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# LAPACK-3

## man page of LAPACK-3

### LAPACK-3: computes an LQ factorization of a complex M-by-N matrix A

```NAME
LAPACK-3 - computes an LQ factorization of a complex M-by-N matrix A

SYNOPSIS
SUBROUTINE ZGELQF( M, N, A, LDA, TAU, WORK, LWORK, INFO )

INTEGER        INFO, LDA, LWORK, M, N

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

PURPOSE
ZGELQF computes an LQ factorization of a complex M-by-N matrix A:
A = L * 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, the elements on and below the diagonal of the array
contain the m-by-min(m,n) lower trapezoidal matrix L (L is
lower triangular if m <= n); the elements above 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 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/output) COMPLEX*16 array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK   (input) INTEGER
The dimension of the array WORK.  LWORK >= max(1,M).
For optimum performance LWORK >= M*NB, where NB is the
optimal blocksize.
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.

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(k)' . . . H(2)' H(1)', 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; conjg(v(i+1:n)) is stored on exit in
A(i,i+1:n), and tau in TAU(i).

LAPACK routine (version 3.2)     March 2011                       LAPACK-3(3)
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