WOLFRAM SYSTEM MODELER

# dormhr

overwrites the general real M-by-N matrix C with Q * C or C * Q or Q' * C or C * Q', where Q is an orthogonal matrix as returned by dgehrd # Wolfram Language

In:= `SystemModel["Modelica.Math.Matrices.LAPACK.dormhr"]`
Out:= # Information

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```

# Syntax

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

# Inputs (7)

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

# Outputs (2)

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 Type: Integer