Multiply matrix with previous result

Hey,

I'm looking to make function that can oversee changes in population. The population is set by having 3 different ages that have different survival rates and possibilities to have children etc. Basicly it goes like this: M*x=b, where M is set propabilities of change for next year, x is the current population number by three groups, and b is the answer for next years number of children, young adults and adults.

M = [0 0 2; 0.25 0 0; 0 0.52 0.73]

x_k = [24; 15; 28]

Now I need to make a loop that multiplys the first population number (x_k) with M, and after that M with previous result.

b = M*x_k

b_2 = M*b

b_3 = M*b_2

etc... until a set amout of years has passed, example 10 years for n = 10

x_k(1,1,1) = [24; 15; 28]

for n=1:10

x(n) = M*x_k(n); %filter

x_k(n+1)=x(n)

end

How could I fix this for loop to get to my desired results? I know my first problem is with x_k(1) since im trying to shove 3 numbers to one variable, but still have trouble typing it differently. Thank you!

Answer 1

[Steven Lord]

Use a matrix to store the population at each year, not a vector.

M = [0 0 2; 0.25 0 0; 0 0.52 0.73];

M = 3×3

0 0 2.0000 0.2500 0 0 0 0.5200 0.7300

x_k = [24; 15; 28];

x_k = 3×1

24 15 28

population = zeros(size(x_k, 1), 20); % each column holds the population for a year
population(:, 1) = x_k;
for year = 2:20
    population(:, year) = M*population(:, year-1);
end
populationAtYear20 = population(:, 20)

populationAtYear20 = 3×1

45.2917 11.3976 22.4973

[Valtteri Virtanen]

This works perfect, Thank you.