sggsvp.f File Reference

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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	(	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	INFO
	)

SGGSVP

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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:

[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(3*N,M,P))
[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.

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.

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