NAME

       zhbtrd.f -

SYNOPSIS

   Functions/Subroutines
       subroutine zhbtrd (VECT, UPLO, N, KD, AB, LDAB, D, E, Q, LDQ, WORK, INFO)
           ZHBTRD

Function/Subroutine Documentation

   subroutine zhbtrd (characterVECT, characterUPLO, integerN, integerKD, complex*16, dimension(
       ldab, * )AB, integerLDAB, double precision, dimension( * )D, double precision, dimension(
       * )E, complex*16, dimension( ldq, * )Q, integerLDQ, complex*16, dimension( * )WORK,
       integerINFO)
       ZHBTRD

       Purpose:

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

       Parameters:
           VECT

                     VECT is CHARACTER*1
                     = 'N':  do not form Q;
                     = 'V':  form Q;
                     = 'U':  update a matrix X, by forming X*Q.

           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.

           KD

                     KD is INTEGER
                     The number of superdiagonals of the matrix A if UPLO = 'U',
                     or the number of subdiagonals if UPLO = 'L'.  KD >= 0.

           AB

                     AB is COMPLEX*16 array, dimension (LDAB,N)
                     On entry, the upper or lower triangle of the Hermitian band
                     matrix A, stored in the first KD+1 rows of the array.  The
                     j-th column of A is stored in the j-th column of the array AB
                     as follows:
                     if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
                     if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).
                     On exit, the diagonal elements of AB are overwritten by the
                     diagonal elements of the tridiagonal matrix T; if KD > 0, the
                     elements on the first superdiagonal (if UPLO = 'U') or the
                     first subdiagonal (if UPLO = 'L') are overwritten by the
                     off-diagonal elements of T; the rest of AB is overwritten by
                     values generated during the reduction.

           LDAB

                     LDAB is INTEGER
                     The leading dimension of the array AB.  LDAB >= KD+1.

           D

                     D is DOUBLE PRECISION array, dimension (N)
                     The diagonal elements of the tridiagonal matrix T.

           E

                     E is DOUBLE PRECISION array, dimension (N-1)
                     The off-diagonal elements of the tridiagonal matrix T:
                     E(i) = T(i,i+1) if UPLO = 'U'; E(i) = T(i+1,i) if UPLO = 'L'.

           Q

                     Q is COMPLEX*16 array, dimension (LDQ,N)
                     On entry, if VECT = 'U', then Q must contain an N-by-N
                     matrix X; if VECT = 'N' or 'V', then Q need not be set.

                     On exit:
                     if VECT = 'V', Q contains the N-by-N unitary matrix Q;
                     if VECT = 'U', Q contains the product X*Q;
                     if VECT = 'N', the array Q is not referenced.

           LDQ

                     LDQ is INTEGER
                     The leading dimension of the array Q.
                     LDQ >= 1, and LDQ >= N if VECT = 'V' or 'U'.

           WORK

                     WORK is COMPLEX*16 array, dimension (N)

           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:
           November 2011

       Further Details:

             Modified by Linda Kaufman, Bell Labs.

       Definition at line 163 of file zhbtrd.f.

Author

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