SRC/zggsvp3.f(3) Library Functions Manual SRC/zggsvp3.f(3)

SRC/zggsvp3.f


subroutine zggsvp3 (jobu, jobv, jobq, m, p, n, a, lda, b, ldb, tola, tolb, k, l, u, ldu, v, ldv, q, ldq, iwork, rwork, tau, work, lwork, info)
ZGGSVP3

ZGGSVP3

Purpose:

 ZGGSVP3 computes unitary matrices U, V and Q such that
                    N-K-L  K    L
  U**H*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**H*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**H,B**H)**H.
 This decomposition is the preprocessing step for computing the
 Generalized Singular Value Decomposition (GSVD), see subroutine
 ZGGSVD3.

Parameters

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

JOBV

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

JOBQ

          JOBQ is CHARACTER*1
          = 'Q':  Unitary 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 COMPLEX*16 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 COMPLEX*16 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)*MAZHEPS,
             TOLB = MAX(P,N)*norm(B)*MAZHEPS.
          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**H,B**H)**H.

U

          U is COMPLEX*16 array, dimension (LDU,M)
          If JOBU = 'U', U contains the unitary 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 COMPLEX*16 array, dimension (LDV,P)
          If JOBV = 'V', V contains the unitary 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 COMPLEX*16 array, dimension (LDQ,N)
          If JOBQ = 'Q', Q contains the unitary 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)

RWORK

          RWORK is DOUBLE PRECISION array, dimension (2*N)

TAU

          TAU is COMPLEX*16 array, dimension (N)

WORK

          WORK is COMPLEX*16 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.
          If LWORK = -1, then a workspace query is assumed; the routine
          only calculates the optimal size of the WORK array, returns
          this value as the first entry of the WORK array, and no error
          message related to LWORK is issued by XERBLA.

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.

Further Details:

  The subroutine uses LAPACK subroutine ZGEQP3 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.
  ZGGSVP3 replaces the deprecated subroutine ZGGSVP.

Definition at line 275 of file zggsvp3.f.

Generated automatically by Doxygen for LAPACK from the source code.

Version 3.12.0 LAPACK