# zgerq2.f(3) [centos man page]

```zgerq2.f(3)							      LAPACK							       zgerq2.f(3)

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

Version 3.4.2							  Tue Sep 25 2012						       zgerq2.f(3)```

## Check Out this Related Man Page

```zgeql2.f(3)							      LAPACK							       zgeql2.f(3)

NAME
zgeql2.f -

SYNOPSIS
Functions/Subroutines
subroutine zgeql2 (M, N, A, LDA, TAU, WORK, INFO)
ZGEQL2 computes the QL factorization of a general rectangular matrix using an unblocked algorithm.

Function/Subroutine Documentation
subroutine zgeql2 (integerM, integerN, complex*16, dimension( lda, * )A, integerLDA, complex*16, dimension( * )TAU, complex*16, dimension( *
)WORK, integerINFO)
ZGEQL2 computes the QL factorization of a general rectangular matrix using an unblocked algorithm.

Purpose:

ZGEQL2 computes a QL factorization of a complex m by n matrix A:
A = Q * L.

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 lower triangle of the subarray
A(m-n+1:m,1:n) contains the n by n lower triangular matrix L;
if m <= n, the elements on and below the (n-m)-th
superdiagonal contain the m by n lower trapezoidal matrix L;
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 (N)

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(k) . . . H(2) H(1), 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(m-k+i+1:m) = 0 and v(m-k+i) = 1; v(1:m-k+i-1) is stored on exit in
A(1:m-k+i-1,n-k+i), and tau in TAU(i).

Definition at line 124 of file zgeql2.f.

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

Version 3.4.2							  Tue Sep 25 2012						       zgeql2.f(3)```
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