
NAMEzgesvd.f SYNOPSISFunctions/Subroutinessubroutine zgesvd (JOBU, JOBVT, M, N, A, LDA, S, U, LDU, VT, LDVT, WORK, LWORK, RWORK, INFO) Function/Subroutine Documentationsubroutine zgesvd (characterJOBU, characterJOBVT, integerM, integerN, complex*16, dimension( lda, * )A, integerLDA, double precision, dimension( * )S, complex*16, dimension( ldu, * )U, integerLDU, complex*16, dimension( ldvt, * )VT, integerLDVT, complex*16, dimension( * )WORK, integerLWORK, double precision, dimension( * )RWORK, integerINFO)ZGESVD computes the singular value decomposition (SVD) for GE matrices 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 written A = U * SIGMA * conjugatetranspose(V) where 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. JOBU
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JOBU is CHARACTER*1 Specifies options for computing all or part of the matrix U: = 'A': all M columns of U are returned in array U: = 'S': the first min(m,n) columns of U (the left singular vectors) are returned in the array U; = 'O': the first min(m,n) columns of U (the left singular vectors) are overwritten on the array A; = 'N': no columns of U (no left singular vectors) are computed.JOBVT JOBVT is CHARACTER*1 Specifies options for computing all or part of the matrix V**H: = 'A': all N rows of V**H are returned in the array VT; = 'S': the first min(m,n) rows of V**H (the right singular vectors) are returned in the array VT; = 'O': the first min(m,n) rows of V**H (the right singular vectors) are overwritten on the array A; = 'N': no rows of V**H (no right singular vectors) are computed. JOBVT and JOBU cannot both be 'O'.M M is INTEGER The number of rows of the input matrix A. M >= 0.N N is INTEGER The number of columns of the input matrix A. N >= 0.A A is COMPLEX*16 array, dimension (LDA,N) On entry, the MbyN matrix A. On exit, if JOBU = 'O', A is overwritten with the first min(m,n) columns of U (the left singular vectors, stored columnwise); if JOBVT = 'O', A is overwritten with the first min(m,n) rows of V**H (the right singular vectors, stored rowwise); if JOBU .ne. 'O' and JOBVT .ne. 'O', the contents of A are destroyed.LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).S S is DOUBLE PRECISION array, dimension (min(M,N)) The singular values of A, sorted so that S(i) >= S(i+1).U U is COMPLEX*16 array, dimension (LDU,UCOL) (LDU,M) if JOBU = 'A' or (LDU,min(M,N)) if JOBU = 'S'. If JOBU = 'A', U contains the MbyM unitary matrix U; if JOBU = 'S', U contains the first min(m,n) columns of U (the left singular vectors, stored columnwise); if JOBU = 'N' or 'O', U is not referenced.LDU LDU is INTEGER The leading dimension of the array U. LDU >= 1; if JOBU = 'S' or 'A', LDU >= M.VT VT is COMPLEX*16 array, dimension (LDVT,N) If JOBVT = 'A', VT contains the NbyN unitary matrix V**H; if JOBVT = 'S', VT contains the first min(m,n) rows of V**H (the right singular vectors, stored rowwise); if JOBVT = 'N' or 'O', VT is not referenced.LDVT LDVT is INTEGER The leading dimension of the array VT. LDVT >= 1; if JOBVT = 'A', LDVT >= N; if JOBVT = 'S', LDVT >= min(M,N).WORK WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK.LWORK LWORK is 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 RWORK is 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 INFO is 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. Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
April 2012
Definition at line 214 of file zgesvd.f.
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