function b = r8pbu_mv ( m, n, mu, a, x )

%*****************************************************************************80
%
%% r8pbu_mv() multiplies an R8PBU matrix by an R8VEC.
%
%  Discussion:
%
%    The R8PBU storage format is for a symmetric positive definite band matrix.
%
%    To save storage, only the diagonal and upper triangle of A is stored,
%    in a compact diagonal format that preserves columns.
%
%    The diagonal is stored in row MU+1 of the array.
%    The first superdiagonal in row MU, columns 2 through N.
%    The second superdiagonal in row MU-1, columns 3 through N.
%    The MU-th superdiagonal in row 1, columns MU+1 through N.
%
%  Licensing:
%
%    This code is distributed under the MIT license. 
%
%  Modified:
%
%    15 October 1998
%
%  Author:
%
%    John Burkardt
%
%  Input:
%
%    integer N, the order of the matrix.
%    N must be positive.
%
%    integer MU, the number of superdiagonals in the matrix.
%    MU must be at least 0 and no more than N-1.
%
%    real A(MU+1,N), the R8PBU matrix.
%
%    real X(N), the vector to be multiplied by A.
%
%  Output:
%
%    real B(N), the result vector A * x.
%
  b = zeros(n,1);
%
%  Multiply X by the diagonal of the matrix.
%
  for i = 1 : n
    b(i,1) = a(mu+1,i) * x(i);
  end
%
%  Multiply X by the superdiagonals of the matrix.
%
  for i = mu : -1 : 1
    for j = mu + 2 - i : n
      ieqn = i + j - mu - 1;
      b(ieqn) = b(ieqn) + a(i,j) * x(j);
      b(j) = b(j) + a(i,j) * x(ieqn);
    end
  end

  return
end
