chetd2.f(3)

NAME
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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