---
name: "dormqr.f"
section: "3"
platform: "linux"
package: "lapack-doc"
version: "3.12.1-2"
release: "Arch Linux 2026-11-01"
platforms: ["linux"]
url: "https://new.carta.tech/dormqr.f"
---

# dormqr.f(3)

## NAME

SRC/dormqr.f

## SYNOPSIS

### Functions/Subroutines

subroutine **dormqr** (side, trans, m, n, k, a, lda, tau, c, ldc, work, lwork, info)\
 **DORMQR**

## Function/Subroutine Documentation

### subroutine dormqr (character side, character trans, integer m, integer n, integer k, double precision, dimension( lda, \* ) a, integer lda, double precision, dimension( \* ) tau, double precision, dimension( ldc, \* ) c, integer ldc, double precision, dimension( \* ) work, integer lwork, integer info)

**DORMQR**

**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'.
!>
```

**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 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.
!>
```

*LDA*

```
!>          LDA is INTEGER
!>          The leading dimension of the array A.
!>          If SIDE = 'L', LDA >= max(1,M);
!>          if SIDE = 'R', LDA >= max(1,N).
!>
```

*TAU*

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

*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**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 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 good performance, LWORK should generally be larger.
!>
!>          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.

Definition at line **165** of file **dormqr.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.