# cgelqt.f

Section: LAPACK (3)
Updated: Tue Nov 14 2017
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cgelqt.f

## SYNOPSIS

### Functions/Subroutines

subroutine cgelqt (M, N, MB, A, LDA, T, LDT, WORK, INFO)

## Function/Subroutine Documentation

### subroutine cgelqt (integer M, integer N, integer MB, complex, dimension( lda, * ) A, integer LDA, complex, dimension( ldt, * ) T, integer LDT, complex, dimension( * ) WORK, integer INFO)

Purpose:

CGELQT computes a blocked LQ factorization of a complex 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 COMPLEX 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 COMPLEX 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 COMPLEX 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.

Date:

June 2017

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 125 of file cgelqt.f.

## Author

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