zggglm(3P) Sun Performance Library zggglm(3P)NAMEzggglm - solve a general Gauss-Markov linear model (GLM) problem
SYNOPSIS
SUBROUTINE ZGGGLM(N, M, P, A, LDA, B, LDB, D, X, Y, WORK, LDWORK,
INFO)
DOUBLE COMPLEX A(LDA,*), B(LDB,*), D(*), X(*), Y(*), WORK(*)
INTEGER N, M, P, LDA, LDB, LDWORK, INFO
SUBROUTINE ZGGGLM_64(N, M, P, A, LDA, B, LDB, D, X, Y, WORK, LDWORK,
INFO)
DOUBLE COMPLEX A(LDA,*), B(LDB,*), D(*), X(*), Y(*), WORK(*)
INTEGER*8 N, M, P, LDA, LDB, LDWORK, INFO
F95 INTERFACE
SUBROUTINE GGGLM([N], [M], [P], A, [LDA], B, [LDB], D, X, Y, [WORK],
[LDWORK], [INFO])
COMPLEX(8), DIMENSION(:) :: D, X, Y, WORK
COMPLEX(8), DIMENSION(:,:) :: A, B
INTEGER :: N, M, P, LDA, LDB, LDWORK, INFO
SUBROUTINE GGGLM_64([N], [M], [P], A, [LDA], B, [LDB], D, X, Y, [WORK],
[LDWORK], [INFO])
COMPLEX(8), DIMENSION(:) :: D, X, Y, WORK
COMPLEX(8), DIMENSION(:,:) :: A, B
INTEGER(8) :: N, M, P, LDA, LDB, LDWORK, INFO
C INTERFACE
#include <sunperf.h>
void zggglm(int n, int m, int p, doublecomplex *a, int lda, doublecom‐
plex *b, int ldb, doublecomplex *d, doublecomplex *x, double‐
complex *y, int *info);
void zggglm_64(long n, long m, long p, doublecomplex *a, long lda, dou‐
blecomplex *b, long ldb, doublecomplex *d, doublecomplex *x,
doublecomplex *y, long *info);
PURPOSEzggglm 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)
On exit, X and Y are the solutions of the GLM problem.
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 ZGEQRF,
ZGERQF, ZUNMQR and ZUNMRQ.
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 zggglm(3P)
