zhetd2.f File Reference

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Functions/Subroutines
subroutine	zhetd2 (UPLO, N, A, LDA, D, E, TAU, INFO)
	ZHETD2 reduces a Hermitian matrix to real symmetric tridiagonal form by an unitary similarity transformation (unblocked algorithm).

---

Function/Subroutine Documentation

subroutine zhetd2	(	character	UPLO,
		integer	N,
		complex*16, dimension( lda, * )	A,
		integer	LDA,
		double precision, dimension( * )	D,
		double precision, dimension( * )	E,
		complex*16, dimension( * )	TAU,
		integer	INFO
	)

ZHETD2 reduces a Hermitian matrix to real symmetric tridiagonal form by an unitary similarity transformation (unblocked algorithm).

Download ZHETD2 + dependencies [TGZ] [ZIP] [TXT]

Purpose:

 ZHETD2 reduces a complex Hermitian matrix A to real symmetric
 tridiagonal form T by a unitary similarity transformation:
 Q**H * A * Q = T.

Parameters:

[in]	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
[in]	N	N is INTEGER The order of the matrix A. N >= 0.
[in,out]	A	A is COMPLEX*16 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.
[in]	LDA	LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).
[out]	D	D is DOUBLE PRECISION array, dimension (N) The diagonal elements of the tridiagonal matrix T: D(i) = A(i,i).
[out]	E	E is DOUBLE PRECISION 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'.
[out]	TAU	TAU is COMPLEX*16 array, dimension (N-1) The scalar factors of the elementary reflectors (see Further Details).
[out]	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 zhetd2.f.

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