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//! Taylor mode forward automatic differentiation //! //! **Caution**: In this documentation, `{i}` means number `i` (ex: AD{2} means AD2) //! //! ## Important Features //! //! * Can automatic differentiate up to 10th order (`AD1` ~ `AD10`) //! * All `AD{i}` are in stack (Guarantee high performance) //! * You can see `AD{i}` via `.print()` //! * You can use n-th derivative value of `AD{i}` via `.d{i}` //! //! ## Implemented Traits for `AD{i}` //! //! * `#[derive(Debug, Copy, Clone, PartialEq, Default)]` //! * `std::fmt::Display` //! * `From<AD{j}>`, `From<&'a AD{j}>` //! * `IntoIterator<Item = f64>` //! * `FromIterator<f64>` //! * `Index`, `IndexMut` //! * `std::ops::{Neg, Add, Sub, Mul, Div}` //! * `peroxide::traits::num::{PowOps, ExpLogOps, TrigOps}` //! //! ## Iterator of `AD{i}` //! //! There are three iterators. //! //! * `ADIntoIter{i}` //! * `ADIter{i}<'a>` //! * `ADIterMut{i}<'a>` //! //! Each implements `DoubleEndedIterator`, `ExactSizeIterator` also. //! //! ## Methods //! //! * `new(d0: f64, ... , d{i}: f64) -> AD{i}` //! * `print(&self)` //! * `iter(&self) -> ADIter{i}` //! * `iter_mut(&self) -> ADIterMut{i}` //! * `len(&self) -> usize` //! //! ## Implemented Operations //! //! * `Add, Sub, Mul, Div` //! * `sin, cos, tan` //! * `sinh, cosh, tanh` //! * `sin_cos`, `sinh_cosh` //! * `exp, ln, log, log2, log10` //! * `powi, powf, sqrt` //! //! ## Not yet implemented //! //! * `asin`, `acos`, `atan` //! * `asinh`, `acosh`, `atanh` //! * `pow` //! //! ## Usage //! //! ### Construction //! //! ``` //! extern crate peroxide; //! use peroxide::fuga::*; //! //! fn main() { //! // Declare x where x = 2 //! let a = AD1::new(2f64, 1f64); //! // Declare x^2 where x = 2 //! let b = AD2::new(4f64, 4f64, 2f64); //! // Convert AD1 -> AD2 //! let c = AD2::from(a); //! // Zeros //! let d = AD2::default(); //! //! assert_eq!(c, AD2::new(2f64, 1f64, 0f64)); //! assert_eq!(d, AD2::new(0f64, 0f64, 0f64)); //! } //! ``` //! //! ### Operation //! //! For every binary operation, it returns higher order AD //! (ex: AD1 + AD2 = AD2) //! //! ``` //! extern crate peroxide; //! use peroxide::fuga::*; //! //! fn main() { //! let a = AD1::new(2f64, 1f64); // x at x = 2 //! let b = AD2::new(4f64, 4f64, 2f64); // x^2 at x = 2 //! let c = a + b; // x^2 + x at x = 2 //! let d = a * b; // x^3 at x = 2 //! let e = a / b; // 1/x at x = 2 //! assert_eq!(c, AD2::new(6f64, 5f64, 2f64)); //! assert_eq!(d, AD2::new(8f64, 12f64, 12f64)); //! assert_eq!(e, AD2::new(0.5, -0.25, 0.25)); //! } //! ``` //! //! ### Generic //! //! * All of `AD{i}` implements `AD` trait //! //! ``` //! extern crate peroxide; //! use peroxide::fuga::*; //! //! fn main() { //! let a = AD1::new(2f64, 1f64); //! let b = AD2::new(4f64, 4f64, 2f64); //! assert_eq!(f(a, b), AD1::new(6f64, 5f64)); //! } //! //! fn f<T: AD, S: AD>(x: T, y: S) -> T { //! T::from(x.to_ad2() + y.to_ad2()) //! } //! ``` use crate::statistics::ops::C; use crate::traits::{ num::{ExpLogOps, PowOps, TrigOps}, stable::StableFn, }; use peroxide_ad::{ ad_display, ad_impl, ad_impl_ad, ad_impl_add, ad_impl_div, ad_impl_double_ended_iter, ad_impl_exact_size_iter, ad_impl_explogops, ad_impl_from, ad_impl_from_iter, ad_impl_index, ad_impl_into_iter, ad_impl_iter, ad_impl_mul, ad_impl_neg, ad_impl_powops, ad_impl_sub, ad_impl_trigops, ad_iter_def, ad_struct_def, ad_impl_from_type, ad_impl_add_f64, ad_impl_sub_f64, ad_impl_mul_f64, ad_impl_div_f64, f64_impl_add_ad, f64_impl_sub_ad, f64_impl_mul_ad, f64_impl_div_ad, f64_impl_from_ad, ad_impl_stable_fn, def_ad }; use std::iter::FromIterator; use std::ops::{Add, Div, Index, IndexMut, Mul, Neg, Sub}; use std::marker::PhantomData; ad_struct_def!