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# LAPACK-3

## man page of LAPACK-3

### LAPACK-3: computes an RQ factorization of a complex m by n matrix A

```NAME
LAPACK-3 - computes 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

FURTHER DETAILS
The matrix Q is represented as a product of elementary reflectors
Q = H(1)' 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(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).

LAPACK routine (version 3.2.2)   March 2011                       LAPACK-3(3)
```