SRC/zhbtrd.f(3)

NAME
SRC/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 (character vect, character uplo, integer n, integer kd, complex*16, dimension( ldab, * ) ab, integer ldab, double precision, dimension( * ) d, double precision, dimension( * ) e, complex*16, dimension( ldq, * ) q, integer ldq, complex*16, dimension( * ) work, integer info)

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.

Further Details:

      Modified by Linda Kaufman, Bell Labs.

Definition at line 161 of file zhbtrd.f.

Author

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