479 lines
12 KiB
Rust
479 lines
12 KiB
Rust
#![allow(clippy::too_many_arguments)] // Clippy, shut
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use crate::egui_app::AppSettings;
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use crate::function_output::FunctionOutput;
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use crate::misc::*;
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use crate::parsing::BackingFunction;
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use eframe::{egui, epaint};
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use egui::{
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plot::{BarChart, PlotUi, Value},
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widgets::plot::Bar,
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};
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use epaint::Color32;
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use std::fmt::{self, Debug};
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#[cfg(not(target_arch = "wasm32"))]
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use rayon::iter::ParallelIterator;
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/// Represents the possible variations of Riemann Sums
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#[derive(PartialEq, Debug, Copy, Clone)]
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pub enum Riemann {
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Left,
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Middle,
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Right,
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}
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impl fmt::Display for Riemann {
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fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result { write!(f, "{:?}", self) }
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}
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lazy_static::lazy_static! {
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/// Represents a "default" instance of `FunctionEntry`
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pub static ref DEFAULT_FUNCTION_ENTRY: FunctionEntry = FunctionEntry::default();
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}
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/// `FunctionEntry` is a function that can calculate values, integrals,
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/// derivatives, etc etc
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#[derive(Clone)]
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pub struct FunctionEntry {
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/// The `BackingFunction` instance that is used to generate `f(x)`, `f'(x)`,
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/// and `f''(x)`
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function: BackingFunction,
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/// Stores a function string (that hasn't been processed via
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/// `process_func_str`) to display to the user
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func_str: String,
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/// Minimum and Maximum values of what do display
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min_x: f64,
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max_x: f64,
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/// output/cached data
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output: FunctionOutput,
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/// If calculating/displayingintegrals are enabled
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pub integral: bool,
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/// If displaying derivatives are enabled (note, they are still calculated
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/// for other purposes)
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pub derivative: bool,
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}
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impl Default for FunctionEntry {
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/// Creates default FunctionEntry instance (which is empty)
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fn default() -> FunctionEntry {
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FunctionEntry {
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function: BackingFunction::new(""),
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func_str: String::new(),
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min_x: -1.0,
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max_x: 1.0,
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output: FunctionOutput::new_empty(),
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integral: false,
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derivative: false,
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}
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}
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}
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impl FunctionEntry {
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/// Update function settings
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pub fn update(&mut self, func_str: &str, integral: bool, derivative: bool) {
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// If the function string changes, just wipe and restart from scratch
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if func_str != self.func_str {
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self.func_str = func_str.to_string();
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self.function = BackingFunction::new(func_str);
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self.output.invalidate_whole();
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}
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self.derivative = derivative;
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self.integral = integral;
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}
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/// Creates and does the math for creating all the rectangles under the
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/// graph
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fn integral_rectangles(
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&self, integral_min_x: f64, integral_max_x: f64, sum: Riemann, integral_num: usize,
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) -> (Vec<(f64, f64)>, f64) {
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if integral_min_x.is_nan() {
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panic!("integral_min_x is NaN")
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} else if integral_max_x.is_nan() {
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panic!("integral_max_x is NaN")
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}
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let step = (integral_min_x - integral_max_x).abs() / (integral_num as f64);
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let data2: Vec<(f64, f64)> = dyn_iter(&step_helper(integral_num, integral_min_x, step))
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.map(|x| {
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let step_offset = step * x.signum(); // store the offset here so it doesn't have to be calculated multiple times
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let x2: f64 = x + step_offset;
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let (left_x, right_x) = match x.is_sign_positive() {
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true => (*x, x2),
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false => (x2, *x),
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};
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let y = match sum {
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Riemann::Left => self.function.get(left_x),
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Riemann::Right => self.function.get(right_x),
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Riemann::Middle => {
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(self.function.get(left_x) + self.function.get(right_x)) / 2.0
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}
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};
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(x + (step_offset / 2.0), y)
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})
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.filter(|(_, y)| !y.is_nan())
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.collect();
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let area = data2.iter().map(|(_, y)| y * step).sum();
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(data2, area)
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}
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/// Returns `self.func_str`
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pub fn get_func_str(&self) -> &str { &self.func_str }
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/// Helps with processing newton's method depending on level of derivative
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fn newtons_method_helper(&self, threshold: f64, derivative_level: usize) -> Option<Vec<Value>> {
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let range = self.min_x..self.max_x;
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let newtons_method_output: Vec<f64> = match derivative_level {
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0 => newtons_method_helper(
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threshold,
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range,
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self.output.back.to_owned().unwrap(),
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&|x: f64| self.function.get(x),
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&|x: f64| self.function.get_derivative_1(x),
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),
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1 => newtons_method_helper(
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threshold,
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range,
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self.output.derivative.to_owned().unwrap(),
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&|x: f64| self.function.get_derivative_1(x),
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&|x: f64| self.function.get_derivative_2(x),
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),
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_ => unreachable!(),
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};
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if newtons_method_output.is_empty() {
