dggglm(3P) Sun Performance Library dggglm(3P)NAMEdggglm - solve a general Gauss-Markov linear model (GLM) problem
SYNOPSIS
SUBROUTINE DGGGLM(N, M, P, A, LDA, B, LDB, D, X, Y, WORK, LDWORK,
INFO)
INTEGER N, M, P, LDA, LDB, LDWORK, INFO
DOUBLE PRECISION A(LDA,*), B(LDB,*), D(*), X(*), Y(*), WORK(*)
SUBROUTINE DGGGLM_64(N, M, P, A, LDA, B, LDB, D, X, Y, WORK, LDWORK,
INFO)
INTEGER*8 N, M, P, LDA, LDB, LDWORK, INFO
DOUBLE PRECISION A(LDA,*), B(LDB,*), D(*), X(*), Y(*), WORK(*)
F95 INTERFACE
SUBROUTINE GGGLM([N], [M], [P], A, [LDA], B, [LDB], D, X, Y, [WORK],
[LDWORK], [INFO])
INTEGER :: N, M, P, LDA, LDB, LDWORK, INFO
REAL(8), DIMENSION(:) :: D, X, Y, WORK
REAL(8), DIMENSION(:,:) :: A, B
SUBROUTINE GGGLM_64([N], [M], [P], A, [LDA], B, [LDB], D, X, Y, [WORK],
[LDWORK], [INFO])
INTEGER(8) :: N, M, P, LDA, LDB, LDWORK, INFO
REAL(8), DIMENSION(:) :: D, X, Y, WORK
REAL(8), DIMENSION(:,:) :: A, B
C INTERFACE
#include <sunperf.h>
void dggglm(int n, int m, int p, double *a, int lda, double *b, int
ldb, double *d, double *x, double *y, int *info);
void dggglm_64(long n, long m, long p, double *a, long lda, double *b,
long ldb, double *d, double *x, double *y, long *info);
PURPOSEdggglm 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 N-
vector. 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.
ARGUMENTS
N (input) The number of rows of the matrices A and B. N >= 0.
M (input) The number of columns of the matrix A. 0 <= M <= N.
P (input) The number of columns of the matrix B. P >= N-M.
A (input/output)
On entry, the N-by-M matrix A. On exit, A is destroyed.
LDA (input)
The leading dimension of the array A. LDA >= max(1,N).
B (input/output)
On entry, the N-by-P matrix B. On exit, B is destroyed.
LDB (input)
The leading dimension of the array B. LDB >= max(1,N).
D (input/output)
On entry, D is the left hand side of the GLM equation. On
exit, D is destroyed.
X (output)
On exit, X and Y are the solutions of the GLM problem.
Y (output)
See the description of X.
WORK (workspace)
On exit, if INFO = 0, WORK(1) returns the optimal LDWORK.
LDWORK (input)
The dimension of the array WORK. LDWORK >= max(1,N+M+P). For
optimum performance, LDWORK >= M+min(N,P)+max(N,P)*NB, where
NB is an upper bound for the optimal blocksizes for DGEQRF,
DGERQF, DORMQR and DORMRQ.
If LDWORK = -1, then a workspace query is assumed; the rou‐
tine 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 LDWORK is issued by XERBLA.
INFO (output)
= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an illegal value.
6 Mar 2009 dggglm(3P)
