sum_polynomials¶

probnum.problems.zoo.quad.sum_polynomials(dim, a=None, b=None, var=1.0)[source]¶

Quadrature problem with an integrand taking the form of a sum of polynomials over \(\mathbb{R}^d\).

\[f(x) = \sum_{j=0}^p \prod_{i=1}^dim a_{ji} x_i^{b_ji}\]

The integrand is integrated against a multivariate normal \(\mathcal{N}(0,var * I_d)\). See [1].

Parameters:

dim (int) – Dimension d of the integration domain
a (ndarray | None) – 2d-array of size (p+1)xd giving coefficients of the polynomials.
b (ndarray | None) – 2d-array of size (p+1)xd giving orders of the polynomials. All entries should be natural numbers.
var (float | Real | floating) – diagonal elements of the covariance function.

Returns:

array of size (n,1) giving integrand evaluations at points in ‘x’.

Return type:

Raises:

ValueError – If the given parameters have the wrong shape or contain invalid values.

References