Contents
sggglm - solve a general Gauss-Markov linear model (GLM)
problem
SUBROUTINE SGGGLM(N, M, P, A, LDA, B, LDB, D, X, Y, WORK, LDWORK,
INFO)
INTEGER N, M, P, LDA, LDB, LDWORK, INFO
REAL A(LDA,*), B(LDB,*), D(*), X(*), Y(*), WORK(*)
SUBROUTINE SGGGLM_64(N, M, P, A, LDA, B, LDB, D, X, Y, WORK, LDWORK,
INFO)
INTEGER*8 N, M, P, LDA, LDB, LDWORK, INFO
REAL 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, DIMENSION(:) :: D, X, Y, WORK
REAL, 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, DIMENSION(:) :: D, X, Y, WORK
REAL, DIMENSION(:,:) :: A, B
C INTERFACE
#include <sunperf.h>
void sggglm(int n, int m, int p, float *a, int lda, float
*b, int ldb, float *d, float *x, float *y, int
*info);
void sggglm_64(long n, long m, long p, float *a, long lda,
float *b, long ldb, float *d, float *x, float *y,
long *info);
sggglm 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.
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 des-
troyed.
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 des-
troyed.
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 equa-
tion. 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 SGEQRF, SGERQF,
SORMQR and SORMRQ.
If LDWORK = -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 LDWORK is issued by XERBLA.
INFO (output)
= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an ille-
gal value.