zgesvd (l)  Linux Manuals
zgesvd: computes the singular value decomposition (SVD) of a complex MbyN matrix A, optionally computing the left and/or right singular vectors
NAME
ZGESVD  computes the singular value decomposition (SVD) of a complex MbyN matrix A, optionally computing the left and/or right singular vectorsSYNOPSIS
 SUBROUTINE ZGESVD(
 JOBU, JOBVT, M, N, A, LDA, S, U, LDU, VT, LDVT, WORK, LWORK, RWORK, INFO )
 CHARACTER JOBU, JOBVT
 INTEGER INFO, LDA, LDU, LDVT, LWORK, M, N
 DOUBLE PRECISION RWORK( * ), S( * )
 COMPLEX*16 A( LDA, * ), U( LDU, * ), VT( LDVT, * ), WORK( * )
PURPOSE
ZGESVD computes the singular value decomposition (SVD) of a complex MbyN matrix A, optionally computing the left and/or right singular vectors. The SVD is writtenwhere SIGMA is an MbyN matrix which is zero except for its min(m,n) diagonal elements, U is an MbyM unitary matrix, and V is an NbyN unitary matrix. The diagonal elements of SIGMA are the singular values of A; they are real and nonnegative, 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.
ARGUMENTS
 JOBU (input) CHARACTER*1

Specifies options for computing all or part of the matrix U:
= aqAaq: all M columns of U are returned in array U:
= aqSaq: the first min(m,n) columns of U (the left singular vectors) are returned in the array U; = aqOaq: the first min(m,n) columns of U (the left singular vectors) are overwritten on the array A; = aqNaq: no columns of U (no left singular vectors) are computed.  JOBVT (input) CHARACTER*1

Specifies options for computing all or part of the matrix
V**H:
= aqAaq: all N rows of V**H are returned in the array VT;
= aqSaq: the first min(m,n) rows of V**H (the right singular vectors) are returned in the array VT; = aqOaq: the first min(m,n) rows of V**H (the right singular vectors) are overwritten on the array A; = aqNaq: no rows of V**H (no right singular vectors) are computed. JOBVT and JOBU cannot both be aqOaq.  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*16 array, dimension (LDA,N)
 On entry, the MbyN matrix A. On exit, if JOBU = aqOaq, A is overwritten with the first min(m,n) columns of U (the left singular vectors, stored columnwise); if JOBVT = aqOaq, A is overwritten with the first min(m,n) rows of V**H (the right singular vectors, stored rowwise); if JOBU .ne. aqOaq and JOBVT .ne. aqOaq, the contents of A are destroyed.
 LDA (input) INTEGER
 The leading dimension of the array A. LDA >= max(1,M).
 S (output) DOUBLE PRECISION array, dimension (min(M,N))
 The singular values of A, sorted so that S(i) >= S(i+1).
 U (output) COMPLEX*16 array, dimension (LDU,UCOL)
 (LDU,M) if JOBU = aqAaq or (LDU,min(M,N)) if JOBU = aqSaq. If JOBU = aqAaq, U contains the MbyM unitary matrix U; if JOBU = aqSaq, U contains the first min(m,n) columns of U (the left singular vectors, stored columnwise); if JOBU = aqNaq or aqOaq, U is not referenced.
 LDU (input) INTEGER
 The leading dimension of the array U. LDU >= 1; if JOBU = aqSaq or aqAaq, LDU >= M.
 VT (output) COMPLEX*16 array, dimension (LDVT,N)
 If JOBVT = aqAaq, VT contains the NbyN unitary matrix V**H; if JOBVT = aqSaq, VT contains the first min(m,n) rows of V**H (the right singular vectors, stored rowwise); if JOBVT = aqNaq or aqOaq, VT is not referenced.
 LDVT (input) INTEGER
 The leading dimension of the array VT. LDVT >= 1; if JOBVT = aqAaq, LDVT >= N; if JOBVT = aqSaq, LDVT >= min(M,N).
 WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK))
 On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
 LWORK (input) INTEGER
 The dimension of the array WORK. LWORK >= MAX(1,2*MIN(M,N)+MAX(M,N)). For good performance, LWORK should generally be larger. If LWORK = 1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.
 RWORK (workspace) DOUBLE PRECISION array, dimension (5*min(M,N))
 On exit, if INFO > 0, RWORK(1:MIN(M,N)1) contains the unconverged superdiagonal elements of an upper bidiagonal matrix B whose diagonal is in S (not necessarily sorted). B satisfies A = U * B * VT, so it has the same singular values as A, and singular vectors related by U and VT.
 INFO (output) INTEGER

= 0: successful exit.
< 0: if INFO = i, the ith argument had an illegal value.
> 0: if ZBDSQR did not converge, INFO specifies how many superdiagonals of an intermediate bidiagonal form B did not converge to zero. See the description of RWORK above for details.