# cgelqf(3) [centos man page]

```cgelqf.f(3)							      LAPACK							       cgelqf.f(3)

NAME
cgelqf.f -

SYNOPSIS
Functions/Subroutines
subroutine cgelqf (M, N, A, LDA, TAU, WORK, LWORK, INFO)
CGELQF

Function/Subroutine Documentation
subroutine cgelqf (integerM, integerN, complex, dimension( lda, * )A, integerLDA, complex, dimension( * )TAU, complex, dimension( * )WORK,
integerLWORK, integerINFO)
CGELQF

Purpose:

CGELQF computes an LQ factorization of a complex M-by-N matrix A:
A = L * 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 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

LDA is INTEGER
The leading dimension of the array A.  LDA >= max(1,M).

TAU

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

WORK

WORK is COMPLEX array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK

LWORK is 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

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:
November 2011

Further Details:

The matrix Q is represented as a product of elementary reflectors

Q = H(k)**H . . . H(2)**H H(1)**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(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).

Definition at line 136 of file cgelqf.f.

Author
Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2							  Tue Sep 25 2012						       cgelqf.f(3)```

## Check Out this Related Man Page

```zgelqf.f(3)							      LAPACK							       zgelqf.f(3)

NAME
zgelqf.f -

SYNOPSIS
Functions/Subroutines
subroutine zgelqf (M, N, A, LDA, TAU, WORK, LWORK, INFO)
ZGELQF

Function/Subroutine Documentation
subroutine zgelqf (integerM, integerN, complex*16, dimension( lda, * )A, integerLDA, complex*16, dimension( * )TAU, complex*16, dimension( *
)WORK, integerLWORK, integerINFO)
ZGELQF

Purpose:

ZGELQF computes an LQ factorization of a complex M-by-N matrix A:
A = L * 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, 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

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 (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK

LWORK is 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

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:
November 2011

Further Details:

The matrix Q is represented as a product of elementary reflectors

Q = H(k)**H . . . H(2)**H H(1)**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(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).

Definition at line 136 of file zgelqf.f.

Author
Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2							  Tue Sep 25 2012						       zgelqf.f(3)```
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