Approximation of e using random points
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I have plotted one random thousand points on an axis. I have also plotted a line y=1/x. Now I am trying to display the points below the line in blue and the points above the line in orange. I have tried using an if loop but have not been successful. Any ideas how I could do this? Thanks
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Rick Rosson
le 9 Sep 2011
Hi Austin,
I have not tested the following code, so it may not be 100 percent correct, but it should give you the basic idea. I am assuming that you have two variables x and y, each one is a 1000 x 1 array of numbers:
idx = (y < 1./x);
figure;
scatter(x(idx),y(idx),'markerfacecolor','blue');
hold on;
scatter(x(~idx),y(~idx),'markerfacecolor','red');
HTH.
Rick
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Rick Rosson
le 9 Sep 2011
Please try the following:
countBelow = sum(idx);
countTotal = size(x,1);
ratio = countBelow/countTotal;
HTH.
Rick
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Rick Rosson
le 9 Sep 2011
Yes, you can solve it with either a for loop or a while loop in conjunction with an if statement. So you were on a perfectly valid path. But in MATLAB, it is almost always possible (and usually desirable) to eliminate for loops and while loops, and replace them with what is called vectorized code (which is what the idx = ... line is doing). Some of the benefits of vectorization include:
- Faster execution time
- More readable code
- More compact code
- More expressive code
- A higher level of abstraction
Also, in almost all programming languages, you generally want to avoid using if statements within loops if at all possible.
HTH.
Best,
Rick
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Rick Rosson
le 9 Sep 2011
BTW, were you able to compute a good value for e using this method? How close to the correct value did you get?
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Rick Rosson
le 9 Sep 2011
Please post a new question on MATLAB Answers with a link to this one for background info.
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