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None
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} else {
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Some(
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dyn_iter(&newtons_method_output)
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.map(|x| (*x, self.function.get(*x)))
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.map(|(x, y)| Value::new(x, y))
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.collect(),
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)
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}
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}
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/// Does the calculations and stores results in `self.output`
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pub fn calculate(
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&mut self, min_x: f64, max_x: f64, width_changed: bool, settings: AppSettings,
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) {
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let resolution: f64 = settings.plot_width as f64 / (max_x.abs() + min_x.abs());
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let resolution_iter = resolution_helper(settings.plot_width + 1, min_x, resolution);
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// Makes sure proper arguments are passed when integral is enabled
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if self.integral && settings.integral_changed {
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self.output.invalidate_integral();
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}
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let mut partial_regen = false;
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let min_max_changed = (min_x != self.min_x) | (max_x != self.max_x);
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if width_changed {
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self.output.invalidate_back();
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self.output.invalidate_derivative();
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self.min_x = min_x;
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self.max_x = max_x;
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} else if min_max_changed && self.output.back.is_some() {
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partial_regen = true;
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let back_cache = self.output.back.as_ref().unwrap();
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let x_data: SteppedVector = back_cache
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.iter()
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.map(|ele| ele.x)
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.collect::<Vec<f64>>()
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.into();
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let back_data: Vec<Value> = dyn_iter(&resolution_iter)
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.cloned()
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.map(|x| {
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if let Some(i) = x_data.get_index(x) {
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back_cache[i]
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} else {
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Value::new(x, self.function.get(x))
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}
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})
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.collect();
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assert_eq!(back_data.len(), settings.plot_width + 1);
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self.output.back = Some(back_data);
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let derivative_cache = self.output.derivative.as_ref().unwrap();
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let new_derivative_data: Vec<Value> = dyn_iter(&resolution_iter)
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.map(|x| {
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if let Some(i) = x_data.get_index(*x) {
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derivative_cache[i]
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} else {
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Value::new(*x, self.function.get_derivative_1(*x))
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}
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})
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.collect();
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assert_eq!(new_derivative_data.len(), settings.plot_width + 1);
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self.output.derivative = Some(new_derivative_data);
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} else {
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self.output.invalidate_back();
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self.output.invalidate_derivative();
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}
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self.min_x = min_x;
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self.max_x = max_x;
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let threshold: f64 = resolution / 2.0;
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if !partial_regen {
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self.output.back = Some({
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if self.output.back.is_none() {
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let data: Vec<Value> = dyn_iter(&resolution_iter)
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.map(|x| Value::new(*x, self.function.get(*x)))
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.collect();
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assert_eq!(data.len(), settings.plot_width + 1);
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self.output.back = Some(data);
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}
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self.output.back.as_ref().unwrap().clone()
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});
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self.output.derivative = {
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if self.output.derivative.is_none() {
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let data: Vec<Value> = dyn_iter(&resolution_iter)
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.map(|x| Value::new(*x, self.function.get_derivative_1(*x)))
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.collect();
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assert_eq!(data.len(), settings.plot_width + 1);
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self.output.derivative = Some(data);
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}
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Some(self.output.derivative.as_ref().unwrap().clone())
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};
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}
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self.output.integral = match self.integral {
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true => {
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if self.output.integral.is_none() {
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let (data, area) = self.integral_rectangles(
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settings.integral_min_x,
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settings.integral_max_x,
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settings.riemann_sum,
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settings.integral_num,
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);
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self.output.integral =
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Some((data.iter().map(|(x, y)| Bar::new(*x, *y)).collect(), area));
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}
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let cache = self.output.integral.as_ref().unwrap();
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Some((cache.0.clone(), cache.1))
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}
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false => None,
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};
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// Calculates extrema
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if settings.do_extrema && (min_max_changed | self.output.extrema.is_none()) {
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self.output.extrema = self.newtons_method_helper(threshold, 1);
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}
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// Calculates roots
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if settings.do_roots && (min_max_changed | self.output.roots.is_none()) {
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self.output.roots = self.newtons_method_helper(threshold, 0);
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}
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}
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/// Displays the function's output on PlotUI `plot_ui` with settings
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/// `settings`. Returns an `Option<f64>` of the calculated integral
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pub fn display(&self, plot_ui: &mut PlotUi, settings: AppSettings) -> Option<f64> {
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let func_str = self.get_func_str();
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let derivative_str = self.function.get_derivative_str();
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let step = (settings.integral_min_x - settings.integral_max_x).abs()
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/ (settings.integral_num as f64);
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// Plot back data
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plot_ui.line(
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vec_tuple_to_line(self.output.back.clone().unwrap())
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.color(Color32::RED)
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.name(func_str),
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);
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// Plot derivative data
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if self.derivative {
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if let Some(derivative_data) = self.output.derivative.clone() {
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plot_ui.line(
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vec_tuple_to_line(derivative_data)
