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polymultiindex

Returns the multi-indices of the degree d multivariate polynomials with p variables.

Calling Sequence

a=mmcool_polymultiindex(p,d)

Parameters

p :

a 1-by-1 matrix of doubles, integer value, greater or equal than 1, the number of variables

d :

a 1-by-1 matrix of doubles, integer value, greater or equal than 0, the total degree of each polynomial

a :

a nbpoly-by-p matrix of doubles, integer value, greater or equal than 0, the exponents

Description

Each row a(i,:) represents the i-th polynomial. The number of rows is the number of degree d polynomials with p variables. For each row i, a(i,j) is the exponent of the j-th variable, for j=1,2,...,p. The sum of exponents for each row is lower or equal to d: sum(a(i,:))<=d. The first row is the zero-degree polynomial with all exponents equal to zero. The rows 2 to p+1 are the first degree polynomials: all columns are zero, except one entry equal to 1.

Examples

p=4; // 4 variables
d=2; // Total degree = 2
a=mmcool_polymultiindex(p,d)

References
http://en.wikipedia.org/wiki/Monomial

O.P. Le Maitre and O.M. Knio. Spectral methods for uncertainty quantification. Springer, 2010. Appendix C Implementation of Product and Moment Formulas, C.2.1 Multi-Index Construction

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