sggsvp3()

subroutine sggsvp3	(	character	jobu,
		character	jobv,
		character	jobq,
		integer	m,
		integer	p,
		integer	n,
		real, dimension( lda, * )	a,
		integer	lda,
		real, dimension( ldb, * )	b,
		integer	ldb,
		real	tola,
		real	tolb,
		integer	k,
		integer	l,
		real, dimension( ldu, * )	u,
		integer	ldu,
		real, dimension( ldv, * )	v,
		integer	ldv,
		real, dimension( ldq, * )	q,
		integer	ldq,
		integer, dimension( * )	iwork,
		real, dimension( * )	tau,
		real, dimension( * )	work,
		integer	lwork,
		integer	info )

SGGSVP3

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Purpose:

!>
!> SGGSVP3 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
!> SGGSVD3.
!> 

Parameters

[in]	JOBU	!> JOBU is CHARACTER*1 !> = 'U': Orthogonal matrix U is computed; !> = 'N': U is not computed. !>
[in]	JOBV	!> JOBV is CHARACTER*1 !> = 'V': Orthogonal matrix V is computed; !> = 'N': V is not computed. !>
[in]	JOBQ	!> JOBQ is CHARACTER*1 !> = 'Q': Orthogonal matrix Q is computed; !> = 'N': Q is not computed. !>
[in]	M	!> M is INTEGER !> The number of rows of the matrix A. M >= 0. !>
[in]	P	!> P is INTEGER !> The number of rows of the matrix B. P >= 0. !>
[in]	N	!> N is INTEGER !> The number of columns of the matrices A and B. N >= 0. !>
[in,out]	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. !>
[in]	LDA	!> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,M). !>
[in,out]	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. !>
[in]	LDB	!> LDB is INTEGER !> The leading dimension of the array B. LDB >= max(1,P). !>
[in]	TOLA	!> TOLA is REAL !>
[in]	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. !>
[out]	K	!> K is INTEGER !>
[out]	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. !>
[out]	U	!> U is REAL array, dimension (LDU,M) !> If JOBU = 'U', U contains the orthogonal matrix U. !> If JOBU = 'N', U is not referenced. !>
[in]	LDU	!> LDU is INTEGER !> The leading dimension of the array U. LDU >= max(1,M) if !> JOBU = 'U'; LDU >= 1 otherwise. !>
[out]	V	!> V is REAL array, dimension (LDV,P) !> If JOBV = 'V', V contains the orthogonal matrix V. !> If JOBV = 'N', V is not referenced. !>
[in]	LDV	!> LDV is INTEGER !> The leading dimension of the array V. LDV >= max(1,P) if !> JOBV = 'V'; LDV >= 1 otherwise. !>
[out]	Q	!> Q is REAL array, dimension (LDQ,N) !> If JOBQ = 'Q', Q contains the orthogonal matrix Q. !> If JOBQ = 'N', Q is not referenced. !>
[in]	LDQ	!> LDQ is INTEGER !> The leading dimension of the array Q. LDQ >= max(1,N) if !> JOBQ = 'Q'; LDQ >= 1 otherwise. !>
[out]	IWORK	!> IWORK is INTEGER array, dimension (N) !>
[out]	TAU	!> TAU is REAL array, dimension (N) !>
[out]	WORK	!> WORK is REAL array, dimension (MAX(1,LWORK)) !> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. !>
[in]	LWORK	!> LWORK is INTEGER !> The dimension of the array WORK. LWORK >= 1. !> !> 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. !>
[out]	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 SGEQP3 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.
!>
!>  SGGSVP3 replaces the deprecated subroutine SGGSVP.
!>
!>