# sgehd2.f - Man Page

## Synopsis

### Functions/Subroutines

subroutine sgehd2 (N, ILO, IHI, A, LDA, TAU, WORK, INFO)
SGEHD2 reduces a general square matrix to upper Hessenberg form using an unblocked algorithm.

## Function/Subroutine Documentation

### subroutine sgehd2 (integer N, integer ILO, integer IHI, real, dimension( lda, * ) A, integer LDA, real, dimension( * ) TAU, real, dimension( * ) WORK, integer INFO)

SGEHD2 reduces a general square matrix to upper Hessenberg form using an unblocked algorithm.

Purpose:

``` SGEHD2 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 <= max(1,N).```

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).```

WORK

`          WORK is REAL 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:

December 2016

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 151 of file sgehd2.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page sgehd2(3) is an alias of sgehd2.f(3).

Tue Nov 14 2017 Version 3.8.0 LAPACK