From a85ff186e7dd0ad0d6b1b19be398eb47a57e9178 Mon Sep 17 00:00:00 2001 From: axect Date: Mon, 8 Apr 2024 09:42:42 +0900 Subject: [PATCH 1/9] DEP: Add `thiserror` as a dependency --- Cargo.toml | 1 + 1 file changed, 1 insertion(+) diff --git a/Cargo.toml b/Cargo.toml index 3c0f238d..57127874 100644 --- a/Cargo.toml +++ b/Cargo.toml @@ -28,6 +28,7 @@ puruspe = "0.2" matrixmultiply = { version = "0.3", features = ["threading"] } peroxide-ad = "0.3" peroxide-num = "0.1" +thiserror = "1.0" #num-complex = "0.3" netcdf = { version = "0.7", optional = true, default_features = false } pyo3 = { version = "0.21", optional = true, features = ["auto-initialize", "gil-refs"] } From a0efff572daf1611dedc61ea4d829fe1314369ed Mon Sep 17 00:00:00 2001 From: axect Date: Mon, 8 Apr 2024 09:58:41 +0900 Subject: [PATCH 2/9] CHGE: Replace all panics & asserts in spline with Result --- examples/ode_env.rs | 6 +- src/numerical/ode.rs | 11 +- src/numerical/spline.rs | 319 ++++++++++++++++++++++++---------------- src/prelude/simpler.rs | 22 +-- tests/numerical.rs | 14 +- 5 files changed, 224 insertions(+), 148 deletions(-) diff --git a/examples/ode_env.rs b/examples/ode_env.rs index 535e08d1..2e820480 100644 --- a/examples/ode_env.rs +++ b/examples/ode_env.rs @@ -2,7 +2,7 @@ extern crate peroxide; use peroxide::fuga::*; -fn main() { +fn main() -> Result<(), Box> { let x = seq(0, 10, 1); x.print(); let y = x @@ -11,7 +11,7 @@ fn main() { .map(|(i, &t)| t.powi(5 - i as i32)) .collect::>(); - let c = CubicSpline::from_nodes(&x, &y); + let c = CubicSpline::from_nodes(&x, &y)?; let init_state = State::::new(0f64, c!(1), c!(0)); @@ -26,6 +26,8 @@ fn main() { let result = ode_solver.integrate(); result.print(); + + Ok(()) } fn test_fn(st: &mut State, env: &CubicSpline) { diff --git a/src/numerical/ode.rs b/src/numerical/ode.rs index 2255e096..727bd911 100644 --- a/src/numerical/ode.rs +++ b/src/numerical/ode.rs @@ -106,12 +106,12 @@ //! extern crate peroxide; //! use peroxide::fuga::*; //! -//! fn main() { +//! fn main() -> Result<(), Box> { //! let x = seq(0, 10, 1); //! x.print(); //! let y = x.iter().enumerate().map(|(i, &t)| t.powi(5-i as i32)).collect::>(); //! -//! let c = CubicSpline::from_nodes(&x, &y); +//! let c = cubic_hermite_spline(&x, &y, Quadratic)?; //! //! let init_state = State::::new(0f64, c!(1), c!(0)); //! @@ -126,9 +126,11 @@ //! //! let result = ode_solver.integrate(); //! result.print(); +//! +//! Ok(()) //! } //! -//! fn test_fn(st: &mut State, env: &CubicSpline) { +//! fn test_fn(st: &mut State, env: &CubicHermiteSpline) { //! let x = st.param; //! let dy = &mut st.deriv; //! dy[0] = env.eval(x); @@ -381,6 +383,7 @@ use crate::traits::{ }; use crate::util::non_macro::{cat, concat, eye, zeros}; use std::collections::HashMap; +use crate::fuga::CubicHermiteSpline; //#[cfg(feature = "O3")] //use {blas_daxpy, blas_daxpy_return}; @@ -1175,3 +1178,5 @@ impl Environment for Matrix {} impl Environment for Vec {} impl Environment for Polynomial {} + +impl Environment for CubicHermiteSpline {} \ No newline at end of file diff --git a/src/numerical/spline.rs b/src/numerical/spline.rs index 74d0dbe4..82cf04f0 100644 --- a/src/numerical/spline.rs +++ b/src/numerical/spline.rs @@ -1,14 +1,14 @@ //! Spline interpolations -//! +//! //! # Available splines -//! +//! //! * Cubic spline //! * Cubic Hermite spline -//! +//! //! # `Spline` trait -//! +//! //! ## Methods -//! +//! //! Let `T: Into + Copy` //! * `fn eval(&self, x: T) -> f64` : Evaluate the spline at x //! * `fn eval_vec(&self, v: &[T]) -> Vec` : Evaluate spline values for an array v @@ -17,11 +17,11 @@ //! * `fn get_ranged_polynomials(&self) -> &Vec<(Range, Polynomial)>` : Get the polynomials //! * `fn eval_with_cond(&self, x: f64, cond: F) -> f64` : Evaluate the spline at x, with a condition //! * `fn eval_vec_with_cond(&self, v: &[f64], cond: F) -> Vec` : Evaluate spline values for an array v, with a condition -//! +//! //! # Low-level interface -//! +//! //! ## Members -//! +//! //! * `CubicSpline`: Structure for cubic spline //! * `fn from_nodes(node_x: &[f64], node_y: &[f64]) -> Self` : Create a cubic spline from nodes //! * `fn extend_with_nodes(&mut self, node_x: Vec, node_y: Vec)` : Extend the spline with nodes @@ -31,41 +31,41 @@ //! * `SlopeMethod`: Enum for slope estimation methods //! * `Akima`: Akima's method to estimate slopes ([Akima (1970)](https://dl.acm.org/doi/abs/10.1145/321607.321609)) //! * `Quadratic`: Using quadratic interpolation to estimate slopes -//! +//! //! ## Usage -//! +//! //! ```rust //! use peroxide::fuga::*; -//! -//! fn main() { +//! +//! fn main() -> Result<(), Box> { //! let x = seq(0, 10, 1); //! let y = x.fmap(|t| t.sin()); //! -//! let cs = CubicSpline::from_nodes(&x, &y); -//! let cs_akima = CubicHermiteSpline::from_nodes(&x, &y, SlopeMethod::Akima); -//! let cs_quad = CubicHermiteSpline::from_nodes(&x, &y, SlopeMethod::Quadratic); -//! +//! let cs = CubicSpline::from_nodes(&x, &y)?; +//! let cs_akima = CubicHermiteSpline::from_nodes(&x, &y, Akima)?; +//! let cs_quad = CubicHermiteSpline::from_nodes(&x, &y, Quadratic)?; +//! //! cs.polynomial_at(0f64).print(); //! cs_akima.polynomial_at(0f64).print(); //! cs_quad.polynomial_at(0f64).print(); //! // -0.1523x^3 + 0.9937x //! // 0.1259x^3 - 0.5127x^2 + 1.2283x //! // -0.0000x^3 - 0.3868x^2 + 1.2283x -//! +//! //! let new_x = seq(4, 6, 0.1); //! let new_y = new_x.fmap(|t| t.sin()); -//! +//! //! let y_cs = cs.eval_vec(&new_x); //! let y_akima = cs_akima.eval_vec(&new_x); //! let y_quad = cs_quad.eval_vec(&new_x); -//! +//! //! let mut df = DataFrame::new(vec![]); //! df.push("x", Series::new(new_x)); //! df.push("y", Series::new(new_y)); //! df.push("y_cs", Series::new(y_cs)); //! df.push("y_akima", Series::new(y_akima)); //! df.push("y_quad", Series::new(y_quad)); -//! +//! //! df.print(); //! // x y y_cs y_akima y_quad //! // r[0] 5 -0.9589 -0.9589 -0.9589 -0.9589 @@ -74,50 +74,52 @@ //! // r[3] 5.6 -0.6313 -0.6288 -0.5960 -0.6120 //! // r[4] 5.8 -0.4646 -0.4631 -0.4424 -0.4459 //! // r[5] 6 -0.2794 -0.2794 -0.2794 -0.2794 +//! +//! Ok(()) //! } //! ``` -//! +//! //! # High-level interface -//! +//! //! ## Functions -//! +//! //! * `fn cubic_spline(node_x: &[f64], node_y: &[f64]) -> CubicSpline` : Create a cubic spline from nodes //! * `fn cubic_hermite_spline(node_x: &[f64], node_y: &[f64], m: &[f64]) -> CubicHermiteSpline` : Create a cubic Hermite spline from nodes with slopes -//! +//! //! ## Usage -//! +//! //! ```rust //! use peroxide::fuga::*; -//! -//! fn main() { +//! +//! fn main() -> Result<(), Box> { //! let x = seq(0, 10, 1); //! let y = x.fmap(|t| t.sin()); //! -//! let cs = cubic_spline(&x, &y); -//! let cs_akima = cubic_hermite_spline(&x, &y, SlopeMethod::Akima); -//! let cs_quad = cubic_hermite_spline(&x, &y, SlopeMethod::Quadratic); -//! +//! let cs = cubic_spline(&x, &y)?; +//! let cs_akima = cubic_hermite_spline(&x, &y, Akima)?; +//! let cs_quad = cubic_hermite_spline(&x, &y, Quadratic)?; +//! //! cs.polynomial_at(0f64).print(); //! cs_akima.polynomial_at(0f64).print(); //! cs_quad.polynomial_at(0f64).print(); //! // -0.1523x^3 + 0.9937x //! // 0.1259x^3 - 0.5127x^2 + 1.2283x //! // -0.0000x^3 - 0.3868x^2 + 1.2283x -//! +//! //! let new_x = seq(4, 6, 0.1); //! let new_y = new_x.fmap(|t| t.sin()); -//! +//! //! let y_cs = cs.eval_vec(&new_x); //! let y_akima = cs_akima.eval_vec(&new_x); //! let y_quad = cs_quad.eval_vec(&new_x); -//! +//! //! let mut df = DataFrame::new(vec![]); //! df.push("x", Series::new(new_x)); //! df.push("y", Series::new(new_y)); //! df.push("y_cs", Series::new(y_cs)); //! df.push("y_akima", Series::new(y_akima)); //! df.push("y_quad", Series::new(y_quad)); -//! +//! //! df.print(); //! // x y y_cs y_akima y_quad //! // r[0] 5 -0.9589 -0.9589 -0.9589 -0.9589 @@ -126,49 +128,51 @@ //! // r[3] 5.6 -0.6313 -0.6288 -0.5960 -0.6120 //! // r[4] 5.8 -0.4646 -0.4631 -0.4424 -0.4459 //! // r[5] 6 -0.2794 -0.2794 -0.2794 -0.2794 +//! +//! Ok(()) //! } //! ``` -//! +//! //! # Calculus with splines -//! +//! //! ## Usage -//! +//! //! ```rust //! use peroxide::fuga::*; //! use std::f64::consts::PI; -//! -//! fn main() { +//! +//! fn main() -> Result<(), Box> { //! let x = seq(0, 10, 1); //! let y = x.fmap(|t| t.sin()); //! -//! let cs = cubic_spline(&x, &y); -//! let cs_akima = cubic_hermite_spline(&x, &y, SlopeMethod::Akima); -//! let cs_quad = cubic_hermite_spline(&x, &y, SlopeMethod::Quadratic); -//! +//! let cs = cubic_spline(&x, &y)?; +//! let cs_akima = cubic_hermite_spline(&x, &y, Akima)?; +//! let cs_quad = cubic_hermite_spline(&x, &y, Quadratic)?; +//! //! println!("============ Polynomial at x=0 ============"); -//! +//! //! cs.polynomial_at(0f64).print(); //! cs_akima.polynomial_at(0f64).print(); //! cs_quad.polynomial_at(0f64).print(); -//! +//! //! println!("============ Derivative at x=0 ============"); -//! +//! //! cs.derivative().polynomial_at(0f64).print(); //! cs_akima.derivative().polynomial_at(0f64).print(); //! cs_quad.derivative().polynomial_at(0f64).print(); -//! +//! //! println!("============ Integral at x=0 ============"); -//! +//! //! cs.integral().polynomial_at(0f64).print(); //! cs_akima.integral().polynomial_at(0f64).print(); //! cs_quad.integral().polynomial_at(0f64).print(); -//! +//! //! println!("============ Integrate from x=0 to x=pi ============"); -//! +//! //! cs.integrate((0f64, PI)).print(); //! cs_akima.integrate((0f64, PI)).print(); //! cs_quad.integrate((0f64, PI)).print(); -//! +//! //! // ============ Polynomial at x=0 ============ //! // -0.1523x^3 + 0.9937x //! // 0.1259x^3 - 0.5127x^2 + 1.2283x @@ -185,43 +189,47 @@ //! // 1.9961861265456702 //! // 2.0049920614062775 //! // 2.004327391790717 +//! +//! Ok(()) //! } //! ``` -//! +//! //! # References -//! +//! //! * Gary D. Knott, *Interpolating Splines*, Birkhäuser Boston, MA, (2000). +use self::SplineError::{NotEnoughNodes, NotEqualNodes, NotEqualSlopes, RedundantNodeX}; #[allow(unused_imports)] use crate::structure::matrix::*; #[allow(unused_imports)] use crate::structure::polynomial::*; #[allow(unused_imports)] use crate::structure::vector::*; -use peroxide_num::PowOps; #[allow(unused_imports)] use crate::util::non_macro::*; use crate::util::useful::zip_range; +use peroxide_num::PowOps; #[cfg(feature = "serde")] use serde::{Deserialize, Serialize}; use std::cmp::{max, min}; use std::convert::{From, Into}; use std::ops::{Index, Range}; +use thiserror::Error; /// Trait for spline interpolation -/// +/// /// # Available Splines -/// +/// /// - `CubicSpline` /// - `CubicHermiteSpline` pub trait Spline { - fn eval + Copy>(&self, x: T) -> f64 { + fn eval + Copy>(&self, x: T) -> f64 { let x = x.into(); self.polynomial_at(x).eval(x) } - fn eval_vec + Copy>(&self, v: &[T]) -> Vec { + fn eval_vec + Copy>(&self, v: &[T]) -> Vec { let mut result = vec![0f64; v.len()]; for (i, x) in v.iter().enumerate() { @@ -231,7 +239,7 @@ pub trait Spline { result } - fn polynomial_at + Copy>(&self, x: T) -> &Polynomial { + fn polynomial_at + Copy>(&self, x: T) -> &Polynomial { let x = x.into(); let poly = self.get_ranged_polynomials(); @@ -285,11 +293,11 @@ pub trait Spline { /// extern crate peroxide; /// use peroxide::fuga::*; /// -/// fn main() { +/// fn main() -> Result<(), Box> { /// let x = c!(0.9, 1.3, 1.9, 2.1); /// let y = c!(1.3, 1.5, 1.85, 2.1); /// -/// let s = cubic_spline(&x, &y); +/// let s = cubic_spline(&x, &y)?; /// /// let new_x = c!(1, 1.5, 2.0); /// @@ -305,13 +313,19 @@ pub trait Spline { /// for t in new_x.iter() { /// s.eval(*t).print(); /// } +/// +/// Ok(()) /// } /// ``` -pub fn cubic_spline(node_x: &[f64], node_y: &[f64]) -> CubicSpline { +pub fn cubic_spline(node_x: &[f64], node_y: &[f64]) -> Result { CubicSpline::from_nodes(node_x, node_y) } -pub fn cubic_hermite_spline(node_x: &[f64], node_y: &[f64], slope_method: SlopeMethod) -> CubicHermiteSpline { +pub fn cubic_hermite_spline( + node_x: &[f64], + node_y: &[f64], + slope_method: SlopeMethod, +) -> Result { CubicHermiteSpline::from_nodes(node_x, node_y, slope_method) } @@ -333,11 +347,11 @@ pub fn cubic_hermite_spline(node_x: &[f64], node_y: &[f64], slope_method: SlopeM /// extern crate peroxide; /// use peroxide::fuga::*; /// -/// fn main() { +/// fn main() -> Result<(), Box> { /// let x = c!(0.9, 1.3, 1.9, 2.1); /// let y = c!(1.3, 1.5, 1.85, 2.1); /// -/// let s = CubicSpline::from_nodes(&x, &y); +/// let s = cubic_spline(&x, &y)?; /// /// let new_x = c!(1, 1.5, 2.0); /// @@ -353,6 +367,8 @@ pub fn cubic_hermite_spline(node_x: &[f64], node_y: &[f64], slope_method: SlopeM /// for t in new_x.iter() { /// s.eval(*t).print(); /// } +/// +/// Ok(()) /// } /// ``` #[derive(Debug, Clone, Default)] @@ -367,6 +383,18 @@ impl Spline for CubicSpline { } } +#[derive(Debug, Copy, Clone, Error)] +pub enum SplineError { + #[error("node_x has less than 3 elements")] + NotEnoughNodes, + #[error("node_x and node_y have different lengths")] + NotEqualNodes, + #[error("nodes and slopes have different lengths")] + NotEqualSlopes, + #[error("there are redundant nodes in node_x")] + RedundantNodeX, +} + impl CubicSpline { /// # Examples /// ``` @@ -374,25 +402,27 @@ impl CubicSpline { /// extern crate peroxide; /// use peroxide::fuga::*; /// - /// fn main() { + /// fn main() -> Result<(), Box> { /// let x = c!(0.9, 1.3, 1.9, 2.1); /// let y = c!(1.3, 1.5, 1.85, 2.1); /// - /// let s = CubicSpline::from_nodes(&x, &y); + /// let s = CubicSpline::from_nodes(&x, &y)?; /// /// for i in 0 .. 4 { /// println!("{}", s.eval(i as f64 / 2.0)); /// } + /// + /// Ok(()) /// } /// ``` - pub fn from_nodes(node_x: &[f64], node_y: &[f64]) -> Self { - let polynomials = CubicSpline::cubic_spline(node_x, node_y); - CubicSpline { + pub fn from_nodes(node_x: &[f64], node_y: &[f64]) -> Result { + let polynomials = CubicSpline::cubic_spline(node_x, node_y)?; + Ok(CubicSpline { polynomials: zip_range(node_x, &polynomials), - } + }) } - fn cubic_spline(node_x: &[f64], node_y: &[f64]) -> Vec { + fn cubic_spline(node_x: &[f64], node_y: &[f64]) -> Result, SplineError> { //! Pre calculated variables //! node_x: n+1 //! node_y: n+1 @@ -402,7 +432,12 @@ impl CubicSpline { //! u : n //! z : n+1 let n = node_x.len() - 1; - assert_eq!(n, node_y.len() - 1); + if n < 2 { + return Err(NotEnoughNodes); + } + if n != node_y.len() - 1 { + return Err(NotEqualNodes); + } // Pre-calculations let mut h = vec![0f64; n]; @@ -459,17 +494,17 @@ impl CubicSpline { s.push(term1 + term2 + term3 + term4); } - return s; + Ok(s) } /// Extends the spline with the given nodes. /// /// # Description - /// + /// /// The method ensures that the transition between each polynomial is smooth and that the spline /// interpolation of the new nodes is calculated around `x = 0` in order to avoid that /// successive spline extensions with large x values become inaccurate. - pub fn extend_with_nodes(&mut self, node_x: Vec, node_y: Vec) { + pub fn extend_with_nodes(&mut self, node_x: Vec, node_y: Vec) -> Result<(), SplineError> { let mut ext_node_x = Vec::with_capacity(node_x.len() + 1); let mut ext_node_y = Vec::with_capacity(node_x.len() + 1); @@ -484,7 +519,7 @@ impl CubicSpline { let polynomials = zip_range( &ext_node_x, - &CubicSpline::cubic_spline(&ext_node_x, &ext_node_y), + &CubicSpline::cubic_spline(&ext_node_x, &ext_node_y)?, ); self.polynomials @@ -497,10 +532,12 @@ impl CubicSpline { p.translate_x(tx), ) })); + + Ok(()) } } -impl std::convert::Into> for CubicSpline { +impl Into> for CubicSpline { fn into(self) -> Vec { self.polynomials .into_iter() @@ -577,7 +614,7 @@ impl Calculus for CubicSpline { // ============================================================================= // Cubic Hermite Spline // ============================================================================= -#[derive(Debug, Clone)] +#[derive(Debug, Clone, Default)] #[cfg_attr(feature = "serde", derive(Serialize, Deserialize))] pub struct CubicHermiteSpline { polynomials: Vec<(Range, Polynomial)>, @@ -590,43 +627,69 @@ impl Spline for CubicHermiteSpline { } impl CubicHermiteSpline { - pub fn from_nodes_with_slopes(node_x: &[f64], node_y: &[f64], m: &[f64]) -> Self { - let mut r = vec![Range::default(); node_x.len()-1]; - let mut u = vec![Polynomial::default(); node_x.len()-1]; - - for i in 0 .. node_x.len()-1 { + pub fn from_nodes_with_slopes( + node_x: &[f64], + node_y: &[f64], + m: &[f64], + ) -> Result { + let n = node_x.len(); + if n < 3 { + return Err(NotEnoughNodes); + } + if n != node_y.len() { + return Err(NotEqualNodes); + } + if n != m.len() { + return Err(NotEqualSlopes); + } + + let mut r = vec![Range::default(); node_x.len() - 1]; + let mut u = vec![Polynomial::default(); node_x.len() - 1]; + + for i in 0..node_x.len() - 1 { let a_i = node_y[i]; let b_i = m[i]; - let dx = node_x[i+1] - node_x[i]; - let dy = node_y[i+1] - node_y[i]; - let c_i = (3f64 * dy/dx - 2f64*m[i] - m[i+1]) / dx; - let d_i = (m[i] + m[i+1] - 2f64 * dy/dx) / dx.powi(2); - + let dx = node_x[i + 1] - node_x[i]; + let dy = node_y[i + 1] - node_y[i]; + let c_i = (3f64 * dy / dx - 2f64 * m[i] - m[i + 1]) / dx; + let d_i = (m[i] + m[i + 1] - 2f64 * dy / dx) / dx.powi(2); + let p = Polynomial::new(vec![1f64, -node_x[i]]); - - r[i] = Range { start: node_x[i], end: node_x[i+1] }; + + r[i] = Range { + start: node_x[i], + end: node_x[i + 1], + }; u[i] = p.powi(3) * d_i + p.powi(2) * c_i + p.clone() * b_i; u[i].coef[3] += a_i; } - CubicHermiteSpline { + Ok(CubicHermiteSpline { polynomials: r.into_iter().zip(u).collect(), - } + }) } - pub fn from_nodes(node_x: &[f64], node_y: &[f64], slope_method: SlopeMethod) -> Self { + pub fn from_nodes( + node_x: &[f64], + node_y: &[f64], + slope_method: SlopeMethod, + ) -> Result { match slope_method { - SlopeMethod::Akima => { - CubicHermiteSpline::from_nodes_with_slopes(node_x, node_y, &akima_slopes(node_x, node_y)) - }, - SlopeMethod::Quadratic => { - CubicHermiteSpline::from_nodes_with_slopes(node_x, node_y, &quadratic_slopes(node_x, node_y)) - }, + SlopeMethod::Akima => CubicHermiteSpline::from_nodes_with_slopes( + node_x, + node_y, + &akima_slopes(node_x, node_y)?, + ), + SlopeMethod::Quadratic => CubicHermiteSpline::from_nodes_with_slopes( + node_x, + node_y, + &quadratic_slopes(node_x, node_y)?, + ), } } } -impl std::convert::Into> for CubicHermiteSpline { +impl Into> for CubicHermiteSpline { fn into(self) -> Vec { self.polynomials .into_iter() @@ -655,7 +718,6 @@ impl Index for CubicHermiteSpline { } } - impl Calculus for CubicHermiteSpline { fn derivative(&self) -> Self { let mut polynomials: Vec<(Range, Polynomial)> = self.clone().into(); @@ -710,21 +772,21 @@ pub enum SlopeMethod { Quadratic, } -fn akima_slopes(x: &[f64], y: &[f64]) -> Vec { +fn akima_slopes(x: &[f64], y: &[f64]) -> Result, SplineError> { if x.len() < 3 { - panic!("Cubic spline need at least 3 nodes"); + return Err(NotEnoughNodes); } let mut m = vec![0f64; x.len()]; - let mut s = vec![0f64; x.len()+3]; // -2, -1, 0, ..., x.len()-1, x.len() + let mut s = vec![0f64; x.len() + 3]; // -2, -1, 0, ..., x.len()-1, x.len() let l_i = lagrange_polynomial(x[0..3].to_vec(), y[0..3].to_vec()); - let l_f = lagrange_polynomial(x[x.len()-3..].to_vec(), y[y.len()-3..].to_vec()); + let l_f = lagrange_polynomial(x[x.len() - 3..].to_vec(), y[y.len() - 3..].to_vec()); let x_i = x[0] - (x[1] - x[0]) / 10f64; let x_ii = x_i - (x[1] - x[0]) / 10f64; - let x_f = x[x.len()-1] + (x[x.len()-1] - x[x.len()-2]) / 10f64; - let x_ff = x_f + (x[x.len()-1] - x[x.len()-2]) / 10f64; + let x_f = x[x.len() - 1] + (x[x.len() - 1] - x[x.len() - 2]) / 10f64; + let x_ff = x_f + (x[x.len() - 1] - x[x.len() - 2]) / 10f64; let y_i = l_i.eval(x_i); let y_ii = l_i.eval(x_ii); @@ -734,40 +796,43 @@ fn akima_slopes(x: &[f64], y: &[f64]) -> Vec { let new_x = concat(&concat(&vec![x_ii, x_i], &x.to_vec()), &vec![x_f, x_ff]); let new_y = concat(&concat(&vec![y_ii, y_i], &y.to_vec()), &vec![y_f, y_ff]); - for i in 0 .. new_x.len()-1 { - let dx = new_x[i+1] - new_x[i]; + for i in 0..new_x.len() - 1 { + let dx = new_x[i + 1] - new_x[i]; if dx == 0f64 { - panic!