How to transform multiple similar outputs into a single output array? - arrays

Question

I have two issues that I desperately need help with, so I'm posting here.
I know this may sound like a much-asked question at first, but I didn't find anything like it in my research.
I'm trying to obtain an entire row of results, using this code:
mu = [0 0];
sigma = [1 0.3; 0.3 1];
for r1 = 1:7;
r2 = 1;
xu = [r1+1, r2+1];
xl = [r1, r2];
p1 = mvncdf(xl,xu,mu,sigma)
end
What I am trying to say is that, for every value that r1 takes (between 1 and 7), r2 will assume the value 1, and I want to generate the values for those 7 combinations. When I run the scripts, I get excatly the values that I want, but in this form:
p1 =
0.0301
p1 =
0.0062
p1 =
4.5904e-04
p1 =
1.2186e-05
p1 =
1.1389e-07
p1 =
3.7054e-10
p1 =
4.1622e-13
After that, when I go to my workspace, I have a variable there named p1, but is only equal to the last value generated - in this case, 4.1622e-13. Is it possible to make this generate an array with all the 7 numbers instead?
My second question is related to this one. As you saw, I use r1 ranging from 1 to 7, and r2 takes the value of 1. Truth is, I want to assess all combinations of them, with r2 also ranging from 1 to 7, but I'm doing it manually, with 7 other similar pieces of code, each one for a value of r2. Is it possible to combine everything and code it in a way that it generates a matrix of values based on all the combinations? I understand that might be more difficult, and I am more concerned with the first question.

Answer 1

For you first question, you want to create a vector of p1 values, so just modify your code like this:
p1(r1) = mvncdf(xl,xu,mu,sigma)
which when r1=1, the first time you loop, will put the result into the first element of p1 and so on.
For the second part of your question, you can nest another for loop, as follows:
for r1 = 1:7;
for r2 = 1:7;
xu = [r1+1, r2+1];
xl = [r1, r2];
p1(r1,r2) = mvncdf(xl,xu,mu,sigma)
end
end
and now you will have a matrix p1 where, for example, the entry in the (4,6) position corresponds to r1=4 and r2=6.
It is possible to compress this,
r1=1:7;
r2=1:7;
[R1,R2]=meshgrid(r1,r2);
p1=arrayfun(#(r1,r2) mvncdf([r1 r2],[r1+1 r2+1],mu,sigma),R1,R2)
but there is no real need to do so.