# sgelqt.f - Man Page

SRC/sgelqt.f

## Synopsis

### Functions/Subroutines

subroutine sgelqt (m, n, mb, a, lda, t, ldt, work, info)
SGELQT

## Function/Subroutine Documentation

### subroutine sgelqt (integer m, integer n, integer mb, real, dimension( lda, * ) a, integer lda, real, dimension( ldt, * ) t, integer ldt, real, dimension( * ) work, integer info)

SGELQT

Purpose:

``` DGELQT computes a blocked LQ factorization of a real M-by-N matrix A
using the compact WY representation of Q.```
Parameters

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 A.  N >= 0.```

MB

```          MB is INTEGER
The block size to be used in the blocked QR.  MIN(M,N) >= MB >= 1.```

A

```          A is REAL array, dimension (LDA,N)
On entry, the M-by-N matrix A.
On exit, the elements on and below the diagonal of the array
contain the M-by-MIN(M,N) lower trapezoidal matrix L (L is
lower triangular if M <= N); the elements above the diagonal
are the rows of V.```

LDA

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

T

```          T is REAL array, dimension (LDT,MIN(M,N))
The 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.```

WORK

`          WORK is REAL array, dimension (MB*N)`

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:

```  The matrix V stores the elementary reflectors H(i) in the i-th row
above the diagonal. For example, if M=5 and N=3, the matrix V is

V = (  1  v1 v1 v1 v1 )
(     1  v2 v2 v2 )
(         1 v3 v3 )

where the vi's represent the vectors which define H(i), which are returned
in the matrix A.  The 1's along the diagonal of V are not stored in A.
Let K=MIN(M,N).  The number of blocks is B = ceiling(K/MB), where each
block is of order MB except for the last block, which is of order
IB = K - (B-1)*MB.  For each of the B blocks, a upper triangular block
reflector factor is computed: T1, T2, ..., TB.  The MB-by-MB (and IB-by-IB
for the last block) T's are stored in the MB-by-K matrix T as

T = (T1 T2 ... TB).```

Definition at line 123 of file sgelqt.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

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

Tue Nov 28 2023 12:08:42 Version 3.12.0 LAPACK