# dormrz.f man page

dormrz.f —

## Synopsis

### Functions/Subroutines

subroutinedormrz(SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)DORMRZ

## Function/Subroutine Documentation

### subroutine dormrz (characterSIDE, characterTRANS, integerM, integerN, integerK, integerL, double precision, dimension( lda, * )A, integerLDA, double precision, dimension( * )TAU, double precision, dimension( ldc, * )C, integerLDC, double precision, dimension( * )WORK, integerLWORK, integerINFO)

**DORMRZ**

**Purpose:**

```
DORMRZ 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 DTZRZF. 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**T from the Left;
= 'R': apply Q or Q**T from the Right.
```

*TRANS*

```
TRANS is CHARACTER*1
= 'N': No transpose, apply Q;
= 'T': Transpose, apply Q**T.
```

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

*C*

```
C is DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
```

*LWORK*

```
LWORK is 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*

```
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

Univ. of Colorado Denver

NAG Ltd.

**Date:**

November 2011

**Contributors:**

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

**Further Details:**

Definition at line 189 of file dormrz.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

dormrz(3) is an alias of dormrz.f(3).

Sat Nov 16 2013 Version 3.4.2 LAPACK