function [c, d, e] = dorr(n, theta)
%DORR  Dorr matrix - diagonally dominant, ill conditioned, tridiagonal.
%      [C, D, E] = DORR(N, THETA) returns the vectors defining a row diagonally
%      dominant, tridiagonal M-matrix that is ill conditioned for small
%      values of the parameter THETA >= 0.
%      If only one output parameter is supplied then
%      C = FULL(TRIDIAG(C,D,E)), i.e., the matrix iself is returned.
%      The columns of INV(C) vary greatly in norm.  THETA defaults to 0.01.
%      The amount of diagonal dominance is given by (ignoring rounding errors):
%            COMP(C)*ONES(N,1) = THETA*(N+1)^2 * [1 0 0 ... 0 1]'.

%      Reference:
%      F.W. Dorr, An example of ill-conditioning in the numerical
%      solution of singular perturbation problems, Math. Comp., 25 (1971),
%      pp. 271-283.

if nargin < 2, theta = 0.01; end

c = zeros(n,1); e = c; d = c;
% All length n for convenience.  Make c, e of length n-1 later.

h = 1/(n+1);
m = floor( (n+1)/2 );
term = theta/h^2;

i = (1:m)';
    c(i) = -term*ones(m,1);
    e(i) = c(i) - (0.5-i*h)/h;
    d(i) = -(c(i) + e(i));

i = (m+1:n)';
    e(i) = -term*ones(n-m,1);
    c(i) = e(i) + (0.5-i*h)/h;
    d(i) = -(c(i) + e(i));

c = c(2:n);
e = e(1:n-1);

if nargout <= 1
   c = tridiag(c, d, e);
end