WDggglm WDgglse

WDgglse() Function WDgglse ( M As  Long, N As  Long, P As  Long, A As  Variant, B As  Variant, C As  Variant, D As  Variant  ) Linear equality-constrained least squares (LSE) problem Purpose WDgglse solves the linear equality-constrained least squares (LSE) problem: minimize || c - Ax ||_2 subject to B*x = d where A is an M x N matrix, B is a P x N matrix, c is a given M-vector, and d is a given P-vector. It is assumed that P <= N <= M + P, and rank(B) = P and rank( (A) ) = N ( (B) ) These conditions ensure that the LSE problem has a unique solution, which is obtained using a generalized RQ factorization of the matrices (B, A) given by B = (0 R)*Q, A = Z*T*Q Returns N+2 x 1 Column 1 Rows 1 to N Least squares solution vector x Row N+1 2-norm of residual sum of squares Row N+2 Return code Return code = 0: Successful exit = 1: The least squares solution could not be computed. The upper triangular factor R associated with B in the generalized RQ factorization of the pair (B, A) is singular, so that rank(B) < P. = 2: The least squares solution could not be computed. The N-P x N-P part of the upper trapezoidal factor T associated with A in the generalized RQ factorization of the pair (B, A) is singular, so that rank(A^T B^T)^T < N. Parameters [in] M Number of rows of the matrix A. (M >= 1) [in] N Number of columns of the matrices A and B. (N >= 1) [in] P Number of rows of the matrix B. (1 <= P <= N <= M + P) [in] A (M x N) M x N coefficient matrix A of the least squares part of the LSE problem. [in] B (P x N) P x N coefficient matrix B of the constrained equation. [in] C (M) Right hand side vector c for the least squares part of the LSE problem. [in] D (P) Right hand side vector d for the constrained equation. Reference LAPACK Example Solve the linear equality-constrained least squares (LSE) problem, i.e. minimize || c - Ax ||_2 subject to B*x = d, where ( -1.06 0.48 -0.04 ) A = ( -1.19 0.73 -0.24 ) ( 1.97 -0.89 0.56 ) ( 0.68 -0.53 0.08 ) ( -0.58 -0.79 0.82 ) B = ( 0.77 0.71 -0.55 ) ( -1.36 -1.22 1.66 ) ( 0.3884 ) c = ( 0.1120 ) ( -0.3644 ) ( -0.0002 ) ( 1.8250 ) d = ( -1.7058 ) ( 3.4904 )