---
name: "dlamswlq.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/dlamswlq.f"
---

# dlamswlq.f(3)

## NAME

SRC/dlamswlq.f

## SYNOPSIS

### Functions/Subroutines

subroutine **dlamswlq** (side, trans, m, n, k, mb, nb, a, lda, t, ldt, c, ldc, work, lwork, info)\
 **DLAMSWLQ**

## Function/Subroutine Documentation

### subroutine dlamswlq (character side, character trans, integer m, integer n, integer k, integer mb, integer nb, double precision, dimension( lda, \* ) a, integer lda, double precision, dimension( ldt, \* ) t, integer ldt, double precision, dimension( ldc, \* ) c, integer ldc, double precision, dimension( \* ) work, integer lwork, integer info)

**DLAMSWLQ**

**Purpose:**

```
!>
!>    DLAMSWLQ 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 (DLASWLQ)
!>
```

**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.
!>          M >= K >= 0;
!>
!>
```

*MB*

```
!>          MB is INTEGER
!>          The row block size to be used in the blocked LQ.
!>          M >= MB >= 1
!>
```

*NB*

```
!>          NB is INTEGER
!>          The column block size to be used in the blocked LQ.
!>          NB > M.
!>
```

*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 blocked
!>          elementary reflector H(i), for i = 1,2,...,k, as returned by
!>          DLASWLQ in the first k rows of its array argument A.
!>
```

*LDA*

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

*T*

```
!>          T is DOUBLE PRECISION array, dimension
!>          ( M * Number of blocks(CEIL(N-K/NB-K)),
!>          The blocked upper triangular block reflectors stored in compact form
!>          as a sequence of upper triangular blocks.  See below
!>          for further details.
!>
```

*LDT*

```
!>          LDT is INTEGER
!>          The leading dimension of the array T.  LDT >= MB.
!>
```

*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*

```
!>          (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.
!>
!>          If MIN(M,N,K) = 0, LWORK >= 1.
!>          If SIDE = 'L', LWORK >= max(1,NB*MB).
!>          If SIDE = 'R', LWORK >= max(1,M*MB).
!>          If LWORK = -1, then a workspace query is assumed; the routine
!>          only calculates the minimal 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.

**Further Details:**

```
!> Short-Wide LQ (SWLQ) performs LQ by a sequence of orthogonal transformations,
!> representing Q as a product of other orthogonal matrices
!>   Q = Q(1) * Q(2) * . . . * Q(k)
!> where each Q(i) zeros out upper diagonal entries of a block of NB rows of A:
!>   Q(1) zeros out the upper diagonal entries of rows 1:NB of A
!>   Q(2) zeros out the bottom MB-N rows of rows [1:M,NB+1:2*NB-M] of A
!>   Q(3) zeros out the bottom MB-N rows of rows [1:M,2*NB-M+1:3*NB-2*M] of A
!>   . . .
!>
!> Q(1) is computed by GELQT, which represents Q(1) by Householder vectors
!> stored under the diagonal of rows 1:MB of A, and by upper triangular
!> block reflectors, stored in array T(1:LDT,1:N).
!> For more information see Further Details in GELQT.
!>
!> Q(i) for i>1 is computed by TPLQT, which represents Q(i) by Householder vectors
!> stored in columns [(i-1)*(NB-M)+M+1:i*(NB-M)+M] of A, and by upper triangular
!> block reflectors, stored in array T(1:LDT,(i-1)*M+1:i*M).
!> The last Q(k) may use fewer rows.
!> For more information see Further Details in TPLQT.
!>
!> For more details of the overall algorithm, see the description of
!> Sequential TSQR in Section 2.2 of [1].
!>
!> [1] “Communication-Optimal Parallel and Sequential QR and LU Factorizations,”
!>     J. Demmel, L. Grigori, M. Hoemmen, J. Langou,
!>     SIAM J. Sci. Comput, vol. 34, no. 1, 2012
!>
```

Definition at line **198** of file **dlamswlq.f**.

## Author

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