WOLFRAM SYSTEM MODELER

# dormqr

Overwrite 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 of a QR factorization as returned by dgeqrf

# Wolfram Language

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

# Information

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

```Lapack documentation
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 (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) = dormqr(C, A, tau, side, trans)

# Inputs (5)

C Type: Real[:,:] Type: Real[:,:] Type: Real[:] Default Value: "L" Type: String Default Value: "N" Type: String

# Outputs (2)

Cout Default Value: C Type: Real[size(C, 1),size(C, 2)] Description: Contains Q*C or Q**T*C or C*Q**T or C*Q Type: Integer