
NAMEzgesdd.f SYNOPSISFunctions/Subroutinessubroutine zgesdd (JOBZ, M, N, A, LDA, S, U, LDU, VT, LDVT, WORK, LWORK, RWORK, IWORK, INFO) Function/Subroutine Documentationsubroutine zgesdd (characterJOBZ, 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, integer, dimension( * )IWORK, integerINFO)ZGESDD Purpose: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. JOBZ
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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.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 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 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) 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.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.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.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).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 >= 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.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)IWORK IWORK is INTEGER array, dimension (8*min(M,N))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. Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
Contributors:
Ming Gu and Huan Ren, Computer Science Division,
University of California at Berkeley, USA
Definition at line 222 of file zgesdd.f.
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