cgehd2-f(3)

cgehd2.f –

Synopsis

Functions/Subroutines

subroutine cgehd2 (N, ILO, IHI, A, LDA, TAU, WORK, INFO)
CGEHD2 reduces a general square matrix to upper Hessenberg form using an unblocked algorithm.

Function/Subroutine Documentation

subroutine cgehd2 (integerN, integerILO, integerIHI, complex, dimension( lda, * )A, integerLDA, complex, dimension( * )TAU, complex, dimension( * )WORK, integerINFO)

CGEHD2 reduces a general square matrix to upper Hessenberg form using an unblocked algorithm.

Purpose:

 CGEHD2 reduces a complex general matrix A to upper Hessenberg form H
 by a unitary similarity transformation: Q**H * A * Q = H .

Parameters:

 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 CGEBAL; otherwise they should be
 set to 1 and N respectively. See Further Details.
 1 <= ILO <= IHI <= max(1,N).

 A is COMPLEX 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 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,N).

TAU

 TAU is COMPLEX array, dimension (N-1)
 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

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**H
 where tau is a complex scalar, and v is a complex 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 cgehd2.f.

Author

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