indexCardinal
(Package: GPC) :
Get the order of canonical polynomial chaos expansion
For a d-dimensional polynomial chaos expansion up to order p, there are a total of M polynomials, determine from get(d,p). Each polynomial $phi_m(x)$ is expressed as the product of the polynomial from each random variables, i.e. $phi_m(x) = phi_m,1(x_1)phi_m,2(x_2)...phi_m,d(x_d)$, each with a different polynomial order. We can thus very succintly denote phi_m(x) with a n-tuple vector containing the polynomial order from each dimension and the entire canonical PCE expansion can be express as a (m x n) matrix.
● Data Source:
CranContrib
● Keywords:
● Alias: indexCardinal
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GPCE.quad
(Package: GPC) :
Solve polynomial chaos expansion with numerical quadrature
The GPCE.quad function implements a polynomial chaos expansion of a given model or an external model. The strategy for the expansion of the model into a polynomial chaos basis is the Gauss quadrature method where the Gauss quadrature points are used to estimate the integrales corresponding to the coefficients of the expansion. A statistical and a global sensitivity analysis of the model is then carried out.
● Data Source:
CranContrib
● Keywords:
● Alias: GPCE.quad
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Print results of adaptive sparse generalized polynomial chaos expansion.
● Data Source:
CranContrib
● Keywords:
● Alias: print,GPCE.sparse-method, print.GPCE.sparse
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Plot results of adaptive sparse generalized polynomial chaos expansion based on least angle regression
● Data Source:
CranContrib
● Keywords:
● Alias: plot,GPCE.lar-method, plot.GPCE.lar
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Print results of adaptive lar generalized polynomial chaos expansion based on least angle regression
● Data Source:
CranContrib
● Keywords:
● Alias: print,GPCE.lar-method, print.GPCE.lar
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getM
(Package: GPC) :
Get canonical polynomial chaos expansion size
The getM is a very simple function that determines the size of the canonical polynomial chaos expansion for d random variables up to and including degree p in the expansion. The size is determined from choose(d+p,d) or factorial(d+p)/factorial(d)/factorial(p).
● Data Source:
CranContrib
● Keywords:
● Alias: getM
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Print results of adaptive quad generalized polynomial chaos expansion.
● Data Source:
CranContrib
● Keywords:
● Alias: print,GPCE.quad-method, print.GPCE.quad
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expansion.
● Data Source:
CranContrib
● Keywords:
● Alias: polyNorm
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GPCE.lar
(Package: GPC) :
Adaptive sparse generalized polynomial chaos expansion based on least angle regression
The GPCE.lar function implements a polynomial chaos expansion of a given model or an external model. The strategy for the expansion of the model into a polynomial chaos basis is the adaptive sparse method based on the least angle regression. A statistical and a global sensitivity analysis of the model is then carried out.
● Data Source:
CranContrib
● Keywords:
● Alias: GPCE.lar
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getSobol
(Package: GPC) :
Determine Sobol indices from PCE solutions
Computes the Sobol sensitivity indices from the coefficient of the polynomial chaos expansion.
● Data Source:
CranContrib
● Keywords:
● Alias: getSobol
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providing 
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