Problem 501. Let's do Markov Chains!

Created by Stephen

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Markov Chains are really useful in a lot of fields. This problem will ask a question about a simple system with 3 states: A,B and C. The probability that one state will go to another can be given in a matrix such as:
mc = [0.5 0.2  0;
      0.2  0  0.6;
      0.3 0.8 0.4];
So, the first element is the probability that something in state A will remain in state A (0.5 here). The zero as the 5th element means nothing in state B will remain in state B. Now, if you are given the current state of the system, say state=[1 0 0], you can get the next state.
In this problem, I will given an incomplete matrix (A zero in place of one value), and then an initial state and the next state like:
states=[1 0.5;
        0 0.2;
        0 0.3]
You will have to provide the correct markov matrix as the output.
Round the output to 2 digits after decimal.

Solve

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Last Solution submitted on Jul 01, 2023

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@bmtran (Bryant Tran) on 15 Mar 2012

test case 2 is underconstrained (either of the two zeros could be changed) and test case 3 doesn't account for increased precision.

Stephen on 15 Mar 2012

hmm, sorry man. This was just for fun so people might get interested in markov chains, so I didn't think too hard about the test cases :)

Alfonso Nieto-Castanon on 15 Mar 2012

perhaps it's been changed already, test 2 does not look underconstrained (one additional constrain of mc is that its columns should add up to 1)

Alfonso Nieto-Castanon on 16 Mar 2012

In fact tests 2 and 3 are 'overconstrained' (you do not need the 'states' information to solve these)

Rafael S.T. Vieira on 12 Oct 2020

Please, do not use isequal with floats, check them against some tolerance: abs(a-b) < tol. Currently rounding numbers to 2 decimal places seems to fix the issue if the test suite is not updated. Good problem.

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Problem 501. Let's do Markov Chains!

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Problem 501. Let's do Markov Chains!

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