
cgesdd.f(3) LAPACK cgesdd.f(3)
NAME
cgesdd.f 
SYNOPSIS
Functions/Subroutines
subroutine cgesdd (JOBZ, M, N, A, LDA, S, U, LDU, VT, LDVT, WORK, LWORK, RWORK, IWORK,
INFO)
CGESDD
Function/Subroutine Documentation
subroutine cgesdd (characterJOBZ, integerM, integerN, complex, dimension( lda, * )A,
integerLDA, real, dimension( * )S, complex, dimension( ldu, * )U, integerLDU, complex,
dimension( ldvt, * )VT, integerLDVT, complex, dimension( * )WORK, integerLWORK, real,
dimension( * )RWORK, integer, dimension( * )IWORK, integerINFO)
CGESDD
Purpose:
CGESDD 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.
Parameters:
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.
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 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 REAL array, dimension (min(M,N))
The singular values of A, sorted so that S(i) >= S(i+1).
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 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 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 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 REAL 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 SBDSDC did not converge.
Author:
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 cgesdd.f.
Author
Generated automatically by Doxygen for LAPACK from the source code.
Version 3.4.2 Tue Sep 25 2012 cgesdd.f(3) 
