cgehrd-f(3)

cgehrd.f –

Synopsis

Functions/Subroutines

subroutine cgehrd (N, ILO, IHI, A, LDA, TAU, WORK, LWORK, INFO)
CGEHRD

Function/Subroutine Documentation

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

CGEHRD

Purpose:

 CGEHRD reduces a complex general matrix A to upper Hessenberg form H by
 an 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 <= N, if N > 0; ILO=1 and IHI=0, if N=0.

 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). Elements 1:ILO-1 and IHI:N-1 of TAU are set to
 zero.

WORK

 WORK is COMPLEX array, dimension (LWORK)
 On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK

 LWORK is INTEGER
 The length of the array WORK. LWORK >= max(1,N).
 For optimum performance LWORK >= N*NB, where NB is the
 optimal blocksize.
 If LWORK = -1, then a workspace query is assumed; the routine
 only calculates the optimal size of the WORK array, returns
 this value as the first entry of the WORK array, and no error
 message related to LWORK is issued by XERBLA.

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:

November 2011

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).
 This file is a slight modification of LAPACK-3.0's DGEHRD
 subroutine incorporating improvements proposed by Quintana-Orti and
 Van de Geijn (2006). (See DLAHR2.)

Definition at line 169 of file cgehrd.f.

Author

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