("x nodes should be different!"); + return Err(RedundantNodeX); } - s[i] = (new_y[i+1] - new_y[i]) / dx; + s[i] = (new_y[i + 1] - new_y[i]) / dx; } - - for i in 0 .. x.len() { - let j = i+2; - let ds_f = (s[j+1] - s[j]).abs(); - let ds_i = (s[j-1] - s[j-2]).abs(); + + for i in 0..x.len() { + let j = i + 2; + let ds_f = (s[j + 1] - s[j]).abs(); + let ds_i = (s[j - 1] - s[j - 2]).abs(); m[i] = if ds_f == 0f64 && ds_i == 0f64 { - (s[j-1] + s[j]) / 2f64 + (s[j - 1] + s[j]) / 2f64 } else { - (ds_f * s[j-1] + ds_i * s[j]) / (ds_f + ds_i) + (ds_f * s[j - 1] + ds_i * s[j]) / (ds_f + ds_i) }; } - m + Ok(m) } -fn quadratic_slopes(x: &[f64], y: &[f64]) -> Vec { +fn quadratic_slopes(x: &[f64], y: &[f64]) -> Result, SplineError> { + if x.len() < 3 { + return Err(NotEnoughNodes); + } let mut m = vec![0f64; x.len()]; let q_i = lagrange_polynomial(x[0..3].to_vec(), y[0..3].to_vec()); - let q_f = lagrange_polynomial(x[x.len()-3..].to_vec(), y[y.len()-3..].to_vec()); + let q_f = lagrange_polynomial(x[x.len() - 3..].to_vec(), y[y.len() - 3..].to_vec()); m[0] = q_i.derivative().eval(x[0]); - m[x.len()-1] = q_f.derivative().eval(x[x.len()-1]); + m[x.len() - 1] = q_f.derivative().eval(x[x.len() - 1]); - for i in 1 .. x.len()-1 { - let q = lagrange_polynomial(x[i-1..i+2].to_vec(), y[i-1..i+2].to_vec()); + for i in 1..x.len() - 1 { + let q = lagrange_polynomial(x[i - 1..i + 2].to_vec(), y[i - 1..i + 2].to_vec()); m[i] = q.derivative().eval(x[i]); } - m + Ok(m) } diff --git a/src/prelude/simpler.rs b/src/prelude/simpler.rs index 22025957..5436ea5c 100644 --- a/src/prelude/simpler.rs +++ b/src/prelude/simpler.rs @@ -6,7 +6,7 @@ use crate::numerical::{ integral, integral::Integral::G7K15R, spline, - spline::{CubicHermiteSpline, SlopeMethod::Quadratic}, + spline::{CubicHermiteSpline, SlopeMethod::Quadratic, SplineError}, }; use crate::structure::matrix::{self, Matrix}; use crate::structure::polynomial; @@ -87,18 +87,23 @@ impl SimplerLinearAlgebra for Matrix { matrix::LinearAlgebra::lu(self) } - fn waz(&self) -> Option { - matrix::LinearAlgebra::waz(self, matrix::Form::Identity) - } - fn waz_diag(&self) -> Option { matrix::LinearAlgebra::waz(self, matrix::Form::Diagonal) } + fn waz(&self) -> Option { + matrix::LinearAlgebra::waz(self, matrix::Form::Identity) + } + fn qr(&self) -> matrix::QR { matrix::LinearAlgebra::qr(self) } + #[cfg(feature="O3")] + fn cholesky(&self) -> Matrix { + matrix::LinearAlgebra::cholesky(self, matrix::UPLO::Lower) + } + fn rref(&self) -> Matrix { matrix::LinearAlgebra::rref(self) } @@ -127,11 +132,6 @@ impl SimplerLinearAlgebra for Matrix { matrix::LinearAlgebra::solve_mat(self, m, matrix::SolveKind::LU) } - #[cfg(feature="O3")] - fn cholesky(&self) -> Matrix { - matrix::LinearAlgebra::cholesky(self, matrix::UPLO::Lower) - } - fn is_symmetric(&self) -> bool { matrix::LinearAlgebra::is_symmetric(self) } @@ -148,7 +148,7 @@ pub fn chebyshev_polynomial(n: usize) -> polynomial::Polynomial { polynomial::chebyshev_polynomial(n, polynomial::SpecialKind::First) } -pub fn cubic_hermite_spline(node_x: &[f64], node_y: &[f64]) -> CubicHermiteSpline { +pub fn cubic_hermite_spline(node_x: &[f64], node_y: &[f64]) -> Result { spline::cubic_hermite_spline(node_x, node_y, Quadratic) } diff --git a/tests/numerical.rs b/tests/numerical.rs index f1ba63d7..fd6091c2 100644 --- a/tests/numerical.rs +++ b/tests/numerical.rs @@ -12,7 +12,7 @@ fn f(x: f64) -> f64 { } #[test] -fn test_cubic_spline_initialization() { +fn test_cubic_spline_initialization() -> Result<(), Box>{ let mut vx = Vec::new(); let mut vy = Vec::new(); for i in 0..11 { @@ -21,7 +21,7 @@ fn test_cubic_spline_initialization() { vy.push(f(x)); } - let spline = CubicSpline::from_nodes(&vx, &vy); + let spline = cubic_spline(&vx, &vy)?; for i in 0..11 { let x = i as f64; @@ -29,10 +29,12 @@ fn test_cubic_spline_initialization() { assert_eq!(rnd!(y), rnd!(f(x))); } + + Ok(()) } #[test] -fn test_cubic_spline_extension() { +fn test_cubic_spline_extension() -> Result<(), Box>{ let mut vx = Vec::new(); let mut vy = Vec::new(); for i in 0..11 { @@ -41,7 +43,7 @@ fn test_cubic_spline_extension() { vy.push(f(x)); } - let mut spline = CubicSpline::from_nodes(&vx, &vy); + let mut spline = cubic_spline(&vx, &vy)?; vx = Vec::new(); vy = Vec::new(); @@ -52,7 +54,7 @@ fn test_cubic_spline_extension() { vy.push(f(x)); } - spline.extend_with_nodes(vx, vy); + spline.extend_with_nodes(vx, vy)?; for i in 0..21 { let x = (i - 10) as f64; @@ -63,4 +65,6 @@ fn test_cubic_spline_extension() { format!("{} = {}", x, rnd!(f(x))) ); } + + Ok(()) } From f1f08f709d21718dd3a41fd6aefc6134361bbd78 Mon Sep 17 00:00:00 2001 From: axect Date: Mon, 8 Apr 2024 11:34:58 +0900 Subject: [PATCH 3/9] IMPL: Implement seedable distribution & sampling --- Cargo.toml | 2 +- src/statistics/dist.rs | 158 ++++++++++++++++++++++++++++++++--------- src/statistics/rand.rs | 118 +++++++++++++++++++++++++++++- 3 files changed, 242 insertions(+), 36 deletions(-) diff --git a/Cargo.toml b/Cargo.toml index 57127874..29c514e6 100644 --- a/Cargo.toml +++ b/Cargo.toml @@ -21,7 +21,7 @@ float-cmp = "0.9" [dependencies] csv = { version = "1", optional = true, default_features = false } -rand = "0.8" +rand = { version = "0.8", features = ["small_rng"] } rand_distr = "0.4" order-stat = "0.1" puruspe = "0.2" diff --git a/src/statistics/dist.rs b/src/statistics/dist.rs index fd533405..e37145eb 100644 --- a/src/statistics/dist.rs +++ b/src/statistics/dist.rs @@ -24,15 +24,17 @@ //! //! * `RNG` trait is composed of two fields //! * `sample`: Extract samples +//! * `sample_with_rng`: Extract samples with specific rng //! * `pdf` : Calculate pdf value at specific point -//! ```rust -//! extern crate rand; -//! use rand::distributions::uniform::SampleUniform; -//! +//! ```no_run +//! use rand::{Rng, distributions::uniform::SampleUniform}; //! pub trait RNG { //! /// Extract samples of distributions //! fn sample(&self, n: usize) -> Vec; //! +//! /// Extract samples of distributions with rng +//! fn sample_with_rng(&self, rng: &mut R, n: usize) -> Vec; +//! //! /// Probability Distribution Function //! /// //! /// # Type @@ -58,12 +60,14 @@ //! use peroxide::fuga::*; //! //! fn main() { -//! let b = Bernoulli(0.1); // Bern(x | 0.1) -//! b.sample(100).print(); // Generate 100 samples -//! b.pdf(0).print(); // 0.9 -//! b.mean().print(); // 0.1 -//! b.var().print(); // 0.09 (approximately) -//! b.sd().print(); // 0.3 (approximately) +//! let mut rng = smallrng_from_seed(42); +//! let b = Bernoulli(0.1); // Bern(x | 0.1) +//! b.sample(100).print(); // Generate 100 samples +//! b.sample_with_rng(&mut rng, 100).print(); // Generate 100 samples with specific rng +//! b.pdf(0).print(); // 0.9 +//! b.mean().print(); // 0.1 +//! b.var().print(); // 0.09 (approximately) +//! b.sd().print(); // 0.3 (approximately) //! } //! ``` //! @@ -119,15 +123,103 @@ //! a.sd().print(); //! } //! ``` -//! + //! ### Beta Distribution //! +//! * Definition +//! $$\text{Beta}(x | \alpha, \beta) = \frac{1}{\text{B}(\alpha, \beta)} x^{\alpha-1} (1-x)^{\beta-1}$$ +//! where $\text{B}(\alpha, \beta) = \frac{\Gamma(\alpha)\Gamma(\beta)}{\Gamma(\alpha+\beta)}$ is the Beta function. +//! * Representative value +//! * Mean: $\frac{\alpha}{\alpha+\beta}$ +//! * Var: $\frac{\alpha\beta}{(\alpha+\beta)^2(\alpha+\beta+1)}$ +//! * To generate beta random samples, Peroxide uses the `rand_distr::Beta` distribution from the `rand_distr` crate. +//! +//! ```rust +//! extern crate peroxide; +//! use peroxide::fuga::*; +//! +//! fn main() { +//! // Beta(alpha, beta) +//! let a = Beta(2.0, 5.0); +//! a.sample(100).print(); +//! a.pdf(0.3).print(); +//! a.mean().print(); +//! a.var().print(); +//! } +//! ``` +//! //! ### Gamma Distribution //! +//! * Definition +//! $$\text{Gamma}(x | \alpha, \beta) = \frac{\beta^\alpha}{\Gamma(\alpha)} x^{\alpha-1} e^{-\beta x}$$ +//! where $\Gamma(\alpha) = \int_0^\infty x^{\alpha-1} e^{-x} dx$ is the Gamma function. +//! * Representative value +//! * Mean: $\frac{\alpha}{\beta}$ +//! * Var: $\frac{\alpha}{\beta^2}$ +//! * To generate gamma random samples, Peroxide uses the `rand_distr::Gamma` distribution from the `rand_distr` crate. +//! +//! ```rust +//! extern crate peroxide; +//! use peroxide::fuga::*; +//! +//! fn main() { +//! // Gamma(shape, scale) +//! let a = Gamma(2.0, 1.0); +//! a.sample(100).print(); +//! a.pdf(1.5).print(); +//! a.mean().print(); +//! a.var().print(); +//! } +//! ``` +//! //! ### Binomial Distribution //! +//! * Definition +//! $$\text{Binom}(k | n, p) = \binom{n}{k} p^k (1-p)^{n-k}$$ +//! where $\binom{n}{k} = \frac{n!}{k!(n-k)!}$ is the binomial coefficient. +//! * Representative value +//! * Mean: $np$ +//! * Var: $np(1-p)$ +//! * To generate binomial random samples, Peroxide uses the `rand_distr::Binomial` distribution from the `rand_distr` crate. +//! +//! ```rust +//! extern crate peroxide; +//! use peroxide::fuga::*; +//! +//! fn main() { +//! // Binomial(n, p) +//! let a = Binomial(10, 0.3); +//! a.sample(100).print(); +//! a.pdf(3).print(); +//! a.mean().print(); +//! a.var().print(); +//! } +//! ``` +//! //! ### Student's t Distribution //! +//! * Definition +//! $$\text{StudentT}(x | \nu) = \frac{\Gamma(\frac{\nu+1}{2})}{\sqrt{\nu\pi}\,\Gamma(\frac{\nu}{2})} \left(1+\frac{x^2}{\nu} \right)^{-\frac{\nu+1}{2}}$$ +//! where $\nu$ is the degrees of freedom and $\Gamma$ is the Gamma function. +//! * Representative value +//! * Mean: 0 (for $\nu > 1$) +//! * Var: $\frac{\nu}{\nu-2}$ (for $\nu > 2$) +//! * To generate Student's t random samples, Peroxide uses the `rand_distr::StudentT` distribution from the `rand_distr` crate. +//! +//! ```rust +//! extern crate peroxide; +//! use peroxide::fuga::*; +//! +//! fn main() { +//! // StudentT(nu) +//! let a = StudentT(5.0); +//! a.sample(100).print(); +//! a.pdf(1.0).print(); +//! a.mean().print(); // Undefined for nu <= 1 +//! a.var().print(); // Undefined for nu <= 2 +//! } +//! ``` +//! //! ### Weighted Uniform Distribution //! //! * Definition @@ -393,7 +485,13 @@ impl> ParametricDist for Weight /// * `sample`: extract samples pub trait RNG { /// Extract samples of distributions - fn sample(&self, n: usize) -> Vec; + fn sample(&self, n: usize) -> Vec { + let mut rng = thread_rng(); + self.sample_with_rng(&mut rng, n) + } + + /// Extract samples of distributions with rng + fn sample_with_rng(&self, rng: &mut R, n: usize) -> Vec; /// Probability Distribution Function /// @@ -410,7 +508,7 @@ pub trait RNG { /// RNG for OPDist impl> RNG for OPDist { - fn sample(&self, n: usize) -> Vec { + fn sample_with_rng(&self, rng: &mut R, n: usize) -> Vec { match self { Bernoulli(prob) => { assert!( @@ -418,7 +516,6 @@ impl> RNG for OPDist { "Probability should be smaller than 1" ); - let mut rng = thread_rng(); let mut v = vec![0f64; n]; for i in 0..n { @@ -432,9 +529,8 @@ impl> RNG for OPDist { v } StudentT(nu) => { - let mut rng = thread_rng(); let stud = rand_distr::StudentT::::new((*nu).into()).unwrap(); - stud.sample_iter(&mut rng).take(n).collect() + stud.sample_iter(rng).take(n).collect() } } } @@ -491,10 +587,9 @@ impl> RNG for OPDist { /// RNG for TPDist impl> RNG for TPDist { - fn sample(&self, n: usize) -> Vec { + fn sample_with_rng(&self, rng: &mut R, n: usize) -> Vec { match self { Uniform(start, end) => { - let mut rng = thread_rng(); let mut v = vec![0f64; n]; for i in 0..n { @@ -504,19 +599,17 @@ impl> RNG for TPDist { } Binomial(num, mu) => { - let mut rng = thread_rng(); let binom = rand_distr::Binomial::new(*num as u64, (*mu).into()).unwrap(); binom - .sample_iter(&mut rng) + .sample_iter(rng) .take(n) .map(|t| t as f64) .collect() } Normal(m, s) => { - let mut rng = thread_rng(); let normal = rand_distr::Normal::::new((*m).into(), (*s).into()).unwrap(); - normal.sample_iter(&mut rng).take(n).collect() + normal.sample_iter(rng).take(n).collect() } // Normal(m, s) => { // let mut rng = thread_rng(); @@ -528,9 +621,8 @@ impl> RNG for TPDist { // v // } Beta(a, b) => { - let mut rng = thread_rng(); let beta = rand_distr::Beta::::new((*a).into(), (*b).into()).unwrap(); - beta.sample_iter(&mut rng).take(n).collect() + beta.sample_iter(rng).take(n).collect() } // Beta(a, b) => { // let mut rng1 = thread_rng(); @@ -558,10 +650,9 @@ impl> RNG for TPDist { // v // } Gamma(shape, scale) => { - let mut rng = thread_rng(); let gamma = rand_distr::Gamma::::new((*shape).into(), (*scale).into()).unwrap(); - gamma.sample_iter(&mut rng).take(n).collect() + gamma.sample_iter(rng).take(n).collect() } // Gamma(a, b) => { // let a_f64 = (*a).into(); // let b_f64 = (*b).into(); @@ -673,17 +764,16 @@ impl> RNG for TPDist { } impl RNG for WeightedUniform { - fn sample(&self, n: usize) -> Vec { - let mut rng = thread_rng(); + fn sample_with_rng(&self, rng: &mut R, n: usize) -> Vec { let w = WeightedAliasIndex::new(self.weights.clone()).unwrap(); - let ics: Vec = w.sample_iter(&mut rng).take(n).collect(); + let mut rng_clip = rng.clone(); + let ics: Vec = w.sample_iter(&mut rng_clip).take(n).collect(); + *rng = rng_clip; - let mut result = vec![0f64; n]; - for (i, idx) in ics.into_iter().enumerate() { + ics.into_iter().map(|idx| { let (l, r) = self.intervals[idx]; - result[i] = rng.gen_range(l ..=r); - } - result + rng.gen_range(l ..=r) + }).collect::>() } fn pdf>(&self, x: S) -> f64 { diff --git a/src/statistics/rand.rs b/src/statistics/rand.rs index 4ebae66e..2cb736ce 100644 --- a/src/statistics/rand.rs +++ b/src/statistics/rand.rs @@ -27,9 +27,40 @@ use std::u32; #[allow(unused_imports)] use crate::structure::matrix::*; - use super::dist::{RNG, WeightedUniform}; +/// Small random number generator from seed +/// +/// # Examples +/// ``` +/// use peroxide::fuga::*; +/// +/// fn main() { +/// let mut rng = smallrng_from_seed(42); +/// +/// let n = Normal(0f64, 1f64); +/// n.sample_with_rng(&mut rng, 10).print(); +/// } +pub fn smallrng_from_seed(seed: u64) -> SmallRng { + SmallRng::seed_from_u64(seed) +} + +/// Std random number generator from seed +/// +/// # Examples +/// ``` +/// use peroxide::fuga::*; +/// +/// fn main() { +/// let mut rng = stdrng_from_seed(42); +/// +/// let n = Normal(0f64, 1f64); +/// n.sample_with_rng(&mut rng, 10).print(); +/// } +pub fn stdrng_from_seed(seed: u64) -> StdRng { + StdRng::seed_from_u64(seed) +} + /// Simple uniform random number generator with ThreadRng /// /// # Examples @@ -410,6 +441,30 @@ pub fn ziggurat(rng: &mut ThreadRng, sigma: f64) -> f64 { // Rejection Sampling // ============================================================================= /// Piecewise Rejection Sampling +/// +/// # Arguments +/// * `f` - Function to sample (unnormalized function is allowed) +/// * `n` - Number of samples +/// * `(a, b)` - Range of sampling +/// * `m` - Number of pieces +/// * `eps` - Epsilon for max pooling +/// +/// # Examples +/// ``` +/// use peroxide::fuga::*; +/// +/// fn main() { +/// let f = |x: f64| { +/// if (0f64..=2f64).contains(&x) { +/// -(x - 1f64).powi(2) + 1f64 +/// } else { +/// 0f64 +/// } +/// }; +/// +/// let samples = prs(f, 1000, (-1f64, 3f64), 200, 1e-4); +/// samples.mean().print(); // near 1 +/// } pub fn prs(f: F, n: usize, (a, b): (f64, f64), m: usize, eps: f64) -> Vec where F: Fn(f64) -> f64 + Copy { let mut rng = thread_rng(); @@ -445,3 +500,64 @@ where F: Fn(f64) -> f64 + Copy { } panic!("Error: failed to generate {} samples", n); } + +/// Piecewise Rejection Sampling with specific Rng +/// +/// # Arguments +/// * `f` - Function to sample (unnormalized function is allowed) +/// * `n` - Number of samples +/// * `(a, b)` - Range of sampling +/// * `m` - Number of pieces +/// * `eps` - Epsilon for max pooling +/// * `rng` - Random number generator +/// +/// # Examples +/// ``` +/// use peroxide::fuga::*; +/// +/// fn main() { +/// let mut rng = smallrng_from_seed(42); +/// let f = |x: f64| { +/// if (0f64..=2f64).contains(&x) { +/// -(x - 1f64).powi(2) + 1f64 +/// } else { +/// 0f64 +/// } +/// }; +/// +/// let samples = prs_with_rng(f, 1000, (-1f64, 3f64), 200, 1e-4, &mut rng); +/// assert!((samples.mean() - 1f64).abs() < 1e-1); +/// } +pub fn prs_with_rng(f: F, n: usize, (a, b): (f64, f64), m: usize, eps: f64, rng: &mut R) -> Vec + where F: Fn(f64) -> f64 + Copy { + let mut result = vec![0f64; n]; + + let w = WeightedUniform::from_max_pool_1d(f, (a, b), m, eps); + if w.weights().iter().any(|w| w <= &0f64) { + println!("Warning: some weights are zero"); + } + + let mut initial_x = w.sample_with_rng(rng, n); + let mut left_num = n; + + while left_num > 0 { + for &x in initial_x.iter() { + let weight = w.weight_at(x); + if weight <= 0f64 { + continue; + } else { + let y = rng.gen_range(0f64 ..=weight); + + if y <= f(x) { + result[n - left_num] = x; + left_num -= 1; + if left_num == 0 { + return result; + } + } + } + } + initial_x = w.sample_with_rng(rng, left_num); + } + panic!("Error: failed to generate {} samples", n); +} From b804e7aecb3e55fb93e60039759daef11766cb84 Mon Sep 17 00:00:00 2001 From: axect Date: Mon, 8 Apr 2024 11:59:21 +0900 Subject: [PATCH 4/9] CHGE: Replace all panics & asserts in weighted uniform with Result --- src/statistics/dist.rs | 67 ++++++++++++++++++++++++++------------- src/statistics/rand.rs | 32 +++++++++---------- tests/weighted_uniform.rs | 15 +++++---- 3 files changed, 68 insertions(+), 46 deletions(-) diff --git a/src/statistics/dist.rs b/src/statistics/dist.rs index e37145eb..7516a855 100644 --- a/src/statistics/dist.rs +++ b/src/statistics/dist.rs @@ -250,6 +250,8 @@ use crate::util::non_macro::{linspace, seq}; use crate::util::useful::{auto_zip, find_interval}; use std::convert::Into; use std::f64::consts::E; +use thiserror::Error; +use self::WeightedUniformError::*; /// One parameter distribution /// @@ -281,6 +283,18 @@ pub struct WeightedUniform> { intervals: Vec<(T, T)> } +#[derive(Debug, Clone, Copy, Error)] +pub enum WeightedUniformError { + #[error("all weights are zero")] + AllZeroWeightError, + #[error("weights and intervals have different length")] + LengthMismatchError, + #[error("no non-zero interval found")] + NoNonZeroIntervalError, + #[error("weights are empty")] + EmptyWeightError, +} + impl WeightedUniform { /// Create a new weighted uniform distribution /// @@ -289,17 +303,28 @@ impl WeightedUniform { /// extern crate peroxide; /// use peroxide::fuga::*; /// - /// fn main() { + /// fn main() -> Result<(), Box> { /// let weights = vec![1f64, 3f64, 0f64, 2f64]; /// let intervals = vec![0f64, 1f64, 2f64, 4f64, 5f64]; - /// let w = WeightedUniform::new(weights, intervals); + /// let w = WeightedUniform::new(weights, intervals)?; /// assert_eq!(w.weights(), &vec![1f64, 3f64, 2f64]); /// assert_eq!(w.intervals(), &vec![(0f64, 1f64), (1f64, 2f64), (4f64, 5f64)]); + /// + /// Ok(()) /// } /// ``` - pub fn new(weights: Vec, intervals: Vec) -> Self { + pub fn new(weights: Vec, intervals: Vec) -> Result { let mut weights = weights; + if weights.len() == 0 { + return Err(EmptyWeightError); + } + if weights.iter().all(|&x| x == 0f64) { + return Err(AllZeroWeightError); + } let mut intervals = auto_zip(&intervals); + if weights.len() != intervals.len() { + return Err(LengthMismatchError); + } // Remove zero weights & corresponding intervals let mut i = 0; @@ -317,12 +342,14 @@ impl WeightedUniform { let sum = weights.iter() .zip(intervals.iter()) .fold(0f64, |acc, (w, (a, b))| acc + w * (b - a)); - - WeightedUniform { - weights, - sum, - intervals - } + + Ok( + WeightedUniform { + weights, + sum, + intervals + } + ) } /// Create WeightedUniform from max pooling @@ -332,9 +359,11 @@ impl WeightedUniform { /// extern crate peroxide; /// use peroxide::fuga::*; /// - /// fn main() { - /// let w = WeightedUniform::from_max_pool_1d(f, (-2f64, 3f64), 10, 1e-3); + /// fn main() -> Result<(), Box> { + /// let w = WeightedUniform::from_max_pool_1d(f, (-2f64, 3f64), 10, 1e-3)?; /// w.weights().print(); + /// + /// Ok(()) /// } /// /// fn f(x: f64) -> f64 { @@ -345,7 +374,7 @@ impl WeightedUniform { /// } /// } /// ``` - pub fn from_max_pool_1d(f: F, (a, b): (f64, f64), n: usize, eps: f64) -> Self + pub fn from_max_pool_1d(f: F, (a, b): (f64, f64), n: usize, eps: f64) -> Result where F: Fn(f64) -> f64 + Copy { // Find non-zero intervals let mut a = a; @@ -365,7 +394,9 @@ impl WeightedUniform { break; } } - assert!(a < b, "No non-zero interval found"); + if a >= b { + return Err(NoNonZeroIntervalError); + } let domain = linspace(a, b, n+1); // Find intervals @@ -380,15 +411,7 @@ impl WeightedUniform { ) .collect(); - let sum = weights.iter() - .zip(intervals.iter()) - .fold(0f64, |acc, (w, (x, y))| acc + w * (y - x)); - - WeightedUniform { - weights, - sum, - intervals - } + Self::new(weights, domain) } pub fn weights(&self) -> &Vec { diff --git a/src/statistics/rand.rs b/src/statistics/rand.rs index 2cb736ce..2db9557c 100644 --- a/src/statistics/rand.rs +++ b/src/statistics/rand.rs @@ -27,7 +27,7 @@ use std::u32; #[allow(unused_imports)] use crate::structure::matrix::*; -use super::dist::{RNG, WeightedUniform}; +use crate::statistics::dist::{RNG, WeightedUniform, WeightedUniformError}; /// Small random number generator from seed /// @@ -453,7 +453,7 @@ pub fn ziggurat(rng: &mut ThreadRng, sigma: f64) -> f64 { /// ``` /// use peroxide::fuga::*; /// -/// fn main() { +/// fn main() -> Result<(), Box> { /// let f = |x: f64| { /// if (0f64..=2f64).contains(&x) { /// -(x - 1f64).powi(2) + 1f64 @@ -462,19 +462,18 @@ pub fn ziggurat(rng: &mut ThreadRng, sigma: f64) -> f64 { /// } /// }; /// -/// let samples = prs(f, 1000, (-1f64, 3f64), 200, 1e-4); +/// let samples = prs(f, 1000, (-1f64, 3f64), 200, 1e-4)?; /// samples.mean().print(); // near 1 +/// +/// Ok(()) /// } -pub fn prs(f: F, n: usize, (a, b): (f64, f64), m: usize, eps: f64) -> Vec +pub fn prs(f: F, n: usize, (a, b): (f64, f64), m: usize, eps: f64) -> Result, WeightedUniformError> where F: Fn(f64) -> f64 + Copy { let mut rng = thread_rng(); let mut result = vec![0f64; n]; - let w = WeightedUniform::from_max_pool_1d(f, (a, b), m, eps); - if w.weights().iter().any(|w| w <= &0f64) { - println!("Warning: some weights are zero"); - } + let w = WeightedUniform::from_max_pool_1d(f, (a, b), m, eps)?; let mut initial_x = w.sample(n); let mut left_num = n; @@ -491,7 +490,7 @@ where F: Fn(f64) -> f64 + Copy { result[n - left_num] = x; left_num -= 1; if left_num == 0 { - return result; + return Ok(result); } } } @@ -515,7 +514,7 @@ where F: Fn(f64) -> f64 + Copy { /// ``` /// use peroxide::fuga::*; /// -/// fn main() { +/// fn main() -> Result<(), Box> { /// let mut rng = smallrng_from_seed(42); /// let f = |x: f64| { /// if (0f64..