WOLFRAM SYSTEM MODELER

# dorghr

Generate a real orthogonal matrix Q which is defined as the product of IHI-ILO elementary reflectors of order N, as returned by DGEHRD

# Wolfram Language

In[1]:=
`SystemModel["Modelica.Math.Matrices.LAPACK.dorghr"]`
Out[1]:=

# Information

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

```Lapack documentation
Purpose
=======

DORGHR generates a real orthogonal matrix Q which is defined as the
product of IHI-ILO elementary reflectors of order N, as returned by
DGEHRD:

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

Arguments
=========

N       (input) INTEGER
The order of the matrix Q. 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).
1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.

A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
On entry, the vectors which define the elementary reflectors,
as returned by DGEHRD.
On exit, the N-by-N orthogonal matrix Q.

LDA     (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).

TAU     (input) DOUBLE PRECISION array, dimension (N-1)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by DGEHRD.

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. LWORK >= IHI-ILO.
For optimum performance LWORK >= (IHI-ILO)*NB, 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

(Aout, info) = dorghr(A, ilo, ihi, tau)

# Inputs (4)

A Type: Real[:,size(A, 1)] Description: Square matrix with the elementary reflectors Default Value: 1 Type: Integer Description: Lowest index where the original matrix is not in upper triangular form - ilo must have the same value as in the previous call of DGEHRD Default Value: size(A, 1) Type: Integer Description: Highest index where the original matrix is not in upper triangular form - ihi must have the same value as in the previous call of DGEHRD Type: Real[max(0, size(A, 1) - 1)] Description: Scalar factors of the elementary reflectors

# Outputs (2)

Aout Default Value: A Type: Real[size(A, 1),size(A, 2)] Description: Orthogonal matrix as a result of elementary reflectors Type: Integer