reward : array Reward matrices or vectors. This is different from the Jacobi method where all the components in. In the Gauss-Seidel method, the system is solved using forward substitution so that each component uses the most recent value obtained for the previous component. See the documentation for the MDP class for details. The Gauss-Seidel method offers a slight modification to the Jacobi method which can cause it to converge faster. Parameters-transitions : array Transition probability matrices. This code was originally written for Jacobi, and I provided the modification for making it into Gauss-Seidel. class ValueIterationGS (ValueIteration): ''' A discounted MDP solved using the value iteration Gauss-Seidel algorithm. If you want, there is another way to calculate Jacobi and Gauss-Seidel, and you can take a look at that post here: Jacobi iteration doesn't end. Once we pass this point, then we use the variables calculated from the current iteration from the first variable up to the point where we are calculating, then use the rest of the variables for calculating the solution. If we are working on calculating the first variable, then we don't have any new information yet, and so we simply just update the solution using all of the previous information from the previous iteration. If idx = 1 %// Case where we are solving for the first variable Therefore: function z=gaussseidel(A,B) %// Change the function name

This has to be done in the while loop, because that's where you're doing the iterations. For Gauss-Seidel, for each variable that you solve for, you must use the solutions of the previous variables calculated from the current iteration as part of the solution for the variable you are focusing on.Īs such, for your particular version of the code (though not optimal.), you simply need to add in a for loop where we solve for each variable one at a time, then keep feeding this information into the other variables.

For Jacobi, you are simply using the previous iteration's solution to formulate the current solution. , x_) as part of the solution for the current variable x_i. It is a minor modification.The difference between a Jacobi solver and a Gauss-Seidel solver is that when you're solving for the solution of a variable x_i at the current iteration, you need to use the information from the previous variables ( x_1, x_2. Gauss-Seidel with Successive OverRelaxation Solver For projected Gauss Seidel, you need to project (or clamp) the solution within lower and upper limits: public static double Solve (double matrix, double right,

You implemented Gauss Seidel without projection.

Mdp gauss seidel python