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(*)
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
#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.
WORK(1)
returns the optimal LDWORK.
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.
= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an illegal value.