.Modelica.Math.Matrices.LAPACK.dorghr

Information

Lapack documentation
    Purpose
    =======

    DORGHR generates a real orthogonal matrix Q which is defined as the
    product of IHI-ILO elementary reflectors of order N, as returned by
    DGEHRD:

    Q = H(ilo) H(ilo+1) . . . H(ihi-1).

    Arguments
    =========

    N       (input) INTEGER
            The order of the matrix Q. N >= 0.

    ILO     (input) INTEGER
    IHI     (input) INTEGER
            ILO and IHI must have the same values as in the previous call
            of DGEHRD. Q is equal to the unit matrix except in the
            submatrix Q(ilo+1:ihi,ilo+1:ihi).
            1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.

    A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
            On entry, the vectors which define the elementary reflectors,
            as returned by DGEHRD.
            On exit, the N-by-N orthogonal matrix Q.

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

    TAU     (input) DOUBLE PRECISION array, dimension (N-1)
            TAU(i) must contain the scalar factor of the elementary
            reflector H(i), as returned by DGEHRD.

    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 >= IHI-ILO.
            For optimum performance LWORK >= (IHI-ILO)*NB, where NB is
            the optimal blocksize.

            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

Interface

pure function dorghr
  extends Modelica.Icons.Function;
  input Real A[:, size(A, 1)] "Square matrix with the elementary reflectors";
  input Integer ilo = 1 "Lowest index where the original matrix is not in upper triangular form - ilo must have the same value as in the previous call of DGEHRD";
  input Integer ihi = size(A, 1) "Highest index where the original matrix is not in upper triangular form - ihi must have the same value as in the previous call of DGEHRD";
  input Real tau[max(0, size(A, 1) - 1)] "Scalar factors of the elementary reflectors";
  output Real Aout[size(A, 1), size(A, 2)] = A "Orthogonal matrix as a result of elementary reflectors";
  output Integer info;
end dorghr;