# zgehd2.f man page

zgehd2.f —

## Synopsis

### Functions/Subroutines

subroutinezgehd2(N, ILO, IHI, A, LDA, TAU, WORK, INFO)ZGEHD2reduces a general square matrix to upper Hessenberg form using an unblocked algorithm.

## Function/Subroutine Documentation

### subroutine zgehd2 (integerN, integerILO, integerIHI, complex*16, dimension( lda, * )A, integerLDA, complex*16, dimension( * )TAU, complex*16, dimension( * )WORK, integerINFO)

**ZGEHD2** reduces a general square matrix to upper Hessenberg form using an unblocked algorithm.

**Purpose:**

```
ZGEHD2 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.
```

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

*A*

```
A is COMPLEX*16 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*16 array, dimension (N-1)
The scalar factors of the elementary reflectors (see Further
Details).
```

*WORK*

`WORK is COMPLEX*16 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 zgehd2.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

zgehd2(3) is an alias of zgehd2.f(3).