sggsvp (3)  Linux Manuals
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 NKL K L U**T*A*Q = K ( 0 A12 A13 ) if MKL >= 0; L ( 0 0 A23 ) MKL ( 0 0 0 ) NKL K L = K ( 0 A12 A13 ) if MKL < 0; MK ( 0 0 A23 ) NKL K L V**T*B*Q = L ( 0 0 B13 ) PL ( 0 0 0 ) where the KbyK matrix A12 and LbyL matrix B13 are nonsingular upper triangular; A23 is LbyL upper triangular if MKL >= 0, otherwise A23 is (MK)byL upper trapezoidal. K+L = the effective numerical rank of the (M+P)byN 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.
JOBVJOBV is CHARACTER*1 = 'V': Orthogonal matrix V is computed; = 'N': V is not computed.
JOBQJOBQ is CHARACTER*1 = 'Q': Orthogonal matrix Q is computed; = 'N': Q is not computed.
MM is INTEGER The number of rows of the matrix A. M >= 0.
PP is INTEGER The number of rows of the matrix B. P >= 0.
NN is INTEGER The number of columns of the matrices A and B. N >= 0.
AA is REAL array, dimension (LDA,N) On entry, the MbyN matrix A. On exit, A contains the triangular (or trapezoidal) matrix described in the Purpose section.
LDALDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).
BB is REAL array, dimension (LDB,N) On entry, the PbyN matrix B. On exit, B contains the triangular matrix described in the Purpose section.
LDBLDB is INTEGER The leading dimension of the array B. LDB >= max(1,P).
TOLATOLA is REAL
TOLBTOLB 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.
KK is INTEGER
LL 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.
UU is REAL array, dimension (LDU,M) If JOBU = 'U', U contains the orthogonal matrix U. If JOBU = 'N', U is not referenced.
LDULDU is INTEGER The leading dimension of the array U. LDU >= max(1,M) if JOBU = 'U'; LDU >= 1 otherwise.
VV is REAL array, dimension (LDV,P) If JOBV = 'V', V contains the orthogonal matrix V. If JOBV = 'N', V is not referenced.
LDVLDV is INTEGER The leading dimension of the array V. LDV >= max(1,P) if JOBV = 'V'; LDV >= 1 otherwise.
QQ is REAL array, dimension (LDQ,N) If JOBQ = 'Q', Q contains the orthogonal matrix Q. If JOBQ = 'N', Q is not referenced.
LDQLDQ is INTEGER The leading dimension of the array Q. LDQ >= max(1,N) if JOBQ = 'Q'; LDQ >= 1 otherwise.
IWORKIWORK is INTEGER array, dimension (N)
TAUTAU is REAL array, dimension (N)
WORKWORK is REAL array, dimension (max(3*N,M,P))
INFOINFO is INTEGER = 0: successful exit < 0: if INFO = i, the ith 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
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