LAPACK  3.4.2 LAPACK: Linear Algebra PACKage
sggsvp.f File Reference

Go to the source code of this file.

## 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

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.```
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.

Here is the call graph for this function:

Here is the caller graph for this function: