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RedHat 9 (Linux i386) - man page for dggsvp (redhat section l)

DGGSVP(l)					)					DGGSVP(l)

NAME
       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

SYNOPSIS
       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( * )

PURPOSE
       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 trans-
       pose 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 trape-
	       zoidal) 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 refer-
	       enced.

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

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

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

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

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

       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.

LAPACK version 3.0			   15 June 2000 				DGGSVP(l)


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