
CHETD2(l) ) CHETD2(l)
NAME
CHETD2  reduce a complex Hermitian matrix A to real symmetric tridiagonal form T by a
unitary similarity transformation
SYNOPSIS
SUBROUTINE CHETD2( UPLO, N, A, LDA, D, E, TAU, INFO )
CHARACTER UPLO
INTEGER INFO, LDA, N
REAL D( * ), E( * )
COMPLEX A( LDA, * ), TAU( * )
PURPOSE
CHETD2 reduces a complex Hermitian matrix A to real symmetric tridiagonal form T by a uni
tary similarity transformation: Q' * A * Q = T.
ARGUMENTS
UPLO (input) CHARACTER*1
Specifies whether the upper or lower triangular part of the Hermitian matrix A is
stored:
= 'U': Upper triangular
= 'L': Lower triangular
N (input) INTEGER
The order of the matrix A. N >= 0.
A (input/output) COMPLEX array, dimension (LDA,N)
On entry, the Hermitian matrix A. If UPLO = 'U', the leading nbyn upper trian
gular part of A contains the upper triangular part of the matrix A, and the
strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading
nbyn lower triangular part of A contains the lower triangular part of the matrix
A, and the strictly upper triangular part of A is not referenced. On exit, if
UPLO = 'U', the diagonal and first superdiagonal of A are overwritten by the cor
responding elements of the tridiagonal matrix T, and the elements above the first
superdiagonal, with the array TAU, represent the unitary matrix Q as a product of
elementary reflectors; if UPLO = 'L', the diagonal and first subdiagonal of A are
over written by the corresponding elements of the tridiagonal matrix T, 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
(input) INTEGER The leading dimension of the array A. LDA >= max(1,N).
D (output) REAL array, dimension (N)
The diagonal elements of the tridiagonal matrix T: D(i) = A(i,i).
E (output) REAL array, dimension (N1)
The offdiagonal elements of the tridiagonal matrix T: E(i) = A(i,i+1) if UPLO =
'U', E(i) = A(i+1,i) if UPLO = 'L'.
TAU (output) COMPLEX array, dimension (N1)
The scalar factors of the elementary reflectors (see Further Details).
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = i, the ith argument had an illegal value.
FURTHER DETAILS
If UPLO = 'U', the matrix Q is represented as a product of elementary reflectors
Q = H(n1) . . . H(2) H(1).
Each H(i) has the form
H(i) = I  tau * v * v'
where tau is a complex scalar, and v is a complex vector with v(i+1:n) = 0 and v(i) = 1;
v(1:i1) is stored on exit in
A(1:i1,i+1), and tau in TAU(i).
If UPLO = 'L', the matrix Q is represented as a product of elementary reflectors
Q = H(1) H(2) . . . H(n1).
Each H(i) has the form
H(i) = I  tau * v * v'
where tau is a complex scalar, and v is a complex vector with v(1:i) = 0 and v(i+1) = 1;
v(i+2:n) is stored on exit in A(i+2:n,i), and tau in TAU(i).
The contents of A on exit are illustrated by the following examples with n = 5:
if UPLO = 'U': if UPLO = 'L':
( d e v2 v3 v4 ) ( d )
( d e v3 v4 ) ( e d )
( d e v4 ) ( v1 e d )
( d e ) ( v1 v2 e d )
( d ) ( v1 v2 v3 e d )
where d and e denote diagonal and offdiagonal elements of T, and vi denotes an element of
the vector defining H(i).
LAPACK version 3.0 15 June 2000 CHETD2(l) 
