How to interpret the meaning of the data in myPCE.PCE.Basis.Indices

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How to understand the meaning of the data in myPCE.PCE.Basis.Indices

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Dear @MinzeXu

The field myPCE.PCE.Basis.Indices specifies the multi-indices exactly like they are used for example in Eq. 1.5 in the manual.

Let’s assume the following indices for simplicity:

     0     0     0
     0     0     1
     0     1     0
     1     0     0
     0     0     2
     0     2     0
     2     0     0
     0     1     1
     1     0     1
     1     1     0

For this specific example:

  • The matrix has 10 rows which means the PCE model has 10 terms (i.e. the PCE output is the weighted sum of these 10 terms).
  • The matrix has 3 columns which means the problem has 3 input variables.
  • For simplicity, let us assume standard monomials instead of orthonormal polynomials. A row (i, j, k) then corresponds to the polynomial term x_1^i \cdot x_2^j \cdot x_3^k.

Hope this helps!

Best regards
Styfen