chetd2.f (3) Linux Manual Page

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

 N is INTEGER

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

A

 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

 D is REAL array, dimension (N)

 The diagonal elements of the tridiagonal matrix T:

 D(i) = A(i,i).

E

 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

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