \fIINFO\fP .PP .nf INFO is INTEGER = 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value. > 0: DBDSDC did not converge, updating process failed. .fi .PP .RE .PP \fBAuthor:\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP \fBDate:\fP .RS 4 November 2013 .RE .PP \fBContributors: \fP .RS 4 Ming Gu and Huan Ren, Computer Science Division, University of California at Berkeley, USA .RE .PP .PP Definition at line 216 of file dgesdd\&.f\&. .SH "Author" .PP Generated automatically by Doxygen for LAPACK from the source code\&.