LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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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
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ZGESDD computes the singular value decomposition (SVD) of a complex M-by-N matrix A, optionally computing the left and/or right singular vectors, by using divide-and-conquer method. The SVD is written A = U * SIGMA * conjugate-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 unitary matrix, and V is an N-by-N unitary 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**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 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.
[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 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**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 M-by-M 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 N-by-N 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 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. Let mx = max(M,N) and mn = min(M,N). If JOBZ = 'N', LWORK >= 2*mn + mx. If JOBZ = 'O', LWORK >= 2*mn*mn + 2*mn + mx. If JOBZ = 'S', LWORK >= mn*mn + 3*mn. If JOBZ = 'A', LWORK >= mn*mn + 2*mn + mx. These are not tight minimums in all cases; see comments inside code. For good performance, LWORK should generally be larger; a query is recommended. |
[out] | RWORK | RWORK is DOUBLE PRECISION array, dimension (MAX(1,LRWORK)) Let mx = max(M,N) and mn = min(M,N). If JOBZ = 'N', LRWORK >= 5*mn (LAPACK <= 3.6 needs 7*mn); else if mx >> mn, LRWORK >= 5*mn*mn + 5*mn; else LRWORK >= max( 5*mn*mn + 5*mn, 2*mx*mn + 2*mn*mn + mn ). |
[out] | IWORK | IWORK is INTEGER array, dimension (8*min(M,N)) |
[out] | INFO | INFO is INTEGER < 0: if INFO = -i, the i-th argument had an illegal value. = -4: if A had a NAN entry. > 0: The updating process of DBDSDC did not converge. = 0: successful exit. |