# Ubuntu Feisty 7.04 manual page repository

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` `

### NAME

```        ZGERQ2 - compute an RQ factorization of a complex m by n matrix A
```

### SYNOPSIS

```        SUBROUTINE ZGERQ2( M, N, A, LDA, TAU, WORK, INFO )

INTEGER        INFO, LDA, M, N

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

### PURPOSE

```        ZGERQ2 computes an RQ factorization of a complex m by n matrix A: A = R
* Q.
```

### 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, if m <= n,  the  upper
triangle  of  the  subarray  A(1:m,n-m+1:n) contains the m by m
upper triangular matrix R; if m >= n, the elements on and above
the  (m-n)-th  subdiagonal contain the m by n upper trapezoidal
matrix R; the remaining elements, with the array TAU, represent
the unitary matrix Q as a product of elementary reflectors (see
Further Details).

LDA     (input) INTEGER
The leading dimension 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 (M)

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)ā . . . H(k)ā, where k = min(m,n).

Each H(i) has the form

H(i) = I - tau * v * vā

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

```
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