=2f64).contains(&x) { @@ -525,17 +524,16 @@ where F: Fn(f64) -> f64 + Copy { /// } /// }; /// -/// let samples = prs_with_rng(f, 1000, (-1f64, 3f64), 200, 1e-4, &mut rng); +/// let samples = prs_with_rng(f, 1000, (-1f64, 3f64), 200, 1e-4, &mut rng)?; /// assert!((samples.mean() - 1f64).abs() < 1e-1); +/// +/// Ok(()) /// } -pub fn prs_with_rng(f: F, n: usize, (a, b): (f64, f64), m: usize, eps: f64, rng: &mut R) -> Vec +pub fn prs_with_rng(f: F, n: usize, (a, b): (f64, f64), m: usize, eps: f64, rng: &mut R) -> Result, WeightedUniformError> where F: Fn(f64) -> f64 + Copy { let mut result = vec![0f64; n]; - let w = WeightedUniform::from_max_pool_1d(f, (a, b), m, eps); - if w.weights().iter().any(|w| w <= &0f64) { - println!("Warning: some weights are zero"); - } + let w = WeightedUniform::from_max_pool_1d(f, (a, b), m, eps)?; let mut initial_x = w.sample_with_rng(rng, n); let mut left_num = n; @@ -552,7 +550,7 @@ pub fn prs_with_rng(f: F, n: usize, (a, b): (f64, f64), m: us result[n - left_num] = x; left_num -= 1; if left_num == 0 { - return result; + return Ok(result); } } } diff --git a/tests/weighted_uniform.rs b/tests/weighted_uniform.rs index 06b547d8..b5f8c176 100644 --- a/tests/weighted_uniform.rs +++ b/tests/weighted_uniform.rs @@ -2,21 +2,20 @@ extern crate peroxide; use peroxide::fuga::*; #[test] -fn test_stats() { +fn test_stats() -> Result<(), Box> { let intervals = vec![0f64, 3f64, 6f64]; let weights = vec![2f64, 1f64]; - let unif = WeightedUniform::new(weights, intervals); + let unif = WeightedUniform::new(weights, intervals)?; assert_eq!(unif.mean(), 2.5); assert_eq!(unif.var(), 2.75); + + Ok(()) } #[test] -fn test_max_pool_1d() { - let w = WeightedUniform::from_max_pool_1d(f, (-2f64, 3f64), 10, 1e-5); - // w.weights().print(); +fn test_max_pool_1d() -> Result<(), Box> { + let w = WeightedUniform::from_max_pool_1d(f, (-2f64, 3f64), 10, 1e-5)?; println!("{:?}", w.intervals()); - // w.sample(100000).mean().print(); - // w.mean().print(); let x = linspace(w.intervals()[0].0, w.intervals()[8].1, 11); let y1 = x.fmap(f); let y2 = x.fmap(|t| w.weight_at(t)); @@ -24,6 +23,8 @@ fn test_max_pool_1d() { println!("a: {}, b: {}", a, b); assert!(a <= b); } + + Ok(()) } fn f(x: f64) -> f64 { From f98a0eb96a894bbe7ebd3fedc4aaf0ff610f42b7 Mon Sep 17 00:00:00 2001 From: axect Date: Mon, 8 Apr 2024 18:26:57 +0900 Subject: [PATCH 5/9] CHGE: Change whole ODE structures --- example_data/rk4_test.png | Bin 82585 -> 62207 bytes example_data/rkf45_test.png | Bin 0 -> 63160 bytes examples/ode_test_rk4.rs | 74 +- examples/ode_test_rkf45.rs | 40 + src/{numerical => grave}/bdf.rs | 0 src/grave/ode.rs | 1300 ++++++++++++++++++++++++--- src/grave/ode_old.rs | 156 ++++ src/numerical/mod.rs | 2 +- src/numerical/ode.rs | 1467 ++++++++----------------------- 9 files changed, 1798 insertions(+), 1241 deletions(-) create mode 100644 example_data/rkf45_test.png create mode 100644 examples/ode_test_rkf45.rs rename src/{numerical => grave}/bdf.rs (100%) create mode 100644 src/grave/ode_old.rs diff --git a/example_data/rk4_test.png b/example_data/rk4_test.png index 5f18481979887e24fa91f704f21ad4ae612fb90a..62660519c98e154a31d1986ae4b58918d0a4ed37 100644 GIT binary patch literal 62207 zcmdSBc|4T+|2ICJPRBWIj-<_2sVE^y_N9~Jgb<>TG9=lu@5VWuWF3j9tfj~jN%pO> zOx8)VFH>FEuIqYlul@OaU7`9HHMecvw;6}S 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use peroxide::fuga::*; -fn main() { - let init_state = State::::new(0f64, c!(1), c!(0)); +//fn main() { +// let init_state = State::::new(0f64, c!(1), c!(0)); +// +// let mut ode_solver = ExplicitODE::new(test_fn); +// +// ode_solver +// .set_method(ExMethod::RK4) +// .set_initial_condition(init_state) +// .set_step_size(0.01) +// .set_times(1000); +// +// let _result = ode_solver.integrate(); +// +// // let mut st = SimpleWriter::new(); +// // st.set_path("example_data/rk4_test.pickle") +// // .insert_matrix(result) +// // .write_pickle(); +//} +// +//fn test_fn(st: &mut State, _: &NoEnv) { +// let x = st.param; +// let y = &st.value; +// let dy = &mut st.deriv; +// dy[0] = (5f64 * x.powi(2) - y[0]) / (x + y[0]).exp(); +//} - let mut ode_solver = ExplicitODE::new(test_fn); +fn main() -> Result<(), Box> { + let basic_ode_solver = BasicODESolver::new(RK4); + let (t_vec, y_vec) = basic_ode_solver.solve( + &Test, + (0f64, 10f64), + 1e-3, + )?; + let y_vec = y_vec.into_iter().flatten().collect(); - ode_solver - .set_method(ExMethod::RK4) - .set_initial_condition(init_state) - .set_step_size(0.01) - .set_times(1000); + let mut plt = Plot2D::new(); + plt + .set_domain(t_vec) + .insert_image(y_vec) + .set_xlabel(r"$t$") + .set_ylabel(r"$y$") + .set_style(PlotStyle::Nature) + .tight_layout() + .set_dpi(600) + .set_path("example_data/rk4_test.png") + .savefig()?; - let _result = ode_solver.integrate(); - - // let mut st = SimpleWriter::new(); - // st.set_path("example_data/rk4_test.pickle") - // .insert_matrix(result) - // .write_pickle(); + Ok(()) } -fn test_fn(st: &mut State, _: &NoEnv) { - let x = st.param; - let y = &st.value; - let dy = &mut st.deriv; - dy[0] = (5f64 * x.powi(2) - y[0]) / (x + y[0]).exp(); +struct Test; + +impl ODEProblem for Test { + fn initial_conditions(&self) -> Vec { + vec![1f64] + } + + fn rhs(&self, t: f64, y: &[f64], dy: &mut [f64]) -> Result<(), ODEError> { + Ok(dy[0] = (5f64 * t.powi(2) - y[0]) / (t + y[0]).exp()) + } } diff --git a/examples/ode_test_rkf45.rs b/examples/ode_test_rkf45.rs new file mode 100644 index 00000000..6b88469a --- /dev/null +++ b/examples/ode_test_rkf45.rs @@ -0,0 +1,40 @@ +#[macro_use] +extern crate peroxide; +use peroxide::fuga::*; + +fn main() -> Result<(), Box> { + let rkf = RKF45::new(1e-4, 0.9, 1e-6, 1e-1, 100); + let basic_ode_solver = BasicODESolver::new(rkf); + let (t_vec, y_vec) = basic_ode_solver.solve( + &Test, + (0f64, 10f64), + 0.01, + )?; + let y_vec = y_vec.into_iter().flatten().collect(); + + let mut plt = Plot2D::new(); + plt + .set_domain(t_vec) + .insert_image(y_vec) + .set_xlabel(r"$t$") + .set_ylabel(r"$y$") + .set_style(PlotStyle::Nature) + .tight_layout() + .set_dpi(600) + .set_path("example_data/rkf45_test.png") + .savefig()?; + + Ok(()) +} + +struct Test; + +impl ODEProblem for Test { + fn initial_conditions(&self) -> Vec { + vec![1f64] + } + + fn rhs(&self, t: f64, y: &[f64], dy: &mut [f64]) -> Result<(), ODEError> { + Ok(dy[0] = (5f64 * t.powi(2) - y[0]) / (t + y[0]).exp()) + } +} diff --git a/src/numerical/bdf.rs b/src/grave/bdf.rs similarity index 100% rename from src/numerical/bdf.rs rename to src/grave/bdf.rs diff --git a/src/grave/ode.rs b/src/grave/ode.rs index e3b6c4b9..727bd911 100644 --- a/src/grave/ode.rs +++ b/src/grave/ode.rs @@ -1,156 +1,1182 @@ -use structure::matrix::*; -use structure::vector::*; -use std::convert::Into; -pub use self::ODEMethod::*; -use numerical::runge_kutta::rk4; -use numerical::bdf::bdf1; -use structure::dual::*; -use numerical::gauss_legendre::gl4; -use util::non_macro::zeros; -use util::non_macro::cat; -use numerical::runge_kutta::one_step_rk; -use numerical::bdf::one_step_bdf1; -use numerical::gauss_legendre::k_newton; - -#[derive(Debug, Copy, Clone)] -pub enum ODEMethod { +//! Solver for ordinary differential equations +//! +//! ## Introduce `ODE` Trait & Structure +//! +//! ### `ODE` Trait +//! +//! * `ODE` structures are divided by two kinds +//! * `ExplicitODE` +//! * `ImplicitODE` +//! * `ODE` trait is given as +//! +//! ```rust +//! extern crate peroxide; +//! use peroxide::fuga::{Real, State, BoundaryCondition, Environment}; +//! +//! pub trait ODE { +//! type Records; +//! type Vector; +//! type Param; +//! type ODEMethod; +//! +//! fn mut_update(&mut self); +//! fn integrate(&mut self) -> Self::Records; +//! fn set_initial_condition(&mut self, init: State) -> &mut Self; +//! fn set_boundary_condition( +//! &mut self, +//! bound1: (State, BoundaryCondition), +//! bound2: (State, BoundaryCondition), +//! ) -> &mut Self; +//! fn set_step_size(&mut self, dt: f64) -> &mut Self; +//! fn set_method(&mut self, method: Self::ODEMethod) -> &mut Self; +//! fn set_stop_condition(&mut self, f: fn(&Self) -> bool) -> &mut Self; +//! fn has_stopped(&self) -> bool; +//! fn set_times(&mut self, n: usize) -> &mut Self; +//! fn check_enough(&self) -> bool; +//! fn set_env(&mut self, env: E) -> &mut Self; +//! } +//! ``` +//! +//! * `Records` : The type to save results of ODE. Usually `Matrix` is used. +//! * `Vector` : Vector can be below things. +//! * `Vec` : Used for `ExplicitODE` +//! * `Vec` : Used for `ImplicitODE` +//! * `Param` : Also it can be `f64` or `AD` +//! * `ODEMethod` : Method for solving ODE +//! * `ExMethod` : Explicit method +//! * `Euler` : Euler first order +//! * `RK4` : Runge Kutta 4th order +//! * `ImMethod` : Implicit method +//! * `BDF` : Backward Euler 1st order (To be fixed) +//! * `GL4` : Gauss Legendre 4th order +//! * `Environment` : External environment (`CubicSpline`, `Vec`, `Matrix` or Another external table) +//! +//! +//! ### `State` structure +//! +//! * To use `ODE` trait, you should understand `State` first. +//! +//! ```rust +//! extern crate peroxide; +//! use peroxide::fuga::Real; +//! +//! #[derive(Debug, Clone, Default)] +//! pub struct State { +//! pub param: T, +//! pub value: Vec, +//! pub deriv: Vec, +//! } +//! ``` +//! +//! * `T` can be `f64` or `AD` +//! * `f64` for `ExplicitODE` +//! * `AD` for `ImplicitODE` +//! * `param` is parameter for ODE. Usually it is represented by time. +//! * `value` is value of each node. +//! * `deriv` is value of derivative of each node. +//! +//! For example, +//! +//! $$ \frac{dy_n}{dt} = f(t, y_n) $$ +//! +//! * $t$ is `param` +//! * $y_n$ is `value` +//! * $f(t,y_n)$ is `deriv` +//! +//! Methods for `State` are as follows. +//! +//! * `to_f64(&self) -> State` +//! * `to_ad(&self) -> State` +//! * `new(T, Vec, Vec) -> Self` +//! +//! ### `Environment` +//! +//! * `Environment` needs just `Default` +//! * To use custom `Environment`, just type follows : `impl Environment for CustomType {}` +//! * If you don't want to use `Environment`, then use `NoEnv` +//! * Implemented Data Types +//! * `Vec` +//! * `Polynomial` +//! * `Matrix` +//! * `CubicSpline` +//! * `NoEnv` +//! +//! ``` +//! #[macro_use] +//! extern crate peroxide; +//! use peroxide::fuga::*; +//! +//! fn main() -> Result<(), Box> { +//! let x = seq(0, 10, 1); +//! x.print(); +//! let y = x.iter().enumerate().map(|(i, &t)| t.powi(5-i as i32)).collect::>(); +//! +//! let c = cubic_hermite_spline(&x, &y, Quadratic)?; +//! +//! let init_state = State::::new(0f64, c!(1), c!(0)); +//! +//! let mut ode_solver = ExplicitODE::new(test_fn); +//! +//! ode_solver +//! .set_method(ExMethod::RK4) +//! .set_initial_condition(init_state) +//! .set_step_size(0.01) +//! .set_times(1000) +//! .set_env(c); +//! +//! let result = ode_solver.integrate(); +//! result.print(); +//! +//! Ok(()) +//! } +//! +//! fn test_fn(st: &mut State, env: &CubicHermiteSpline) { +//! let x = st.param; +//! let dy = &mut st.deriv; +//! dy[0] = env.eval(x); +//! } +//! ``` +//! +//! ### `ExplicitODE` struct +//! +//! `ExplicitODE` is given as follow : +//! +//! ```rust +//! extern crate peroxide; +//! use std::collections::HashMap; +//! use peroxide::fuga::{State, ExMethod, BoundaryCondition, ODEOptions, Environment}; +//! +//! #[derive(Clone)] +//! pub struct ExplicitODE { +//! state: State, +//! func: fn(&mut State, &E), +//! step_size: f64, +//! method: ExMethod, +//! init_cond: State, +//! bound_cond1: (State, BoundaryCondition), +//! bound_cond2: (State, BoundaryCondition), +//! stop_cond: fn(&Self) -> bool, +//! has_stopped: bool, +//! times: usize, +//! to_use: HashMap, +//! env: E, +//! } +//! ``` +//! +//! * `state` : Current param, value, derivative +//! * `func` : Function to update `state` +//! * `init_cond` : Initial condition +//! * `bound_cond1` : If boundary problem, then first boundary condition +//! * `bound_cond2` : second boundary condition +//! * `stop_cond` : Stop condition (stop before `times`) +//! * `has_stopped`: Has the stop condition been reached +//! * `times` : How many times do you want to update? +//! * `to_use` : Just check whether information is enough +//! * `env` : Environment +//! +//! # `ImplicitODE` struct +//! +//! `ImplicitODE` is struct to solve stiff ODE with implicit methods. +//! +//! ```no_run +//! extern crate peroxide; +//! use std::collections::HashMap; +//! use peroxide::fuga::{State, ImMethod, BoundaryCondition, ODEOptions, Environment, AD}; +//! +//! #[derive(Clone)] +//! pub struct ImplicitODE { +//! state: State, +//! func: fn(&mut State, &E), +//! step_size: f64, +//! method: ImMethod, +//! init_cond: State, +//! bound_cond1: (State, BoundaryCondition), +//! bound_cond2: (State, BoundaryCondition), +//! stop_cond: fn(&Self) -> bool, +//! has_stopped: bool, +//! times: usize, +//! to_use: HashMap, +//! env: E, +//! } +//! ``` +//! +//! ## Example +//! +//! ### Lorenz Butterfly +//! +//! ```rust +//! extern crate peroxide; +//! use peroxide::fuga::*; +//! +//! fn main() { +//! // ========================================= +//! // Declare ODE (Euler) +//! // ========================================= +//! let mut ex_test = ExplicitODE::new(f); +//! +//! let init_state: State = State::new( +//! 0.0, +//! vec![10.0, 1.0, 1.0], +//! vec![0.0, 0.0, 0.0], +//! ); +//! +//! ex_test +//! .set_initial_condition(init_state) +//! .set_method(ExMethod::Euler) +//! .set_step_size(0.01f64) +//! .set_times(10000); +//! +//! // ========================================= +//! // Declare ODE (RK4) +//! // ========================================= +//! let mut ex_test2 = ex_test.clone(); +//! ex_test2.set_method(ExMethod::RK4); +//! +//! // ========================================= +//! // Declare ODE (GL4) +//! // ========================================= +//! let mut im_test = ImplicitODE::new(g); +//! +//! let init_state: State = State::new( +//! AD0(0.0), +//! vec![AD0(10f64), AD0(1f64), AD0(1f64)], +//! vec![AD0(0.0), AD0(0.0), AD0(0.0)], +//! ); +//! +//! im_test +//! .set_initial_condition(init_state) +//! .set_method(ImMethod::GL4) +//! .set_step_size(0.01f64) +//! .set_times(10000); +//! +//! // ========================================= +//! // Save results +//! // ========================================= +//! let results = ex_test.integrate(); +//! let results2 = ex_test2.integrate(); +//! let results3 = im_test.integrate(); +//! +//! // Extract data +//! let mut df = DataFrame::new(vec![]); +//! df.push("x_euler", Series::new(results.col(1))); +//! df.push("z_euler", Series::new(results.col(3))); +//! df.push("x_rk4", Series::new(results2.col(1))); +//! df.push("z_rk4", Series::new(results2.col(3))); +//! df.push("x_gl4", Series::new(results3.col(1))); +//! df.push("z_gl4", Series::new(results3.col(3))); +//! +//! # #[cfg(feature="nc")] +//! # { +//! // Write netcdf file (`nc` feature required) +//! df.write_nc("example_data/lorenz.nc") +//! .expect("Can't write lorenz.nc"); +//! # } +//! } +//! +//! fn f(st: &mut State, _: &NoEnv) { +//! let x = &st.value; +//! let dx = &mut st.deriv; +//! dx[0] = 10f64 * (x[1] - x[0]); +//! dx[1] = 28f64 * x[0] - x[1] - x[0] * x[2]; +//! dx[2] = -8f64/3f64 * x[2] + x[0] * x[1]; +//! } +//! +//! fn g(st: &mut State, _: &NoEnv) { +//! let x = &st.value; +//! let dx = &mut st.deriv; +//! dx[0] = 10f64 * (x[1] - x[0]); +//! dx[1] = 28f64 * x[0] - x[1] - x[0] * x[2]; +//! dx[2] = -8f64/3f64 * x[2] + x[0] * x[1]; +//! } +//! ``` +//! +//! ### Simple 1D Runge-Kutta +//! +//! $$\begin{gathered} \frac{dy}{dx} = \frac{5x^2 - y}{e^{x+y}} \\\ y(0) = 1 \end{gathered}$$ +//! +//! ```rust +//! #[macro_use] +//! extern crate peroxide; +//! use peroxide::fuga::*; +//! +//! fn main() { +//! let init_state = State::::new(0f64, c!(1), c!(0)); +//! +//! let mut ode_solver = ExplicitODE::new(test_fn); +//! +//! ode_solver +//! .set_method(ExMethod::RK4) +//! .set_initial_condition(init_state) +//! .set_step_size(0.01) +//! .set_times(1000); +//! +//! let result = ode_solver.integrate(); +//! +//! // Plot or Extract.. +//! } +//! +//! fn test_fn(st: &mut State, _: &NoEnv) { +//! let x = st.param; +//! let y = &st.value; +//! let dy = &mut st.deriv; +//! dy[0] = (5f64 * x.powi(2) - y[0]) / (x + y[0]).exp(); +//! } +//! ``` +//! +//! ### With stop condition +//! +//! ```rust +//! #[macro_use] +//! extern crate peroxide; +//! use peroxide::fuga::*; +//! +//! fn main() { +//! let init_state = State::::new(0f64, c!(1), c!(0)); +//! +//! let mut ode_solver = ExplicitODE::new(test_fn); +//! +//! ode_solver +//! .set_method(ExMethod::RK4) +//! .set_initial_condition(init_state) +//! .set_step_size(0.01) +//! .set_stop_condition(stop) // Add stop condition +//! .set_times(1000); +//! +//! let result = ode_solver.integrate(); +//! if ode_solver.has_stopped() { +//! println!("It reached to stop condition"); +//! } else { +//! println!("It didn't reach to stop condition"); +//! } +//! +//! // Plot or Extract.. +//! } +//! +//! fn test_fn(st: &mut State, _: &NoEnv) { +//! let x = st.param; +//! let y = &st.value; +//! let dy = &mut st.deriv; +//! dy[0] = (5f64 * x.powi(2) - y[0]) / (x + y[0]).exp(); +//! } +//! +//! fn stop(st: &ExplicitODE) -> bool { +//! let y = &st.get_state().value[0]; +//! (*y - 2.4).abs() < 0.01 +//! } +//! ``` + +use self::BoundaryCondition::Dirichlet; +use self::ExMethod::{Euler, RK4}; +use self::ImMethod::{BDF1, GL4}; +use self::ODEOptions::{BoundCond, InitCond, Method, StepSize, StopCond, Times}; +use crate::numerical::{spline::CubicSpline, utils::jacobian}; +use crate::structure::{ + ad::{ADVec, AD, AD::*}, + matrix::{LinearAlgebra, Matrix}, + polynomial::Polynomial, +}; +use crate::traits::{ + fp::{FPMatrix, FPVector}, + math::{Norm, Normed, Vector}, + mutable::MutFP, + num::Real, +}; +use crate::util::non_macro::{cat, concat, eye, zeros}; +use std::collections::HashMap; +use crate::fuga::CubicHermiteSpline; +//#[cfg(feature = "O3")] +//use {blas_daxpy, blas_daxpy_return}; + +/// Explicit ODE Methods +/// +/// * Euler : Euler 1st Order +/// * RK4 : Runge-Kutta 4th Order +#[derive(Debug, Copy, Clone, Hash, PartialOrd, PartialEq, Eq)] +pub enum ExMethod { + Euler, RK4, - BDF1(f64), - GL4(f64), } -/// ODE Solver -/// -/// # Parameters -/// * `f = f(t, y)` -/// * `init_value = y_start` -/// * `param_range = (t_start, t_end)` -/// -/// # Type -/// `solve: (F, Vec, (T, T), f64, ODEMethod) -> Matrix where Fn(Dual, Vec) -> Vec + Copy, T: Into + Copy` -/// -/// # Methods -/// * `RK4`: Explicit Runge-Kutta 4th order -/// * `BDF1`: Backward Differentiation Formula 1st order (Backward Euler) -/// * `GL4`: Gauss-Legendre 4th order -/// -/// # Examples -/// ``` -/// extern crate peroxide; -/// use peroxide::*; +#[derive(Debug, Copy, Clone, Hash, PartialOrd, PartialEq, Eq)] +pub enum ImMethod { + BDF1, + GL4, +} + +/// Kinds of Boundary Conditions /// -/// let init_val = c!