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zgerq2.f -

# SYNOPSIS

## Functions/Subroutines

subroutine zgerq2 (M, N, A, LDA, TAU, WORK, INFO)

ZGERQ2 computes the RQ factorization of a general rectangular matrix using an unblocked algorithm.

# Function/Subroutine Documentation

## subroutine zgerq2 (integerM, integerN, complex*16, dimension( lda, * )A, integerLDA, complex*16, dimension( * )TAU, complex*16, dimension( * )WORK, integerINFO)

ZGERQ2 computes the RQ factorization of a general rectangular matrix using an unblocked algorithm.
Purpose:
``` ZGERQ2 computes an RQ factorization of a complex m by n matrix A:
A = R * 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.
```
A
```          A is 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
```          LDA is INTEGER
The leading dimension of the array A.  LDA >= max(1,M).
```
TAU
```          TAU is COMPLEX*16 array, dimension (min(M,N))
The scalar factors of the elementary reflectors (see Further
Details).
```
WORK
```          WORK is COMPLEX*16 array, dimension (M)
```
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:
September 2012
Further Details:
```  The matrix Q is represented as a product of elementary reflectors

Q = H(1)**H H(2)**H . . . H(k)**H, where k = min(m,n).

Each H(i) has the form

H(i) = I - tau * v * v**H

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).
```
Definition at line 124 of file zgerq2.f.

# Author

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