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
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
void zggglm(int n, int m, int p, doublecomplex *a, int lda, doublecomplex *b, int ldb, doublecomplex *d, doublecomplex *x, doublecomplex *y, int *info);
void zggglm_64(long n, long m, long p, doublecomplex *a, long lda, doublecomplex *b, long ldb, doublecomplex *d, doublecomplex *x, doublecomplex *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.