ZGGGLM(3F) ZGGGLM(3F)
ZGGGLM - solve a general Gauss-Markov linear model (GLM) problem
SUBROUTINE ZGGGLM( N, M, P, A, LDA, B, LDB, D, X, Y, WORK, LWORK, INFO )
INTEGER INFO, LDA, LDB, LWORK, M, N, P
COMPLEX*16 A( LDA, * ), B( LDB, * ), D( * ), WORK( * ), X( * ),
Y( * )
ZGGGLM solves a general Gauss-Markov linear model (GLM) problem:
minimize || y ||_2 subject to d = A*x + B*y
x
where A is an N-by-M matrix, B is an N-by-P matrix, and d is a given Nvector.
It is assumed that M <= N <= M+P, and
rank(A) = M and rank( A B ) = N.
Under these assumptions, the constrained equation is always consistent,
and there is a unique solution x and a minimal 2-norm solution y, which
is obtained using a generalized QR factorization of A and B.
In particular, if matrix B is square nonsingular, then the problem GLM is
equivalent to the following weighted linear least squares problem
minimize || inv(B)*(d-A*x) ||_2
x
where inv(B) denotes the inverse of B.
N (input) INTEGER
The number of rows of the matrices A and B. N >= 0.
M (input) INTEGER
The number of columns of the matrix A. 0 <= M <= N.
P (input) INTEGER
The number of columns of the matrix B. P >= N-M.
A (input/output) COMPLEX*16 array, dimension (LDA,M)
On entry, the N-by-M matrix A. On exit, A is destroyed.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
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ZGGGLM(3F) ZGGGLM(3F)
B (input/output) COMPLEX*16 array, dimension (LDB,P)
On entry, the N-by-P matrix B. On exit, B is destroyed.
LDB (input) INTEGER
The leading dimension of the array B. LDB >= max(1,N).
D (input/output) COMPLEX*16 array, dimension (N)
On entry, D is the left hand side of the GLM equation. On exit,
D is destroyed.
X (output) COMPLEX*16 array, dimension (M)
Y (output) COMPLEX*16 array, dimension (P) On exit, X and Y
are the solutions of the GLM 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,N+M+P). For
optimum performance, LWORK >= M+min(N,P)+max(N,P)*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.
ZGGGLM(3F) ZGGGLM(3F)
ZGGGLM - solve a general Gauss-Markov linear model (GLM) problem
SUBROUTINE ZGGGLM( N, M, P, A, LDA, B, LDB, D, X, Y, WORK, LWORK, INFO )
INTEGER INFO, LDA, LDB, LWORK, M, N, P
COMPLEX*16 A( LDA, * ), B( LDB, * ), D( * ), WORK( * ), X( * ),
Y( * )
ZGGGLM solves a general Gauss-Markov linear model (GLM) problem:
minimize || y ||_2 subject to d = A*x + B*y
x
where A is an N-by-M matrix, B is an N-by-P matrix, and d is a given Nvector.
It is assumed that M <= N <= M+P, and
rank(A) = M and rank( A B ) = N.
Under these assumptions, the constrained equation is always consistent,
and there is a unique solution x and a minimal 2-norm solution y, which
is obtained using a generalized QR factorization of A and B.
In particular, if matrix B is square nonsingular, then the problem GLM is
equivalent to the following weighted linear least squares problem
minimize || inv(B)*(d-A*x) ||_2
x
where inv(B) denotes the inverse of B.
N (input) INTEGER
The number of rows of the matrices A and B. N >= 0.
M (input) INTEGER
The number of columns of the matrix A. 0 <= M <= N.
P (input) INTEGER
The number of columns of the matrix B. P >= N-M.
A (input/output) COMPLEX*16 array, dimension (LDA,M)
On entry, the N-by-M matrix A. On exit, A is destroyed.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
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ZGGGLM(3F) ZGGGLM(3F)
B (input/output) COMPLEX*16 array, dimension (LDB,P)
On entry, the N-by-P matrix B. On exit, B is destroyed.
LDB (input) INTEGER
The leading dimension of the array B. LDB >= max(1,N).
D (input/output) COMPLEX*16 array, dimension (N)
On entry, D is the left hand side of the GLM equation. On exit,
D is destroyed.
X (output) COMPLEX*16 array, dimension (M)
Y (output) COMPLEX*16 array, dimension (P) On exit, X and Y
are the solutions of the GLM 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,N+M+P). For
optimum performance, LWORK >= M+min(N,P)+max(N,P)*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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