sggsvp.f(3)							      LAPACK							       sggsvp.f(3)

NAME

       sggsvp.f -

SYNOPSIS

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

Function/Subroutine Documentation
   subroutine sggsvp (characterJOBU, characterJOBV, characterJOBQ, integerM, integerP, integerN, real, dimension( lda, * )A, integerLDA, real,
       dimension( ldb, * )B, integerLDB, realTOLA, realTOLB, integerK, integerL, real, dimension( ldu, * )U, integerLDU, real, dimension( ldv, *
       )V, integerLDV, real, dimension( ldq, * )Q, integerLDQ, integer, dimension( * )IWORK, real, dimension( * )TAU, real, dimension( * )WORK,
       integerINFO)
       SGGSVP

       Purpose:

	    SGGSVP 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
	    SGGSVD.

       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 REAL 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 REAL 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 REAL

	   TOLB

		     TOLB is REAL

		     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 REAL 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 REAL 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 REAL 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 REAL array, dimension (N)

	   WORK

		     WORK is REAL 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 SGEQPF 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 sggsvp.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2							  Tue Sep 25 2012						       sggsvp.f(3)