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LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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| subroutine cgesdd | ( | character | JOBZ, |
| integer | M, | ||
| integer | N, | ||
| complex, dimension( lda, * ) | A, | ||
| integer | LDA, | ||
| real, dimension( * ) | S, | ||
| complex, dimension( ldu, * ) | U, | ||
| integer | LDU, | ||
| complex, dimension( ldvt, * ) | VT, | ||
| integer | LDVT, | ||
| complex, dimension( * ) | WORK, | ||
| integer | LWORK, | ||
| real, dimension( * ) | RWORK, | ||
| integer, dimension( * ) | IWORK, | ||
| integer | INFO | ||
| ) |
CGESDD
Download CGESDD + dependencies [TGZ] [ZIP] [TXT]
CGESDD 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 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 REAL array, dimension (min(M,N))
The singular values of A, sorted so that S(i) >= S(i+1). |
| [out] | U | U is COMPLEX 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 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 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 REAL 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 SBDSDC did not converge.
= 0: successful exit. |
1.9.4