subroutine zggsvp3 (JOBU, JOBV, JOBQ, M, P, N, A, LDA, B, LDB, TOLA, TOLB, K, L, U, LDU, V, LDV, Q, LDQ, IWORK, RWORK, TAU, WORK, LWORK, INFO)
ZGGSVP3
ZGGSVP3
Purpose:
ZGGSVP3 computes unitary matrices U, V and Q such that
N-K-L K L
U**H*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**H*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**H,B**H)**H.
This decomposition is the preprocessing step for computing the
Generalized Singular Value Decomposition (GSVD), see subroutine
ZGGSVD3.
Parameters:
JOBU is CHARACTER*1
= 'U': Unitary matrix U is computed;
= 'N': U is not computed.
JOBV
JOBV is CHARACTER*1
= 'V': Unitary matrix V is computed;
= 'N': V is not computed.
JOBQ
JOBQ is CHARACTER*1
= 'Q': Unitary matrix Q is computed;
= 'N': Q is not computed.
M
M is INTEGER
The number of rows of the matrix A. M >= 0.
P
P is INTEGER
The number of rows of the matrix B. P >= 0.
N
N is INTEGER
The number of columns of the matrices A and B. N >= 0.
A
A is COMPLEX*16 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
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,M).
B
B is COMPLEX*16 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
LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,P).
TOLA
TOLA is DOUBLE PRECISION
TOLB
TOLB is DOUBLE PRECISION
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)*MAZHEPS,
TOLB = MAX(P,N)*norm(B)*MAZHEPS.
The size of TOLA and TOLB may affect the size of backward
errors of the decomposition.
K
K is INTEGER
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**H,B**H)**H.
U
U is COMPLEX*16 array, dimension (LDU,M)
If JOBU = 'U', U contains the unitary matrix U.
If JOBU = 'N', U is not referenced.
LDU
LDU is INTEGER
The leading dimension of the array U. LDU >= max(1,M) if
JOBU = 'U'; LDU >= 1 otherwise.
V
V is COMPLEX*16 array, dimension (LDV,P)
If JOBV = 'V', V contains the unitary matrix V.
If JOBV = 'N', V is not referenced.
LDV
LDV is INTEGER
The leading dimension of the array V. LDV >= max(1,P) if
JOBV = 'V'; LDV >= 1 otherwise.
Q
Q is COMPLEX*16 array, dimension (LDQ,N)
If JOBQ = 'Q', Q contains the unitary matrix Q.
If JOBQ = 'N', Q is not referenced.
LDQ
LDQ is INTEGER
The leading dimension of the array Q. LDQ >= max(1,N) if
JOBQ = 'Q'; LDQ >= 1 otherwise.
IWORK
IWORK is INTEGER array, dimension (N)
RWORK
RWORK is DOUBLE PRECISION array, dimension (2*N)
TAU
TAU is COMPLEX*16 array, dimension (N)
WORK
WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK
LWORK is INTEGER
The dimension of the array WORK.
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.
INFO
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value.
Author:
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
Further Details:
The subroutine uses LAPACK subroutine ZGEQP3 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.
ZGGSVP3 replaces the deprecated subroutine ZGGSVP.
Definition at line 280 of file zggsvp3.f.
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