.Modelica.Math.Matrices.LAPACK.dgglse_vec

Information

Lapack documentation
    Purpose
    =======

    DGGLSE solves the linear equality-constrained least squares (LSE)
    problem:

            minimize || c - A*x ||_2   subject to   B*x = d

    where A is an M-by-N matrix, B is a P-by-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.

    Arguments
    =========

    M       (input) INTEGER
            The number of rows of the matrix A.  M >= 0.

    N       (input) INTEGER
            The number of columns of the matrices A and B. N >= 0.

    P       (input) INTEGER
            The number of rows of the matrix B. 0 <= P <= N <= M+P.

    A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
            On entry, the M-by-N matrix A.
            On exit, the elements on and above the diagonal of the array
            contain the min(M,N)-by-N upper trapezoidal matrix T.

    LDA     (input) INTEGER
            The leading dimension of the array A. LDA >= max(1,M).

    B       (input/output) DOUBLE PRECISION array, dimension (LDB,N)
            On entry, the P-by-N matrix B.
            On exit, the upper triangle of the subarray B(1:P,N-P+1:N)
            contains the P-by-P upper triangular matrix R.

    LDB     (input) INTEGER
            The leading dimension of the array B. LDB >= max(1,P).

    C       (input/output) DOUBLE PRECISION array, dimension (M)
            On entry, C contains the right hand side vector for the
            least squares part of the LSE problem.
            On exit, the residual sum of squares for the solution
            is given by the sum of squares of elements N-P+1 to M of
            vector C.

    D       (input/output) DOUBLE PRECISION array, dimension (P)
            On entry, D contains the right hand side vector for the
            constrained equation.
            On exit, D is destroyed.

    X       (output) DOUBLE PRECISION array, dimension (N)
            On exit, X is the solution of the LSE problem.

    WORK    (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK))
            On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

    LWORK   (input) INTEGER
            The dimension of the array WORK. LWORK >= max(1,M+N+P).
            For optimum performance LWORK >= P+min(M,N)+max(M,N)*NB,
            where NB is an upper bound for the optimal blocksizes for
            DGEQRF, SGERQF, DORMQR and SORMRQ.

            If LWORK = -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 LWORK is issued by XERBLA.

    INFO    (output) INTEGER
            = 0:  successful exit.
            < 0:  if INFO = -i, the i-th argument had an illegal value.
            = 1:  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; the least squares
                  solution could not be computed.
            = 2:  the (N-P) by (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) ) < N; the least squares solution could not
                      ( (B) )
                  be computed.

Interface

pure function dgglse_vec
  extends Modelica.Icons.Function;
  input Real A[:, :] "Minimize |A*x - c|^2";
  input Real c[size(A, 1)];
  input Real B[:, size(A, 2)] "Subject to B*x=d";
  input Real d[size(B, 1)];
  output Real x[size(A, 2)] "Solution vector";
  output Integer info;
end dgglse_vec;