zhptrd(3)

NAME

ZHPTRD - reduce a complex Hermitian matrix A stored in

packed form to real symmetric tridiagonal form T by a unitary

similarity transformation

SYNOPSIS

SUBROUTINE ZHPTRD( UPLO, N, AP, D, E, TAU, INFO )
    CHARACTER      UPLO
    INTEGER        INFO, N
    DOUBLE         PRECISION D( * ), E( * )
    COMPLEX*16     AP( * ), TAU( * )

PURPOSE

ZHPTRD reduces a complex Hermitian matrix A stored in

packed form to real symmetric tridiagonal form T by a unitary

similarity transformation: Q**H * A * Q = T.

ARGUMENTS

UPLO (input) CHARACTER*1

= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.

N (input) INTEGER

The order of the matrix A. N >= 0.

AP (input/output) COMPLEX*16 array, dimension

(N*(N+1)/2)

On entry, the upper or lower triangle of the Her

mitian matrix A, packed columnwise in a linear array. The j-th

column of A is stored in the array AP as follows: if UPLO = 'U',

AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i +

(j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n. On exit, if UPLO = 'U',

the diagonal and first superdiagonal of A are overwritten by the

corresponding elements of the tridiagonal matrix T, and the ele

ments above the first superdiagonal, with the array TAU, repre

sent 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. D (output) DOUBLE PRECI

SION array, dimension (N) The diagonal elements of the tridiago

nal matrix T: D(i) = A(i,i).

E (output) DOUBLE PRECISION array, dimension (N-1)

The off-diagonal elements of the tridiagonal ma

trix T: E(i) = A(i,i+1) if UPLO = 'U', E(i) = A(i+1,i) if UPLO =

'L'.

TAU (output) COMPLEX*16 array, dimension (N-1)

The scalar factors of the elementary reflectors

(see Further Details).

INFO (output) INTEGER

= 0: successful exit
< 0: if INFO = -i, the i-th argument had an ille

gal value

FURTHER DETAILS

If UPLO = 'U', the matrix Q is represented as a product of

elementary reflectors

Q = H(n-1) . . . 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:i-1) is stored on exit in AP,

overwriting A(1:i-1,i+1), and tau is stored in TAU(i).

If UPLO = 'L', the matrix Q is represented as a product of

elementary reflectors

Q = H(1) H(2) . . . H(n-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(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in AP,

overwriting A(i+2:n,i), and tau is stored in TAU(i).

LAPACK version 3.0 15 June 2000

ZHPTRD(3)