Provided by: liblapack-doc_3.3.1-1_all bug

NAME

       LAPACK-3  - reduces a complex Hermitian matrix A to real symmetric tridiagonal form T by a
       unitary similarity transformation

SYNOPSIS

       SUBROUTINE CHETRD( UPLO, N, A, LDA, D, E, TAU, WORK, LWORK, INFO )

           CHARACTER      UPLO

           INTEGER        INFO, LDA, LWORK, N

           REAL           D( * ), E( * )

           COMPLEX        A( LDA, * ), TAU( * ), WORK( * )

PURPOSE

       CHETRD reduces a complex Hermitian matrix A to real symmetric  tridiagonal  form  T  by  a
       unitary similarity transformation:
        Q**H * A * Q = T.

ARGUMENTS

        UPLO    (input) CHARACTER*1
                = 'U':  Upper triangle of A is stored;
                = 'L':  Lower triangle of A is stored.

        N       (input) INTEGER
                The order of the matrix A.  N >= 0.

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

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

        E       (output) 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     (output) COMPLEX array, dimension (N-1)
                The scalar factors of the elementary reflectors (see Further
                Details).

        WORK    (workspace/output) COMPLEX array, dimension (MAX(1,LWORK))
                On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

        LWORK   (input) 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    (output) INTEGER
                = 0:  successful exit
                < 0:  if INFO = -i, the i-th argument had an illegal value

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).

 LAPACK routine (version 3.3.1)             April 2011                            CHETRD(3lapack)