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jonathf / chaospy

Chaospy - Toolbox for performing uncertainty quantification.
https://chaospy.readthedocs.io/
MIT License
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How did we selected the point in the Monte Carlo, point collocation and Psuedo-spectral method ? #112

Closed nguyenhoaiThanhbk2811 closed 5 years ago

nguyenhoaiThanhbk2811 commented 5 years ago

Hi you, Now I have the distribution by Uniform. I want to select the point int the this Distribution. How do I select the point three methods. for instance the distribution is A (1,5) and B (0.2,0.6). Thank you

jonathf commented 5 years ago

Point collocation is a flexible method that can use the nodes from both Mone Carlo and pseudo-spectral projection in its own scheme. I usually go for Monte Carlo samples, but either way works.

For monte carlo samples, you do: samples = distribution.sample(size).

For pseudo-spectral you do: samples, weights = chaospy.generate_quadrature(order, distribution).

Hope this helps.

nguyenhoaiThanhbk2811 commented 5 years ago

Thanks you for help me. Please! could you recommend for me the books about non-instructive point collocation polynomial method? thank you.

jonathf commented 5 years ago

To understand NIPC, I recommend you look into two sources:

Primary book is: "Numerical Methods for Stochastic Computations: A Spectral Method Approach" by Dongbin Xiu Gives an overview over polynomial chaos theory in general.

To get into NIPC specifically, I propose you read the paper: "Comparison of Non-Intrusive Polynomial Chaos and Stochastic Collocation Methods for Uncertainty Quantification" by Michael Eldred and John Burkardt They make the Dakota tool and made a decent overview in their paper.