# cunmr3.f - Man Page

SRC/cunmr3.f

## Synopsis

### Functions/Subroutines

subroutine cunmr3 (side, trans, m, n, k, l, a, lda, tau, c, ldc, work, info)
CUNMR3 multiplies a general matrix by the unitary matrix from a RZ factorization determined by ctzrzf (unblocked algorithm).

## Function/Subroutine Documentation

### subroutine cunmr3 (character side, character trans, integer m, integer n, integer k, integer l, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) tau, complex, dimension( ldc, * ) c, integer ldc, complex, dimension( * ) work, integer info)

CUNMR3 multiplies a general matrix by the unitary matrix from a RZ factorization determined by ctzrzf (unblocked algorithm).

Purpose:

``` CUNMR3 overwrites the general complex m by n matrix C with

Q * C  if SIDE = 'L' and TRANS = 'N', or

Q**H* C  if SIDE = 'L' and TRANS = 'C', or

C * Q  if SIDE = 'R' and TRANS = 'N', or

C * Q**H if SIDE = 'R' and TRANS = 'C',

where Q is a complex unitary matrix defined as the product of k
elementary reflectors

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

as returned by CTZRZF. Q is of order m if SIDE = 'L' and of order n
if SIDE = 'R'.```
Parameters

SIDE

```          SIDE is CHARACTER*1
= 'L': apply Q or Q**H from the Left
= 'R': apply Q or Q**H from the Right```

TRANS

```          TRANS is CHARACTER*1
= 'N': apply Q  (No transpose)
= 'C': apply Q**H (Conjugate transpose)```

M

```          M is INTEGER
The number of rows of the matrix C. M >= 0.```

N

```          N is INTEGER
The number of columns of the matrix C. N >= 0.```

K

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

L

```          L is INTEGER
The number of columns of the matrix A containing
the meaningful part of the Householder reflectors.
If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0.```

A

```          A is COMPLEX array, dimension
(LDA,M) if SIDE = 'L',
(LDA,N) if SIDE = 'R'
The i-th row must contain the vector which defines the
elementary reflector H(i), for i = 1,2,...,k, as returned by
CTZRZF in the last k rows of its array argument A.
A is modified by the routine but restored on exit.```

LDA

```          LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,K).```

TAU

```          TAU is COMPLEX array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by CTZRZF.```

C

```          C is COMPLEX array, dimension (LDC,N)
On entry, the m-by-n matrix C.
On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.```

LDC

```          LDC is INTEGER
The leading dimension of the array C. LDC >= max(1,M).```

WORK

```          WORK is COMPLEX array, dimension
(N) if SIDE = 'L',
(M) if SIDE = 'R'```

INFO

```          INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value```
Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Contributors:

A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA

Further Details:

Definition at line 176 of file cunmr3.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page cunmr3(3) is an alias of cunmr3.f(3).

Tue Nov 28 2023 12:08:41 Version 3.12.0 LAPACK