For loops on a space

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Saeid Hajizadeh
Saeid Hajizadeh 2014-5-20
编辑： Saeid Hajizadeh 2014-5-20
Dear Guys,
I want to compute the borders of a region. The region is like below:
R <= f1(p1,p2,p3,p4,p5,p6,p7,p8)
R <= f2(p1,p2,p3,p4,p5,p6,p7,p8)
over all p1, p2, p3, p4, p5, p6, p7, and p8 where p1+p2+p3+p4+p5+p6+p7+p8 = 1 (probability space)
So I have seven randoms in p1, p2 , p3, p4, p5, p6, and p7 (or seven degrees of freedom).
My problem is that I can not find a way to cover the whole space. To be brief,
I have given my code for the same problem with three degrees of freedom, where
R <= f1(p1,p2,p3,p4)
R <= f2(p1,p2,p3,p4)
over all p1, p2, p3, and p4 where p1+p2+p3+p4 = 1:
********
clear all
Rf = 0;
p1(1) = 0.00001;
p2(1) = 0.00001;
for j1 = 1:1:101
if j1 > 1
p1(j1) = 0.00001 + 0.004998*(j1-1);
p2(j1) = 0.00001 + 0.004998*(j1-1);
end
p3(j1) = 1 - p1(j1) - p2(j1);
end
for i1 = 1:1:101
for i2 = 1:1:101
for i3 = 1:1:101
R1(i1,i2,i3) = f1 (p1(i1),p2(i2),p3(i3)) ;
R2(i1,i2,i3) = f2 (p1(i1),p2(i2),p3(i3)) ;
R(i1,i2,i3) = min(R1(i1,i2,i3),R2(i1,i2,i3));
Rf = max(R(i1,i2,i3),Rf);
if R(i1,i2,i3) > Rf
a1 = i1;
a2 = i2;
a3 = i3;
end
end
end
end
***************

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