function [ v ] = markovchain( A, init, steps )
%MARKOVCHAIN Summary of this function goes here
%   Detailed explanation goes here

    % Check that A is a matrix
    if ndims(A) ~= 2
        throw(MException('markovchain:A','A is not a matrix'));
    end
    
    % Check that A is a square matrix
    [rowsA colsA] = size(A);
    if rowsA ~= colsA
        throw(MException('markovchain:A','A is not a square matrix'));
    end
        
    % Check that A is a transition matrix (i.e. non-negative entries, rows
    %   sum to 1).
    if min(min(A)) < 0
        throw(MException('markovchain:A','A is not a matrix with non-negative entries'));
    end
    rowsumsA = sum(A,2);
    if min(rowsumsA) < 1 || max(rowsumsA) > 1
        throw(MException('markovchain:A','A is not a matrix with rows that sum to 1'));
    end
    
    % Check that init is a compatible vector
    [ rowsinit colsinit ] = size(init);
    if rowsinit ~= 1 || colsinit ~= rowsA
        throw(MException('markovchain:init','init is not the right size'));
    end
    % Check that steps is a positive integer
    if steps <= 0
        throw(MException('markovchain:steps','steps must be positive'));
    end        
    if steps ~= round(steps)
        throw(MException('markovchain:steps','steps must be an integer'));
    end
    
    v = init*(A^steps);
    
    
end