.Modelica_LinearSystems2.Math.Matrices.Internal.multiplyWithOrthogonalQ_qr

Information

   Purpose
   =======

   DORMQR 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 defined as the product of k
   elementary reflectors

         Q = H(1) H(2) . . . H(k)

   as returned by DGEQRF. Q is of order M if SIDE = 'L' and of order N
   if SIDE = 'R'.

   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.

   K       (input) INTEGER
           The number of elementary reflectors whose product defines
           the matrix Q.
           If SIDE = 'L', M >= K >= 0;
           if SIDE = 'R', N >= K >= 0.

   A       (input) DOUBLE PRECISION array, dimension (LDA,K)
           The i-th column must contain the vector which defines the
           elementary reflector H(i), for i = 1,2,...,k, as returned by
           DGEQRF in the first k columns of its array argument A.
           A is modified by the routine but restored on exit.

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

   TAU     (input) DOUBLE PRECISION array, dimension (K)
           TAU(i) must contain the scalar factor of the elementary
           reflector H(i), as returned by DGEQRF.

   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_qr
  input Real C[:, :];
  input Real Q[:, :];
  input Real tau[:];
  input String side = "L";
  input String trans = "N";
  output Real Cout[size(C, 1), size(C, 2)] = C "contains Q*C or Q**T*C or C*Q**T or C*Q";
  output Integer info;
end multiplyWithOrthogonalQ_qr;