ZHETRD 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


          = 'U':  Upper triangle of A is stored;


          = 'L':  Lower triangle of A is stored.

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).

WORK

          WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))


          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK

          LWORK is INTEGER


          The dimension of the array WORK.  LWORK >= 1.


          For optimum performance LWORK >= N*NB, where NB is the


          optimal blocksize.


          If LWORK = -1, then a workspace query is assumed; the routine


          only calculates the optimal size of the WORK array, returns


          this value as the first entry of the WORK array, and no error


          message related to LWORK is issued by XERBLA.

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.

November 2011

  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).