# zgehd2.f - Man Page

## Synopsis

### Functions/Subroutines

subroutine **zgehd2** (**N**, ILO, IHI, A, **LDA**, TAU, WORK, INFO)**ZGEHD2** reduces a general square matrix to upper Hessenberg form using an unblocked algorithm.

## Function/Subroutine Documentation

### subroutine zgehd2 (integer N, integer ILO, integer IHI, complex*16, dimension( lda, * ) A, integer LDA, complex*16, dimension( * ) TAU, complex*16, dimension( * ) WORK, integer INFO)

**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:**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**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 151 of file zgehd2.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page zgehd2(3) is an alias of zgehd2.f(3).

Tue Nov 14 2017 Version 3.8.0 LAPACK