(2, 1); -/// let result = solve(lotka_volterra, init_val, (0, 10), 1e-3, RK4); -/// result.print(); +/// * Dirichlet +/// * Neumann +#[derive(Debug, Copy, Clone, Hash, PartialOrd, PartialEq, Eq)] +pub enum BoundaryCondition { + Dirichlet, + Neumann, +} + +/// Options for ODE /// -/// fn lotka_volterra(t: Dual, xs: Vec) -> Vec { -/// let a = 4.; -/// let c = 1.; +/// * `InitCond` : Initial condition +/// * `BoundCond` : Boundary condition +/// * `Method` : methods of `ExMethod` or `ImMethod` +/// * `StopCond` : Stop condition +/// * `StepSize` : Step size +/// * `Times` : A number of times to integrate with specific step size +#[derive(Debug, Clone, Copy, Hash, PartialOrd, PartialEq, Eq)] +pub enum ODEOptions { + InitCond, + BoundCond, + Method, + StopCond, + StepSize, + Times, +} + +pub trait Environment: Default {} + +/// State for ODE /// -/// let x = xs[0]; -/// let y = xs[1]; +/// * `param` : Parameter of ODE (ex) time) +/// * `value` : Current value of ODE +/// * `deriv` : Current differential of values +#[derive(Debug, Clone, Default)] +pub struct State { + pub param: T, + pub value: Vec, + pub deriv: Vec, +} + +impl State { + pub fn to_f64(&self) -> State { + State { + param: self.param.to_f64(), + value: self + .value + .clone() + .into_iter() + .map(|x| x.to_f64()) + .collect::>(), + deriv: self + .deriv + .clone() + .into_iter() + .map(|x| x.to_f64()) + .collect::>(), + } + } + + pub fn to_ad(&self) -> State { + State { + param: self.param.to_ad(), + value: self + .value + .clone() + .into_iter() + .map(|x| x.to_ad()) + .collect::>(), + deriv: self + .deriv + .clone() + .into_iter() + .map(|x| x.to_ad()) + .collect::>(), + } + } + + pub fn new(param: T, state: Vec, deriv: Vec) -> Self { + State { + param, + value: state, + deriv, + } + } +} + +/// ODE solver /// -/// vec![ -/// a * (x - x*y), -/// -c * (y - x*y) -/// ] -/// } -/// ``` -pub fn solve(f: F, init_value: Vec, param_range: (T, T), step: f64, method: ODEMethod) -> Matrix - where F: Fn(Dual, Vec) -> Vec + Copy, - T: Into + Copy -{ - let t_start = param_range.0.into(); - let t_end = param_range.1.into(); - let num = ((t_end - t_start) / step).round() as usize; - - match method { - RK4 => { - let g = |t: f64, xs: Vec| f(dual(t, 0.), merge_dual(xs.clone(), vec![0f64;xs.len()])).values(); - let result = rk4( - t_start, - init_value.into_iter().map(|p| p.into()).collect::>(), - g, - step, - num, - ); - result - }, - BDF1(rtol) => { - let result = bdf1(t_start, init_value, f, step, rtol, num); - result - }, - GL4(rtol) => { - let result = gl4(f, t_start, init_value, step, rtol, num); - result +/// * `Records` : Type of container to contain results +/// * `Param` : Type of parameter +/// * `ODEMethod` : Explicit or Implicit +pub trait ODE { + type Records; + type Param; + type ODEMethod; + + fn mut_update(&mut self); + //fn mut_integrate(&mut self, rec: &mut Self::Records); + fn integrate(&mut self) -> Self::Records; + fn set_initial_condition(&mut self, init: State) -> &mut Self; + fn set_boundary_condition( + &mut self, + bound1: (State, BoundaryCondition), + bound2: (State, BoundaryCondition), + ) -> &mut Self; + fn set_step_size(&mut self, dt: f64) -> &mut Self; + fn set_method(&mut self, method: Self::ODEMethod) -> &mut Self; + fn set_stop_condition(&mut self, f: fn(&Self) -> bool) -> &mut Self; + fn has_stopped(&self) -> bool; + fn set_times(&mut self, n: usize) -> &mut Self; + fn check_enough(&self) -> bool; + fn set_env(&mut self, env: E) -> &mut Self; +} + +#[derive(Clone)] +pub struct ExplicitODE { + state: State, + func: fn(&mut State, &E), + step_size: f64, + method: ExMethod, + init_cond: State, + bound_cond1: (State, BoundaryCondition), + bound_cond2: (State, BoundaryCondition), + stop_cond: fn(&Self) -> bool, + has_stopped: bool, + times: usize, + options: HashMap, + env: E, +} + +impl ExplicitODE { + pub fn new(f: fn(&mut State, &E)) -> Self { + let mut default_to_use: HashMap = HashMap::new(); + default_to_use.insert(InitCond, false); + default_to_use.insert(StepSize, false); + default_to_use.insert(BoundCond, false); + default_to_use.insert(Method, false); + default_to_use.insert(StopCond, false); + default_to_use.insert(Times, false); + + ExplicitODE { + state: Default::default(), + func: f, + step_size: 0.0, + method: Euler, + init_cond: Default::default(), + bound_cond1: (Default::default(), Dirichlet), + bound_cond2: (Default::default(), Dirichlet), + stop_cond: |_x| false, + has_stopped: false, + times: 0, + options: default_to_use, + env: E::default(), } } + + pub fn get_state(&self) -> &State { + &self.state + } + + pub fn get_env(&self) -> &E { + &self.env + } + + pub fn get_step_size(&self) -> f64 { + self.step_size + } + + pub fn get_times(&self) -> usize { + self.times + } + + pub fn get_method(&self) -> ExMethod { + self.method + } + + pub fn get_stop_condition(&self) -> fn(&Self) -> bool { + self.stop_cond + } + + pub fn get_has_stopped(&self) -> bool { + self.has_stopped + } + + pub fn get_init_cond(&self) -> &State { + &self.init_cond + } + + pub fn get_bound_cond1(&self) -> &(State, BoundaryCondition) { + &self.bound_cond1 + } + + pub fn get_bound_cond2(&self) -> &(State, BoundaryCondition) { + &self.bound_cond2 + } } -pub fn solve_with_condition(f: F, init_value: Vec, param_range: (T, T), step: f64, method: ODEMethod, cond: G) -> Matrix -where F: Fn(Dual, Vec) -> Vec + Copy, - T: Into + Copy, - G: Fn(Vec) -> bool + Copy, -{ - let t_start = param_range.0.into(); - let t_end = param_range.1.into(); - let num = ((t_end - t_start) / step).round() as usize; - - match method { - RK4 => { - let g = |t: f64, xs: Vec| f(dual(t, 0.), merge_dual(xs.clone(), vec![0f64;xs.len()])).values(); - let mut xs = init_value.clone(); - let mut t = t_start; - let mut result = zeros(num+1, xs.len() + 1); - result.subs_row(0, cat(t, xs.clone())); - let mut key = 0usize; - for i in 1 .. num + 1 { - if !cond(xs.clone()) { - key = i - 1; - break; - } else { - xs = one_step_rk(t, xs.clone(), g, step); - t += step; - result.subs_row(i, cat(t, xs.clone())); +impl ODE for ExplicitODE { + type Records = Matrix; + type Param = f64; + type ODEMethod = ExMethod; + + fn mut_update(&mut self) { + match self.method { + Euler => { + // Set Derivative from state + (self.func)(&mut self.state, &self.env); + let dt = self.step_size; + + //match () { + // #[cfg(feature = "oxidize")] + // () => { + // blas_daxpy(dt, &self.state.deriv, &mut self.state.value); + // } + // _ => { + self.state + .value + .mut_zip_with(|x, y| x + y * dt, &self.state.deriv); + // } + //} + self.state.param += dt; + } + RK4 => { + let h = self.step_size; + let h2 = h / 2f64; + + // Set Derivative from state + let yn = self.state.value.clone(); + (self.func)(&mut self.state, &self.env); + + let k1 = self.state.deriv.clone(); + let k1_add = k1.mul_scalar(h2); + self.state.param += h2; + self.state.value.mut_zip_with(|x, y| x + y, &k1_add); + (self.func)(&mut self.state, &self.env); + + let k2 = self.state.deriv.clone(); + let k2_add = k2.zip_with(|x, y| h2 * x - y, &k1_add); + self.state.value.mut_zip_with(|x, y| x + y, &k2_add); + (self.func)(&mut self.state, &self.env); + + let k3 = self.state.deriv.clone(); + let k3_add = k3.zip_with(|x, y| h * x - y, &k2_add); + self.state.param += h2; + self.state.value.mut_zip_with(|x, y| x + y, &k3_add); + (self.func)(&mut self.state, &self.env); + + let k4 = self.state.deriv.clone(); + + for i in 0..k1.len() { + self.state.value[i] = + yn[i] + (k1[i] + 2f64 * k2[i] + 2f64 * k3[i] + k4[i]) * h / 6f64; } } - result.take(key, Row) - }, - BDF1(rtol) => { - let mut t = t_start; - let mut xs = init_value.clone(); - let mut records = zeros(num + 1, xs.len() + 1); - let mut key = 0usize; - for i in 0 .. (num+1) { - if !cond(xs.clone()) { - key =i; - break; + } + } + + fn integrate(&mut self) -> Self::Records { + assert!(self.check_enough(), "Not enough fields!"); + + let mut result = zeros(self.times + 1, self.state.value.len() + 1); + + result.subs_row(0, &cat(self.state.param, &self.state.value)); + + match self.options.get(&StopCond) { + Some(stop) if *stop => { + let mut key = 1usize; + for i in 1..self.times + 1 { + self.mut_update(); + result.subs_row(i, &cat(self.state.param, &self.state.value)); + key += 1; + if (self.stop_cond)(&self) { + self.has_stopped = true; + break; + } } - records.subs_row(i, cat(t, xs.clone())); - t += step; - xs = one_step_bdf1(t, xs.clone(), f, step, rtol); - } - records.take(key, Row) - }, - GL4(rtol) => { - let mut t = t_start; - let mut y_curr = init_value.clone(); - let mut records = zeros(num + 1, y_curr.len() + 1); - records.subs_row(0, cat(t, y_curr.clone())); - let mut key = 0usize; - - for i in 0 .. num { - if !cond(y_curr.clone()) { - key = i; - break; + return result.take_row(key); + } + _ => { + for i in 1..self.times + 1 { + self.mut_update(); + result.subs_row(i, &cat(self.state.param, &self.state.value)); } - let (k1, k2) = k_newton(f, t, y_curr.clone(), step, rtol); - y_curr = y_curr.add(&k1.fmap(|x| 0.5 * x * step).add(&k2.fmap(|x| 0.5 * x * step))); - t += step; - records.subs_row(i+1, cat(t, y_curr.clone())) + return result; } + } + } + + fn set_initial_condition(&mut self, init: State) -> &mut Self { + if let Some(x) = self.options.get_mut(&InitCond) { + *x = true + } + self.init_cond = init.to_f64(); + self.state = init.to_f64(); + self + } + + fn set_boundary_condition( + &mut self, + bound1: (State, BoundaryCondition), + bound2: (State, BoundaryCondition), + ) -> &mut Self { + if let Some(x) = self.options.get_mut(&BoundCond) { + *x = true + } + self.bound_cond1 = (bound1.0.to_f64(), bound1.1); + self.bound_cond2 = (bound2.0.to_f64(), bound2.1); + self + } - records.take(key, Row) + fn set_step_size(&mut self, dt: f64) -> &mut Self { + if let Some(x) = self.options.get_mut(&StepSize) { + *x = true } + self.step_size = dt; + self + } + + fn set_method(&mut self, method: Self::ODEMethod) -> &mut Self { + if let Some(x) = self.options.get_mut(&Method) { + *x = true + } + self.method = method; + self + } + + fn set_stop_condition(&mut self, f: fn(&Self) -> bool) -> &mut Self { + if let Some(x) = self.options.get_mut(&StopCond) { + *x = true + } + self.stop_cond = f; + self + } + + fn has_stopped(&self) -> bool { + self.has_stopped + } + + fn set_times(&mut self, n: usize) -> &mut Self { + if let Some(x) = self.options.get_mut(&Times) { + *x = true + } + self.times = n; + self + } + + fn check_enough(&self) -> bool { + // Method + match self.options.get(&Method) { + Some(x) => { + if !*x { + return false; + } + } + None => { + return false; + } + } + + // Step size + match self.options.get(&StepSize) { + Some(x) => { + if !*x { + return false; + } + } + None => { + return false; + } + } + + // Initial or Boundary + match self.options.get(&InitCond) { + None => { + return false; + } + Some(x) => { + if !*x { + match self.options.get(&BoundCond) { + None => { + return false; + } + Some(_) => (), + } + } + } + } + + // Set Time? + match self.options.get(&Times) { + None => { + return false; + } + Some(x) => { + if !*x { + return false; + } + } + } + true + } + + fn set_env(&mut self, env: E) -> &mut Self { + self.env = env; + self } -} \ No newline at end of file +} + +#[derive(Clone)] +pub struct ImplicitODE { + state: State, + func: fn(&mut State, &E), + step_size: f64, + rtol: f64, + method: ImMethod, + init_cond: State, + bound_cond1: (State, BoundaryCondition), + bound_cond2: (State, BoundaryCondition), + stop_cond: fn(&Self) -> bool, + has_stopped: bool, + times: usize, + options: HashMap, + env: E, +} + +impl ImplicitODE { + pub fn new(f: fn(&mut State, &E)) -> Self { + let mut default_to_use: HashMap = HashMap::new(); + default_to_use.insert(InitCond, false); + default_to_use.insert(StepSize, false); + default_to_use.insert(BoundCond, false); + default_to_use.insert(Method, false); + default_to_use.insert(StopCond, false); + default_to_use.insert(Times, false); + + ImplicitODE { + state: State::new(AD0(0f64), vec![], vec![]), + func: f, + step_size: 0.0, + rtol: 1e-6, + method: GL4, + init_cond: Default::default(), + bound_cond1: (Default::default(), Dirichlet), + bound_cond2: (Default::default(), Dirichlet), + stop_cond: |_x| false, + has_stopped: false, + times: 0, + options: default_to_use, + env: E::default(), + } + } + + pub fn get_state(&self) -> &State { + &self.state + } + + pub fn set_rtol(&mut self, rtol: f64) -> &mut Self { + self.rtol = rtol; + self + } + + pub fn get_env(&self) -> &E { + &self.env + } + + pub fn get_step_size(&self) -> f64 { + self.step_size + } + + pub fn get_times(&self) -> usize { + self.times + } + + pub fn get_method(&self) -> ImMethod { + self.method + } + + pub fn get_stop_condition(&self) -> fn(&Self) -> bool { + self.stop_cond + } + + pub fn get_has_stopped(&self) -> bool { + self.has_stopped + } + + pub fn get_init_cond(&self) -> &State { + &self.init_cond + } + + pub fn get_bound_cond1(&self) -> &(State, BoundaryCondition) { + &self.bound_cond1 + } + + pub fn get_bound_cond2(&self) -> &(State, BoundaryCondition) { + &self.bound_cond2 + } + + pub fn get_rtol(&self) -> f64 { + self.rtol + } +} + +/// Value of 3f64.sqrt() +const SQRT3: f64 = 1.7320508075688772; + +/// Butcher tableau for Gauss_legendre 4th order +const GL4_TAB: [[f64; 3]; 2] = [ + [0.5 - SQRT3 / 6f64, 0.25, 0.25 - SQRT3 / 6f64], + [0.5 + SQRT3 / 6f64, 0.25 + SQRT3 / 6f64, 0.25], +]; + +#[allow(non_snake_case)] +impl ODE for ImplicitODE { + type Records = Matrix; + type Param = AD; + type ODEMethod = ImMethod; + fn mut_update(&mut self) { + match self.method { + BDF1 => unimplemented!(), + GL4 => { + let f = |t: AD, y: Vec| { + let mut st = State::new(t, y.clone(), y); + (self.func)(&mut st, &self.env); + st.deriv + }; + + let h = self.step_size; + let t = self.state.param; + let t1: AD = t + GL4_TAB[0][0] * h; + let t2: AD = t + GL4_TAB[1][0] * h; + let yn = &self.state.value; + let n = yn.len(); + + // 0. Initial Guess + let k1_init: Vec = f(t, yn.clone()).to_f64_vec(); + let k2_init: Vec = f(t, yn.clone()).to_f64_vec(); + let mut k_curr: Vec = concat(&k1_init, &k2_init); + let mut err = 1f64; + + // 1. Combine two functions to one function + let g = |k: &Vec| -> Vec { + let k1 = k.take(n); + let k2 = k.skip(n); + concat( + &f( + t1, + yn.add_vec( + &k1.mul_scalar(AD::from(GL4_TAB[0][1] * h)) + .add_vec(&k2.mul_scalar(AD::from(GL4_TAB[0][2] * h))), + ), + ), + &f( + t2, + yn.add_vec( + &k1.mul_scalar(AD::from(GL4_TAB[1][1] * h)) + .add_vec(&k2.mul_scalar(AD::from(GL4_TAB[1][2] * h))), + ), + ), + ) + }; + + // 2. Obtain Jacobian + let I = eye(2 * n); + + let mut Dg = jacobian(Box::new(g), &k_curr); + let mut DG = &I - &Dg; + let mut DG_inv = DG.inv(); + let mut G = k_curr.sub_vec(&g(&k_curr.to_ad_vec()).to_f64_vec()); + let mut num_iter: usize = 0; + + // 3. Iteration + while err >= self.rtol && num_iter <= 10 { + let DGG = &DG_inv * &G; + let k_prev = k_curr.clone(); + k_curr.mut_zip_with(|x, y| x - y, &DGG); + Dg = jacobian(Box::new(g), &k_curr); + DG = &I - &Dg; + DG_inv = DG.inv(); + G = k_curr.sub_vec(&g(&k_curr.to_ad_vec()).to_f64_vec()); + err = k_curr.sub_vec(&k_prev).norm(Norm::L2); + num_iter += 1; + } + + // 4. Find k1, k2 + let (k1, k2) = (k_curr.take(n), k_curr.skip(n)); + + // Set Derivative from state + (self.func)(&mut self.state, &self.env); + + // 5. Merge k1, k2 + let mut y_curr = self.state.value.to_f64_vec(); + y_curr = y_curr.add_vec(&k1.mul_scalar(0.5 * h).add_vec(&k2.mul_scalar(0.5 * h))); + self.state.value = y_curr.to_ad_vec(); + self.state.param = self.state.param + h; + } + } + } + + fn integrate(&mut self) -> Self::Records { + assert!(self.check_enough(), "Not enough fields!"); + + let mut result = zeros(self.times + 1, self.state.value.len() + 1); + + result.subs_row( + 0, + &cat(self.state.param.to_f64(), &self.state.value.to_f64_vec()), + ); + + match self.options.get(&StopCond) { + Some(stop) if *stop => { + let mut key = 1usize; + for i in 1..self.times + 1 { + self.mut_update(); + result.subs_row( + i, + &cat(self.state.param.to_f64(), &self.state.value.to_f64_vec()), + ); + key += 1; + if (self.stop_cond)(&self) { + self.has_stopped = true; + break; + } + } + return result.take_row(key); + } + _ => { + for i in 1..self.times + 1 { + self.mut_update(); + result.subs_row( + i, + &cat(self.state.param.to_f64(), &self.state.value.to_f64_vec()), + ); + } + return result; + } + } + } + + fn set_initial_condition(&mut self, init: State) -> &mut Self { + if let Some(x) = self.options.get_mut(&InitCond) { + *x = true + } + self.init_cond = init.to_f64(); + self.state = init.to_ad(); + self + } + + fn set_boundary_condition( + &mut self, + bound1: (State, BoundaryCondition), + bound2: (State, BoundaryCondition), + ) -> &mut Self { + if let Some(x) = self.options.get_mut(&BoundCond) { + *x = true + } + self.bound_cond1 = (bound1.0.to_f64(), bound1.1); + self.bound_cond2 = (bound2.0.to_f64(), bound2.1); + self + } + + fn set_step_size(&mut self, dt: f64) -> &mut Self { + if let Some(x) = self.options.get_mut(&StepSize) { + *x = true + } + self.step_size = dt; + self + } + + fn set_method(&mut self, method: Self::ODEMethod) -> &mut Self { + if let Some(x) = self.options.get_mut(&Method) { + *x = true + } + self.method = method; + self + } + + fn set_stop_condition(&mut self, f: fn(&Self) -> bool) -> &mut Self { + if let Some(x) = self.options.get_mut(&StopCond) { + *x = true + } + self.stop_cond = f; + self + } + + fn has_stopped(&self) -> bool { + self.has_stopped + } + + fn set_times(&mut self, n: usize) -> &mut Self { + if let Some(x) = self.options.get_mut(&Times) { + *x = true + } + self.times = n; + self + } + + fn check_enough(&self) -> bool { + // Method + match self.options.get(&Method) { + Some(x) => { + if !*x { + return false; + } + } + None => { + return false; + } + } + + // Step size + match self.options.get(&StepSize) { + Some(x) => { + if !*x { + return false; + } + } + None => { + return false; + } + } + + // Initial or Boundary + match self.options.get(&InitCond) { + None => { + return false; + } + Some(x) => { + if !*x { + match self.options.get(&BoundCond) { + None => { + return false; + } + Some(_) => (), + } + } + } + } + + // Set Time? + match self.options.get(&Times) { + None => { + return false; + } + Some(x) => { + if !*x { + return false; + } + } + } + true + } + + fn set_env(&mut self, env: E) -> &mut Self { + self.env = env; + self + } +} + +// ============================================================================= +// Some Environments +// ============================================================================= +#[derive(Debug, Copy, Clone, Default)] +pub struct NoEnv {} + +impl Environment for NoEnv {} + +impl Environment for CubicSpline {} + +impl Environment for Matrix {} + +impl Environment for Vec {} + +impl Environment for Polynomial {} + +impl Environment for CubicHermiteSpline {} \ No newline at end of file diff --git a/src/grave/ode_old.rs b/src/grave/ode_old.rs new file mode 100644 index 00000000..e3b6c4b9 --- /dev/null +++ b/src/grave/ode_old.rs @@ -0,0 +1,156 @@ +use structure::matrix::*; +use structure::vector::*; +use std::convert::Into; +pub use self::ODEMethod::*; +use numerical::runge_kutta::rk4; +use numerical::bdf::bdf1; +use structure::dual::*; +use numerical::gauss_legendre::gl4; +use util::non_macro::zeros; +use util::non_macro::cat; +use numerical::runge_kutta::one_step_rk; +use numerical::bdf::one_step_bdf1; +use numerical::gauss_legendre::k_newton; + +#[derive(Debug, Copy, Clone)] +pub enum ODEMethod { + RK4, + BDF1(f64), + GL4(f64), +} + +/// ODE Solver +/// +/// # Parameters +/// * `f = f(t, y)` +/// * `init_value = y_start` +/// * `param_range = (t_start, t_end)` +/// +/// # Type +/// `solve: (F, Vec, (T, T), f64, ODEMethod) -> Matrix where Fn(Dual, Vec) -> Vec + Copy, T: Into + Copy` +/// +/// # Methods +/// * `RK4`: Explicit Runge-Kutta 4th order +/// * `BDF1`: Backward Differentiation Formula 1st order (Backward Euler) +/// * `GL4`: Gauss-Legendre 4th order +/// +/// # Examples +/// ``` +/// extern crate peroxide; +/// use peroxide::*; +/// +/// let init_val = c!