cggsvp (l) - Linux Man Pages

cggsvp: computes unitary matrices U, V and Q such that N-K-L K L Uaq*A*Q = K ( 0 A12 A13 ) if M-K-L >= 0

NAME

CGGSVP - computes unitary matrices U, V and Q such that N-K-L K L Uaq*A*Q = K ( 0 A12 A13 ) if M-K-L >= 0

SYNOPSIS

SUBROUTINE CGGSVP(
JOBU, JOBV, JOBQ, M, P, N, A, LDA, B, LDB, TOLA, TOLB, K, L, U, LDU, V, LDV, Q, LDQ, IWORK, RWORK, TAU, WORK, INFO )

    
CHARACTER JOBQ, JOBU, JOBV

    
INTEGER INFO, K, L, LDA, LDB, LDQ, LDU, LDV, M, N, P

    
REAL TOLA, TOLB

    
INTEGER IWORK( * )

    
REAL RWORK( * )

    
COMPLEX A( LDA, * ), B( LDB, * ), Q( LDQ, * ), TAU( * ), U( LDU, * ), V( LDV, * ), WORK( * )

PURPOSE

CGGSVP computes unitary matrices U, V and Q such that
              A23 )

    M-K-L         )

           N-K-L     L

         A12  A13  if M-K-L 0;

      M-K       A23 )

         N-K-L     L

 Vaq*B*Q         B13 )

    P-L         )
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 (Aaq,Baq)aq. Zaq denotes the conjugate transpose of Z.
This decomposition is the preprocessing step for computing the Generalized Singular Value Decomposition (GSVD), see subroutine CGGSVD.

ARGUMENTS

JOBU (input) CHARACTER*1
= aqUaq: Unitary matrix U is computed;
= aqNaq: U is not computed.
JOBV (input) CHARACTER*1

= aqVaq: Unitary matrix V is computed;
= aqNaq: V is not computed.
JOBQ (input) CHARACTER*1

= aqQaq: Unitary matrix Q is computed;
= aqNaq: 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) COMPLEX 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) COMPLEX array, dimension (LDB,N)
On entry, the P-by-N matrix B. On exit, B contains the triangular matrix described in the Purpose section.
LDB (input) INTEGER
The leading dimension of the array B. LDB >= max(1,P).
TOLA (input) REAL
TOLB (input) 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.
K (output) INTEGER
L (output) INTEGER On exit, K and L specify the dimension of the subblocks described in Purpose section. K + L = effective numerical rank of (Aaq,Baq)aq.
U (output) COMPLEX array, dimension (LDU,M)
If JOBU = aqUaq, U contains the unitary matrix U. If JOBU = aqNaq, U is not referenced.
LDU (input) INTEGER
The leading dimension of the array U. LDU >= max(1,M) if JOBU = aqUaq; LDU >= 1 otherwise.
V (output) COMPLEX array, dimension (LDV,P)
If JOBV = aqVaq, V contains the unitary matrix V. If JOBV = aqNaq, V is not referenced.
LDV (input) INTEGER
The leading dimension of the array V. LDV >= max(1,P) if JOBV = aqVaq; LDV >= 1 otherwise.
Q (output) COMPLEX array, dimension (LDQ,N)
If JOBQ = aqQaq, Q contains the unitary matrix Q. If JOBQ = aqNaq, Q is not referenced.
LDQ (input) INTEGER
The leading dimension of the array Q. LDQ >= max(1,N) if JOBQ = aqQaq; LDQ >= 1 otherwise.
IWORK (workspace) INTEGER array, dimension (N)
RWORK (workspace) REAL array, dimension (2*N)
TAU (workspace) COMPLEX array, dimension (N)
WORK (workspace) COMPLEX array, dimension (max(3*N,M,P))
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 CGEQPF 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.