Crate quadrature

The primary function of this library is integrate, witch uses the double exponential algorithm. It is a port of the Fast Numerical Integration from c++ to rust. The original code is by John D. Cook, and is licensed under the BSD.

Other Algorithms are provided in modules.

Reexports

pub use double_exponential::integrate;

Modules

clenshaw_curtis

The clenshaw_curtis module provides a integrate function with the same signature as quadrature::integrate. The implemented variant of clenshaw curtis quadrature is adaptive, however the weights change for each adaptation. This unfortunately means that the sum needs to be recalculated for each layer of adaptation. It also does not allocate on the heap, however it does use a [f64; 129] to store the function values. It has a hard coded maximum of approximately 257 function evaluations. This guarantees that the algorithm will return. The clenshaw curtis algorithm exactly integrates polynomials of order N. This implementation starts with an N of approximately 5 and increases up to an N of approximately 257. In general the error in the algorithm decreases exponentially in the number of function evaluations. In summery clenshaw curtis will in general use more stack space and run slower than the double exponential algorithm, unless clenshaw curtis can get the exact solution.

double_exponential

The double exponential algorithm is naturally adaptive, it stops calling the integrand when the error is reduced to below the desired threshold. It also does not allocate. No box, no vec, etc. It has a hard coded maximum of approximately 350 function evaluations. This guarantees that the algorithm will return. The error in the algorithm decreases exponentially in the number of function evaluations, specifically O(exp(-cN/log(N))). So if 350 function evaluations is not giving the desired accuracy than the programmer probably needs to give some guidance by splitting up the range at singularities or other preparation techniques.

Structs

Output