compute matrix power Lambda^(k-1) more efficiently

not sure how much my method drifts over the course of thousands of timesteps.

dmd.m

@@ -94,11 +94,14 @@ classdef dmd < handle
             xhat(:,1) = initial_condition;
             b0 = obj.Phi\initial_condition;
             
+			LambdaPowKMinus1 = eye(size(obj.Lambda));
             for k = 2:num_timesteps
-                xhat(:,k) = obj.Phi*obj.Lambda^(k-1)*b0;
-            end
-            
-            assert(norm(imag(xhat)) <= 1e-6);
+				LambdaPowKMinus1 = obj.Lambda*LambdaPowKMinus1;
+% 				check = obj.Lambda^(k-1);
+% 				checknorm = norm(LambdaPowKMinus1 - check)/norm(check);
+                xhat(:,k) = obj.Phi*LambdaPowKMinus1*b0;
+			end
+			           
 %             assert(norm(imag(xhat)) <= 1e-6);
 			if (norm(imag(xhat))/norm(xhat) >= 1e-6) % rel norm of imag components 
 				warning('rel norm of imaginary component of X2hat nontrivial: %e. Proceeding anyway.',norm(imag(xhat))/norm(xhat))