Plot piecewise function with couple of kink points

Thank you so much beforehand if anyone could help me with this. I have used Matlab in the past. However, I am a bit overwhelmed trying to plot this piecewise function.

I need to plot a piece wise function (q) where the parameters are i2, r, sigma1, sigma2, sigma3, v and beta and the variable is i1. The function is:

q= 1 {if i1=(1+r)(1-sigma3/(sigma3+v*sigma2))+sigma3/(sigma3+v*sigma2)*(i2-v*sigma2)}

q=1-(i1-1/beta)/sigma1 {if i1>=sigma1*((i2-1/beta)/v*sigma2 -1) -1/beta}

q=1-(i1-r-1)/sigma1*(1-(sigma3/sigma1)*(1+sigma3/sigma1+sigma3/(sigma2*v))**(-1))+(sigma3/sigma1)*(1+sigma3/sigma1+sigma3/(sigma2*v))**(-1)*((i2-r-1)/v*sigma2-1) {if if i1<sigma1*((i2-1/beta)/v*sigma2 -1) -1/beta}

q=1-(i1-1/beta)/(sigma1+sigma3) {if sigma2=0 or v=0}

q=0 {if sigma1=0}

The values for the parameters is:

r=(1-beta)/beta

beta=0.9

i2=4

sigma1=0.1

sigma2=0.2

sigma3=0.7

v=0.5

I would greatly appreciate if anyone could show me how to do it for an array of values for i1 that has a range from 0 to 10 separated by 0.1.

Answer 1

[Voss]

You can use logical indexing for this:

beta=0.9;
r=(1-beta)/beta;
i2=4;
sigma1=0.1;
sigma2=0.2;
sigma3=0.7;
v=0.5;

i1 = 0:0.1:10;
q = NaN(size(i1));

if sigma1 == 0
    
    q(:) = 0;
    
elseif sigma2 == 0 || v == 0
    
    q(:) = 1-(i1-1/beta)/(sigma1+sigma3);
    
else
    
    % idx is an array of logical type (i.e., each element is true or
    % false) which is the same size as i1.
    % each element of idx tells you whether or not the corresponding 
    % element of i1 satisfies the condition (i1 == (1+r)*...):
    idx = i1 == (1+r)*(1-sigma3/(sigma3+v*sigma2))+sigma3/(sigma3+v*sigma2)*(i2-v*sigma2);
    % now set the elements of q where idx is true (i.e., that condition is
    % true) to 1:
    q(idx) = 1;
    
    % idx is another logical array, this time based on a different
    % condition (i1 >= sigma1*...):
    idx = i1 >= sigma1*((i2-1/beta)/v*sigma2 -1)-1/beta;
    % set the elements of q where this second condition is true to
    % the values calculated from the expression below.
    % (note that i1(idx) is used - only using the elements of i1 where the 
    % condition is true)
    q(idx) = 1-(i1(idx)-1/beta)/sigma1;
    
    % final condition to check (i1 < sigma1*...)
    idx = i1 < sigma1*((i2-1/beta)/v*sigma2 -1) -1/beta;
    % set the corresponding elements of q, again based on i1(idx)
    q(idx) = 1-(i1(idx)-r-1)/sigma1*(1-(sigma3/sigma1)*(1+sigma3/sigma1+sigma3/(sigma2*v))^(-1))+(sigma3/sigma1)*(1+sigma3/sigma1+sigma3/(sigma2*v))^(-1)*((i2-r-1)/v*sigma2-1);
    
end

plot(i1,q);

References:

https://www.mathworks.com/matlabcentral/answers/129-how-does-logical-indexing-work

https://www.mathworks.com/company/newsletters/articles/matrix-indexing-in-matlab.html (scroll down to near the bottom for the logical indexing section)

[Jorge Martinez Compains]

Thanks a lot! That helped me a lot!

[Voss]

You're welcome!