ZHETD2 reduces a complex Hermitian matrix A to real symmetric


 tridiagonal form T by a unitary similarity transformation:


 Q**H * A * Q = T.

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*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.

LDA

          LDA is INTEGER


          The leading dimension of the array A.  LDA >= max(1,N).

D

          D is DOUBLE PRECISION array, dimension (N)


          The diagonal elements of the tridiagonal matrix T:


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

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'.

TAU

          TAU is COMPLEX*16 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.

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NAG Ltd.

September 2012

  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).