3 ms·

I was always amazed that R can do: > integrate(dnorm, -Inf, +Inf) 1 with absolute error < 9.4e-05 Can we do the same in this library?

Buttons840 2y ago
How many evaluations of the underlying function does it make? (Hoping someone will fire up their R interpreter and find out.) Or, probably, dnorm is a probability distribution which includes a likeliness function, and a cumulative likeliness function, etc. I bet it doesn't work on arbitrary functions.
- thrasibule 2y ago
  R integrate is just a wrapper around quadpack. It works with arbitrary functions, but arguably dnorm is pretty well behaved.
legobmw99 2y ago
It seems like it is lacking the functionality R's integrate has for handling infinite boundaries, but I suppose you could implement that yourself on the outside. For what it's worth, use integrate::adaptive_quadrature::simpson::adaptive_simpson_method; use statrs::distribution::{Continuous, Normal}; fn dnorm(x: f64) -> f64 { Normal::new(0.0, 1.0).unwrap().pdf(x) } fn main() { let result = adaptive_simpson_method(dnorm, -100.0, 100.0, 1e-2, 1e-8); println!("Result: {:?}", result); } prints Result: Ok(1.000000000053865) It does seem to be a usability hazard that the function being integrated is defined as a fn, rather than a Fn, as you can't pass closures that capture variables, requiring the weird dnorm definition
antononcube 2y ago
You will be completely blown away, then, from what Wolfram Language (aka Mathematica) can do. (When it comes to numerical integration.) https://reference.wolfram.com/language/tutorial/NIntegrateOverview.html https://reference.wolfram.com/language/tutorial/NIntegrateOv...
mtantaoui 2y ago
for ]-inf, inf[ integrals, you can use Gauss Hermite method, just keep in mind to multiply your function with exp(x^2). use integrate::{ gauss_quadrature::hermite::gauss_hermite_rule, }; use statrs::distribution::{Continuous, Normal}; fn dnorm(x: f64) -> f64 { Normal::new(0.0, 1.0).unwrap().pdf(x)* x.powi(2).exp() } fn main() { let n: usize = 170; let result = gauss_hermite_rule(dnorm, n); println!("Result: {:?}", result); } I got Result: 1.0000000183827922.

Buttons840 2y ago

How many evaluations of the underlying function does it make? (Hoping someone will fire up their R interpreter and find out.) Or, probably, dnorm is a probability distribution which includes a likeliness function, and a cumulative likeliness function, etc. I bet it doesn't work on arbitrary functions.

thrasibule 2y ago
R integrate is just a wrapper around quadpack. It works with arbitrary functions, but arguably dnorm is pretty well behaved.

legobmw99 2y ago

It seems like it is lacking the functionality R's integrate has for handling infinite boundaries, but I suppose you could implement that yourself on the outside. For what it's worth, use integrate::adaptive_quadrature::simpson::adaptive_simpson_method; use statrs::distribution::{Continuous, Normal}; fn dnorm(x: f64) -> f64 { Normal::new(0.0, 1.0).unwrap().pdf(x) } fn main() { let result = adaptive_simpson_method(dnorm, -100.0, 100.0, 1e-2, 1e-8); println!("Result: {:?}", result); } prints Result: Ok(1.000000000053865) It does seem to be a usability hazard that the function being integrated is defined as a fn, rather than a Fn, as you can't pass closures that capture variables, requiring the weird dnorm definition

antononcube 2y ago

You will be completely blown away, then, from what Wolfram Language (aka Mathematica) can do. (When it comes to numerical integration.) https://reference.wolfram.com/language/tutorial/NIntegrateOverview.html https://reference.wolfram.com/language/tutorial/NIntegrateOv...

mtantaoui 2y ago

for ]-inf, inf[ integrals, you can use Gauss Hermite method, just keep in mind to multiply your function with exp(x^2). use integrate::{ gauss_quadrature::hermite::gauss_hermite_rule, }; use statrs::distribution::{Continuous, Normal}; fn dnorm(x: f64) -> f64 { Normal::new(0.0, 1.0).unwrap().pdf(x)* x.powi(2).exp() } fn main() { let n: usize = 170; let result = gauss_hermite_rule(dnorm, n); println!("Result: {:?}", result); } I got Result: 1.0000000183827922.