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