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## chetd2()

subroutine chetd2 | ( | character | uplo,
|  | integer | n,
|  | complex, dimension( lda, * ) | a,
|  | integer | lda,
|  | real, dimension( * ) | d,
|  | real, dimension( * ) | e,
|  | complex, dimension( * ) | tau,
|  | integer | info )

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

Download CHETD2 + dependencies [TGZ] [ZIP] [TXT]

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

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

  [out]

  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'.
      !>

  [out]

  TAU

      !>          TAU is COMPLEX 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.

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).
      !>