(); ad_display!(); ad_impl!(); ad_impl_from!(); ad_iter_def!(); ad_impl_into_iter!(); ad_impl_iter!(); ad_impl_from_iter!(); ad_impl_double_ended_iter!(); ad_impl_exact_size_iter!(); ad_impl_index!(); ad_impl_neg!(); ad_impl_add!(); ad_impl_sub!(); ad_impl_mul!(); ad_impl_div!(); ad_impl_explogops!(); ad_impl_powops!(); ad_impl_trigops!(); ad_impl_ad!(); def_ad!(); ad_impl_from_type!(f64); // ad_impl_from_type!(f32); // ad_impl_from_type!(i64); // ad_impl_from_type!(i32); ad_impl_add_f64!(); ad_impl_sub_f64!(); ad_impl_mul_f64!(); ad_impl_div_f64!(); f64_impl_add_ad!(); f64_impl_sub_ad!(); f64_impl_mul_ad!(); f64_impl_div_ad!(); f64_impl_from_ad!(); ad_impl_stable_fn!(); // pub trait AD: // std::fmt::Display // + Clone // + Copy // + PartialEq // + From<AD1> // + From<AD2> // + From<AD3> // + From<AD4> // + From<AD5> // + From<AD6> // + From<AD7> // + From<AD8> // + From<AD9> // + From<AD10> // + Into<AD1> // + Into<AD2> // + Into<AD3> // + Into<AD4> // + Into<AD5> // + Into<AD6> // + Into<AD7> // + Into<AD8> // + Into<AD9> // + Into<AD10> // + From<f64> // + Into<f64> // + Add<Output = Self> // + Sub<Output = Self> // + Mul<Output = Self> // + Div<Output = Self> // + Add<f64, Output = Self> // + Sub<f64, Output = Self> // + Mul<f64, Output = Self> // + Div<f64, Output = Self> // + PowOps // + ExpLogOps // + TrigOps // { // fn to_ad1(self) -> AD1 { // self.into() // } // // fn to_ad2(self) -> AD2 { // self.into() // } // // fn to_ad3(self) -> AD3 { // self.into() // } // // fn to_ad4(self) -> AD4 { // self.into() // } // // fn to_ad5(self) -> AD5 { // self.into() // } // // fn to_ad6(self) -> AD6 { // self.into() // } // // fn to_ad7(self) -> AD7 { // self.into() // } // // fn to_ad8(self) -> AD8 { // self.into() // } // // fn to_ad9(self) -> AD9 { // self.into() // } // // fn to_ad10(self) -> AD10 { // self.into() // } // } //impl AD for f64 {} /// Lift AD functions /// /// # Description /// To lift `AD` functions /// /// # Implementation /// /// * All `Fn(T) -> T where T:AD` functions can be lift to `Fn(f64) -> f64` /// * If `j > i`, then `Fn(AD{j}) -> AD{j}` can be lift to `Fn(AD{i}) -> AD{i}` /// /// # Usage /// ``` /// extern crate peroxide; /// use peroxide::fuga::*; /// /// fn main() { /// let ad0 = 2f64; /// let ad1 = AD1::new(2f64, 1f64); /// /// let lift1 = ADLift::<_, AD1>::new(f_ad); /// let lift2 = ADLift::<_, AD2>::new(f_ad2); /// /// let ans_ad0 = ad0.powi(2); /// let ans_ad1 = ad1.powi(2); /// /// // All AD function can be lift to f64 /// assert_eq!(ans_ad0, lift1.call_stable(ad0)); /// assert_eq!(ans_ad0, lift2.call_stable(ad0)); /// /// // AD2 is higher than AD1 (AD2 -> AD1 lifting is allowed) /// assert_eq!(ans_ad1, lift2.call_stable(ad1)); /// } /// /// fn f_ad<T: AD>(x: T) -> T { /// x.powi(2) /// } /// /// fn f_ad2(x: AD2) -> AD2 { /// x.powi(2) /// } /// ``` pub struct ADLift<F, T> { f: Box<F>, _marker: PhantomData<T>, } impl<F: Fn(T) -> T, T> ADLift<F, T> { pub fn new(f: F) -> Self { Self { f: Box::new(f), _marker: PhantomData } } pub fn f(&self, t: T) -> T { (self.f)(t) } } impl<F: Fn(T) -> T, T: AD> StableFn<f64> for ADLift<F, T> { type Output = f64; fn call_stable(&self, target: f64) -> Self::Output { self.f(T::from(target)).into() } } impl<F: Fn(T) -> T, T: AD> StableFn<AD1> for ADLift<F, T> { type Output = AD1; fn call_stable(&self, target: AD1) -> Self::Output { self.f(T::from(target)).into() } } // Nightly only //pub struct ADLift<F>(F); // //impl<F: FnOnce<(T)>, T> FnOnce<f64> for ADLift<F> { // type Output = f64; // //}