CXML
        	    
LAPACK version 3.0
dggsvp(3)

PURPOSE
  DGGSVP - compute orthogonal matrices U, V and Q such that  N-K-L K L U'*A*Q
  = K ( 0 A12 A13 ) if M-K-L >= 0

SYNTAX
  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 )

      CHARACTER	     JOBQ, JOBU, JOBV

      INTEGER	     INFO, K, L, LDA, LDB, LDQ, LDU, LDV, M, N, P

      DOUBLE	     PRECISION TOLA, TOLB

      INTEGER	     IWORK( * )

      DOUBLE	     PRECISION A( LDA, * ), B( LDB, * ), Q( LDQ, * ), TAU( *
		     ), U( LDU, * ), V( LDV, * ), WORK( * )

DESCRIPTION
  DGGSVP computes orthogonal matrices U, V and Q such that N-K-L K L U'*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'*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 transpose of Z.

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

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

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

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

  M	  (input) INTEGER
	  The number of rows of the matrix A.  M >= 0.

  P	  (input) INTEGER
	  The number of rows of the matrix B.  P >= 0.

  N	  (input) INTEGER
	  The number of columns of the matrices A and B.  N >= 0.

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

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

  TOLA	  (input) DOUBLE PRECISION
	  TOLB	  (input) 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	  (output) INTEGER
	  L	  (output) INTEGER On exit, K and L specify the dimension of
	  the subblocks described in Purpose.  K + L = effective numerical
	  rank of (A',B')'.

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

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

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

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

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

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

  IWORK	  (workspace) INTEGER array, dimension (N)

  TAU	  (workspace) DOUBLE PRECISION array, dimension (N)

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

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

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.