Integration for only positive values

2020 6 18
2 个回答
更新时间：2021 12 20
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Hi!
I would like to calculate the integral of an already estimated probability density function. This PDF was estimated with a SPLINE, which is "slightly" negative in certain areas. My SPLINE is saved as a "struct" and integrating it works just fine fnint(PDF). However, the resulting CDF is decreasing in those areas of negative densities, which I would like to avoid by simply replacing those areas of the PDF with 0.
My question: Is it possible to set those regions of the function equal to 0, or to integrate just over the positive values ot this PDF? I would like to avoid transforming the function into a vector of resulting densities, and instead use the (spline) function directly?
Thanks in advance!

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回答（2 个）

the cyclist
the cyclist 2020-6-19

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Can you just replace your PDF with max(0,PDF) and proceed?

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Sim Kron
Sim Kron 2020-6-19
No, unfortunately this doesn't work :/
It gives me the error message: "Error using max. Invalid data type. Second argument must be numeric or logical."
I guess this has something to do with the application of the max function on a spine? Because the function is saved as a combination of several polynomials, which are all in that struct.
the cyclist
the cyclist 2020-6-19
Sorry, I meant my comment to be more conceptual that an exact MATLAB syntax. If you upload the data, it should be possible to give more specific advice.
Walter Roberson
Walter Roberson 2020-6-19
NNPDF = @(x) max(0, PDF(x))
Unless your PDF is symbolic. If it is symbolic then
NNPDF = symfun(piecewise(PDF(x) < 0, 0, PDF(x)),x)
Sim Kron
Sim Kron 2020-6-19
I tried to search for commands that act like a "max-function for individual elements", but for a whole function (I hope this makes sense, idk how to explain it any better). But unfortunately I couldn't find anything.
Sry, I'm pretty new to Matlab. How should I upload the data? Do you mean just the code or also the data set?
the cyclist
the cyclist 2020-6-19
In the "Insert" section, there is an icon that looks like a paper-clip, that can be used to upload files. Uploading both code and data is usually helpful.
Sim Kron
Sim Kron 2020-6-19
Thank you so much for helping me cyclist!
Sim Kron
Sim Kron 2020-6-19
@Walter Robertson Thanks for your help!
Does this command apply a function on my function? Sry, I'm new here and I don't really know what this is doing...
For your @(x) max(0, PDF(x)) command I get the message
function_handle with value: @(x)max(0,PDF(x))
How do I continue from there? Do I need to define a vector of "x-values" and apply my NNPDF on those values?
Thanks a lot for your help!
the cyclist
the cyclist 2020-6-19
It wasn't clear to me which field of the structure you need to modify, but for example if it is coefs,then
PDF.coefs = max(PDF.coefs,0)
Sim Kron
Sim Kron 2020-6-19
Sry, I made a mistake: The whole file was too large to upload, so I just uploaded the data of an arbitrary PDF. By sheer coincidence, exatly this data set doesn't exhibit any negative densities... The data set I uploaded now should include negative densities.
Concerning your comment: This command just replaces negative coefficients with 0, right? But my intention would be to replace a potential negative output of each function of the spline with 0. In my case, the different parts of the spline are linear functions, so I would like to adjust the outcome f(x) of each part of the spline and not the coefficients itself.

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Pasindu Ranasinghe
Pasindu Ranasinghe 2021-12-20
Ran in:

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Ran in:
How to integrate over the positive part of the function
lower_limit=-5; %Lower Limit of the integration
upper_limit=5; %Upper limit of the integration
Point_number=1000; %NUmber of points to be in the function
x_range=linspace(lower_limit,upper_limit,Point_number);
% Enter Function
syms x
f(x)=x^2+3*x-5
f(x) = 
y=f(x_range); %Getting function values
y_plus=subplus(y); %Getting only the Positive part
fprintf("Integration of the Positive Part %f",trapz(y_plus))
Integration of the Positive Part 5930.246783
%more plots
figure
plot(x_range,y_plus,"g","LineWidth",2);
hold on
plot(x_range,y,"r","LineWidth",1);
hold off
legend({'Positive Part','Input Function'});
xline(0);
yline(0);
title("Function")

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