---
name: "dorm2l.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/dorm2l.f"
---

# dorm2l.f(3)

## NAME

SRC/dorm2l.f

## SYNOPSIS

### Functions/Subroutines

subroutine **dorm2l** (side, trans, m, n, k, a, lda, tau, c, ldc, work, info)\
 **DORM2L** multiplies a general matrix by the orthogonal matrix from a QL factorization determined by sgeqlf (unblocked algorithm).

## Function/Subroutine Documentation

### subroutine dorm2l (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 info)

**DORM2L** multiplies a general matrix by the orthogonal matrix from a QL factorization determined by sgeqlf (unblocked algorithm).

**Purpose:**

```
!>
!> DORM2L overwrites the general real m by n matrix C with
!>
!>       Q * C  if SIDE = 'L' and TRANS = 'N', or
!>
!>       Q**T * C  if SIDE = 'L' and TRANS = 'T', or
!>
!>       C * Q  if SIDE = 'R' and TRANS = 'N', or
!>
!>       C * Q**T if SIDE = 'R' and TRANS = 'T',
!>
!> where Q is a real orthogonal matrix defined as the product of k
!> elementary reflectors
!>
!>       Q = H(k) . . . H(2) H(1)
!>
!> as returned by DGEQLF. 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': apply Q  (No transpose)
!>          = 'T': apply Q**T (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.
!>
```

*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
!>          DGEQLF in the last 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 DGEQLF.
!>
```

*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
!>                                   (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

Univ. of Colorado Denver

NAG Ltd.

Definition at line **156** of file **dorm2l.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.