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Polynomial chaos approximation

version (8.84 KB) by Felipe Uribe
Several 1D probability distributions are approximated using the polynomial chaos expansion method


Updated 12 Jun 2015

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The main file 'PC_examples_1D.m' contains basic examples, in which several probability distributions are approximated using the polynomial chaos (PC) expansion. The key components of this method lie in the calculation of the orthogonal polynomials and the computation of the PC coefficients:
i). Functions to compute N-dimensional Hermite, Charlier and Jacobi polynomial are provided; extension to other types of orthogonal polynomials is straightforward.
ii). The PC coefficients are estimated using the projection method, where the integral is solved using a Gauss-Hermite quadrature. This step was only programmed for the case of 1D Hermite polynomials. Therefore, further extension to other types of orthogonal polynomials is required. An implementation of the regression method for the estimation of the PC coefficients can deal with this problem (hopefully, it will be included in a future version).

Cite As

Felipe Uribe (2021). Polynomial chaos approximation (, MATLAB Central File Exchange. Retrieved .

Comments and Ratings (16)

Maryam Rezaie

Chao Fu

baiyang shi

Oussama GASSAB

thank you so much, it is very useful. I would like to ask you, do you have a file that generates Legendre polynomials? (legendre_PC.m)

haisong zhao

Tianmou Liu

Very helpful to the beginner of PCE. Same Error message on line 84. Replace sym2poly(PsiPol{k}) as double(sym2poly(PsiPol{k}) and executed normally. Thank you very much.

Putika Ashfar

Moslem Moradi

marc rocas

yijun xu


Tathagata Roy

Error in line 84. Undefined function or method 'sym2poly' for input arguments of type 'double'


george veropoulos

Hi good work thera an explanation fo filles tnank you

Allen Zhu

i 'm confused about the equation in line 84 of ‘PC_examples_1D.m', and cannot find the original equation in the corresponding reference you gave. Would you please name another reference that is more accurate and easy to understand?
Thank you!

Allen Zhu

very helpful to the beginner of PCE

MATLAB Release Compatibility
Created with R2014a
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