This information is part of the Modelica Standard Library maintained by the Modelica Association.

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

(Cout, info) = dormhr(C, A, tau, side, trans, ilo, ihi)

C	Type: Real[:,:]
A	Type: Real[:,:]
tau	Type: Real[if side == "L" then size(C, 2) - 1 else size(C, 1) - 1]
side	Default Value: "L" Type: String
trans	Default Value: "N" Type: String
ilo	Default Value: 1 Type: Integer Description: lowest index where the original matrix had been Hessenbergform
ihi	Default Value: if side == "L" then size(C, 1) else size(C, 2) Type: Integer Description: highest index where the original matrix had been Hessenbergform

Cout	Default Value: C Type: Real[size(C, 1),size(C, 2)] Description: 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
info	Type: Integer