(2, 1); +/// let result = solve(lotka_volterra, init_val, (0, 10), 1e-3, RK4); +/// result.print(); +/// +/// fn lotka_volterra(t: Dual, xs: Vec) -> Vec { +/// let a = 4.; +/// let c = 1.; +/// +/// let x = xs[0]; +/// let y = xs[1]; +/// +/// vec![ +/// a * (x - x*y), +/// -c * (y - x*y) +/// ] +/// } +/// ``` +pub fn solve(f: F, init_value: Vec, param_range: (T, T), step: f64, method: ODEMethod) -> Matrix + where F: Fn(Dual, Vec) -> Vec + Copy, + T: Into + Copy +{ + let t_start = param_range.0.into(); + let t_end = param_range.1.into(); + let num = ((t_end - t_start) / step).round() as usize; + + match method { + RK4 => { + let g = |t: f64, xs: Vec| f(dual(t, 0.), merge_dual(xs.clone(), vec![0f64;xs.len()])).values(); + let result = rk4( + t_start, + init_value.into_iter().map(|p| p.into()).collect::>(), + g, + step, + num, + ); + result + }, + BDF1(rtol) => { + let result = bdf1(t_start, init_value, f, step, rtol, num); + result + }, + GL4(rtol) => { + let result = gl4(f, t_start, init_value, step, rtol, num); + result + } + } +} + +pub fn solve_with_condition(f: F, init_value: Vec, param_range: (T, T), step: f64, method: ODEMethod, cond: G) -> Matrix +where F: Fn(Dual, Vec) -> Vec + Copy, + T: Into + Copy, + G: Fn(Vec) -> bool + Copy, +{ + let t_start = param_range.0.into(); + let t_end = param_range.1.into(); + let num = ((t_end - t_start) / step).round() as usize; + + match method { + RK4 => { + let g = |t: f64, xs: Vec| f(dual(t, 0.), merge_dual(xs.clone(), vec![0f64;xs.len()])).values(); + let mut xs = init_value.clone(); + let mut t = t_start; + let mut result = zeros(num+1, xs.len() + 1); + result.subs_row(0, cat(t, xs.clone())); + let mut key = 0usize; + for i in 1 .. num + 1 { + if !cond(xs.clone()) { + key = i - 1; + break; + } else { + xs = one_step_rk(t, xs.clone(), g, step); + t += step; + result.subs_row(i, cat(t, xs.clone())); + } + } + result.take(key, Row) + }, + BDF1(rtol) => { + let mut t = t_start; + let mut xs = init_value.clone(); + let mut records = zeros(num + 1, xs.len() + 1); + let mut key = 0usize; + for i in 0 .. (num+1) { + if !cond(xs.clone()) { + key =i; + break; + } + records.subs_row(i, cat(t, xs.clone())); + t += step; + xs = one_step_bdf1(t, xs.clone(), f, step, rtol); + } + records.take(key, Row) + }, + GL4(rtol) => { + let mut t = t_start; + let mut y_curr = init_value.clone(); + let mut records = zeros(num + 1, y_curr.len() + 1); + records.subs_row(0, cat(t, y_curr.clone())); + let mut key = 0usize; + + for i in 0 .. num { + if !cond(y_curr.clone()) { + key = i; + break; + } + let (k1, k2) = k_newton(f, t, y_curr.clone(), step, rtol); + y_curr = y_curr.add(&k1.fmap(|x| 0.5 * x * step).add(&k2.fmap(|x| 0.5 * x * step))); + t += step; + records.subs_row(i+1, cat(t, y_curr.clone())) + } + + records.take(key, Row) + } + } +} \ No newline at end of file diff --git a/src/numerical/mod.rs b/src/numerical/mod.rs index 20de60cc..3a26b42c 100644 --- a/src/numerical/mod.rs +++ b/src/numerical/mod.rs @@ -10,4 +10,4 @@ pub mod ode; pub mod optimize; pub mod root; pub mod spline; -pub mod utils; +pub mod utils; \ No newline at end of file diff --git a/src/numerical/ode.rs b/src/numerical/ode.rs index 727bd911..bb5b0505 100644 --- a/src/numerical/ode.rs +++ b/src/numerical/ode.rs @@ -1,1182 +1,481 @@ -//! Solver for ordinary differential equations -//! -//! ## Introduce `ODE` Trait & Structure -//! -//! ### `ODE` Trait -//! -//! * `ODE` structures are divided by two kinds -//! * `ExplicitODE` -//! * `ImplicitODE` -//! * `ODE` trait is given as -//! -//! ```rust -//! extern crate peroxide; -//! use peroxide::fuga::{Real, State, BoundaryCondition, Environment}; -//! -//! pub trait ODE { -//! type Records; -//! type Vector; -//! type Param; -//! type ODEMethod; -//! -//! fn mut_update(&mut self); -//! fn integrate(&mut self) -> Self::Records; -//! fn set_initial_condition(&mut self, init: State) -> &mut Self; -//! fn set_boundary_condition( -//! &mut self, -//! bound1: (State, BoundaryCondition), -//! bound2: (State, BoundaryCondition), -//! ) -> &mut Self; -//! fn set_step_size(&mut self, dt: f64) -> &mut Self; -//! fn set_method(&mut self, method: Self::ODEMethod) -> &mut Self; -//! fn set_stop_condition(&mut self, f: fn(&Self) -> bool) -> &mut Self; -//! fn has_stopped(&self) -> bool; -//! fn set_times(&mut self, n: usize) -> &mut Self; -//! fn check_enough(&self) -> bool; -//! fn set_env(&mut self, env: E) -> &mut Self; -//! } -//! ``` -//! -//! * `Records` : The type to save results of ODE. Usually `Matrix` is used. -//! * `Vector` : Vector can be below things. -//! * `Vec` : Used for `ExplicitODE` -//! * `Vec` : Used for `ImplicitODE` -//! * `Param` : Also it can be `f64` or `AD` -//! * `ODEMethod` : Method for solving ODE -//! * `ExMethod` : Explicit method -//! * `Euler` : Euler first order -//! * `RK4` : Runge Kutta 4th order -//! * `ImMethod` : Implicit method -//! * `BDF` : Backward Euler 1st order (To be fixed) -//! * `GL4` : Gauss Legendre 4th order -//! * `Environment` : External environment (`CubicSpline`, `Vec`, `Matrix` or Another external table) -//! -//! -//! ### `State` structure -//! -//! * To use `ODE` trait, you should understand `State` first. -//! -//! ```rust -//! extern crate peroxide; -//! use peroxide::fuga::Real; -//! -//! #[derive(Debug, Clone, Default)] -//! pub struct State { -//! pub param: T, -//! pub value: Vec, -//! pub deriv: Vec, -//! } -//! ``` -//! -//! * `T` can be `f64` or `AD` -//! * `f64` for `ExplicitODE` -//! * `AD` for `ImplicitODE` -//! * `param` is parameter for ODE. Usually it is represented by time. -//! * `value` is value of each node. -//! * `deriv` is value of derivative of each node. -//! -//! For example, -//! -//! $$ \frac{dy_n}{dt} = f(t, y_n) $$ -//! -//! * $t$ is `param` -//! * $y_n$ is `value` -//! * $f(t,y_n)$ is `deriv` -//! -//! Methods for `State` are as follows. -//! -//! * `to_f64(&self) -> State` -//! * `to_ad(&self) -> State` -//! * `new(T, Vec, Vec) -> Self` -//! -//! ### `Environment` -//! -//! * `Environment` needs just `Default` -//! * To use custom `Environment`, just type follows : `impl Environment for CustomType {}` -//! * If you don't want to use `Environment`, then use `NoEnv` -//! * Implemented Data Types -//! * `Vec` -//! * `Polynomial` -//! * `Matrix` -//! * `CubicSpline` -//! * `NoEnv` -//! -//! ``` -//! #[macro_use] -//! extern crate peroxide; -//! use peroxide::fuga::*; -//! -//! fn main() -> Result<(), Box> { -//! let x = seq(0, 10, 1); -//! x.print(); -//! let y = x.iter().enumerate().map(|(i, &t)| t.powi(5-i as i32)).collect::>(); -//! -//! let c = cubic_hermite_spline(&x, &y, Quadratic)?; -//! -//! let init_state = State::::new(0f64, c!(1), c!(0)); -//! -//! let mut ode_solver = ExplicitODE::new(test_fn); -//! -//! ode_solver -//! .set_method(ExMethod::RK4) -//! .set_initial_condition(init_state) -//! .set_step_size(0.01) -//! .set_times(1000) -//! .set_env(c); -//! -//! let result = ode_solver.integrate(); -//! result.print(); -//! -//! Ok(()) -//! } -//! -//! fn test_fn(st: &mut State, env: &CubicHermiteSpline) { -//! let x = st.param; -//! let dy = &mut st.deriv; -//! dy[0] = env.eval(x); -//! } -//! ``` -//! -//! ### `ExplicitODE` struct -//! -//! `ExplicitODE` is given as follow : -//! -//! ```rust -//! extern crate peroxide; -//! use std::collections::HashMap; -//! use peroxide::fuga::{State, ExMethod, BoundaryCondition, ODEOptions, Environment}; -//! -//! #[derive(Clone)] -//! pub struct ExplicitODE { -//! state: State, -//! func: fn(&mut State, &E), -//! step_size: f64, -//! method: ExMethod, -//! init_cond: State, -//! bound_cond1: (State, BoundaryCondition), -//! bound_cond2: (State, BoundaryCondition), -//! stop_cond: fn(&Self) -> bool, -//! has_stopped: bool, -//! times: usize, -//! to_use: HashMap, -//! env: E, -//! } -//! ``` -//! -//! * `state` : Current param, value, derivative -//! * `func` : Function to update `state` -//! * `init_cond` : Initial condition -//! * `bound_cond1` : If boundary problem, then first boundary condition -//! * `bound_cond2` : second boundary condition -//! * `stop_cond` : Stop condition (stop before `times`) -//! * `has_stopped`: Has the stop condition been reached -//! * `times` : How many times do you want to update? -//! * `to_use` : Just check whether information is enough -//! * `env` : Environment -//! -//! # `ImplicitODE` struct -//! -//! `ImplicitODE` is struct to solve stiff ODE with implicit methods. -//! -//! ```no_run -//! extern crate peroxide; -//! use std::collections::HashMap; -//! use peroxide::fuga::{State, ImMethod, BoundaryCondition, ODEOptions, Environment, AD}; -//! -//! #[derive(Clone)] -//! pub struct ImplicitODE { -//! state: State, -//! func: fn(&mut State, &E), -//! step_size: f64, -//! method: ImMethod, -//! init_cond: State, -//! bound_cond1: (State, BoundaryCondition), -//! bound_cond2: (State, BoundaryCondition), -//! stop_cond: fn(&Self) -> bool, -//! has_stopped: bool, -//! times: usize, -//! to_use: HashMap, -//! env: E, -//! } -//! ``` -//! -//! ## Example -//! -//! ### Lorenz Butterfly -//! -//! ```rust -//! extern crate peroxide; -//! use peroxide::fuga::*; -//! -//! fn main() { -//! // ========================================= -//! // Declare ODE (Euler) -//! // ========================================= -//! let mut ex_test = ExplicitODE::new(f); -//! -//! let init_state: State = State::new( -//! 0.0, -//! vec![10.0, 1.0, 1.0], -//! vec![0.0, 0.0, 0.0], -//! ); -//! -//! ex_test -//! .set_initial_condition(init_state) -//! .set_method(ExMethod::Euler) -//! .set_step_size(0.01f64) -//! .set_times(10000); -//! -//! // ========================================= -//! // Declare ODE (RK4) -//! // ========================================= -//! let mut ex_test2 = ex_test.clone(); -//! ex_test2.set_method(ExMethod::RK4); -//! -//! // ========================================= -//! // Declare ODE (GL4) -//! // ========================================= -//! let mut im_test = ImplicitODE::new(g); -//! -//! let init_state: State = State::new( -//! AD0(0.0), -//! vec![AD0(10f64), AD0(1f64), AD0(1f64)], -//! vec![AD0(0.0), AD0(0.0), AD0(0.0)], -//! ); -//! -//! im_test -//! .set_initial_condition(init_state) -//! .set_method(ImMethod::GL4) -//! .set_step_size(0.01f64) -//! .set_times(10000); -//! -//! // ========================================= -//! // Save results -//! // ========================================= -//! let results = ex_test.integrate(); -//! let results2 = ex_test2.integrate(); -//! let results3 = im_test.integrate(); -//! -//! // Extract data -//! let mut df = DataFrame::new(vec![]); -//! df.push("x_euler", Series::new(results.col(1))); -//! df.push("z_euler", Series::new(results.col(3))); -//! df.push("x_rk4", Series::new(results2.col(1))); -//! df.push("z_rk4", Series::new(results2.col(3))); -//! df.push("x_gl4", Series::new(results3.col(1))); -//! df.push("z_gl4", Series::new(results3.col(3))); -//! -//! # #[cfg(feature="nc")] -//! # { -//! // Write netcdf file (`nc` feature required) -//! df.write_nc("example_data/lorenz.nc") -//! .expect("Can't write lorenz.nc"); -//! # } -//! } -//! -//! fn f(st: &mut State, _: &NoEnv) { -//! let x = &st.value; -//! let dx = &mut st.deriv; -//! dx[0] = 10f64 * (x[1] - x[0]); -//! dx[1] = 28f64 * x[0] - x[1] - x[0] * x[2]; -//! dx[2] = -8f64/3f64 * x[2] + x[0] * x[1]; -//! } -//! -//! fn g(st: &mut State, _: &NoEnv) { -//! let x = &st.value; -//! let dx = &mut st.deriv; -//! dx[0] = 10f64 * (x[1] - x[0]); -//! dx[1] = 28f64 * x[0] - x[1] - x[0] * x[2]; -//! dx[2] = -8f64/3f64 * x[2] + x[0] * x[1]; -//! } -//! ``` -//! -//! ### Simple 1D Runge-Kutta -//! -//! $$\begin{gathered} \frac{dy}{dx} = \frac{5x^2 - y}{e^{x+y}} \\\ y(0) = 1 \end{gathered}$$ -//! -//! ```rust -//! #[macro_use] -//! extern crate peroxide; -//! use peroxide::fuga::*; -//! -//! fn main() { -//! let init_state = State::::new(0f64, c!(1), c!(0)); -//! -//! let mut ode_solver = ExplicitODE::new(test_fn); -//! -//! ode_solver -//! .set_method(ExMethod::RK4) -//! .set_initial_condition(init_state) -//! .set_step_size(0.01) -//! .set_times(1000); -//! -//! let result = ode_solver.integrate(); -//! -//! // Plot or Extract.. -//! } -//! -//! fn test_fn(st: &mut State, _: &NoEnv) { -//! let x = st.param; -//! let y = &st.value; -//! let dy = &mut st.deriv; -//! dy[0] = (5f64 * x.powi(2) - y[0]) / (x + y[0]).exp(); -//! } -//! ``` -//! -//! ### With stop condition -//! -//! ```rust -//! #[macro_use] -//! extern crate peroxide; -//! use peroxide::fuga::*; -//! -//! fn main() { -//! let init_state = State::::new(0f64, c!(1), c!(0)); -//! -//! let mut ode_solver = ExplicitODE::new(test_fn); -//! -//! ode_solver -//! .set_method(ExMethod::RK4) -//! .set_initial_condition(init_state) -//! .set_step_size(0.01) -//! .set_stop_condition(stop) // Add stop condition -//! .set_times(1000); -//! -//! let result = ode_solver.integrate(); -//! if ode_solver.has_stopped() { -//! println!("It reached to stop condition"); -//! } else { -//! println!("It didn't reach to stop condition"); -//! } -//! -//! // Plot or Extract.. -//! } -//! -//! fn test_fn(st: &mut State, _: &NoEnv) { -//! let x = st.param; -//! let y = &st.value; -//! let dy = &mut st.deriv; -//! dy[0] = (5f64 * x.powi(2) - y[0]) / (x + y[0]).exp(); -//! } -//! -//! fn stop(st: &ExplicitODE) -> bool { -//! let y = &st.get_state().value[0]; -//! (*y - 2.4).abs() < 0.01 -//! } -//! ``` - -use self::BoundaryCondition::Dirichlet; -use self::ExMethod::{Euler, RK4}; -use self::ImMethod::{BDF1, GL4}; -use self::ODEOptions::{BoundCond, InitCond, Method, StepSize, StopCond, Times}; -use crate::numerical::{spline::CubicSpline, utils::jacobian}; -use crate::structure::{ - ad::{ADVec, AD, AD::*}, - matrix::{LinearAlgebra, Matrix}, - polynomial::Polynomial, -}; -use crate::traits::{ - fp::{FPMatrix, FPVector}, - math::{Norm, Normed, Vector}, - mutable::MutFP, - num::Real, -}; -use crate::util::non_macro::{cat, concat, eye, zeros}; -use std::collections::HashMap; -use crate::fuga::CubicHermiteSpline; -//#[cfg(feature = "O3")] -//use {blas_daxpy, blas_daxpy_return}; - -/// Explicit ODE Methods -/// -/// * Euler : Euler 1st Order -/// * RK4 : Runge-Kutta 4th Order -#[derive(Debug, Copy, Clone, Hash, PartialOrd, PartialEq, Eq)] -pub enum ExMethod { - Euler, - RK4, +use thiserror::Error; +use ODEError::*; + +use crate::{util::non_macro::eye, traits::math::LinearOp, traits::fp::FPVector}; + +pub trait ODEProblem { + fn initial_conditions(&self) -> Vec; + fn rhs(&self, t: f64, y: &[f64], dy: &mut [f64]) -> Result<(), ODEError>; } -#[derive(Debug, Copy, Clone, Hash, PartialOrd, PartialEq, Eq)] -pub enum ImMethod { - BDF1, - GL4, + +pub trait ODEIntegrator { + fn step(&self, problem: &P, t: f64, y: &mut [f64], dt: f64) -> Result; } -/// Kinds of Boundary Conditions -/// -/// * Dirichlet -/// * Neumann -#[derive(Debug, Copy, Clone, Hash, PartialOrd, PartialEq, Eq)] -pub enum BoundaryCondition { - Dirichlet, - Neumann, +#[derive(Debug, Clone, Copy, Error)] +pub enum ODEError { + #[error("constraint violation")] + ConstraintViolation, + #[error("reached maximum number of iterations per step")] + ReachedMaxStepIter, } -/// Options for ODE -/// -/// * `InitCond` : Initial condition -/// * `BoundCond` : Boundary condition -/// * `Method` : methods of `ExMethod` or `ImMethod` -/// * `StopCond` : Stop condition -/// * `StepSize` : Step size -/// * `Times` : A number of times to integrate with specific step size -#[derive(Debug, Clone, Copy, Hash, PartialOrd, PartialEq, Eq)] -pub enum ODEOptions { - InitCond, - BoundCond, - Method, - StopCond, - StepSize, - Times, +pub trait ODESolver { + fn solve(&self, problem: &P, t_span: (f64, f64), dt: f64) -> Result<(Vec, Vec>), ODEError>; } -pub trait Environment: Default {} - -/// State for ODE -/// -/// * `param` : Parameter of ODE (ex) time) -/// * `value` : Current value of ODE -/// * `deriv` : Current differential of values -#[derive(Debug, Clone, Default)] -pub struct State { - pub param: T, - pub value: Vec, - pub deriv: Vec, +pub struct BasicODESolver { + integrator: I, } -impl State { - pub fn to_f64(&self) -> State { - State { - param: self.param.to_f64(), - value: self - .value - .clone() - .into_iter() - .map(|x| x.to_f64()) - .collect::>(), - deriv: self - .deriv - .clone() - .into_iter() - .map(|x| x.to_f64()) - .collect::>(), - } +impl BasicODESolver { + pub fn new(integrator: I) -> Self { + Self { integrator } } +} - pub fn to_ad(&self) -> State { - State { - param: self.param.to_ad(), - value: self - .value - .clone() - .into_iter() - .map(|x| x.to_ad()) - .collect::>(), - deriv: self - .deriv - .clone() - .into_iter() - .map(|x| x.to_ad()) - .collect::>(), +impl ODESolver for BasicODESolver { + fn solve(&self, problem: &P, t_span: (f64, f64), dt: f64) -> Result<(Vec, Vec>), ODEError> { + let mut t = t_span.0; + let mut y = problem.initial_conditions(); + let mut t_vec = vec![t]; + let mut y_vec = vec![y.clone()]; + + while t < t_span.1 { + let dt_step = self.integrator.step(problem, t, &mut y, dt)?; + t += dt_step; + t_vec.push(t); + y_vec.push(y.clone()); } + + Ok((t_vec, y_vec)) } +} - pub fn new(param: T, state: Vec, deriv: Vec) -> Self { - State { - param, - value: state, - deriv, - } +// ┌─────────────────────────────────────────────────────────┐ +// Runge-Kutta +// └─────────────────────────────────────────────────────────┘ +/// Runge-Kutta 4th order +#[derive(Debug, Clone, Copy, Default)] +#[cfg_attr(feature = "serde", derive(serde::Serialize, serde::Deserialize))] +pub struct RK4; + +impl ODEIntegrator for RK4 { + fn step(&self, problem: &P, t: f64, y: &mut [f64], dt: f64) -> Result { + let n = y.len(); + let mut k1 = vec![0.0; n]; + let mut k2 = vec![0.0; n]; + let mut k3 = vec![0.0; n]; + let mut k4 = vec![0.0; n]; + + problem.rhs(t, y, &mut k1)?; + k1.iter_mut().for_each(|k| *k *= dt); + + let mut y_temp = y.to_vec(); + y_temp.iter_mut().zip(&k1).for_each(|(y, k)| *y += 0.5 * k); + problem.rhs(t + 0.5 * dt, &y_temp, &mut k2)?; + k2.iter_mut().for_each(|k| *k *= dt); + + y_temp.iter_mut().zip(&k2).for_each(|(y, k)| *y = y.to_owned() + 0.5 * k); + problem.rhs(t + 0.5 * dt, &y_temp, &mut k3)?; + k3.iter_mut().for_each(|k| *k *= dt); + + y_temp.iter_mut().zip(&k3).for_each(|(y, k)| *y = y.to_owned() + k); + problem.rhs(t + dt, &y_temp, &mut k4)?; + k4.iter_mut().for_each(|k| *k *= dt); + + y.iter_mut().zip(&k1).zip(&k2).zip(&k3).zip(&k4) + .for_each(|((((y, k1), k2), k3), k4)| { + *y += (k1 + 2.0 * k2 + 2.0 * k3 + k4) / 6.0; + }); + + Ok(dt) } } -/// ODE solver -/// -/// * `Records` : Type of container to contain results -/// * `Param` : Type of parameter -/// * `ODEMethod` : Explicit or Implicit -pub trait ODE { - type Records; - type Param; - type ODEMethod; - - fn mut_update(&mut self); - //fn mut_integrate(&mut self, rec: &mut Self::Records); - fn integrate(&mut self) -> Self::Records; - fn set_initial_condition(&mut self, init: State) -> &mut Self; - fn set_boundary_condition( - &mut self, - bound1: (State, BoundaryCondition), - bound2: (State, BoundaryCondition), - ) -> &mut Self; - fn set_step_size(&mut self, dt: f64) -> &mut Self; - fn set_method(&mut self, method: Self::ODEMethod) -> &mut Self; - fn set_stop_condition(&mut self, f: fn(&Self) -> bool) -> &mut Self; - fn has_stopped(&self) -> bool; - fn set_times(&mut self, n: usize) -> &mut Self; - fn check_enough(&self) -> bool; - fn set_env(&mut self, env: E) -> &mut Self; +// ┌─────────────────────────────────────────────────────────┐ +// Runge-Kutta-Fehlberg +// └─────────────────────────────────────────────────────────┘ +/// Runge-Kutta-Fehlberg 4/5th order +#[derive(Debug, Clone, Copy)] +#[cfg_attr(feature = "serde", derive(serde::Serialize, serde::Deserialize))] +pub struct RKF45 { + tol: f64, + safety_factor: f64, + min_step_size: f64, + max_step_size: f64, + max_step_iter: usize, } -#[derive(Clone)] -pub struct ExplicitODE { - state: State, - func: fn(&mut State, &E), - step_size: f64, - method: ExMethod, - init_cond: State, - bound_cond1: (State, BoundaryCondition), - bound_cond2: (State, BoundaryCondition), - stop_cond: fn(&Self) -> bool, - has_stopped: bool, - times: usize, - options: HashMap, - env: E, +impl Default for RKF45 { + fn default() -> Self { + Self { + tol: 1e-6, + safety_factor: 0.9, + min_step_size: 1e-6, + max_step_size: 1e-1, + max_step_iter: 100, + } + } } -impl ExplicitODE { - pub fn new(f: fn(&mut State, &E)) -> Self { - let mut default_to_use: HashMap = HashMap::new(); - default_to_use.insert(InitCond, false); - default_to_use.insert(StepSize, false); - default_to_use.insert(BoundCond, false); - default_to_use.insert(Method, false); - default_to_use.insert(StopCond, false); - default_to_use.insert(Times, false); - - ExplicitODE { - state: Default::default(), - func: f, - step_size: 0.0, - method: Euler, - init_cond: Default::default(), - bound_cond1: (Default::default(), Dirichlet), - bound_cond2: (Default::default(), Dirichlet), - stop_cond: |_x| false, - has_stopped: false, - times: 0, - options: default_to_use, - env: E::default(), +impl RKF45 { + pub fn new(tol: f64, safety_factor: f64, min_step_size: f64, max_step_size: f64, max_step_iter: usize) -> Self { + Self { + tol, + safety_factor, + min_step_size, + max_step_size, + max_step_iter, } } - pub fn get_state(&self) -> &State { - &self.state + pub fn set_tol(&mut self, tol: f64) { + self.tol = tol; } - pub fn get_env(&self) -> &E { - &self.env + pub fn set_safety_factor(&mut self, safety_factor: f64) { + self.safety_factor = safety_factor; } - pub fn get_step_size(&self) -> f64 { - self.step_size + pub fn set_min_step_size(&mut self, min_step_size: f64) { + self.min_step_size = min_step_size; } - pub fn get_times(&self) -> usize { - self.times + pub fn set_max_step_size(&mut self, max_step_size: f64) { + self.max_step_size = max_step_size; } - pub fn get_method(&self) -> ExMethod { - self.method + pub fn set_max_step_iter(&mut self, max_step_iter: usize) { + self.max_step_iter = max_step_iter; } - pub fn get_stop_condition(&self) -> fn(&Self) -> bool { - self.stop_cond + pub fn get_tol(&self) -> f64 { + self.tol } - pub fn get_has_stopped(&self) -> bool { - self.has_stopped + pub fn get_safety_factor(&self) -> f64 { + self.safety_factor } - pub fn get_init_cond(&self) -> &State { - &self.init_cond + pub fn get_min_step_size(&self) -> f64 { + self.min_step_size } - pub fn get_bound_cond1(&self) -> &(State, BoundaryCondition) { - &self.bound_cond1 + pub fn get_max_step_size(&self) -> f64 { + self.max_step_size } - pub fn get_bound_cond2(&self) -> &(State, BoundaryCondition) { - &self.bound_cond2 + pub fn get_max_step_iter(&self) -> usize { + self.max_step_iter } } -impl ODE for ExplicitODE { - type Records = Matrix; - type Param = f64; - type ODEMethod = ExMethod; - - fn mut_update(&mut self) { - match self.method { - Euler => { - // Set Derivative from state - (self.func)(&mut self.state, &self.env); - let dt = self.step_size; - - //match () { - // #[cfg(feature = "oxidize")] - // () => { - // blas_daxpy(dt, &self.state.deriv, &mut self.state.value); - // } - // _ => { - self.state - .value - .mut_zip_with(|x, y| x + y * dt, &self.state.deriv); - // } - //} - self.state.param += dt; +impl ODEIntegrator for RKF45 { + fn step(&self, problem: &P, t: f64, y: &mut [f64], dt: f64) -> Result { + let mut iter_count = 0usize; + let mut dt = dt; + let n = y.len(); + + loop { + let mut k1 = vec![0.0; n]; + let mut k2 = vec![0.0; n]; + let mut k3 = vec![0.0; n]; + let mut k4 = vec![0.0; n]; + let mut k5 = vec![0.0; n]; + let mut k6 = vec![0.0; n]; + + problem.rhs(t, y, &mut k1)?; + let mut y_temp = y.to_vec(); + for i in 0..n { + y_temp[i] = y[i] + dt * (1.0 / 4.0) * k1[i]; } - RK4 => { - let h = self.step_size; - let h2 = h / 2f64; - - // Set Derivative from state - let yn = self.state.value.clone(); - (self.func)(&mut self.state, &self.env); - - let k1 = self.state.deriv.clone(); - let k1_add = k1.mul_scalar(h2); - self.state.param += h2; - self.state.value.mut_zip_with(|x, y| x + y, &k1_add); - (self.func)(&mut self.state, &self.env); - - let k2 = self.state.deriv.clone(); - let k2_add = k2.zip_with(|x, y| h2 * x - y, &k1_add); - self.state.value.mut_zip_with(|x, y| x + y, &k2_add); - (self.func)(&mut self.state, &self.env); - - let k3 = self.state.deriv.clone(); - let k3_add = k3.zip_with(|x, y| h * x - y, &k2_add); - self.state.param += h2; - self.state.value.mut_zip_with(|x, y| x + y, &k3_add); - (self.func)(&mut self.state, &self.env); - - let k4 = self.state.deriv.clone(); - - for i in 0..k1.len() { - self.state.value[i] = - yn[i] + (k1[i] + 2f64 * k2[i] + 2f64 * k3[i] + k4[i]) * h / 6f64; - } - } - } - } - - fn integrate(&mut self) -> Self::Records { - assert!