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(*)
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
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);
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.
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.