.Modelica_LinearSystems2.Math.Matrices.Internal.multiplyWithOrthogonalQ_hr

Information

   Purpose
    -- LAPACK routine (version 3.0) --
      Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
      Courant Institute, Argonne National Lab, and Rice University
      June 30, 1999

      .. Scalar Arguments ..
      ..
      .. Array Arguments ..
      ..

   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 (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

function multiplyWithOrthogonalQ_hr
  input Real C[:, :];
  input Real A[:, :];
  input Real tau[size(A, 2) - 1];
  input String side = "L";
  input String trans = "N";
  input Integer ilo = 1 "lowest index where the original matrix had been Hessenbergform";
  input Integer ihi = size(A, 2) "highest index where the original matrix had been Hessenbergform";
  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 multiplyWithOrthogonalQ_hr;