---
name: "sgemlq.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/sgemlq.f"
---

# sgemlq.f(3)

## NAME

SRC/sgemlq.f

## SYNOPSIS

### Functions/Subroutines

subroutine **sgemlq** (side, trans, m, n, k, a, lda, t, tsize, c, ldc, work, lwork, info)\
 **SGEMLQ**

## Function/Subroutine Documentation

### subroutine sgemlq (character side, character trans, integer m, integer n, integer k, real, dimension( lda, \* ) a, integer lda, real, dimension( \* ) t, integer tsize, real, dimension( ldc, \* ) c, integer ldc, real, dimension( \* ) work, integer lwork, integer info)

**SGEMLQ**

**Purpose:**

```
!>
!>     SGEMLQ 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 blocked elementary reflectors computed by short wide LQ
!>    factorization (SGELQ)
!>
!>
```

**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 A.  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'
!>          Part of the data structure to represent Q as returned by SGELQ.
!>
```

*LDA*

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

*T*

```
!>          T is REAL array, dimension (MAX(5,TSIZE)).
!>          Part of the data structure to represent Q as returned by SGELQ.
!>
```

*TSIZE*

```
!>          TSIZE is INTEGER
!>          The dimension of the array T. TSIZE >= 5.
!>
```

*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*

```
!>          (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK))
!>          On exit, if INFO = 0, WORK(1) returns the minimal LWORK.
!>
```

*LWORK*

```
!>          LWORK is INTEGER
!>          The dimension of the array WORK. LWORK >= 1.
!>          If LWORK = -1, then a workspace query is assumed. The routine
!>          only calculates the size of the WORK array, returns this
!>          value as WORK(1), and no error message related to WORK
!>          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.

**Further Details**

```
!>
!> These details are particular for this LAPACK implementation. Users should not
!> take them for granted. These details may change in the future, and are not likely
!> true for another LAPACK implementation. These details are relevant if one wants
!> to try to understand the code. They are not part of the interface.
!>
!> In this version,
!>
!>          T(2): row block size (MB)
!>          T(3): column block size (NB)
!>          T(6:TSIZE): data structure needed for Q, computed by
!>                           SLASWLQ or SGELQT
!>
!>  Depending on the matrix dimensions M and N, and row and column
!>  block sizes MB and NB returned by ILAENV, SGELQ will use either
!>  SLASWLQ (if the matrix is wide-and-short) or SGELQT to compute
!>  the LQ factorization.
!>  This version of SGEMLQ will use either SLAMSWLQ or SGEMLQT to
!>  multiply matrix Q by another matrix.
!>  Further Details in SLAMSWLQ or SGEMLQT.
!>
```

Definition at line **171** of file **sgemlq.f**.

## Author

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