|
Foxes Team
|
Plot bi-variate function f(x,
y) with Monte Carlo method
The
freeware Excel workbooks "Random Plot.xls" can be an usefull
tool for studing didactical problems.
We have
used this file for years when we wanted to get a "quick-and-simple"
result.
For example
find the Max and Min of the following linear function
During the
computing for plotting function, the algorithm find also an approximation for
the absolute max-min of the function inside the domain box
Comparing
with the exact solution (2/3, 2/3), we
get the precision of about 1 % - 1.5 %
|
|
Exact |
Approximate |
Error |
Error
% |
Points |
||
|
x |
y |
x |
y |
||||
|
min |
0.666667 |
0.666667 |
0.653989 |
0.659698 |
0.0145 |
1.5
% |
2077 |
|
max |
2 |
2 |
1.970444 |
1.994513 |
0.0301 |
1 % |
2077 |
Switching
to the "Plot2D" chart, we can see the xy-plane view.
Min and Max
points are also rapresented by two colored dot (yellow for Max and cyan for
Min).
The domain
box - xmin <= x <= xmax and
ymin <= y <= ymax is rapresented by a grey rectangle
download
Random Plot.xls
(zip 240 KB)
fixed ver. 10-2007, thanks to Giulio Venezian
Explanation guide to Random Plot. (Doc 530 KB)
Random_Plot_Examples (Doc 1.7 MB)