dgehd2.f(3) LAPACK dgehd2.f(3)
NAME
dgehd2.f -
SYNOPSIS
Functions/Subroutines
subroutine dgehd2 (N, ILO, IHI, A, LDA, TAU, WORK, INFO)
DGEHD2 reduces a general square matrix to upper Hessenberg form using an unblocked algorithm.
Function/Subroutine Documentation
subroutine dgehd2 (integerN, integerILO, integerIHI, double precision, dimension( lda, * )A, integerLDA, double precision, dimension( * )TAU,
double precision, dimension( * )WORK, integerINFO)
DGEHD2 reduces a general square matrix to upper Hessenberg form using an unblocked algorithm.
Purpose:
DGEHD2 reduces a real general matrix A to upper Hessenberg form H by
an orthogonal similarity transformation: Q**T * A * Q = H .
Parameters:
N
N is INTEGER
The order of the matrix A. N >= 0.
ILO
ILO is INTEGER
IHI
IHI is INTEGER
It is assumed that A is already upper triangular in rows
and columns 1:ILO-1 and IHI+1:N. ILO and IHI are normally
set by a previous call to DGEBAL; otherwise they should be
set to 1 and N respectively. See Further Details.
1 <= ILO <= IHI <= max(1,N).
A
A is DOUBLE PRECISION array, dimension (LDA,N)
On entry, the n by n general matrix to be reduced.
On exit, the upper triangle and the first subdiagonal of A
are overwritten with the upper Hessenberg matrix H, and the
elements below the first subdiagonal, 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,N).
TAU
TAU is DOUBLE PRECISION array, dimension (N-1)
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 (ihi-ilo) elementary
reflectors
Q = H(ilo) H(ilo+1) . . . H(ihi-1).
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(1:i) = 0, v(i+1) = 1 and v(ihi+1:n) = 0; v(i+2:ihi) is stored on
exit in A(i+2:ihi,i), and tau in TAU(i).
The contents of A are illustrated by the following example, with
n = 7, ilo = 2 and ihi = 6:
on entry, on exit,
( a a a a a a a ) ( a a h h h h a )
( a a a a a a ) ( a h h h h a )
( a a a a a a ) ( h h h h h h )
( a a a a a a ) ( v2 h h h h h )
( a a a a a a ) ( v2 v3 h h h h )
( a a a a a a ) ( v2 v3 v4 h h h )
( a ) ( a )
where a denotes an element of the original matrix A, h denotes a
modified element of the upper Hessenberg matrix H, and vi denotes an
element of the vector defining H(i).
Definition at line 150 of file dgehd2.f.
Author
Generated automatically by Doxygen for LAPACK from the source code.
Version 3.4.2 Tue Sep 25 2012 dgehd2.f(3)