(self.check_enough(), "Not enough fields!"); - let mut result = zeros(self.times + 1, self.state.value.len() + 1); - - result.subs_row(0, &cat(self.state.param, &self.state.value)); - - match self.options.get(&StopCond) { - Some(stop) if *stop => { - let mut key = 1usize; - for i in 1..self.times + 1 { - self.mut_update(); - result.subs_row(i, &cat(self.state.param, &self.state.value)); - key += 1; - if (self.stop_cond)(&self) { - self.has_stopped = true; - break; - } - } - return result.take_row(key); - } - _ => { - for i in 1..self.times + 1 { - self.mut_update(); - result.subs_row(i, &cat(self.state.param, &self.state.value)); - } - return result; + problem.rhs(t + dt * (1.0 / 4.0), &y_temp, &mut k2)?; + for i in 0..n { + y_temp[i] = y[i] + dt * (3.0 / 32.0 * k1[i] + 9.0 / 32.0 * k2[i]); } - } - } - fn set_initial_condition(&mut self, init: State) -> &mut Self { - if let Some(x) = self.options.get_mut(&InitCond) { - *x = true - } - self.init_cond = init.to_f64(); - self.state = init.to_f64(); - self - } - - fn set_boundary_condition( - &mut self, - bound1: (State, BoundaryCondition), - bound2: (State, BoundaryCondition), - ) -> &mut Self { - if let Some(x) = self.options.get_mut(&BoundCond) { - *x = true - } - self.bound_cond1 = (bound1.0.to_f64(), bound1.1); - self.bound_cond2 = (bound2.0.to_f64(), bound2.1); - self - } - - fn set_step_size(&mut self, dt: f64) -> &mut Self { - if let Some(x) = self.options.get_mut(&StepSize) { - *x = true - } - self.step_size = dt; - self - } - - fn set_method(&mut self, method: Self::ODEMethod) -> &mut Self { - if let Some(x) = self.options.get_mut(&Method) { - *x = true - } - self.method = method; - self - } + problem.rhs(t + dt * (3.0 / 8.0), &y_temp, &mut k3)?; + for i in 0..n { + y_temp[i] = y[i] + dt * (1932.0 / 2197.0 * k1[i] - 7200.0 / 2197.0 * k2[i] + 7296.0 / 2197.0 * k3[i]); + } - fn set_stop_condition(&mut self, f: fn(&Self) -> bool) -> &mut Self { - if let Some(x) = self.options.get_mut(&StopCond) { - *x = true - } - self.stop_cond = f; - self - } + problem.rhs(t + dt * (12.0 / 13.0), &y_temp, &mut k4)?; + for i in 0..n { + y_temp[i] = y[i] + dt * (439.0 / 216.0 * k1[i] - 8.0 * k2[i] + 3680.0 / 513.0 * k3[i] - 845.0 / 4104.0 * k4[i]); + } - fn has_stopped(&self) -> bool { - self.has_stopped - } + problem.rhs(t + dt, &y_temp, &mut k5)?; + for i in 0..n { + y_temp[i] = y[i] + dt * (-8.0 / 27.0 * k1[i] + 2.0 * k2[i] - 3544.0 / 2565.0 * k3[i] + 1859.0 / 4104.0 * k4[i] - 11.0 / 40.0 * k5[i]); + } - fn set_times(&mut self, n: usize) -> &mut Self { - if let Some(x) = self.options.get_mut(&Times) { - *x = true - } - self.times = n; - self - } + problem.rhs(t + dt * 0.5, &y_temp, &mut k6)?; - fn check_enough(&self) -> bool { - // Method - match self.options.get(&Method) { - Some(x) => { - if !*x { - return false; - } - } - None => { - return false; + let mut error = 0.0; + for i in 0..n { + let y_err = dt * (1.0 / 360.0 * k1[i] - 128.0 / 4275.0 * k3[i] - 2197.0 / 75240.0 * k4[i] + 1.0 / 50.0 * k5[i] + 2.0 / 55.0 * k6[i]); + error += y_err * y_err; } - } - // Step size - match self.options.get(&StepSize) { - Some(x) => { - if !*x { - return false; - } - } - None => { - return false; - } - } + error = error.sqrt() / (n as f64).sqrt(); - // Initial or Boundary - match self.options.get(&InitCond) { - None => { - return false; - } - Some(x) => { - if !*x { - match self.options.get(&BoundCond) { - None => { - return false; - } - Some(_) => (), - } - } - } - } + let new_dt = self.safety_factor * dt * (self.tol * dt / error).powf(0.25); + let new_dt = new_dt.max(self.min_step_size).min(self.max_step_size); - // Set Time? - match self.options.get(&Times) { - None => { - return false; - } - Some(x) => { - if !*x { - return false; + if error <= self.tol { + for i in 0..n { + y[i] += dt * (16.0 / 135.0 * k1[i] + 6656.0 / 12825.0 * k3[i] + 28561.0 / 56430.0 * k4[i] - 9.0 / 50.0 * k5[i] + 2.0 / 55.0 * k6[i]); } + return Ok(new_dt); + } else { + iter_count += 1; + if iter_count >= self.max_step_iter { + return Err(ReachedMaxStepIter); + } + dt = new_dt; } } - true } +} - fn set_env(&mut self, env: E) -> &mut Self { - self.env = env; - self - } +// ┌─────────────────────────────────────────────────────────┐ +// Gauss-Legendre 4th order +// └─────────────────────────────────────────────────────────┘ +#[derive(Debug, Clone, Copy)] +#[cfg_attr(feature = "serde", derive(serde::Serialize, serde::Deserialize))] +pub enum ImplicitSolver { + FixedPoint, + Broyden, + TrustRegion(f64, f64), } -#[derive(Clone)] -pub struct ImplicitODE { - state: State, - func: fn(&mut State, &E), - step_size: f64, - rtol: f64, - method: ImMethod, - init_cond: State, - bound_cond1: (State, BoundaryCondition), - bound_cond2: (State, BoundaryCondition), - stop_cond: fn(&Self) -> bool, - has_stopped: bool, - times: usize, - options: HashMap, - env: E, +#[derive(Debug, Clone, Copy)] +#[cfg_attr(feature = "serde", derive(serde::Serialize, serde::Deserialize))] +pub struct GL4 { + solver: ImplicitSolver, + max_iter: usize, + tol: f64, } -impl ImplicitODE { - pub fn new(f: fn(&mut State, &E)) -> Self { - let mut default_to_use: HashMap = HashMap::new(); - default_to_use.insert(InitCond, false); - default_to_use.insert(StepSize, false); - default_to_use.insert(BoundCond, false); - default_to_use.insert(Method, false); - default_to_use.insert(StopCond, false); - default_to_use.insert(Times, false); - - ImplicitODE { - state: State::new(AD0(0f64), vec![], vec![]), - func: f, - step_size: 0.0, - rtol: 1e-6, - method: GL4, - init_cond: Default::default(), - bound_cond1: (Default::default(), Dirichlet), - bound_cond2: (Default::default(), Dirichlet), - stop_cond: |_x| false, - has_stopped: false, - times: 0, - options: default_to_use, - env: E::default(), +impl GL4 { + pub fn new(solver: ImplicitSolver, max_iter: usize, tol: f64) -> Self { + GL4 { + solver, + max_iter, + tol, } } - - pub fn get_state(&self) -> &State { - &self.state - } - - pub fn set_rtol(&mut self, rtol: f64) -> &mut Self { - self.rtol = rtol; - self - } - - pub fn get_env(&self) -> &E { - &self.env - } - - pub fn get_step_size(&self) -> f64 { - self.step_size - } - - pub fn get_times(&self) -> usize { - self.times - } - - pub fn get_method(&self) -> ImMethod { - self.method - } - - pub fn get_stop_condition(&self) -> fn(&Self) -> bool { - self.stop_cond - } - - pub fn get_has_stopped(&self) -> bool { - self.has_stopped - } - - pub fn get_init_cond(&self) -> &State { - &self.init_cond - } - - pub fn get_bound_cond1(&self) -> &(State, BoundaryCondition) { - &self.bound_cond1 - } - - pub fn get_bound_cond2(&self) -> &(State, BoundaryCondition) { - &self.bound_cond2 - } - - pub fn get_rtol(&self) -> f64 { - self.rtol - } } -/// Value of 3f64.sqrt() -const SQRT3: f64 = 1.7320508075688772; - -/// Butcher tableau for Gauss_legendre 4th order -const GL4_TAB: [[f64; 3]; 2] = [ - [0.5 - SQRT3 / 6f64, 0.25, 0.25 - SQRT3 / 6f64], - [0.5 + SQRT3 / 6f64, 0.25 + SQRT3 / 6f64, 0.25], -]; - -#[allow(non_snake_case)] -impl ODE for ImplicitODE { - type Records = Matrix; - type Param = AD; - type ODEMethod = ImMethod; - fn mut_update(&mut self) { - match self.method { - BDF1 => unimplemented!(), - GL4 => { - let f = |t: AD, y: Vec| { - let mut st = State::new(t, y.clone(), y); - (self.func)(&mut st, &self.env); - st.deriv - }; - - let h = self.step_size; - let t = self.state.param; - let t1: AD = t + GL4_TAB[0][0] * h; - let t2: AD = t + GL4_TAB[1][0] * h; - let yn = &self.state.value; - let n = yn.len(); - - // 0. Initial Guess - let k1_init: Vec = f(t, yn.clone()).to_f64_vec(); - let k2_init: Vec = f(t, yn.clone()).to_f64_vec(); - let mut k_curr: Vec = concat(&k1_init, &k2_init); - let mut err = 1f64; - - // 1. Combine two functions to one function - let g = |k: &Vec| -> Vec { - let k1 = k.take(n); - let k2 = k.skip(n); - concat( - &f( - t1, - yn.add_vec( - &k1.mul_scalar(AD::from(GL4_TAB[0][1] * h)) - .add_vec(&k2.mul_scalar(AD::from(GL4_TAB[0][2] * h))), - ), - ), - &f( - t2, - yn.add_vec( - &k1.mul_scalar(AD::from(GL4_TAB[1][1] * h)) - .add_vec(&k2.mul_scalar(AD::from(GL4_TAB[1][2] * h))), - ), - ), - ) - }; - - // 2. Obtain Jacobian - let I = eye(2 * n); - - let mut Dg = jacobian(Box::new(g), &k_curr); - let mut DG = &I - &Dg; - let mut DG_inv = DG.inv(); - let mut G = k_curr.sub_vec(&g(&k_curr.to_ad_vec()).to_f64_vec()); - let mut num_iter: usize = 0; - - // 3. Iteration - while err >= self.rtol && num_iter <= 10 { - let DGG = &DG_inv * &G; - let k_prev = k_curr.clone(); - k_curr.mut_zip_with(|x, y| x - y, &DGG); - Dg = jacobian(Box::new(g), &k_curr); - DG = &I - &Dg; - DG_inv = DG.inv(); - G = k_curr.sub_vec(&g(&k_curr.to_ad_vec()).to_f64_vec()); - err = k_curr.sub_vec(&k_prev).norm(Norm::L2); - num_iter += 1; +impl ODEIntegrator for GL4 { + #[inline] + fn step(&self, problem: &P, t: f64, y: &mut [f64], dt: f64) -> Result { + let n = y.len(); + let sqrt3 = 3.0_f64.sqrt(); + let c = 0.5 * (3.0 - sqrt3) / 6.0; + let d = 0.5 * (3.0 + sqrt3) / 6.0; + + let mut k1 = vec![0.0; n]; + let mut k2 = vec![0.0; n]; + + let mut y1 = vec![0.0; n]; + let mut y2 = vec![0.0; n]; + + match self.solver { + ImplicitSolver::FixedPoint => { + // Fixed-point iteration + for _ in 0..self.max_iter { + problem.rhs(t + c * dt, &y1, &mut k1)?; + problem.rhs(t + d * dt, &y2, &mut k2)?; + + let mut max_diff = 0f64; + for i in 0..n { + let y1_new = y[i] + dt * (c * k1[i] + d * k2[i] - sqrt3 * (k2[i] - k1[i]) / 2.0); + let y2_new = y[i] + dt * (c * k1[i] + d * k2[i] + sqrt3 * (k2[i] - k1[i]) / 2.0); + max_diff = max_diff.max((y1_new - y1[i]).abs()).max((y2_new - y2[i]).abs()); + y1[i] = y1_new; + y2[i] = y2_new; + } + + if max_diff < self.tol { + break; + } } + } + ImplicitSolver::Broyden => { + // Broyden's method + let mut b = eye(n); + + for _ in 0..self.max_iter { + problem.rhs(t + c * dt, &y1, &mut k1)?; + problem.rhs(t + d * dt, &y2, &mut k2)?; + + let mut f1 = vec![0.0; n]; + let mut f2 = vec![0.0; n]; + for i in 0..n { + f1[i] = y1[i] - y[i] - dt * (c * k1[i] + d * k2[i] - sqrt3 * (k2[i] - k1[i]) / 2.0); + f2[i] = y2[i] - y[i] - dt * (c * k1[i] + d * k2[i] + sqrt3 * (k2[i] - k1[i]) / 2.0); + } - // 4. Find k1, k2 - let (k1, k2) = (k_curr.take(n), k_curr.skip(n)); + let neg_dy1 = b.apply(&f1); + let neg_dy2 = b.apply(&f2); - // Set Derivative from state - (self.func)(&mut self.state, &self.env); + for i in 0..n { + y1[i] -= neg_dy1[i]; + y2[i] -= neg_dy2[i]; + } - // 5. Merge k1, k2 - let mut y_curr = self.state.value.to_f64_vec(); - y_curr = y_curr.add_vec(&k1.mul_scalar(0.5 * h).add_vec(&k2.mul_scalar(0.5 * h))); - self.state.value = y_curr.to_ad_vec(); - self.state.param = self.state.param + h; - } - } - } + let mut max_diff = 0f64; + for i in 0..n { + max_diff = max_diff.max(neg_dy1[i].abs()).max(neg_dy2[i].abs()); + } - fn integrate(&mut self) -> Self::Records { - assert!(self.check_enough(), "Not enough fields!"); - - let mut result = zeros(self.times + 1, self.state.value.len() + 1); - - result.subs_row( - 0, - &cat(self.state.param.to_f64(), &self.state.value.to_f64_vec()), - ); - - match self.options.get(&StopCond) { - Some(stop) if *stop => { - let mut key = 1usize; - for i in 1..self.times + 1 { - self.mut_update(); - result.subs_row( - i, - &cat(self.state.param.to_f64(), &self.state.value.to_f64_vec()), - ); - key += 1; - if (self.stop_cond)(&self) { - self.has_stopped = true; + if max_diff < self.tol { break; } - } - return result.take_row(key); - } - _ => { - for i in 1..self.times + 1 { - self.mut_update(); - result.subs_row( - i, - &cat(self.state.param.to_f64(), &self.state.value.to_f64_vec()), - ); - } - return result; - } - } - } - fn set_initial_condition(&mut self, init: State) -> &mut Self { - if let Some(x) = self.options.get_mut(&InitCond) { - *x = true - } - self.init_cond = init.to_f64(); - self.state = init.to_ad(); - self - } + let mut df1 = vec![0.0; n]; + let mut df2 = vec![0.0; n]; + for i in 0..n { + df1[i] = f1[i] + dt * (c * neg_dy1[i] + d * neg_dy2[i] - sqrt3 * (neg_dy2[i] - neg_dy1[i]) / 2.0); + df2[i] = f2[i] + dt * (c * neg_dy1[i] + d * neg_dy2[i] + sqrt3 * (neg_dy2[i] - neg_dy1[i]) / 2.0); + } - fn set_boundary_condition( - &mut self, - bound1: (State, BoundaryCondition), - bound2: (State, BoundaryCondition), - ) -> &mut Self { - if let Some(x) = self.options.get_mut(&BoundCond) { - *x = true - } - self.bound_cond1 = (bound1.0.to_f64(), bound1.1); - self.bound_cond2 = (bound2.0.to_f64(), bound2.1); - self - } + for i in 0..n { + for j in 0..n { + b[(i, j)] -= (df1[i] * neg_dy1[j] + df2[i] * neg_dy2[j]) / (neg_dy1[j].powi(2) + neg_dy2[j].powi(2)); + } + } + } + } + ImplicitSolver::TrustRegion(eta, rho) => { + // Trust-region method + let mut r = self.tol; + let mut d1 = vec![0.0; n]; + let mut d2 = vec![0.0; n]; + let mut g1 = vec![0.0; n]; + let mut g2 = vec![0.0; n]; + let mut b1 = eye(n); + let mut b2 = eye(n); + + for _ in 0..self.max_iter { + problem.rhs(t + c * dt, &y1, &mut k1)?; + problem.rhs(t + d * dt, &y2, &mut k2)?; + + let mut f1 = vec![0.0; n]; + let mut f2 = vec![0.0; n]; + for i in 0..n { + f1[i] = y1[i] - y[i] - dt * (c * k1[i] + d * k2[i] - sqrt3 * (k2[i] - k1[i]) / 2.0); + f2[i] = y2[i] - y[i] - dt * (c * k1[i] + d * k2[i] + sqrt3 * (k2[i] - k1[i]) / 2.0); + } - fn set_step_size(&mut self, dt: f64) -> &mut Self { - if let Some(x) = self.options.get_mut(&StepSize) { - *x = true - } - self.step_size = dt; - self - } + let mut norm_f1 = 0.0; + let mut norm_f2 = 0.0; + for i in 0..n { + norm_f1 += f1[i] * f1[i]; + norm_f2 += f2[i] * f2[i]; + g1[i] = f1[i]; + g2[i] = f2[i]; + } + norm_f1 = norm_f1.sqrt(); + norm_f2 = norm_f2.sqrt(); + + let mut inner_iter_count = 0; + while norm_f1 > self.tol || norm_f2 > self.tol { + let h1 = b1.apply(&g1).fmap(|x| -x); + let h2 = b2.apply(&g2).fmap(|x| -x); + + let mut norm_h1 = 0.0; + let mut norm_h2 = 0.0; + for i in 0..n { + norm_h1 += h1[i] * h1[i]; + norm_h2 += h2[i] * h2[i]; + } + norm_h1 = norm_h1.sqrt(); + norm_h2 = norm_h2.sqrt(); + + if norm_h1 <= r || norm_h2 <= r { + d1.copy_from_slice(&h1[..]); + d2.copy_from_slice(&h2[..]); + } else { + let sigma1 = (r / norm_h1).powf(2.0); + let sigma2 = (r / norm_h2).powf(2.0); + for i in 0..n { + d1[i] = sigma1 * h1[i]; + d2[i] = sigma2 * h2[i]; + } + } - fn set_method(&mut self, method: Self::ODEMethod) -> &mut Self { - if let Some(x) = self.options.get_mut(&Method) { - *x = true - } - self.method = method; - self - } + let mut y1_new = vec![0.0; n]; + let mut y2_new = vec![0.0; n]; + for i in 0..n { + y1_new[i] = y1[i] + d1[i]; + y2_new[i] = y2[i] + d2[i]; + } - fn set_stop_condition(&mut self, f: fn(&Self) -> bool) -> &mut Self { - if let Some(x) = self.options.get_mut(&StopCond) { - *x = true - } - self.stop_cond = f; - self - } + problem.rhs(t + c * dt, &y1_new, &mut k1)?; + problem.rhs(t + d * dt, &y2_new, &mut k2)?; - fn has_stopped(&self) -> bool { - self.has_stopped - } + let mut f1_new = vec![0.0; n]; + let mut f2_new = vec![0.0; n]; + for i in 0..n { + f1_new[i] = y1_new[i] - y[i] - dt * (c * k1[i] + d * k2[i] - sqrt3 * (k2[i] - k1[i]) / 2.0); + f2_new[i] = y2_new[i] - y[i] - dt * (c * k1[i] + d * k2[i] + sqrt3 * (k2[i] - k1[i]) / 2.0); + } - fn set_times(&mut self, n: usize) -> &mut Self { - if let Some(x) = self.options.get_mut(&Times) { - *x = true - } - self.times = n; - self - } + let mut norm_f1_new = 0.0; + let mut norm_f2_new = 0.0; + for i in 0..n { + norm_f1_new += f1_new[i] * f1_new[i]; + norm_f2_new += f2_new[i] * f2_new[i]; + } + norm_f1_new = norm_f1_new.sqrt(); + norm_f2_new = norm_f2_new.sqrt(); + + let rho1 = (norm_f1 * norm_f1 - norm_f1_new * norm_f1_new) / (norm_f1 * norm_f1 - (g1.iter().zip(&d1).map(|(g, d)| g * d).sum::()).abs()); + let rho2 = (norm_f2 * norm_f2 - norm_f2_new * norm_f2_new) / (norm_f2 * norm_f2 - (g2.iter().zip(&d2).map(|(g, d)| g * d).sum::()).abs()); + + if rho1 > eta && rho2 > eta { + y1.copy_from_slice(&y1_new[..]); + y2.copy_from_slice(&y2_new[..]); + f1.copy_from_slice(&f1_new[..]); + f2.copy_from_slice(&f2_new[..]); + g1.copy_from_slice(&f1_new[..]); + g2.copy_from_slice(&f2_new[..]); + norm_f1 = norm_f1_new; + norm_f2 = norm_f2_new; + r = r.max(rho * r); + } else { + r *= rho; + } - fn check_enough(&self) -> bool { - // Method - match self.options.get(&Method) { - Some(x) => { - if !*x { - return false; - } - } - None => { - return false; - } - } + if r < self.tol { + break; + } - // Step size - match self.options.get(&StepSize) { - Some(x) => { - if !*x { - return false; - } - } - None => { - return false; - } - } + for i in 0..n { + for j in 0..n { + b1[(i, j)] += (f1[i] - g1[i]) * d1[j] / (d1.iter().map(|d| d * d).sum::()); + b2[(i, j)] += (f2[i] - g2[i]) * d2[j] / (d2.iter().map(|d| d * d).sum::()); + } + } - // Initial or Boundary - match self.options.get(&InitCond) { - None => { - return false; - } - Some(x) => { - if !*x { - match self.options.get(&BoundCond) { - None => { - return false; + inner_iter_count += 1; + if inner_iter_count >= self.max_iter { + break; } - Some(_) => (), } } } } - // Set Time? - match self.options.get(&Times) { - None => { - return false; - } - Some(x) => { - if !*x { - return false; - } - } + for i in 0..n { + y[i] += dt * 0.5 * (k1[i] + k2[i]); } - true - } - fn set_env(&mut self, env: E) -> &mut Self { - self.env = env; - self + Ok(dt) } } - -// ============================================================================= -// Some Environments -// ============================================================================= -#[derive(Debug, Copy, Clone, Default)] -pub struct NoEnv {} - -impl Environment for NoEnv {} - -impl Environment for CubicSpline {} - -impl Environment for Matrix {} - -impl Environment for Vec {} - -impl Environment for Polynomial {} - -impl Environment for CubicHermiteSpline {} \ No newline at end of file From 9fc7724036e6a43afe6f84c6718d55556f198431 Mon Sep 17 00:00:00 2001 From: axect Date: Mon, 8 Apr 2024 23:01:41 +0900 Subject: [PATCH 6/9] CHGE: Fix all issues corresponding to new ode & write new examples --- example_data/gl4_plot.png | Bin 86419 -> 0 bytes example_data/gl4_test.png | Bin 0 -> 62558 bytes example_data/lorenz_gl4.png | Bin 939311 -> 389789 bytes example_data/lorenz_rk4.png | Bin 841692 -> 145694 bytes example_data/lorenz_rkf45.png | Bin 0 -> 394524 bytes example_data/ode_env.png | Bin 0 -> 51665 bytes example_data/ode_test.png | Bin 83524 -> 0 bytes example_data/plot_test.png | Bin 75938 -> 0 bytes example_data/rkf45_test.png | Bin 63160 -> 62366 bytes example_data/test_plot.png | Bin 121802 -> 124749 bytes example_data/tov_rk4.png | Bin 73927 -> 0 bytes examples/gl4.rs | 30 ---- examples/lorenz_gl4.rs | 46 +++++ examples/lorenz_rk4.rs | 45 +++++ examples/lorenz_rkf45.rs | 46 +++++ examples/ode_env.rs | 67 ++++--- examples/ode_gl4.rs | 38 ---- examples/ode_test_gl4.rs | 43 +++++ examples/ode_test_lorenz.rs | 35 ---- examples/ode_test_rk4.rs | 55 ++---- examples/ode_test_rkf45.rs | 29 +-- src/numerical/ode.rs | 320 ++++++++++++++++------------------ src/numerical/spline.rs | 2 +- src/statistics/dist.rs | 2 - src/traits/fp.rs | 1 - src/util/non_macro.rs | 2 - 26 files changed, 401 insertions(+), 360 deletions(-) delete mode 100644 example_data/gl4_plot.png create mode 100644 example_data/gl4_test.png create mode 100644 example_data/lorenz_rkf45.png create mode 100644 example_data/ode_env.png delete mode 100644 example_data/ode_test.png delete mode 100644 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z#feGAP%ayP|JKE@I`NyM(V~4_XOq)2GSL2-qDF=?&OH{--v-}jGuyt5oj~G9Q;SOP zq*VNKl zv-+v{ZNLP8f~T)u4fZn(R)~t`G8h*w83{sB1Y#Zim@Ec9)3f(e_*+8?u1&lEngi5D zmYfR?2~iY!