dggsvp.f man page

dggsvp.f —

Synopsis

Functions/Subroutines

subroutine dggsvp (JOBU, JOBV, JOBQ, M, P, N, A, LDA, B, LDB, TOLA, TOLB, K, L, U, LDU, V, LDV, Q, LDQ, IWORK, TAU, WORK, INFO)
DGGSVP

Function/Subroutine Documentation

subroutine dggsvp (characterJOBU, characterJOBV, characterJOBQ, integerM, integerP, integerN, double precision, dimension( lda, * )A, integerLDA, double precision, dimension( ldb, * )B, integerLDB, double precisionTOLA, double precisionTOLB, integerK, integerL, double precision, dimension( ldu, * )U, integerLDU, double precision, dimension( ldv, * )V, integerLDV, double precision, dimension( ldq, * )Q, integerLDQ, integer, dimension( * )IWORK, double precision, dimension( * )TAU, double precision, dimension( * )WORK, integerINFO)

DGGSVP  

Purpose:

 DGGSVP computes orthogonal matrices U, V and Q such that

                    N-K-L  K    L
  U**T*A*Q =     K ( 0    A12  A13 )  if M-K-L >= 0;
                 L ( 0     0   A23 )
             M-K-L ( 0     0    0  )

                  N-K-L  K    L
         =     K ( 0    A12  A13 )  if M-K-L < 0;
             M-K ( 0     0   A23 )

                  N-K-L  K    L
  V**T*B*Q =   L ( 0     0   B13 )
             P-L ( 0     0    0  )

 where the K-by-K matrix A12 and L-by-L matrix B13 are nonsingular
 upper triangular; A23 is L-by-L upper triangular if M-K-L >= 0,
 otherwise A23 is (M-K)-by-L upper trapezoidal.  K+L = the effective
 numerical rank of the (M+P)-by-N matrix (A**T,B**T)**T. 

 This decomposition is the preprocessing step for computing the
 Generalized Singular Value Decomposition (GSVD), see subroutine
 DGGSVD.
Parameters:

JOBU

          JOBU is CHARACTER*1
          = 'U':  Orthogonal matrix U is computed;
          = 'N':  U is not computed.

JOBV

          JOBV is CHARACTER*1
          = 'V':  Orthogonal matrix V is computed;
          = 'N':  V is not computed.

JOBQ

          JOBQ is CHARACTER*1
          = 'Q':  Orthogonal matrix Q is computed;
          = 'N':  Q is not computed.

M

          M is INTEGER
          The number of rows of the matrix A.  M >= 0.

P

          P is INTEGER
          The number of rows of the matrix B.  P >= 0.

N

          N is INTEGER
          The number of columns of the matrices A and B.  N >= 0.

A

          A is DOUBLE PRECISION array, dimension (LDA,N)
          On entry, the M-by-N matrix A.
          On exit, A contains the triangular (or trapezoidal) matrix
          described in the Purpose section.

LDA

          LDA is INTEGER
          The leading dimension of the array A. LDA >= max(1,M).

B

          B is DOUBLE PRECISION array, dimension (LDB,N)
          On entry, the P-by-N matrix B.
          On exit, B contains the triangular matrix described in
          the Purpose section.

LDB

          LDB is INTEGER
          The leading dimension of the array B. LDB >= max(1,P).

TOLA

          TOLA is DOUBLE PRECISION

TOLB

          TOLB is DOUBLE PRECISION

          TOLA and TOLB are the thresholds to determine the effective
          numerical rank of matrix B and a subblock of A. Generally,
          they are set to
             TOLA = MAX(M,N)*norm(A)*MACHEPS,
             TOLB = MAX(P,N)*norm(B)*MACHEPS.
          The size of TOLA and TOLB may affect the size of backward
          errors of the decomposition.

K

          K is INTEGER

L

          L is INTEGER

          On exit, K and L specify the dimension of the subblocks
          described in Purpose section.
          K + L = effective numerical rank of (A**T,B**T)**T.

U

          U is DOUBLE PRECISION array, dimension (LDU,M)
          If JOBU = 'U', U contains the orthogonal matrix U.
          If JOBU = 'N', U is not referenced.

LDU

          LDU is INTEGER
          The leading dimension of the array U. LDU >= max(1,M) if
          JOBU = 'U'; LDU >= 1 otherwise.

V

          V is DOUBLE PRECISION array, dimension (LDV,P)
          If JOBV = 'V', V contains the orthogonal matrix V.
          If JOBV = 'N', V is not referenced.

LDV

          LDV is INTEGER
          The leading dimension of the array V. LDV >= max(1,P) if
          JOBV = 'V'; LDV >= 1 otherwise.

Q

          Q is DOUBLE PRECISION array, dimension (LDQ,N)
          If JOBQ = 'Q', Q contains the orthogonal matrix Q.
          If JOBQ = 'N', Q is not referenced.

LDQ

          LDQ is INTEGER
          The leading dimension of the array Q. LDQ >= max(1,N) if
          JOBQ = 'Q'; LDQ >= 1 otherwise.

IWORK

          IWORK is INTEGER array, dimension (N)

TAU

          TAU is DOUBLE PRECISION array, dimension (N)

WORK

          WORK is DOUBLE PRECISION array, dimension (max(3*N,M,P))

INFO

          INFO is INTEGER
          = 0:  successful exit
          < 0:  if INFO = -i, the i-th argument had an illegal value.
Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

November 2011

Further Details:

The subroutine uses LAPACK subroutine DGEQPF for the QR factorization with column pivoting to detect the effective numerical rank of the a matrix. It may be replaced by a better rank determination strategy.

Definition at line 253 of file dggsvp.f.

Author

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Referenced By

dggsvp(3) is an alias of dggsvp.f(3).

Sat Nov 16 2013 Version 3.4.2 LAPACK