# cgehd2.f - Man Page

SRC/cgehd2.f

## Synopsis

### Functions/Subroutines

subroutine **cgehd2** (n, ilo, ihi, a, lda, tau, work, info)**CGEHD2** reduces a general square matrix to upper Hessenberg form using an unblocked algorithm.

## Function/Subroutine Documentation

### subroutine cgehd2 (integer n, integer ilo, integer ihi, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) tau, complex, dimension( * ) work, integer info)

**CGEHD2** reduces a general square matrix to upper Hessenberg form using an unblocked algorithm.

**Purpose:**

CGEHD2 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 CGEBAL; otherwise they should be set to 1 and N respectively. See Further Details. 1 <= ILO <= IHI <= max(1,N).

*A*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).

*WORK*WORK is COMPLEX 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.

**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 **148** of file **cgehd2.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page cgehd2(3) is an alias of cgehd2.f(3).

Tue Nov 28 2023 12:08:41 Version 3.12.0 LAPACK