LAPACK
3.4.2
LAPACK: Linear Algebra PACKage

Functions/Subroutines  
subroutine  zgesdd (JOBZ, M, N, A, LDA, S, U, LDU, VT, LDVT, WORK, LWORK, RWORK, IWORK, INFO) 
ZGESDD  
subroutine  zgesvd (JOBU, JOBVT, M, N, A, LDA, S, U, LDU, VT, LDVT, WORK, LWORK, RWORK, INFO) 
ZGESVD computes the singular value decomposition (SVD) for GE matrices 
This is the group of complex16 singular value driver functions for GE matrices
subroutine zgesdd  (  character  JOBZ, 
integer  M,  
integer  N,  
complex*16, dimension( lda, * )  A,  
integer  LDA,  
double precision, dimension( * )  S,  
complex*16, dimension( ldu, * )  U,  
integer  LDU,  
complex*16, dimension( ldvt, * )  VT,  
integer  LDVT,  
complex*16, dimension( * )  WORK,  
integer  LWORK,  
double precision, dimension( * )  RWORK,  
integer, dimension( * )  IWORK,  
integer  INFO  
) 
ZGESDD
Download ZGESDD + dependencies [TGZ] [ZIP] [TXT]ZGESDD computes the singular value decomposition (SVD) of a complex MbyN matrix A, optionally computing the left and/or right singular vectors, by using divideandconquer method. 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 VT = V**H, 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 XMP, Cray YMP, Cray C90, or Cray2. It could conceivably fail on hexadecimal or decimal machines without guard digits, but we know of none.
[in]  JOBZ  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**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 in 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 A; = 'N': no columns of U or rows of V**H are computed. 
[in]  M  M is INTEGER The number of rows of the input matrix A. M >= 0. 
[in]  N  N is INTEGER The number of columns of the input matrix A. N >= 0. 
[in,out]  A  A is COMPLEX*16 array, dimension (LDA,N) On entry, the MbyN 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. 
[in]  LDA  LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M). 
[out]  S  S is DOUBLE PRECISION array, dimension (min(M,N)) The singular values of A, sorted so that S(i) >= S(i+1). 
[out]  U  U is COMPLEX*16 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 MbyM 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. 
[in]  LDU  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. 
[out]  VT  VT is COMPLEX*16 array, dimension (LDVT,N) If JOBZ = 'A' or JOBZ = 'O' and M >= N, VT contains the NbyN unitary matrix V**H; if JOBZ = 'S', VT contains the first min(M,N) rows of V**H (the right singular vectors, stored rowwise); if JOBZ = 'O' and M < N, or JOBZ = 'N', VT is not referenced. 
[in]  LDVT  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). 
[out]  WORK  WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK. 
[in]  LWORK  LWORK is 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 generally be larger. If LWORK = 1, a workspace query is assumed. The optimal size for the WORK array is calculated and stored in WORK(1), and no other work except argument checking is performed. 
[out]  RWORK  RWORK is DOUBLE PRECISION array, dimension (MAX(1,LRWORK)) If JOBZ = 'N', LRWORK >= 5*min(M,N). Otherwise, LRWORK >= min(M,N)*max(5*min(M,N)+7,2*max(M,N)+2*min(M,N)+1) 
[out]  IWORK  IWORK is INTEGER array, dimension (8*min(M,N)) 
[out]  INFO  INFO is INTEGER = 0: successful exit. < 0: if INFO = i, the ith argument had an illegal value. > 0: The updating process of DBDSDC did not converge. 
Definition at line 222 of file zgesdd.f.
subroutine zgesvd  (  character  JOBU, 
character  JOBVT,  
integer  M,  
integer  N,  
complex*16, dimension( lda, * )  A,  
integer  LDA,  
double precision, dimension( * )  S,  
complex*16, dimension( ldu, * )  U,  
integer  LDU,  
complex*16, dimension( ldvt, * )  VT,  
integer  LDVT,  
complex*16, dimension( * )  WORK,  
integer  LWORK,  
double precision, dimension( * )  RWORK,  
integer  INFO  
) 
ZGESVD computes the singular value decomposition (SVD) for GE matrices
Download ZGESVD + dependencies [TGZ] [ZIP] [TXT]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.
[in]  JOBU  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. 
[in]  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'. 
[in]  M  M is INTEGER The number of rows of the input matrix A. M >= 0. 
[in]  N  N is INTEGER The number of columns of the input matrix A. N >= 0. 
[in,out]  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. 
[in]  LDA  LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M). 
[out]  S  S is DOUBLE PRECISION array, dimension (min(M,N)) The singular values of A, sorted so that S(i) >= S(i+1). 
[out]  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. 
[in]  LDU  LDU is INTEGER The leading dimension of the array U. LDU >= 1; if JOBU = 'S' or 'A', LDU >= M. 
[out]  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. 
[in]  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). 
[out]  WORK  WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK. 
[in]  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. 
[out]  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. 
[out]  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. 
Definition at line 214 of file zgesvd.f.