%
% min [phi(x) = (1/2)*<Ax,x> + <b,x>]
%
- % using the conjugate_gradient_method (Algorithm 5.2 in Nocedal and
- % Wright).
+ % using the conjugate_gradient_method.
%
% INPUT:
%
%
% All vectors are assumed to be *column* vectors.
%
- zero_vector = zeros(length(x0), 1);
+ n = length(x0);
+ M = eye(n);
- k = 0;
- x = x0; % Eschew the 'k' suffix on 'x' for simplicity.
- rk = A*x - b; % The first residual must be computed the hard way.
- pk = -rk;
-
- for k = [ 0 : max_iterations ]
- if (norm(rk) < tolerance)
- % Success.
- return;
- end
-
- alpha_k = step_length_cgm(rk, A, pk);
- x_next = x + alpha_k*pk;
- r_next = rk + alpha_k*A*pk;
- beta_next = (r_next' * r_next)/(rk' * rk);
- p_next = -r_next + beta_next*pk;
-
- k = k + 1;
- x = x_next;
- rk = r_next;
- pk = p_next;
- end
+ % The standard CGM is equivalent to the preconditioned CGM is you
+ % use the identity matrix as your preconditioner.
+ [x, k] = preconditioned_conjugate_gradient_method(A,
+ M,
+ b,
+ x0,
+ tolerance,
+ max_iterations);
end