NAME

SYNOPSIS

  SUBROUTINE ZGGSVP( JOBU, JOBV, JOBQ, M, P, N, A, LDA, B, LDB, TOLA, 
 *      TOLB, K, L, U, LDU, V, LDV, Q, LDQ, IWORK, RWORK, TAU, WORK, 
 *      INFO)
  CHARACTER * 1 JOBU, JOBV, JOBQ
  DOUBLE COMPLEX A(LDA,*), B(LDB,*), U(LDU,*), V(LDV,*), Q(LDQ,*), TAU(*), WORK(*)
  INTEGER M, P, N, LDA, LDB, K, L, LDU, LDV, LDQ, INFO
  INTEGER IWORK(*)
  DOUBLE PRECISION TOLA, TOLB
  DOUBLE PRECISION RWORK(*)
 
  SUBROUTINE ZGGSVP_64( JOBU, JOBV, JOBQ, M, P, N, A, LDA, B, LDB, 
 *      TOLA, TOLB, K, L, U, LDU, V, LDV, Q, LDQ, IWORK, RWORK, TAU, 
 *      WORK, INFO)
  CHARACTER * 1 JOBU, JOBV, JOBQ
  DOUBLE COMPLEX A(LDA,*), B(LDB,*), U(LDU,*), V(LDV,*), Q(LDQ,*), TAU(*), WORK(*)
  INTEGER*8 M, P, N, LDA, LDB, K, L, LDU, LDV, LDQ, INFO
  INTEGER*8 IWORK(*)
  DOUBLE PRECISION TOLA, TOLB
  DOUBLE PRECISION RWORK(*)
 

F95 INTERFACE

  SUBROUTINE GGSVP( JOBU, JOBV, JOBQ, [M], [P], [N], A, [LDA], B, [LDB], 
 *       TOLA, TOLB, K, L, U, [LDU], V, [LDV], Q, [LDQ], [IWORK], [RWORK], 
 *       [TAU], [WORK], [INFO])
  CHARACTER(LEN=1) :: JOBU, JOBV, JOBQ
  COMPLEX(8), DIMENSION(:) :: TAU, WORK
  COMPLEX(8), DIMENSION(:,:) :: A, B, U, V, Q
  INTEGER :: M, P, N, LDA, LDB, K, L, LDU, LDV, LDQ, INFO
  INTEGER, DIMENSION(:) :: IWORK
  REAL(8) :: TOLA, TOLB
  REAL(8), DIMENSION(:) :: RWORK
 
  SUBROUTINE GGSVP_64( JOBU, JOBV, JOBQ, [M], [P], [N], A, [LDA], B, 
 *       [LDB], TOLA, TOLB, K, L, U, [LDU], V, [LDV], Q, [LDQ], [IWORK], 
 *       [RWORK], [TAU], [WORK], [INFO])
  CHARACTER(LEN=1) :: JOBU, JOBV, JOBQ
  COMPLEX(8), DIMENSION(:) :: TAU, WORK
  COMPLEX(8), DIMENSION(:,:) :: A, B, U, V, Q
  INTEGER(8) :: M, P, N, LDA, LDB, K, L, LDU, LDV, LDQ, INFO
  INTEGER(8), DIMENSION(:) :: IWORK
  REAL(8) :: TOLA, TOLB
  REAL(8), DIMENSION(:) :: RWORK
 

C INTERFACE

void zggsvp(char jobu, char jobv, char jobq, int m, int p, int n, doublecomplex *a, int lda, doublecomplex *b, int ldb, double tola, double tolb, int *k, int *l, doublecomplex *u, int ldu, doublecomplex *v, int ldv, doublecomplex *q, int ldq, int *info);

void zggsvp_64(char jobu, char jobv, char jobq, long m, long p, long n, doublecomplex *a, long lda, doublecomplex *b, long ldb, double tola, double tolb, long *k, long *l, doublecomplex *u, long ldu, doublecomplex *v, long ldv, doublecomplex *q, long ldq, long *info);

PURPOSE

          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'*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',B')'. Z' denotes the conjugate transpose of Z.

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

ARGUMENTS

* JOBU (input)

* JOBV (input)

* JOBQ (input)

* M (input)

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

* P (input)

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

* N (input)

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

* A (input/output)

On entry, the M-by-N matrix A. On exit, A contains the triangular (or trapezoidal) matrix described in the Purpose section.

* LDA (input)

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

* B (input/output)

On entry, the P-by-N matrix B. On exit, B contains the triangular matrix described in the Purpose section.

* LDB (input)

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

* TOLA (input)

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.

* TOLB (input)

See description of TOLA.

* K (output)

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

* L (output)

See the description of K.

* U (input)

If JOBU = 'U', U contains the unitary matrix U. If JOBU = 'N', U is not referenced.

* LDU (input)

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

* V (input)

If JOBV = 'V', V contains the unitary matrix V. If JOBV = 'N', V is not referenced.

* LDV (input)

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

* Q (input)

If JOBQ = 'Q', Q contains the unitary matrix Q. If JOBQ = 'N', Q is not referenced.

* LDQ (input)

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

* IWORK (workspace)

dimension(N)

* RWORK (workspace)

dimension(2*N)

* TAU (workspace)

dimension(N)

* WORK (workspace)

dimension(MAX(3*N,M,P))

* INFO (output)