# zgeqrt3.f man page

zgeqrt3.f —

## Synopsis

### Functions/Subroutines

recursive subroutinezgeqrt3(M, N, A, LDA, T, LDT, INFO)ZGEQRT3recursively computes a QR factorization of a general real or complex matrix using the compact WY representation of Q.

## Function/Subroutine Documentation

### recursive subroutine zgeqrt3 (integerM, integerN, complex*16, dimension( lda, * )A, integerLDA, complex*16, dimension( ldt, * )T, integerLDT, integerINFO)

**ZGEQRT3** recursively computes a QR factorization of a general real or complex matrix using the compact WY representation of Q.

**Purpose:**

```
ZGEQRT3 recursively computes a QR factorization of a complex M-by-N
matrix A, using the compact WY representation of Q.
Based on the algorithm of Elmroth and Gustavson,
IBM J. Res. Develop. Vol 44 No. 4 July 2000.
```

**Parameters:**

*M*

```
M is INTEGER
The number of rows of the matrix A. M >= N.
```

*N*

```
N is INTEGER
The number of columns of the matrix A. N >= 0.
```

*A*

```
A is COMPLEX*16 array, dimension (LDA,N)
On entry, the complex M-by-N matrix A. On exit, the elements on
and above the diagonal contain the N-by-N upper triangular matrix R;
the elements below the diagonal are the columns of V. See below for
further details.
```

*LDA*

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

*T*

```
T is COMPLEX*16 array, dimension (LDT,N)
The N-by-N upper triangular factor of the block reflector.
The elements on and above the diagonal contain the block
reflector T; the elements below the diagonal are not used.
See below for further details.
```

*LDT*

```
LDT is INTEGER
The leading dimension of the array T. LDT >= max(1,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

Univ. of Colorado Denver

NAG Ltd.

**Date:**

September 2012

**Further Details:**

```
The matrix V stores the elementary reflectors H(i) in the i-th column
below the diagonal. For example, if M=5 and N=3, the matrix V is
V = ( 1 )
( v1 1 )
( v1 v2 1 )
( v1 v2 v3 )
( v1 v2 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. The
block reflector H is then given by
H = I - V * T * V**H
where V**H is the conjugate transpose of V.
For details of the algorithm, see Elmroth and Gustavson (cited above).
```

Definition at line 133 of file zgeqrt3.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

zgeqrt3(3) is an alias of zgeqrt3.f(3).