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# cgeql2.f - Man Page

SRC/cgeql2.f

## Synopsis

### Functions/Subroutines

subroutine cgeql2 (m, n, a, lda, tau, work, info)
CGEQL2 computes the QL factorization of a general rectangular matrix using an unblocked algorithm.

## Function/Subroutine Documentation

### subroutine cgeql2 (integer m, integer n, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) tau, complex, dimension( * ) work, integer info)

CGEQL2 computes the QL factorization of a general rectangular matrix using an unblocked algorithm. Ā

Purpose:

CGEQL2 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 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 array, dimension (min(M,N))
The scalar factors of the elementary reflectors (see Further
Details).

WORK

WORK is COMPLEX 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.

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 122 of file cgeql2.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page cgeql2(3) is an alias of cgeql2.f(3).

Tue Nov 28 2023 12:08:41 Version 3.12.0 LAPACK