dgeql2.f(3) LAPACK dgeql2.f(3)
NAME
dgeql2.f -
SYNOPSIS
Functions/Subroutines
subroutine dgeql2 (M, N, A, LDA, TAU, WORK, INFO)
DGEQL2 computes the QL factorization of a general rectangular matrix using an unblocked algorithm.
Function/Subroutine Documentation
subroutine dgeql2 (integerM, integerN, double precision, dimension( lda, * )A, integerLDA, double precision, dimension( * )TAU, double
precision, dimension( * )WORK, integerINFO)
DGEQL2 computes the QL factorization of a general rectangular matrix using an unblocked algorithm.
Purpose:
DGEQL2 computes a QL factorization of a real 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 DOUBLE PRECISION 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
orthogonal 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 DOUBLE PRECISION array, dimension (min(M,N))
The scalar factors of the elementary reflectors (see Further
Details).
WORK
WORK is DOUBLE PRECISION 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
Univ. of Colorado Denver
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**T
where tau is a real scalar, and v is a real 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 dgeql2.f.
Author
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Version 3.4.2 Tue Sep 25 2012 dgeql2.f(3)