# Ubuntu Feisty 7.04 manual page repository

Ubuntu is a free computer operating system based on the Linux kernel. Many IT companies, like DeployIS is using it to provide an up-to-date, stable operating system.

Provided by: lapack3-doc_3.0.20000531a-6ubuntu3_all

` `

### NAME

```        ZGEQR2 - compute a QR factorization of a complex m by n matrix A
```

### SYNOPSIS

```        SUBROUTINE ZGEQR2( M, N, A, LDA, TAU, WORK, INFO )

INTEGER        INFO, LDA, M, N

COMPLEX*16     A( LDA, * ), TAU( * ), WORK( * )
```

### PURPOSE

```        ZGEQR2  computes a QR factorization of a complex m by n matrix A: A = Q
* R.
```

### ARGUMENTS

```        M       (input) INTEGER
The number of rows of the matrix A.  M >= 0.

N       (input) INTEGER
The number of columns of the matrix A.  N >= 0.

A       (input/output) COMPLEX*16 array, dimension (LDA,N)
On entry, the m by n matrix A.  On exit, the  elements  on  and
above the diagonal of the array contain the min(m,n) by n upper
trapezoidal matrix R (R is upper triangular if  m  >=  n);  the
elements  below the diagonal, with the array TAU, represent the
unitary matrix Q as a product  of  elementary  reflectors  (see
Further  Details).   LDA     (input) INTEGER The leading dimen‐
sion of the array A.  LDA >= max(1,M).

TAU     (output) COMPLEX*16 array, dimension (min(M,N))
The scalar factors of the elementary  reflectors  (see  Further
Details).

WORK    (workspace) COMPLEX*16 array, dimension (N)

INFO    (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
The matrix Q is represented as a product of elementary reflectors

H(2) . . . H(k), where k = min(m,n).

Each H(i) has the form

H(i) = I - tau * v * v’

where  tau is a complex scalar, and v is a complex vector with v(1:i-1)
= 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i), and tau  in
TAU(i).

```
Sections

What does Ubuntu mean?
Ubuntu is an African word meaning 'Humanity to others', or 'I am what I am because of who we all are'. The Ubuntu distribution brings the spirit of Ubuntu to the software world.