ZGGLSE(3F) ZGGLSE(3F)
ZGGLSE - solve the linear equality-constrained least squares (LSE)
problem
SUBROUTINE ZGGLSE( M, N, P, A, LDA, B, LDB, C, D, X, WORK, LWORK, INFO )
INTEGER INFO, LDA, LDB, LWORK, M, N, P
COMPLEX*16 A( LDA, * ), B( LDB, * ), C( * ), D( * ), WORK( * ),
X( * )
ZGGLSE solves the linear equality-constrained least squares (LSE)
problem:
minimize || c - A*x ||_2 subject to B*x = d
where A is an M-by-N matrix, B is a P-by-N matrix, c is a given M-vector,
and d is a given P-vector. It is assumed that
P <= N <= M+P, and
rank(B) = P and rank( ( A ) ) = N.
( ( B ) )
These conditions ensure that the LSE problem has a unique solution, which
is obtained using a GRQ factorization of the matrices B and A.
M (input) INTEGER
The number of rows of the matrix A. M >= 0.
N (input) INTEGER
The number of columns of the matrices A and B. N >= 0.
P (input) INTEGER
The number of rows of the matrix B. 0 <= P <= N <= M+P.
A (input/output) COMPLEX*16 array, dimension (LDA,N)
On entry, the M-by-N matrix A. On exit, A is destroyed.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,M).
B (input/output) COMPLEX*16 array, dimension (LDB,N)
On entry, the P-by-N matrix B. On exit, B is destroyed.
LDB (input) INTEGER
The leading dimension of the array B. LDB >= max(1,P).
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ZGGLSE(3F) ZGGLSE(3F)
C (input/output) COMPLEX*16 array, dimension (M)
On entry, C contains the right hand side vector for the least
squares part of the LSE problem. On exit, the residual sum of
squares for the solution is given by the sum of squares of
elements N-P+1 to M of vector C.
D (input/output) COMPLEX*16 array, dimension (P)
On entry, D contains the right hand side vector for the
constrained equation. On exit, D is destroyed.
X (output) COMPLEX*16 array, dimension (N)
On exit, X is the solution of the LSE problem.
WORK (workspace/output) COMPLEX*16 array, dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The dimension of the array WORK. LWORK >= max(1,M+N+P). For
optimum performance LWORK >= P+min(M,N)+max(M,N)*NB, where NB is
an upper bound for the optimal blocksizes for ZGEQRF, CGERQF,
ZUNMQR and CUNMRQ.
INFO (output) INTEGER
= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an illegal value.
ZGGLSE(3F) ZGGLSE(3F)
ZGGLSE - solve the linear equality-constrained least squares (LSE)
problem
SUBROUTINE ZGGLSE( M, N, P, A, LDA, B, LDB, C, D, X, WORK, LWORK, INFO )
INTEGER INFO, LDA, LDB, LWORK, M, N, P
COMPLEX*16 A( LDA, * ), B( LDB, * ), C( * ), D( * ), WORK( * ),
X( * )
ZGGLSE solves the linear equality-constrained least squares (LSE)
problem:
minimize || c - A*x ||_2 subject to B*x = d
where A is an M-by-N matrix, B is a P-by-N matrix, c is a given M-vector,
and d is a given P-vector. It is assumed that
P <= N <= M+P, and
rank(B) = P and rank( ( A ) ) = N.
( ( B ) )
These conditions ensure that the LSE problem has a unique solution, which
is obtained using a GRQ factorization of the matrices B and A.
M (input) INTEGER
The number of rows of the matrix A. M >= 0.
N (input) INTEGER
The number of columns of the matrices A and B. N >= 0.
P (input) INTEGER
The number of rows of the matrix B. 0 <= P <= N <= M+P.
A (input/output) COMPLEX*16 array, dimension (LDA,N)
On entry, the M-by-N matrix A. On exit, A is destroyed.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,M).
B (input/output) COMPLEX*16 array, dimension (LDB,N)
On entry, the P-by-N matrix B. On exit, B is destroyed.
LDB (input) INTEGER
The leading dimension of the array B. LDB >= max(1,P).
Page 1
ZGGLSE(3F) ZGGLSE(3F)
C (input/output) COMPLEX*16 array, dimension (M)
On entry, C contains the right hand side vector for the least
squares part of the LSE problem. On exit, the residual sum of
squares for the solution is given by the sum of squares of
elements N-P+1 to M of vector C.
D (input/output) COMPLEX*16 array, dimension (P)
On entry, D contains the right hand side vector for the
constrained equation. On exit, D is destroyed.
X (output) COMPLEX*16 array, dimension (N)
On exit, X is the solution of the LSE problem.
WORK (workspace/output) COMPLEX*16 array, dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The dimension of the array WORK. LWORK >= max(1,M+N+P). For
optimum performance LWORK >= P+min(M,N)+max(M,N)*NB, where NB is
an upper bound for the optimal blocksizes for ZGEQRF, CGERQF,
ZUNMQR and CUNMRQ.
INFO (output) INTEGER
= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an illegal value.
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