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PolyChaos is a collection of numerical routines for orthogonal polynomials written in the Julia programming language.

Starting from some non-negative weight (aka an absolutely continuous nonnegative measure), PolyChaos allows

  • to compute the coefficients for the monic three-term recurrence relation,
  • to evaluate the orthogonal polynomials at arbitrary points,
  • to compute the quadrature rule,
  • to compute tensors of scalar products,
  • to do all of the above in a multivariate setting (aka product measures).

If the weight function is a probability density function, PolyChaos further provides routines to compute polynomial chaos expansions (PCEs) of random variables with this very density function. These routines allow

  • to compute affine PCE coefficients for arbitrary densities,
  • to compute moments,
  • to compute the tensors of scalar products.

PolyChaos contains several canonical orthogonal polynomials such as Jacobi or Hermite polynomials. For these, closed-form expressions and state-of-the art quadrature rules are used whenever possible. However, a cornerstone principle of PolyChaos is to provide all the functionality for user-specific, arbitrary weights.

Take a look at the documentation.

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