#s6u3b91vjiA3Gy>Ea^PGo%29AqTKE#kt#eVVGVdrYtVKOSF7 A9{>OV diff --git a/examples/gl4.rs b/examples/gl4.rs deleted file mode 100644 index 87dc5933..00000000 --- a/examples/gl4.rs +++ /dev/null @@ -1,30 +0,0 @@ -extern crate peroxide; -use peroxide::fuga::*; - -pub fn main() { - let t = AD0(0f64); - let y = AD1(5f64, 1f64); - let init_state = State::::new(t, vec![y], vec![AD0(0f64)]); - - let mut ode_solver = ImplicitODE::new(f); - - ode_solver - .set_method(ImMethod::GL4) - .set_initial_condition(init_state) - .set_step_size(1e-3) - .set_times(10_000); - - let result = ode_solver.integrate(); - - let mut df = DataFrame::new(vec![]); - df.push("t", Series::new(result.col(0))); - df.push("y", Series::new(result.col(1))); - df.print(); - -} - -fn f(st: &mut State, _: &NoEnv) { - let y = st.value[0]; - let dy = &mut st.deriv; - dy[0] = -0.3 * y; -} diff --git a/examples/lorenz_gl4.rs b/examples/lorenz_gl4.rs new file mode 100644 index 00000000..e0937bf0 --- /dev/null +++ b/examples/lorenz_gl4.rs @@ -0,0 +1,46 @@ +use peroxide::fuga::*; + +fn main() -> Result<(), Box> { + let gl4 = GL4::new(ImplicitSolver::FixedPoint, 100, 1e-6); + let basic_ode_solver = BasicODESolver::new(gl4); + let (_, y_vec) = basic_ode_solver.solve( + &Lorenz, + (0f64, 100f64), + 1e-2, + )?; + let y_mat = py_matrix(y_vec); + let y0 = y_mat.col(0); + let y2 = y_mat.col(2); + + #[cfg(feature = "plot")] + { + let mut plt = Plot2D::new(); + plt + .set_domain(y0) + .insert_image(y2) + .set_xlabel(r"$y_0$") + .set_ylabel(r"$y_2$") + .set_style(PlotStyle::Nature) + .tight_layout() + .set_dpi(600) + .set_path("example_data/lorenz_gl4.png") + .savefig()?; + } + + Ok(()) +} + +struct Lorenz; + +impl ODEProblem for Lorenz { + fn initial_conditions(&self) -> Vec { + vec![10f64, 1f64, 1f64] + } + + fn rhs(&self, _t: f64, y: &[f64], dy: &mut [f64]) -> Result<(), ODEError> { + dy[0] = 10f64 * (y[1] - y[0]); + dy[1] = 28f64 * y[0] - y[1] - y[0] * y[2]; + dy[2] = -8f64 / 3f64 * y[2] + y[0] * y[1]; + Ok(()) + } +} diff --git a/examples/lorenz_rk4.rs b/examples/lorenz_rk4.rs new file mode 100644 index 00000000..ad016087 --- /dev/null +++ b/examples/lorenz_rk4.rs @@ -0,0 +1,45 @@ +use peroxide::fuga::*; + +fn main() -> Result<(), Box> { + let basic_ode_solver = BasicODESolver::new(RK4); + let (_, y_vec) = basic_ode_solver.solve( + &Lorenz, + (0f64, 100f64), + 1e-2, + )?; + let y_mat = py_matrix(y_vec); + let y0 = y_mat.col(0); + let y2 = y_mat.col(2); + + #[cfg(feature = "plot")] + { + let mut plt = Plot2D::new(); + plt + .set_domain(y0) + .insert_image(y2) + .set_xlabel(r"$y_0$") + .set_ylabel(r"$y_2$") + .set_style(PlotStyle::Nature) + .tight_layout() + .set_dpi(600) + .set_path("example_data/lorenz_rk4.png") + .savefig()?; + } + + Ok(()) +} + +struct Lorenz; + +impl ODEProblem for Lorenz { + fn initial_conditions(&self) -> Vec { + vec![10f64, 1f64, 1f64] + } + + fn rhs(&self, t: f64, y: &[f64], dy: &mut [f64]) -> Result<(), ODEError> { + dy[0] = 10f64 * (y[1] - y[0]); + dy[1] = 28f64 * y[0] - y[1] - y[0] * y[2]; + dy[2] = -8f64 / 3f64 * y[2] + y[0] * y[1]; + Ok(()) + } +} diff --git a/examples/lorenz_rkf45.rs b/examples/lorenz_rkf45.rs new file mode 100644 index 00000000..db294511 --- /dev/null +++ b/examples/lorenz_rkf45.rs @@ -0,0 +1,46 @@ +use peroxide::fuga::*; + +fn main() -> Result<(), Box> { + let rkf45 = RKF45::new(1e-4, 0.9, 1e-6, 1e-1, 100); + let basic_ode_solver = BasicODESolver::new(rkf45); + let (_, y_vec) = basic_ode_solver.solve( + &Lorenz, + (0f64, 100f64), + 1e-2, + )?; + let y_mat = py_matrix(y_vec); + let y0 = y_mat.col(0); + let y2 = y_mat.col(2); + + #[cfg(feature = "plot")] + { + let mut plt = Plot2D::new(); + plt + .set_domain(y0) + .insert_image(y2) + .set_xlabel(r"$y_0$") + .set_ylabel(r"$y_2$") + .set_style(PlotStyle::Nature) + .tight_layout() + .set_dpi(600) + .set_path("example_data/lorenz_rkf45.png") + .savefig()?; + } + + Ok(()) +} + +struct Lorenz; + +impl ODEProblem for Lorenz { + fn initial_conditions(&self) -> Vec { + vec![10f64, 1f64, 1f64] + } + + fn rhs(&self, t: f64, y: &[f64], dy: &mut [f64]) -> Result<(), ODEError> { + dy[0] = 10f64 * (y[1] - y[0]); + dy[1] = 28f64 * y[0] - y[1] - y[0] * y[2]; + dy[2] = -8f64 / 3f64 * y[2] + y[0] * y[1]; + Ok(()) + } +} diff --git a/examples/ode_env.rs b/examples/ode_env.rs index 2e820480..fa9c4af1 100644 --- a/examples/ode_env.rs +++ b/examples/ode_env.rs @@ -1,37 +1,54 @@ -#[macro_use] -extern crate peroxide; use peroxide::fuga::*; -fn main() -> Result<(), Box> { - let x = seq(0, 10, 1); - x.print(); - let y = x +fn main() -> Result<(), Box> { + let t = seq(0, 10, 1); + let y = t .iter() .enumerate() .map(|(i, &t)| t.powi(5 - i as i32)) .collect::>(); - let c = CubicSpline::from_nodes(&x, &y)?; - - let init_state = State::::new(0f64, c!(1), c!(0)); - - let mut ode_solver = ExplicitODE::new(test_fn); - - ode_solver - .set_method(ExMethod::RK4) - .set_initial_condition(init_state) - .set_step_size(0.01) - .set_times(1000) - .set_env(c); - - let result = ode_solver.integrate(); - result.print(); + let c = cubic_hermite_spline(&t, &y, Quadratic)?; + + let test_problem = Test { + cs: c, + }; + let basic_ode_solver = BasicODESolver::new(RK4); + let (t_vec, y_vec) = basic_ode_solver.solve( + &test_problem, + (0f64, 10f64), + 0.01, + )?; + let y_vec: Vec = y_vec.into_iter().flatten().collect(); + + #[cfg(feature = "plot")] + { + let mut plt = Plot2D::new(); + plt + .set_domain(t_vec) + .insert_image(y_vec) + .set_xlabel(r"$t$") + .set_ylabel(r"$y$") + .set_style(PlotStyle::Nature) + .tight_layout() + .set_dpi(600) + .set_path("example_data/ode_env.png") + .savefig()?; + } Ok(()) } -fn test_fn(st: &mut State, env: &CubicSpline) { - let x = st.param; - let dy = &mut st.deriv; - dy[0] = env.eval(x); +struct Test { + cs: CubicHermiteSpline, +} + +impl ODEProblem for Test { + fn initial_conditions(&self) -> Vec { + vec![1f64] + } + + fn rhs(&self, t: f64, _y: &[f64], dy: &mut [f64]) -> Result<(), ODEError> { + Ok(dy[0] = self.cs.eval(t)) + } } diff --git a/examples/ode_gl4.rs b/examples/ode_gl4.rs deleted file mode 100644 index dc7985f1..00000000 --- a/examples/ode_gl4.rs +++ /dev/null @@ -1,38 +0,0 @@ -#[macro_use] -extern crate peroxide; -use peroxide::fuga::*; - -fn main() { - let mut im_test = ImplicitODE::new(test_fn); - - let init_state = State::::new(0f64, c!(1), c!(0)); - im_test - .set_initial_condition(init_state) - .set_method(ImMethod::GL4) - .set_step_size(0.01f64) - .set_rtol(1e-6) - .set_times(1000); - - #[cfg(feature = "plot")] - { - let result = im_test.integrate(); - let x = result.col(0); - let y = result.col(1); - let mut plt = Plot2D::new(); - plt.set_domain(x) - .insert_image(y) - .set_title("Test Figure") - .set_fig_size((10, 6)) - .set_dpi(300) - .set_legend(vec!["GL4"]) - .set_path("example_data/gl4_plot.png"); - plt.savefig(); - } -} - -fn test_fn(st: &mut State, _: &NoEnv) { - let x = st.param; - let y = &st.value; - let dy = &mut st.deriv; - dy[0] = (5f64 * x.powi(2) - y[0]) / (x + y[0]).exp(); -} diff --git a/examples/ode_test_gl4.rs b/examples/ode_test_gl4.rs new file mode 100644 index 00000000..bc1f9682 --- /dev/null +++ b/examples/ode_test_gl4.rs @@ -0,0 +1,43 @@ +#[macro_use] +extern crate peroxide; +use peroxide::fuga::*; + +fn main() -> Result<(), Box> { + let gl4 = GL4::new(ImplicitSolver::FixedPoint, 100, 1e-6); + let basic_ode_solver = BasicODESolver::new(gl4); + let (t_vec, y_vec) = basic_ode_solver.solve( + &Test, + (0f64, 10f64), + 0.01, + )?; + let y_vec: Vec = y_vec.into_iter().flatten().collect(); + + #[cfg(feature = "plot")] + { + let mut plt = Plot2D::new(); + plt + .set_domain(t_vec) + .insert_image(y_vec) + .set_xlabel(r"$t$") + .set_ylabel(r"$y$") + .set_style(PlotStyle::Nature) + .tight_layout() + .set_dpi(600) + .set_path("example_data/gl4_test.png") + .savefig()?; + } + + Ok(()) +} + +struct Test; + +impl ODEProblem for Test { + fn initial_conditions(&self) -> Vec { + vec![1f64] + } + + fn rhs(&self, t: f64, y: &[f64], dy: &mut [f64]) -> Result<(), ODEError> { + Ok(dy[0] = (5f64 * t.powi(2) - y[0]) / (t + y[0]).exp()) + } +} diff --git a/examples/ode_test_lorenz.rs b/examples/ode_test_lorenz.rs deleted file mode 100644 index 34e44ed8..00000000 --- a/examples/ode_test_lorenz.rs +++ /dev/null @@ -1,35 +0,0 @@ -extern crate peroxide; -use peroxide::fuga::*; - -fn main() { - let mut ex_test = ExplicitODE::new(f); - - let init_state: State = State::new(0.0, vec![10.0, 1.0, 1.0], vec![0.0, 0.0, 0.0]); - ex_test - .set_initial_condition(init_state) - .set_method(ExMethod::Euler) - .set_step_size(0.01f64) - .set_times(10000); - - let mut ex_test2 = ex_test.clone(); - - let _results = ex_test.integrate(); - - ex_test2.set_method(ExMethod::RK4); - - let _results2 = ex_test2.integrate(); - - // let mut wt = SimpleWriter::new(); - // wt.set_path("example_data/lorenz.pickle") - // .insert_matrix(results) - // .insert_matrix(results2) - // .write_pickle(); -} - -fn f(st: &mut State, _: &NoEnv) { - let x = &st.value; - let dx = &mut st.deriv; - dx[0] = 10f64 * (x[1] - x[0]); - dx[1] = 28f64 * x[0] - x[1] - x[0] * x[2]; - dx[2] = -8f64 / 3f64 * x[2] + x[0] * x[1]; -} diff --git a/examples/ode_test_rk4.rs b/examples/ode_test_rk4.rs index eba6c412..2a22a0b4 100644 --- a/examples/ode_test_rk4.rs +++ b/examples/ode_test_rk4.rs @@ -1,33 +1,5 @@ -#[macro_use] -extern crate peroxide; use peroxide::fuga::*; -//fn main() { -// let init_state = State::::new(0f64, c!(1), c!(0)); -// -// let mut ode_solver = ExplicitODE::new(test_fn); -// -// ode_solver -// .set_method(ExMethod::RK4) -// .set_initial_condition(init_state) -// .set_step_size(0.01) -// .set_times(1000); -// -// let _result = ode_solver.integrate(); -// -// // let mut st = SimpleWriter::new(); -// // st.set_path("example_data/rk4_test.pickle") -// // .insert_matrix(result) -// // .write_pickle(); -//} -// -//fn test_fn(st: &mut State, _: &NoEnv) { -// let x = st.param; -// let y = &st.value; -// let dy = &mut st.deriv; -// dy[0] = (5f64 * x.powi(2) - y[0]) / (x + y[0]).exp(); -//} - fn main() -> Result<(), Box> { let basic_ode_solver = BasicODESolver::new(RK4); let (t_vec, y_vec) = basic_ode_solver.solve( @@ -35,19 +7,22 @@ fn main() -> Result<(), Box> { (0f64, 10f64), 1e-3, )?; - let y_vec = y_vec.into_iter().flatten().collect(); + let y_vec: Vec = y_vec.into_iter().flatten().collect(); - let mut plt = Plot2D::new(); - plt - .set_domain(t_vec) - .insert_image(y_vec) - .set_xlabel(r"$t$") - .set_ylabel(r"$y$") - .set_style(PlotStyle::Nature) - .tight_layout() - .set_dpi(600) - .set_path("example_data/rk4_test.png") - .savefig()?; + #[cfg(feature = "plot")] + { + let mut plt = Plot2D::new(); + plt + .set_domain(t_vec) + .insert_image(y_vec) + .set_xlabel(r"$t$") + .set_ylabel(r"$y$") + .set_style(PlotStyle::Nature) + .tight_layout() + .set_dpi(600) + .set_path("example_data/rk4_test.png") + .savefig()?; + } Ok(()) } diff --git a/examples/ode_test_rkf45.rs b/examples/ode_test_rkf45.rs index 6b88469a..bdd64bcd 100644 --- a/examples/ode_test_rkf45.rs +++ b/examples/ode_test_rkf45.rs @@ -1,5 +1,3 @@ -#[macro_use] -extern crate peroxide; use peroxide::fuga::*; fn main() -> Result<(), Box> { @@ -10,19 +8,22 @@ fn main() -> Result<(), Box> { (0f64, 10f64), 0.01, )?; - let y_vec = y_vec.into_iter().flatten().collect(); + let y_vec: Vec = y_vec.into_iter().flatten().collect(); - let mut plt = Plot2D::new(); - plt - .set_domain(t_vec) - .insert_image(y_vec) - .set_xlabel(r"$t$") - .set_ylabel(r"$y$") - .set_style(PlotStyle::Nature) - .tight_layout() - .set_dpi(600) - .set_path("example_data/rkf45_test.png") - .savefig()?; + #[cfg(feature = "plot")] + { + let mut plt = Plot2D::new(); + plt + .set_domain(t_vec) + .insert_image(y_vec) + .set_xlabel(r"$t$") + .set_ylabel(r"$y$") + .set_style(PlotStyle::Nature) + .tight_layout() + .set_dpi(600) + .set_path("example_data/rkf45_test.png") + .savefig()?; + } Ok(()) } diff --git a/src/numerical/ode.rs b/src/numerical/ode.rs index bb5b0505..95748a66 100644 --- a/src/numerical/ode.rs +++ b/src/numerical/ode.rs @@ -1,18 +1,96 @@ +//! # Ordinary Differential Equation (ODE) Solvers +//! +//! This module provides traits and structs for solving ordinary differential equations (ODEs). +//! +//! ## Example +//! +//! ```rust +//! use peroxide::fuga::*; +//! +//! fn main() -> Result<(), Box> { +//! let rkf = RKF45::new(1e-4, 0.9, 1e-6, 1e-1, 100); +//! let basic_ode_solver = BasicODESolver::new(rkf); +//! let (t_vec, y_vec) = basic_ode_solver.solve( +//! &Test, +//! (0f64, 10f64), +//! 0.01, +//! )?; +//! let y_vec: Vec = y_vec.into_iter().flatten().collect(); +//! println!("{}", y_vec.len()); +//! +//! # #[cfg(feature = "plot")] +//! # { +//! let mut plt = Plot2D::new(); +//! plt +//! .set_domain(t_vec) +//! .insert_image(y_vec) +//! .set_xlabel(r"$t$") +//! .set_ylabel(r"$y$") +//! .set_style(PlotStyle::Nature) +//! .tight_layout() +//! .set_dpi(600) +//! .set_path("example_data/rkf45_test.png") +//! .savefig()?; +//! # } +//! Ok(()) +//! } +//! +//! struct Test; +//! +//! impl ODEProblem for Test { +//! fn initial_conditions(&self) -> Vec { +//! vec![1f64] +//! } +//! +//! fn rhs(&self, t: f64, y: &[f64], dy: &mut [f64]) -> Result<(), ODEError> { +//! Ok(dy[0] = (5f64 * t.powi(2) - y[0]) / (t + y[0]).exp()) +//! } +//! } +//! ``` + use thiserror::Error; use ODEError::*; -use crate::{util::non_macro::eye, traits::math::LinearOp, traits::fp::FPVector}; - +/// Trait for defining an ODE problem. +/// +/// Implement this trait to define your own ODE problem. +/// +/// # Example +/// +/// ``` +/// use peroxide::fuga::*; +/// +/// struct MyODEProblem; +/// +/// impl ODEProblem for MyODEProblem { +/// fn initial_conditions(&self) -> Vec { +/// vec![1.0, 2.0] +/// } +/// +/// fn rhs(&self, t: f64, y: &[f64], dy: &mut [f64]) -> Result<(), ODEError> { +/// dy[0] = -0.5 * y[0]; +/// dy[1] = y[0] - y[1]; +/// Ok(()) +/// } +/// } +/// ``` pub trait ODEProblem { fn initial_conditions(&self) -> Vec; fn rhs(&self, t: f64, y: &[f64], dy: &mut [f64]) -> Result<(), ODEError>; } +/// Trait for ODE integrators. +/// +/// Implement this trait to define your own ODE integrator. pub trait ODEIntegrator { fn step(&self, problem: &P, t: f64, y: &mut [f64], dt: f64) -> Result; } + +/// Enum for ODE errors. + + #[derive(Debug, Clone, Copy, Error)] pub enum ODEError { #[error("constraint violation")] @@ -21,10 +99,45 @@ pub enum ODEError { ReachedMaxStepIter, } +/// Trait for ODE solvers. +/// +/// Implement this trait to define your own ODE solver. pub trait ODESolver { fn solve(&self, problem: &P, t_span: (f64, f64), dt: f64) -> Result<(Vec, Vec>), ODEError>; } +/// A basic ODE solver using a specified integrator. +/// +/// # Example +/// +/// ``` +/// use peroxide::fuga::*; +/// +/// fn main() -> Result<(), Box> { +/// let rkf = RKF45::new(1e-4, 0.9, 1e-6, 1e-1, 100); +/// let basic_ode_solver = BasicODESolver::new(rkf); +/// let (t_vec, y_vec) = basic_ode_solver.solve( +/// &Test, +/// (0f64, 10f64), +/// 0.01, +/// )?; +/// let y_vec: Vec = y_vec.into_iter().flatten().collect(); +/// +/// Ok(()) +/// } +/// +/// struct Test; +/// +/// impl ODEProblem for Test { +/// fn initial_conditions(&self) -> Vec { +/// vec![1f64] +/// } +/// +/// fn rhs(&self, t: f64, y: &[f64], dy: &mut [f64]) -> Result<(), ODEError> { +/// Ok(dy[0] = (5f64 * t.powi(2) - y[0]) / (t + y[0]).exp()) +/// } +/// } +/// ``` pub struct BasicODESolver { integrator: I, } @@ -38,15 +151,17 @@ impl BasicODESolver { impl ODESolver for BasicODESolver { fn solve(&self, problem: &P, t_span: (f64, f64), dt: f64) -> Result<(Vec, Vec>), ODEError> { let mut t = t_span.0; + let mut dt = dt; let mut y = problem.initial_conditions(); let mut t_vec = vec![t]; let mut y_vec = vec![y.clone()]; while t < t_span.1 { let dt_step = self.integrator.step(problem, t, &mut y, dt)?; - t += dt_step; + t += dt; t_vec.push(t); y_vec.push(y.clone()); + dt = dt_step; } Ok((t_vec, y_vec)) @@ -56,7 +171,10 @@ impl ODESolver for BasicODESolver { // ┌─────────────────────────────────────────────────────────┐ // Runge-Kutta // └─────────────────────────────────────────────────────────┘ -/// Runge-Kutta 4th order +/// Runge-Kutta 4th order integrator. +/// +/// This integrator uses the classical 4th order Runge-Kutta method to numerically integrate the ODE system. +/// It calculates four intermediate values (k1, k2, k3, k4) to estimate the next step solution. #[derive(Debug, Clone, Copy, Default)] #[cfg_attr(feature = "serde", derive(serde::Serialize, serde::Deserialize))] pub struct RK4; @@ -97,7 +215,11 @@ impl ODEIntegrator for RK4 { // ┌─────────────────────────────────────────────────────────┐ // Runge-Kutta-Fehlberg // └─────────────────────────────────────────────────────────┘ -/// Runge-Kutta-Fehlberg 4/5th order +/// Runge-Kutta-Fehlberg 4/5th order integrator. +/// +/// This integrator uses the Runge-Kutta-Fehlberg method, which is an adaptive step size integrator. +/// It calculates six intermediate values (k1, k2, k3, k4, k5, k6) to estimate the next step solution and the error. +/// The step size is automatically adjusted based on the estimated error to maintain the desired tolerance. #[derive(Debug, Clone, Copy)] #[cfg_attr(feature = "serde", derive(serde::Serialize, serde::Deserialize))] pub struct RKF45 { @@ -244,14 +366,23 @@ impl ODEIntegrator for RKF45 { // ┌─────────────────────────────────────────────────────────┐ // Gauss-Legendre 4th order // └─────────────────────────────────────────────────────────┘ +/// Enum for implicit solvers. +/// +/// This enum defines the available implicit solvers for the Gauss-Legendre 4th order integrator. +/// Currently, only the fixed-point iteration method is implemented. #[derive(Debug, Clone, Copy)] #[cfg_attr(feature = "serde", derive(serde::Serialize, serde::Deserialize))] pub enum ImplicitSolver { FixedPoint, - Broyden, - TrustRegion(f64, f64), + //Broyden, + //TrustRegion(f64, f64), } +/// Gauss-Legendre 4th order integrator. +/// +/// This integrator uses the 4th order Gauss-Legendre Runge-Kutta method, which is an implicit integrator. +/// It requires solving a system of nonlinear equations at each step, which is done using the specified implicit solver (e.g., fixed-point iteration). +/// The Gauss-Legendre method has better stability properties compared to explicit methods, especially for stiff ODEs. #[derive(Debug, Clone, Copy)] #[cfg_attr(feature = "serde", derive(serde::Serialize, serde::Deserialize))] pub struct GL4 { @@ -260,6 +391,16 @@ pub struct GL4 { tol: f64, } +impl Default for GL4 { + fn default() -> Self { + GL4 { + solver: ImplicitSolver::FixedPoint, + max_iter: 100, + tol: 1e-6, + } + } +} + impl GL4 { pub fn new(solver: ImplicitSolver, max_iter: usize, tol: f64) -> Self { GL4 { @@ -305,171 +446,6 @@ impl ODEIntegrator for GL4 { } } } - ImplicitSolver::Broyden => { - // Broyden's method - let mut b = eye(n); - - for _ in 0..self.max_iter { - problem.rhs(t + c * dt, &y1, &mut k1)?; - problem.rhs(t + d * dt, &y2, &mut k2)?; - - let mut f1 = vec![0.0; n]; - let mut f2 = vec![0.0; n]; - for i in 0..n { - f1[i] = y1[i] - y[i] - dt * (c * k1[i] + d * k2[i] - sqrt3 * (k2[i] - k1[i]) / 2.0); - f2[i] = y2[i] - y[i] - dt * (c * k1[i] + d * k2[i] + sqrt3 * (k2[i] - k1[i]) / 2.0); - } - - let neg_dy1 = b.apply(&f1); - let neg_dy2 = b.apply(&f2); - - for i in 0..n { - y1[i] -= neg_dy1[i]; - y2[i] -= neg_dy2[i]; - } - - let mut max_diff = 0f64; - for i in 0..n { - max_diff = max_diff.max(neg_dy1[i].abs()).max(neg_dy2[i].abs()); - } - - if max_diff < self.tol { - break; - } - - let mut df1 = vec![0.0; n]; - let mut df2 = vec![0.0; n]; - for i in 0..n { - df1[i] = f1[i] + dt * (c * neg_dy1[i] + d * neg_dy2[i] - sqrt3 * (neg_dy2[i] - neg_dy1[i]) / 2.0); - df2[i] = f2[i] + dt * (c * neg_dy1[i] + d * neg_dy2[i] + sqrt3 * (neg_dy2[i] - neg_dy1[i]) / 2.0); - } - - for i in 0..n { - for j in 0..n { - b[(i, j)] -= (df1[i] * neg_dy1[j] + df2[i] * neg_dy2[j]) / (neg_dy1[j].powi(2) + neg_dy2[j].powi(2)); - } - } - } - } - ImplicitSolver::TrustRegion(eta, rho) => { - // Trust-region method - let mut r = self.tol; - let mut d1 = vec![0.0; n]; - let mut d2 = vec![0.0; n]; - let mut g1 = vec![0.0; n]; - let mut g2 = vec![0.0; n]; - let mut b1 = eye(n); - let mut b2 = eye(n); - - for _ in 0..self.max_iter { - problem.rhs(t + c * dt, &y1, &mut k1)?; - problem.rhs(t + d * dt, &y2, &mut k2)?; - - let mut f1 = vec![0.0; n]; - let mut f2 = vec![0.0; n]; - for i in 0..n { - f1[i] = y1[i] - y[i] - dt * (c * k1[i] + d * k2[i] - sqrt3 * (k2[i] - k1[i]) / 2.0); - f2[i] = y2[i] - y[i] - dt * (c * k1[i] + d * k2[i] + sqrt3 * (k2[i] - k1[i]) / 2.0); - } - - let mut norm_f1 = 0.0; - let mut norm_f2 = 0.0; - for i in 0..n { - norm_f1 += f1[i] * f1[i]; - norm_f2 += f2[i] * f2[i]; - g1[i] = f1[i]; - g2[i] = f2[i]; - } - norm_f1 = norm_f1.sqrt(); - norm_f2 = norm_f2.sqrt(); - - let mut inner_iter_count = 0; - while norm_f1 > self.tol || norm_f2 > self.tol { - let h1 = b1.apply(&g1).fmap(|x| -x); - let h2 = b2.apply(&g2).fmap(|x| -x); - - let mut norm_h1 = 0.0; - let mut norm_h2 = 0.0; - for i in 0..n { - norm_h1 += h1[i] * h1[i]; - norm_h2 += h2[i] * h2[i]; - } - norm_h1 = norm_h1.sqrt(); - norm_h2 = norm_h2.sqrt(); - - if norm_h1 <= r || norm_h2 <= r { - d1.copy_from_slice(&h1[..]); - d2.copy_from_slice(&h2[..]); - } else { - let sigma1 = (r / norm_h1).powf(2.0); - let sigma2 = (r / norm_h2).powf(2.0); - for i in 0..n { - d1[i] = sigma1 * h1[i]; - d2[i] = sigma2 * h2[i]; - } - } - - let mut y1_new = vec![0.0; n]; - let mut y2_new = vec![0.0; n]; - for i in 0..n { - y1_new[i] = y1[i] + d1[i]; - y2_new[i] = y2[i] + d2[i]; - } - - problem.rhs(t + c * dt, &y1_new, &mut k1)?; - problem.rhs(t + d * dt, &y2_new, &mut k2)?; - - let mut f1_new = vec![0.0; n]; - let mut f2_new = vec![0.0; n]; - for i in 0..n { - f1_new[i] = y1_new[i] - y[i] - dt * (c * k1[i] + d * k2[i] - sqrt3 * (k2[i] - k1[i]) / 2.0); - f2_new[i] = y2_new[i] - y[i] - dt * (c * k1[i] + d * k2[i] + sqrt3 * (k2[i] - k1[i]) / 2.0); - } - - let mut norm_f1_new = 0.0; - let mut norm_f2_new = 0.0; - for i in 0..n { - norm_f1_new += f1_new[i] * f1_new[i]; - norm_f2_new += f2_new[i] * f2_new[i]; - } - norm_f1_new = norm_f1_new.sqrt(); - norm_f2_new = norm_f2_new.sqrt(); - - let rho1 = (norm_f1 * norm_f1 - norm_f1_new * norm_f1_new) / (norm_f1 * norm_f1 - (g1.iter().zip(&d1).map(|(g, d)| g * d).sum::()).abs()); - let rho2 = (norm_f2 * norm_f2 - norm_f2_new * norm_f2_new) / (norm_f2 * norm_f2 - (g2.iter().zip(&d2).map(|(g, d)| g * d).sum::()).abs()); - - if rho1 > eta && rho2 > eta { - y1.copy_from_slice(&y1_new[..]); - y2.copy_from_slice(&y2_new[..]); - f1.copy_from_slice(&f1_new[..]); - f2.copy_from_slice(&f2_new[..]); - g1.copy_from_slice(&f1_new[..]); - g2.copy_from_slice(&f2_new[..]); - norm_f1 = norm_f1_new; - norm_f2 = norm_f2_new; - r = r.max(rho * r); - } else { - r *= rho; - } - - if r < self.tol { - break; - } - - for i in 0..n { - for j in 0..n { - b1[(i, j)] += (f1[i] - g1[i]) * d1[j] / (d1.iter().map(|d| d * d).sum::()); - b2[(i, j)] += (f2[i] - g2[i]) * d2[j] / (d2.iter().map(|d| d * d).sum::()); - } - } - - inner_iter_count += 1; - if inner_iter_count >= self.max_iter { - break; - } - } - } - } } for i in 0..n { diff --git a/src/numerical/spline.rs b/src/numerical/spline.rs index 82cf04f0..16bbb4ca 100644 --- a/src/numerical/spline.rs +++ b/src/numerical/spline.rs @@ -212,7 +212,7 @@ use peroxide_num::PowOps; #[cfg(feature = "serde")] use serde::{Deserialize, Serialize}; use std::cmp::{max, min}; -use std::convert::{From, Into}; +use std::convert::From; use std::ops::{Index, Range}; use thiserror::Error; diff --git a/src/statistics/dist.rs b/src/statistics/dist.rs index 7516a855..59dd3fa7 100644 --- a/src/statistics/dist.rs +++ b/src/statistics/dist.rs @@ -239,7 +239,6 @@ use rand_distr::WeightedAliasIndex; use self::rand::distributions::uniform::SampleUniform; use self::rand::prelude::*; -use self::rand_distr::Distribution; pub use self::OPDist::*; pub use self::TPDist::*; use crate::traits::fp::FPVector; @@ -248,7 +247,6 @@ use crate::special::function::*; use crate::statistics::{ops::C, stat::Statistics}; use crate::util::non_macro::{linspace, seq}; use crate::util::useful::{auto_zip, find_interval}; -use std::convert::Into; use std::f64::consts::E; use thiserror::Error; use self::WeightedUniformError::*; diff --git a/src/traits/fp.rs b/src/traits/fp.rs index 7a9b5196..41f11463 100644 --- a/src/traits/fp.rs +++ b/src/traits/fp.rs @@ -1,5 +1,4 @@ use crate::structure::matrix::Matrix; -use std::convert::Into; /// Functional Programming tools for Vector pub trait FPVector { diff --git a/src/util/non_macro.rs b/src/util/non_macro.rs index 070c9557..25ee56c0 100644 --- a/src/util/non_macro.rs +++ b/src/util/non_macro.rs @@ -8,8 +8,6 @@ use crate::structure::{ }; use crate::traits::float::FloatWithPrecision; -use std::convert::Into; - /// R like seq function /// /// # Example From 1ce695133f5fa42792bba04e12b8572a0b7d948b Mon Sep 17 00:00:00 2001 From: axect Date: Mon, 8 Apr 2024 23:02:26 +0900 Subject: [PATCH 7/9] UPD: Update list & README & csv version --- Cargo.toml | 2 +- README.md | 1 - list.md | 55 ++++++++++++++++++++++++++++++++++++++++-------------- 3 files changed, 42 insertions(+), 16 deletions(-) diff --git a/Cargo.toml b/Cargo.toml index 29c514e6..efd476f9 100644 --- a/Cargo.toml +++ b/Cargo.toml @@ -20,7 +20,7 @@ maintenance = { status = "actively-developed" } float-cmp = "0.9" [dependencies] -csv = { version = "1", optional = true, default_features = false } +csv = { version = "1.3", optional = true, default_features = false } rand = { version = "0.8", features = ["small_rng"] } rand_distr = "0.4" order-stat = "0.1" diff --git a/README.md b/README.md index 1c9805de..511f7df1 100644 --- a/README.md +++ b/README.md @@ -288,7 +288,6 @@ Corresponding to `0.34.4` - [mod.rs](src/ml/mod.rs) - [reg.rs](src/ml/reg.rs) : Regression tools - __numerical__ : To do numerical things - - [bdf.rs](src/numerical/bdf.rs) : Backward Differentiation Formula (deprecated) - [eigen.rs](src/numerical/eigen.rs) : Eigenvalue, Eigenvector algorithm - [interp.rs](src/numerical/interp.rs) : Interpolation - [integral.rs](src/numerical/integral.rs) : Numerical integration diff --git a/list.md b/list.md index 2ac5902f..7ee3c3c6 100644 --- a/list.md +++ b/list.md @@ -1,39 +1,66 @@ - __src__ - [lib.rs](src/lib.rs) - - __ml__ - - [mod.rs](src/ml/mod.rs) - - [reg.rs](src/ml/reg.rs) - __macros__ - - [matlab_macro.rs](src/macros/matlab_macro.rs) - [mod.rs](src/macros/mod.rs) + - [julia_macro.rs](src/macros/julia_macro.rs) + - [matlab_macro.rs](src/macros/matlab_macro.rs) - [r_macro.rs](src/macros/r_macro.rs) + - __ml__ + - [mod.rs](src/ml/mod.rs) + - [reg.rs](src/ml/reg.rs) - __numerical__ - - [bdf.rs](src/numerical/bdf.rs) - - [interp.rs](src/numerical/interp.rs) - [mod.rs](src/numerical/mod.rs) + - [eigen.rs](src/numerical/eigen.rs) + - [integral.rs](src/numerical/integral.rs) + - [interp.rs](src/numerical/interp.rs) - [newton.rs](src/numerical/newton.rs) - - [runge_kutta.rs](src/numerical/runge_kutta.rs) + - [ode.rs](src/numerical/ode.rs) + - [optimize.rs](src/numerical/optimize.rs) + - [root.rs](src/numerical/root.rs) - [spline.rs](src/numerical/spline.rs) - - [util.rs](src/numerical/utils.rs) - - __operation__ - - [extra_ops.rs](src/operation/extra_ops.rs) - - [mod.rs](src/operation/mod.rs) + - [utils.rs](src/numerical/utils.rs) + - __prelude__ + - [mod.rs](src/prelude/mod.rs) + - [simpler.rs](src/prelude/simpler.rs) + - __special__ + - [mod.rs](src/special/mod.rs) + - [function.rs](src/special/function.rs) + - [lanczos.rs](src/special/lanczos.rs) - __statistics__ - [mod.rs](src/statistics/mod.rs) + - [dist.rs](src/statistics/dist.rs) + - [ops.rs](src/statistics/ops.rs) - [rand.rs](src/statistics/rand.rs) - [stat.rs](src/statistics/stat.rs) - __structure__ + - [mod.rs](src/structure/mod.rs) + - [ad.rs](src/structure/ad.rs) + - [complex.rs](src/structure/complex.rs) - [dataframe.rs](src/structure/dataframe.rs) - - [dual.rs](src/structure/dual.rs) - [matrix.rs](src/structure/matrix.rs) - - [mod.rs](src/structure/mod.rs) - [multinomial.rs](src/structure/multinomial.rs) - [polynomial.rs](src/structure/polynomial.rs) + - [sparse.rs](src/structure/sparse.rs) - [vector.rs](src/structure/vector.rs) + - __traits__ + - [mod.rs](src/traits/mod.rs) + - [float.rs](src/traits/float.rs) + - [fp.rs](src/traits/fp.rs) + - [general.rs](src/traits/general.rs) + - [math.rs](src/traits/math.rs) + - [mutable.rs](src/traits/mutable.rs) + - [num.rs](src/traits/num.rs) + - [pointer.rs](src/traits/pointer.rs) + - [stable.rs](src/traits/stable.rs) + - [sugar.rs](src/traits/sugar.rs) - __util__ - - [api.rs](src/util/api.rs) - [mod.rs](src/util/mod.rs) + - [api.rs](src/util/api.rs) + - [low_level.rs](src/util/low_level.rs) - [non_macro.rs](src/util/non_macro.rs) + - [plot.rs](src/util/plot.rs) - [print.rs](src/util/print.rs) - [useful.rs](src/util/useful.rs) + - [wrapper.rs](src/util/wrapper.rs) + - [writer.rs](src/util/writer.rs) From 26233518c53cf06303b67e742c3992ab5ff82d78 Mon Sep 17 00:00:00 2001 From: axect Date: Mon, 8 Apr 2024 23:35:35 +0900 Subject: [PATCH 8/9] DOCS: Update README --- README.md | 158 ++++++++++++++++++++++++++++++++++++++++++------------ 1 file changed, 123 insertions(+), 35 deletions(-) diff --git a/README.md b/README.md index 511f7df1..f1d9f1d3 100644 --- a/README.md +++ b/README.md @@ -9,6 +9,28 @@ Rust numeric library contains linear algebra, numerical analysis, statistics and machine learning tools with R, MATLAB, Python like macros. +## Table of Contents + +- [Why Peroxide?](#why-peroxide) + - [1. Customize features](#1-customize-features) + - [2. Easy to optimize](#2-easy-to-optimize) + - [3. Friendly syntax](#3-friendly-syntax) + - [4. Can choose two different coding styles](#4-can-choose-two-different-coding-styles) + - [5. Batteries included](#5-batteries-included) + - [6. Compatible with Mathematics](#6-compatible-with-mathematics) + - [7. Written in Rust](#7-written-in-rust) +- [Latest README version](#latest-readme-version) +- [Pre-requisite](#pre-requisite) +- [Install](#install) +- [Useful tips for features](#useful-tips-for-features) +- [Module Structure](#module-structure) +- [Documentation](#documentation) +- [Examples](#examples) +- [Version Info](#version-info) +- [Contributes Guide](#contributes-guide) +- [LICENSE](#license) +- [TODO](#todo) + ## Why Peroxide? ### 1. Customize features @@ -28,16 +50,19 @@ If you don't want to depend C/C++ or Fortran libraries, then choose `default` fe If you want to draw plot with some great templates, then choose `plot` feature. You can choose any features simultaneously. - + ### 2. Easy to optimize -Peroxide uses 1D data structure to describe matrix. So, it's too easy to integrate BLAS. -It means peroxide guarantees perfect performance for linear algebraic computations. +Peroxide uses a 1D data structure to represent matrices, making it straightforward to integrate with BLAS (Basic Linear Algebra Subprograms). +This means that Peroxide can guarantee excellent performance for linear algebraic computations by leveraging the optimized routines provided by BLAS. ### 3. Friendly syntax -Rust is so strange for Numpy, MATLAB, R users. Thus, it's harder to learn the more rusty libraries. -With peroxide, you can do heavy computations with R, Numpy, MATLAB like syntax. +For users familiar with numerical computing libraries like NumPy, MATLAB, or R, Rust's syntax might seem unfamiliar at first. +This can make it more challenging to learn and use Rust libraries that heavily rely on Rust's unique features and syntax. + +However, Peroxide aims to bridge this gap by providing a syntax that resembles the style of popular numerical computing environments. +With Peroxide, you can perform complex computations using a syntax similar to that of R, NumPy, or MATLAB, making it easier for users from these backgrounds to adapt to Rust and take advantage of its performance benefits. For example, @@ -100,7 +125,7 @@ fn main() { } ``` -In `fuga`, use various norms. But you should write longer than `prelude`. +In `fuga`, use various norms. But you should write a little bit longer than `prelude`. ```rust #[macro_use] extern crate peroxide; @@ -132,7 +157,7 @@ Peroxide can do many things. * Column, Row operations * Eigenvalue, Eigenvector * Functional Programming - * More easy functional programming with `Vec` + * Easier functional programming with `Vec` * For matrix, there are three maps * `fmap` : map for all elements * `col_map` : map for column vectors @@ -152,15 +177,16 @@ Peroxide can do many things. * Gradient Descent * Levenberg Marquardt * Ordinary Differential Equation - * Euler - * Runge Kutta 4th order - * Backward Euler (Implicit) - * Gauss Legendre 4th order (Implicit) + * Runge-Kutta 4th order (`RK4`) + * Runge-Kutta-Fehlberg 4/5th order (`RKF45`) + * Gauss-Legendre 4th order (`GL4`; Implicit) * Numerical Integration * Newton-Cotes Quadrature * Gauss-Legendre Quadrature (up to 30 order) * Gauss-Kronrod Quadrature (Adaptive) * G7K15, G10K21, G15K31, G20K41, G25K51, G30K61 + * Gauss-Kronrod Quadrature (Relative tolerance) + * G7K15R, G10K21R, G15K31R, G20K41R, G25K51R, G30K61R * Root Finding * Bisection * False Position (Regula Falsi) @@ -179,6 +205,7 @@ Peroxide can do many things. * Gamma * Beta * Student's-t + * Weighted Uniform * RNG algorithms * Acceptance Rejection * Marsaglia Polar @@ -209,19 +236,73 @@ For future, peroxide will include more & more mathematical concepts. (But still ### 7. Written in Rust -Rust & Cargo are awesome for scientific computations. -You can use any external packages easily with Cargo, not make. -And default runtime performance of Rust is also great. If you use many iterations for computations, -then Rust become great choice. +Rust provides a strong type system, ownership concepts, borrowing rules, and other features that enable developers to write safe and efficient code. It also offers modern programming techniques like trait-based abstraction and convenient error handling. Peroxide is developed to take full advantage of these strengths of Rust. + +The example code demonstrates how Peroxide can be used to simulate the Lorenz attractor and visualize the results. It showcases some of the powerful features provided by Rust, such as the `?` operator for streamlined error handling and the `ODEProblem` trait for abstracting ODE problems. + +```rust +use peroxide::fuga::*; + +fn main() -> Result<(), Box> { + let rkf45 = RKF45::new(1e-4, 0.9, 1e-6, 1e-1, 100); + let basic_ode_solver = BasicODESolver::new(rkf45); + let (_, y_vec) = basic_ode_solver.solve( + &Lorenz, + (0f64, 100f64), + 1e-2, + )?; // Error handling with `?` - can check constraint violation and etc. + let y_mat = py_matrix(y_vec); + let y0 = y_mat.col(0); + let y2 = y_mat.col(2); + + // Simple but effective plotting + let mut plt = Plot2D::new(); + plt + .set_domain(y0) + .insert_image(y2) + .set_xlabel(r"$y_0$") + .set_ylabel(r"$y_2$") + .set_style(PlotStyle::Nature) + .tight_layout() + .set_dpi(600) + .set_path("example_data/lorenz_rkf45.png") + .savefig()?; + + Ok(()) +} + +struct Lorenz; + +impl ODEProblem for Lorenz { + fn initial_conditions(&self) -> Vec { + vec![10f64, 1f64, 1f64] + } + + fn rhs(&self, t: f64, y: &[f64], dy: &mut [f64]) -> Result<(), ODEError> { + dy[0] = 10f64 * (y[1] - y[0]); + dy[1] = 28f64 * y[0] - y[1] - y[0] * y[2]; + dy[2] = -8f64 / 3f64 * y[2] + y[0] * y[1]; + Ok(()) + } +} +``` + +Running the code produces the following visualization of the Lorenz attractor: + +![lorenz_rkf45.png](example_data/lorenz_rkf45.png) + +Peroxide strives to leverage the benefits of the Rust language while providing a user-friendly interface for numerical computing and scientific simulations. + +How's that? Let me know if there's anything else you'd like me to improve! ## Latest README version -Corresponding to `0.34.4` +Corresponding to `0.36.0` ## Pre-requisite * For `O3` feature - Need `OpenBLAS` -* For `plot` feature - Need `matplotlib` of python +* For `plot` feature - Need `matplotlib` and optional `scienceplots` (for publication quality) * For `nc` feature - Need `netcdf` ## Install @@ -263,15 +344,18 @@ Corresponding to `0.34.4` cargo add peroxide --features "O3 plot nc csv parquet serde" ``` - ## Useful tips for features -* If you want to use *QR* or *SVD* or *Cholesky Decomposition* then should use `O3` feature (there are no implementations for these decompositions in `default`) -* If you want to write your numerical results, then use `parquet` or `nc` features (corresponding to `parquet` or `netcdf` format. (It is much more effective than `csv` and `json`.) -* To plot, use `parquet` or `nc` feature to export data as parquet or netcdf format and use python to draw plot. - * `plot` feature has limited plot abilities. - * To read parquet file in python, use `pandas` & `pyarrow` libraries. - * There is a template of python code for netcdf. - [Socialst](https://github.com/Axect/Socialst/blob/master/Templates/PyPlot_Template/nc_plot.py) +* If you want to use _QR_, _SVD_, or _Cholesky Decomposition_, you should use the `O3` feature. These decompositions are not implemented in the `default` feature. + +* If you want to save your numerical results, consider using the `parquet` or `nc` features, which correspond to the `parquet` and `netcdf` file formats, respectively. These formats are much more efficient than `csv` and `json`. + +* For plotting, it is recommended to use the `plot` feature. However, if you require more customization, you can use the `parquet` or `nc` feature to export your data in the parquet or netcdf format and then use Python to create the plots. + + * To read parquet files in Python, you can use the `pandas` and `pyarrow` libraries. + + * A template for Python code that works with netcdf files can be found in the [Socialst](https://github.com/Axect/Socialst/blob/master/Templates/PyPlot_Template/nc_plot.py) repository. + ## Module Structure @@ -285,13 +369,13 @@ Corresponding to `0.34.4` - [mod.rs](src/macros/mod.rs) - [r_macro.rs](src/macros/r_macro.rs) : R like macro - __ml__ : For machine learning (*Beta*) - - [mod.rs](src/ml/mod.rs) - - [reg.rs](src/ml/reg.rs) : Regression tools + - [mod.rs](src/ml/mod.rs) + - [reg.rs](src/ml/reg.rs) : Regression tools - __numerical__ : To do numerical things + - [mod.rs](src/numerical/mod.rs) - [eigen.rs](src/numerical/eigen.rs) : Eigenvalue, Eigenvector algorithm - - [interp.rs](src/numerical/interp.rs) : Interpolation - [integral.rs](src/numerical/integral.rs) : Numerical integration - - [mod.rs](src/numerical/mod.rs) + - [interp.rs](src/numerical/interp.rs) : Interpolation - [newton.rs](src/numerical/newton.rs) : Newton's Method - [ode.rs](src/numerical/ode.rs) : Main ODE solver with various algorithms - [optimize.rs](src/numerical/optimize.rs) : Non-linear regression @@ -308,21 +392,21 @@ Corresponding to `0.34.4` - [mod.rs](src/statistics/mod.rs) - [dist.rs](src/statistics/dist.rs) : Probability distributions - [ops.rs](src/statistics/ops.rs) : Some probabilistic operations - - [rand.rs](src/statistics/rand.rs) : Wrapper for `rand` crate + - [rand.rs](src/statistics/rand.rs) : Wrapper for `rand` crate & Piecewise Rejection Sampling - [stat.rs](src/statistics/stat.rs) : Statistical tools - __structure__ : Fundamental data structures + - [mod.rs](src/structure/mod.rs) - [ad.rs](src/structure/ad.rs) : Automatic Differentation - [dataframe.rs](src/structure/dataframe.rs) : Dataframe - [matrix.rs](src/structure/matrix.rs) : Matrix - - [mod.rs](src/structure/mod.rs) - [polynomial.rs](src/structure/polynomial.rs) : Polynomial - [sparse.rs](src/structure/sparse.rs) : For sparse structure (*Beta*) - [vector.rs](src/structure/vector.rs) : Extra tools for `Vec` - __traits__ + - [mod.rs](src/traits/mod.rs) - [fp.rs](src/traits/fp.rs) : Functional programming toolbox - [general.rs](src/traits/general.rs) : General algorithms - [math.rs](src/traits/math.rs) : Mathematics - - [mod.rs](src/traits/mod.rs) - [mutable.rs](src/traits/mutable.rs) : Mutable toolbox - [num.rs](src/traits/num.rs) : Number, Real and more operations - [pointer.rs](src/traits/pointer.rs) : Matrix pointer and Vector pointer for convenience @@ -332,7 +416,6 @@ Corresponding to `0.34.4` - [mod.rs](src/util/mod.rs) - [api.rs](src/util/api.rs) : Matrix constructor for various language style - [low_level.rs](src/util/low_level.rs) : Low-level tools - - [mod.rs](src/util/mod.rs) - [non_macro.rs](src/util/non_macro.rs) : Primordial version of macros - [plot.rs](src/util/plot.rs) : To draw plot (using `pyo3`) - [print.rs](src/util/print.rs) : To print conveniently @@ -340,14 +423,15 @@ Corresponding to `0.34.4` - [wrapper.rs](src/util/wrapper.rs) : Wrapper for other crates (e.g. rand) - [writer.rs](src/util/writer.rs) : More convenient write system - ## Documentation * [![On docs.rs](https://docs.rs/peroxide/badge.svg)](https://axect.github.io/Peroxide_Doc) -## Example +## Examples + +- In [examples](./examples) directory, there are some examples. -[Peroxide Gallery](https://github.com/Axect/Peroxide_Gallery) +- More examples are in [Peroxide Gallery](https://github.com/Axect/Peroxide_Gallery). ## Version Info @@ -357,6 +441,10 @@ To see [RELEASES.md](./RELEASES.md) See [CONTRIBUTES.md](./CONTRIBUTES.md) +## LICENSE + +Peroxide is licensed under dual licenses - Apache License 2.0 and MIT License. + ## TODO To see [TODO.md](./TODO.md) From 8034930c0829794b88850b3b41ad22794cd10ec9 Mon Sep 17 00:00:00 2001 From: axect Date: Mon, 8 Apr 2024 23:47:29 +0900 Subject: [PATCH 9/9] RLSE: Ver 0.36.0 - Error handling for spline & prs - Whole new ODE --- Cargo.toml | 2 +- RELEASES.md | 32 ++++++++++++++++++++++++++++++++ 2 files changed, 33 insertions(+), 1 deletion(-) diff --git a/Cargo.toml b/Cargo.toml index efd476f9..87a8dbbe 100644 --- a/Cargo.toml +++ b/Cargo.toml @@ -1,6 +1,6 @@ [package] name = "peroxide" -version = "0.35.1" +version = "0.36.0" authors = ["axect "] edition = "2018" description = "Rust comprehensive scientific computation library contains linear algebra, numerical analysis, statistics and machine learning tools with farmiliar syntax" diff --git a/RELEASES.md b/RELEASES.md index 808c1fe9..f3df7bbd 100644 --- a/RELEASES.md +++ b/RELEASES.md @@ -1,3 +1,35 @@ +# Release 0.36.0 (2024-04-08) + +## Huge Update - Error handling & Whole new ODE + +### Error handling + +- Add `thiserror` for error handling +- Implement errors for cubic spline & cubic hermite spline. +- Implement errors for weighted uniform distribution & PRS. + +### Seedable sampling + +- Now, all distribution has `sample_with_rng` method. +- There are two wrappers for `SeedableRng` + - `smallrng_from_seed` : Performant but not secure + - `stdrng_from_seed` : Performant enough and secure enough + +### Whole new ODE + +- Remove all boilerplates. +- Now, `ODE` is composed of traits. + - `ODEProblem`: Trait for defining and ODE problem. + - `ODEIntegrator`: Trait for integrating ODE. + - `RK4`: Runge-Kutta 4th order + - `RKF45`: Runge-Kutta-Fehlberg 4/5th order + - `GL4`: Gauss-Legendre 4th order + - You can implement your own integrator. + - `ODESolver`: Trait for solving ODE. + - `BasicODESolver`: Basic ODE solver - define range of t, initial step size and integrate it. + - You can implement your own solver. +- For more information, see [docs for ode](https://axect.github.io/Peroxide_Doc/peroxide/numerical/ode/index.html). + # Release 0.35.1 (2024-03-29) - Add `PlotType` for `Plot2D`

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