chetd2-f(3)

chetd2.f –

Synopsis

Functions/Subroutines

subroutine chetd2 (UPLO, N, A, LDA, D, E, TAU, INFO)
CHETD2 reduces a Hermitian matrix to real symmetric tridiagonal form by an unitary similarity transformation (unblocked algorithm).

Function/Subroutine Documentation

subroutine chetd2 (characterUPLO, integerN, complex, dimension( lda, * )A, integerLDA, real, dimension( * )D, real, dimension( * )E, complex, dimension( * )TAU, integerINFO)

CHETD2 reduces a Hermitian matrix to real symmetric tridiagonal form by an unitary similarity transformation (unblocked algorithm).

Purpose:

 CHETD2 reduces a complex Hermitian matrix A to real symmetric
 tridiagonal form T by a unitary similarity transformation:
 Q**H * A * Q = T.

Parameters:

UPLO

 UPLO is CHARACTER*1
 Specifies whether the upper or lower triangular part of the
 Hermitian matrix A is stored:
 = 'U': Upper triangular
 = 'L': Lower triangular

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

 A is COMPLEX array, dimension (LDA,N)
 On entry, the Hermitian matrix A. If UPLO = 'U', the leading
 n-by-n upper triangular 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 n-by-n 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 corresponding 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

 LDA is INTEGER
 The leading dimension of the array A. LDA >= max(1,N).

 D is REAL array, dimension (N)
 The diagonal elements of the tridiagonal matrix T:
 D(i) = A(i,i).

 E is REAL array, dimension (N-1)
 The off-diagonal 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

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

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:

 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**H
 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
 A(1:i-1,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(n-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 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 off-diagonal elements of T, and vi
 denotes an element of the vector defining H(i).

Definition at line 176 of file chetd2.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.