# CentOS 7.0 - man page for sgehrd (centos section 3)

```sgehrd.f(3)							      LAPACK							       sgehrd.f(3)

NAME
sgehrd.f -

SYNOPSIS
Functions/Subroutines
subroutine sgehrd (N, ILO, IHI, A, LDA, TAU, WORK, LWORK, INFO)
SGEHRD

Function/Subroutine Documentation
subroutine sgehrd (integerN, integerILO, integerIHI, real, dimension( lda, * )A, integerLDA, real, dimension( * )TAU, real, dimension( * )WORK,
integerLWORK, integerINFO)
SGEHRD

Purpose:

SGEHRD 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 SGEBAL; 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

A is REAL 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 REAL 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 REAL 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

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**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).

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 sgehrd.f.

Author
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Version 3.4.2							  Tue Sep 25 2012						       sgehrd.f(3)```