cgehd2 (3)  Linux Manuals
NAME
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
N is INTEGER The order of the matrix A. N >= 0.
ILOILO is INTEGER
IHIIHI is INTEGER It is assumed that A is already upper triangular in rows and columns 1:ILO1 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).
AA 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.
LDALDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).
TAUTAU is COMPLEX array, dimension (N1) The scalar factors of the elementary reflectors (see Further Details).
WORKWORK is COMPLEX array, dimension (N)
INFOINFO is INTEGER = 0: successful exit < 0: if INFO = i, the ith 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 (ihiilo) elementary reflectors Q = H(ilo) H(ilo+1) . . . H(ihi1). 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
Generated automatically by Doxygen for LAPACK from the source code.