# zlamswlq.f - Man Page

## Synopsis

### Functions/Subroutines

subroutine zlamswlq (SIDE, TRANS, M, N, K, MB, NB, A, LDA, T, LDT, C, LDC, WORK, LWORK, INFO)
ZLAMSWLQ

## Function/Subroutine Documentation

### subroutine zlamswlq (character SIDE, character TRANS, integer M, integer N, integer K, integer MB, integer NB, complex*16, dimension( lda, * ) A, integer LDA, complex*16, dimension( ldt, * ) T, integer LDT, complex*16, dimension(ldc, * ) C, integer LDC, complex*16, dimension( * ) WORK, integer LWORK, integer INFO)

ZLAMSWLQ

Purpose:

```    ZLAMSWLQ overwrites the general complex M-by-N matrix C with

SIDE = 'L'     SIDE = 'R'
TRANS = 'N':      Q * C          C * Q
TRANS = 'C':      Q**H * C       C * Q**H
where Q is a complex unitary matrix defined as the product of blocked
elementary reflectors computed by short wide LQ
factorization (ZLASWLQ)```
Parameters

SIDE

```          SIDE is CHARACTER*1
= 'L': apply Q or Q**H from the Left;
= 'R': apply Q or Q**H from the Right.```

TRANS

```          TRANS is CHARACTER*1
= 'N':  No transpose, apply Q;
= 'C':  Conjugate Transpose, apply Q**H.```

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 COMPLEX*16 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
ZLASWLQ 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 COMPLEX*16 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 COMPLEX*16 array, dimension (LDC,N)
On entry, the M-by-N matrix C.
On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.```

LDC

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

WORK

`         (workspace) COMPLEX*16 array, dimension (MAX(1,LWORK))`

LWORK

```          LWORK is INTEGER
The dimension of the array WORK.
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 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

NAG Ltd.

Further Details:

``` Short-Wide LQ (SWLQ) performs LQ by a sequence of unitary transformations,
representing Q as a product of other unitary 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).

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 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 193 of file zlamswlq.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page zlamswlq(3) is an alias of zlamswlq.f(3).

Tue Apr 12 2022 Version 3.10.1 LAPACK