.Modelica.Math.Matrices.LAPACK.dormhr

Information

Lapack documentation
    Purpose
    =======

    DORMHR overwrites the general real M-by-N matrix C with

                    SIDE = 'L'     SIDE = 'R'
    TRANS = 'N':      Q * C          C * Q
    TRANS = 'T':      Q**T * C       C * Q**T

    where Q is a real orthogonal matrix of order nq, with nq = m if
    SIDE = 'L' and nq = n if SIDE = 'R'. Q is defined as the product of
    IHI-ILO elementary reflectors, as returned by DGEHRD:

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

    Arguments
    =========

    SIDE    (input) CHARACTER*1
            = 'L': apply Q or Q**T from the Left;
            = 'R': apply Q or Q**T from the Right.

    TRANS   (input) CHARACTER*1
            = 'N':  No transpose, apply Q;
            = 'T':  Transpose, apply Q**T.

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

    N       (input) INTEGER
            The number of columns of the matrix C. 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).
            If SIDE = 'L', then 1 <= ILO <= IHI <= M, if M > 0, and
            ILO = 1 and IHI = 0, if M = 0;
            if SIDE = 'R', then 1 <= ILO <= IHI <= N, if N > 0, and
            ILO = 1 and IHI = 0, if N = 0.

    A       (input) DOUBLE PRECISION array, dimension
                                 (LDA,M) if SIDE = 'L'
                                 (LDA,N) if SIDE = 'R'
            The vectors which define the elementary reflectors, as
            returned by DGEHRD.

    LDA     (input) INTEGER
            The leading dimension of the array A.
            LDA >= max(1,M) if SIDE = 'L'; LDA >= max(1,N) if SIDE = 'R'.

    TAU     (input) DOUBLE PRECISION array, dimension
                                 (M-1) if SIDE = 'L'
                                 (N-1) if SIDE = 'R'
            TAU(i) must contain the scalar factor of the elementary
            reflector H(i), as returned by DGEHRD.

    C       (input/output) DOUBLE PRECISION array, dimension (LDC,N)
            On entry, the M-by-N matrix C.
            On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.

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

    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.
            If SIDE = 'L', LWORK >= max(1,N);
            if SIDE = 'R', LWORK >= max(1,M).
            For optimum performance LWORK >= N*NB if SIDE = 'L', and
            LWORK >= M*NB if SIDE = 'R', 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 dormhr
  extends Modelica.Icons.Function;
  input Real C[:, :];
  input Real A[:, :];
  input Real tau[if side == "L" then size(C, 2) - 1 else size(C, 1) - 1];
  input String side = "L";
  input String trans = "N";
  input Integer ilo = 1 "Lowest index where the original matrix is not in upper triangular form";
  input Integer ihi = if side == "L" then size(C, 1) else size(C, 2) "Highest index where the original matrix is not in upper triangular form";
  output Real Cout[size(C, 1), size(C, 2)] = C "Contains the Hessenberg form in the upper triangle and the first subdiagonal and below the first subdiagonal it contains the elementary reflectors which represents (with array tau) as a product the orthogonal matrix Q";
  output Integer info;
end dormhr;