sgesdd.f (3) - Linux Manuals

NAME

sgesdd.f -

SYNOPSIS

Functions/Subroutines

subroutine sgesdd (JOBZ, M, N, A, LDA, S, U, LDU, VT, LDVT, WORK, LWORK, IWORK, INFO)
SGESDD

Function/Subroutine Documentation

subroutine sgesdd (characterJOBZ, integerM, integerN, real, dimension( lda, * )A, integerLDA, real, dimension( * )S, real, dimension( ldu, * )U, integerLDU, real, dimension( ldvt, * )VT, integerLDVT, real, dimension( * )WORK, integerLWORK, integer, dimension( * )IWORK, integerINFO)

SGESDD

Purpose:

 SGESDD computes the singular value decomposition (SVD) of a real
 M-by-N matrix A, optionally computing the left and right singular
 vectors.  If singular vectors are desired, it uses a
 divide-and-conquer algorithm.

 The SVD is written

      A = U * SIGMA * 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 orthogonal matrix, and
 V is an N-by-N orthogonal 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**T, 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.

 

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**T 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**T are returned in the arrays U
                  and VT;
          = 'O':  If M >= N, the first N columns of U are overwritten
                  on the array A and all rows of V**T are returned in
                  the array VT;
                  otherwise, all columns of U are returned in the
                  array U and the first M rows of V**T are overwritten
                  in the array A;
          = 'N':  no columns of U or rows of V**T 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 REAL 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**T (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 REAL 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
          orthogonal 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 REAL array, dimension (LDVT,N)
          If JOBZ = 'A' or JOBZ = 'O' and M >= N, VT contains the
          N-by-N orthogonal matrix V**T;
          if JOBZ = 'S', VT contains the first min(M,N) rows of
          V**T (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 REAL 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 >= 3*min(M,N) + max(max(M,N),6*min(M,N)).
          If JOBZ = 'O',
            LWORK >= 3*min(M,N) + 
                     max(max(M,N),5*min(M,N)*min(M,N)+4*min(M,N)).
          If JOBZ = 'S' or 'A'
            LWORK >= 3*min(M,N) +
                     max(max(M,N),4*min(M,N)*min(M,N)+3*min(M,N)+max(M,N)).
          For good performance, LWORK should generally be larger.
          If LWORK = -1 but other input arguments are legal, WORK(1)
          returns the optimal LWORK.

IWORK

          IWORK is INTEGER array, dimension (8*min(M,N))

INFO

          INFO is INTEGER
          = 0:  successful exit.
          < 0:  if INFO = -i, the i-th argument had an illegal value.
          > 0:  SBDSDC did not converge, updating process failed.

 

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

September 2012

Contributors:

Ming Gu and Huan Ren, Computer Science Division, University of California at Berkeley, USA

Definition at line 217 of file sgesdd.f.

Author

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