Previous: dggsvd Up: ../lapack-d.html Next: dgtcon
NAME
DGGSVP - compute orthogonal matrices U, V and Q such that
U'*A*Q = ( 0 A12 A13 ) K , V'*B*Q = ( 0 0 B13 ) L ( 0 0 A23
) L ( 0 0 0 ) P-L ( 0 0 0 ) M-K-L N-K-L K L N-K-L K L
where the K-by-K matrix A12 and L-by-L matrix B13 are non-
singular upper triangular
SYNOPSIS
SUBROUTINE DGGSVP( JOBU, JOBV, JOBQ, M, P, N, A, LDA, B,
LDB, TOLA, TOLB, K, L, U, LDU, V, LDV, Q,
LDQ, IWORK, TAU, WORK, INFO )
CHARACTER JOBQ, JOBU, JOBV
INTEGER INFO, K, L, LDA, LDB, LDQ, LDU, LDV, M,
N, P
DOUBLE PRECISION TOLA, TOLB
INTEGER IWORK( * )
DOUBLE PRECISION A( LDA, * ), B( LDB, * ), Q(
LDQ, * ), TAU( * ), U( LDU, * ), V( LDV,
* ), WORK( * )
PURPOSE
DGGSVP computes orthogonal matrices U, V and Q such that A23
is upper trapezoidal. K+L = the effective rank of (M+P)-
by-N matrix (A',B')'. Z' denotes the transpose of Z.
This decomposition is the preprocessing step for computing
the Generalized Singular Value Decomposition (GSVD), see
subroutine DGGSVD.
ARGUMENTS
JOBU (input) CHARACTER*1
= 'U': Orthogonal matrix U is computed;
= 'N': U is not computed.
JOBV (input) CHARACTER*1
= 'V': Orthogonal matrix V is computed;
= 'N': V is not computed.
JOBQ (input) CHARACTER*1
= 'Q': Orthogonal matrix Q is computed;
= 'N': Q is not computed.
M (input) INTEGER
The number of rows of the matrix A. M >= 0.
P (input) INTEGER
The number of rows of the matrix B. P >= 0.
N (input) INTEGER
The number of columns of the matrices A and B. N >=
0.
A (input/output) DOUBLE PRECISION 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 (input) INTEGER
The leading dimension of the array A. LDA >=
max(1,M).
B (input/output) DOUBLE PRECISION array, dimension (LDB,N)
On entry, the P-by-N matrix B. On exit, B contains
the triangular matrix described in the Purpose sec-
tion.
LDB (input) INTEGER
The leading dimension of the array B. LDB >=
max(1,P).
TOLA (input) DOUBLE PRECISION
TOLB (input) DOUBLE PRECISION TOLA and TOLB are
the thresholds to determine the effective rank of
matrix B and a subblock of A. Generally, they are
set to TOLA = MAX(M,N)*norm(A)*MAZHEPS, TOLB =
MAX(P,N)*norm(B)*MAZHEPS. The size of TOLA and TOLB
may affect the size of backward errors of the decom-
position.
K (output) INTEGER
L (output) INTEGER On exit, K and L specify
the dimension of the subblocks described in Purpose.
K + L = effective numerical rank of (A',B')'.
U (output) DOUBLE PRECISION array, dimension (LDU,M)
If JOBU = 'U', U contains the orthogonal matrix U.
If JOBU = 'N', U is not referenced.
LDU (input) INTEGER
The leading dimension of the array U. LDU >=
max(1,M).
V (output) DOUBLE PRECISION array, dimension (LDV,M)
If JOBV = 'V', V contains the orthogonal matrix V.
If JOBV = 'N', V is not referenced.
LDV (input) INTEGER
The leading dimension of the array V. LDV >=
max(1,P).
Q (output) DOUBLE PRECISION array, dimension (LDQ,N)
If JOBQ = 'Q', Q contains the orthogonal matrix Q.
If JOBQ = 'N', Q is not referenced.
LDQ (input) INTEGER
The leading dimension of the array Q. LDQ >=
max(1,N).
IWORK (workspace) INTEGER array, dimension (N)
TAU (workspace) DOUBLE PRECISION array, dimension (N)
(MAX(3*N,M,P))
WORK (workspace) DOUBLE PRECISION array, dimension
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal
value.
FURTHER DETAILS
The subroutine uses LAPACK subroutine DGEQPF for the QR fac-
torization with column pivoting to detect the effective
numerical rank of the a matrix. It may be replaced by a
better rank determination strategy.