function b = r8ccs_mv ( m, n, nz_num, colptr, rowind, a, x )

%*****************************************************************************80
%
%% r8ccs_mv() multiplies an r8ccs matrix times a vector.
%
%  Discussion:
%
%    The r8ccs format is the double precision sparse compressed column
%    format.  Associated with this format, we have an M by N matrix
%    with NZ_NUM nonzero entries.  We construct the column pointer
%    vector COL of length N+1, such that entries of column J will be
%    stored in positions COL(J) through COL(J+1)-1.  This indexing
%    refers to both the ROW and A vectors, which store the row indices
%    and the values of the nonzero entries.  The entries of the
%    ROW vector corresponding to each column are assumed to be
%    ascending sorted.
%
%    The r8ccs format is equivalent to the MATLAB "sparse" format,
%    and the Harwell Boeing "real unsymmetric assembled" (RUA) format.
%
%  Licensing:
%
%    This code is distributed under the MIT license.
%
%  Modified:
%
%    01 September 2006
%
%  Author:
%
%    John Burkardt
%
%  Reference:
%
%    Iain Duff, Roger Grimes, John Lewis,
%    User's Guide for the Harwell-Boeing Sparse Matrix Collection,
%    October 1992
%
%  Input:
%
%    integer M, the number of rows of the matrix.
%
%    integer N, the number of columns of the matrix.
%
%    integer NZ_NUM, the number of nonzero elements in A.
%
%    integer COLPTR(N+1), points to the first element of each column.
%
%    integer ROWIND(NZ_NUM), contains the row indices of the elements.
%
%    real A(NZ_NUM), the matrix.
%
%    real X(N), the vector to be multiplied.
%
%  Output:
%
%    real B(M), the product A*X.
%
  b(1:m) = 0.0;

  for j = 1 : n
    for k = colptr(j) : colptr(j+1) - 1
      i = rowind(k);
      b(i) = b(i) + a(k) * x(j);
    end
  end

  return
end
