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#
# order.m
#
# (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
#
global N;
N = 10;
global subdivisions;
subdivisions = 100;
global P;
P = 0.5
function retval = orderF(p, n, k)
retval = 0;
for i = (k:n)
retval = retval + nchoosek(n,i) * p^i * (1-p)^(n-i);
end
end
function retval = orderd(p, n, k)
retval = 0;
for i = (k:n)
s = i * p^(i-1) * (1-p)^(n-i);
s = s - p^i * (n-i) * (1-p)^(n-i-1);
retval = retval + nchoosek(n,i) * s;
end
end
function retval = orders(p, n, k)
retval = k * nchoosek(n, k) * p^(k-1) * (1-p)^(n-k);
end
function orderpath(fn, k, name)
fprintf(fn, "\\def\\order%s{\n\t(0,0)", name);
global N;
global subdivisions;
for i = (0:subdivisions)
p = i/subdivisions;
fprintf(fn, "\n\t-- ({%.4f*\\dx},{%.4f*\\dy})",
p, orderF(p, N, k));
end
fprintf(fn, "\n}\n");
end
function orderdpath(fn, k, name)
fprintf(fn, "\\def\\orderd%s{\n\t(0,0)", name);
global N;
global subdivisions;
for i = (1:subdivisions-1)
p = i/subdivisions;
fprintf(fn, "\n\t-- ({%.4f*\\dx},{%.4f*\\dy})",
p, orderd(p, N, k));
end
fprintf(fn, "\n\t-- ({1*\\dx},0)");
fprintf(fn, "\n}\n");
end
function orderspath(fn, k, name)
fprintf(fn, "\\def\\orders%s{\n\t(0,0)", name);
global N;
global subdivisions;
for i = (1:subdivisions-1)
p = i/subdivisions;
fprintf(fn, "\n\t-- ({%.4f*\\dx},{%.4f*\\dy})",
p, orders(p, N, k));
end
fprintf(fn, "\n\t-- ({1*\\dx},0)");
fprintf(fn, "\n}\n");
end
fn = fopen("orderpath.tex", "w");
orderpath(fn, 0, "zero");
orderdpath(fn, 0, "zero");
orderspath(fn, 0, "zero");
orderpath(fn, 1, "one");
orderdpath(fn, 1, "one");
orderspath(fn, 1, "one");
orderpath(fn, 2, "two");
orderdpath(fn, 2, "two");
orderspath(fn, 2, "two");
orderpath(fn, 3, "three");
orderdpath(fn, 3, "three");
orderspath(fn, 3, "three");
orderpath(fn, 4, "four");
orderdpath(fn, 4, "four");
orderspath(fn, 4, "four");
orderpath(fn, 5, "five");
orderdpath(fn, 5, "five");
orderspath(fn, 5, "five");
orderpath(fn, 6, "six");
orderdpath(fn, 6, "six");
orderspath(fn, 6, "six");
orderpath(fn, 7, "seven");
orderdpath(fn, 7, "seven");
orderspath(fn, 7, "seven");
orderpath(fn, 8, "eight");
orderdpath(fn, 8, "eight");
orderspath(fn, 8, "eight");
orderpath(fn, 9, "nine");
orderdpath(fn, 9, "nine");
orderspath(fn, 9, "nine");
orderpath(fn, 10, "ten");
orderdpath(fn, 10, "ten");
orderspath(fn, 10, "ten");
fclose(fn);
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