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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