# sormrq.f man page

sormrq.f —

## Synopsis

### Functions/Subroutines

subroutinesormrq(SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)SORMRQ

## Function/Subroutine Documentation

### subroutine sormrq (characterSIDE, characterTRANS, integerM, integerN, integerK, real, dimension( lda, * )A, integerLDA, real, dimension( * )TAU, real, dimension( ldc, * )C, integerLDC, real, dimension( * )WORK, integerLWORK, integerINFO)

**SORMRQ**

**Purpose:**

```
SORMRQ 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 SGERQF. 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.
```

*A*

```
A is REAL 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
SGERQF in the last k rows of its array argument A.
```

*LDA*

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

*TAU*

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

*C*

```
C is REAL 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*

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

*WORK*

```
WORK is REAL 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

Definition at line 170 of file sormrq.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

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

Sat Nov 16 2013 Version 3.4.2 LAPACK