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.color(Color32::GREEN)
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.name(derivative_str),
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);
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}
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}
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// Plot extrema points
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if settings.do_extrema {
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if let Some(extrema_data) = self.output.extrema.clone() {
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plot_ui.points(
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vec_tuple_to_points(extrema_data)
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.color(Color32::YELLOW)
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.name("Extrema")
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.radius(5.0), // Radius of points of Extrema
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);
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}
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}
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// Plot roots points
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if settings.do_roots {
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if let Some(roots_data) = self.output.roots.clone() {
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plot_ui.points(
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vec_tuple_to_points(roots_data)
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.color(Color32::LIGHT_BLUE)
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.name("Root")
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.radius(5.0), // Radius of points of Roots
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);
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}
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}
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// Plot integral data
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if let Some(integral_data) = self.output.integral.clone() {
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plot_ui.bar_chart(
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BarChart::new(integral_data.0)
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.color(Color32::BLUE)
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.width(step),
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);
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// return value rounded to 8 decimal places
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Some(crate::misc::decimal_round(integral_data.1, 8))
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} else {
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None
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}
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}
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/// Runs asserts to make sure everything is the expected value
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#[cfg(test)]
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pub fn tests(
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&mut self, settings: AppSettings, back_target: Vec<(f64, f64)>,
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derivative_target: Vec<(f64, f64)>, area_target: f64, min_x: f64, max_x: f64,
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) {
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{
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self.calculate(min_x, max_x, true, settings);
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let settings = settings;
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let back_target = back_target;
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assert!(self.output.back.is_some());
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let back_data = self.output.back.as_ref().unwrap().clone();
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assert_eq!(back_data.len(), settings.plot_width + 1);
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let back_vec_tuple = back_data.to_tuple();
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assert_eq!(back_vec_tuple, back_target);
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assert!(self.integral);
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assert!(self.derivative);
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assert_eq!(self.output.roots.is_some(), settings.do_roots);
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assert_eq!(self.output.extrema.is_some(), settings.do_extrema);
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assert!(self.output.derivative.is_some());
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assert!(self.output.integral.is_some());
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assert_eq!(
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self.output.derivative.as_ref().unwrap().to_tuple(),
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derivative_target
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);
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assert_eq!(self.output.integral.clone().unwrap().1, area_target);
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}
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}
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}
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#[cfg(test)]
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mod tests {
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use super::*;
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fn app_settings_constructor(
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sum: Riemann, integral_min_x: f64, integral_max_x: f64, pixel_width: usize,
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integral_num: usize,
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) -> AppSettings {
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crate::egui_app::AppSettings {
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help_open: false,
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info_open: false,
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show_side_panel: false,
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riemann_sum: sum,
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integral_min_x,
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integral_max_x,
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integral_changed: true,
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integral_num,
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dark_mode: false,
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do_extrema: false,
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do_roots: false,
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plot_width: pixel_width,
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}
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}
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static BACK_TARGET: [(f64, f64); 11] = [
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(-1.0, 1.0),
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(-0.8, 0.6400000000000001),
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(-0.6, 0.36),
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(-0.4, 0.16000000000000003),
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(-0.19999999999999996, 0.03999999999999998),
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(0.0, 0.0),
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(0.19999999999999996, 0.03999999999999998),
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(0.3999999999999999, 0.15999999999999992),
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(0.6000000000000001, 0.3600000000000001),
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(0.8, 0.6400000000000001),
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(1.0, 1.0),
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];
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static DERIVATIVE_TARGET: [(f64, f64); 11] = [
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(-1.0, -2.0),
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(-0.8, -1.6),
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(-0.6, -1.2),
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(-0.4, -0.8),
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(-0.19999999999999996, -0.3999999999999999),
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(0.0, 0.0),
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(0.19999999999999996, 0.3999999999999999),
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(0.3999999999999999, 0.7999999999999998),
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(0.6000000000000001, 1.2000000000000002),
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(0.8, 1.6),
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(1.0, 2.0),
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];
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fn do_test(sum: Riemann, area_target: f64) {
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let settings = app_settings_constructor(sum, -1.0, 1.0, 10, 10);
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let mut function = FunctionEntry::default();
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function.update("x^2", true, true);
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function.tests(
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settings,
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BACK_TARGET.to_vec(),
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DERIVATIVE_TARGET.to_vec(),
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area_target,
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-1.0,
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1.0,
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);
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}
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#[test]
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fn left_function_test() {
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let area_target = 0.9600000000000001;
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do_test(Riemann::Left, area_target);
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}
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#[test]
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fn middle_function_test() {
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let area_target = 0.92;
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do_test(Riemann::Middle, area_target);
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}
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#[test]
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fn right_function_test() {
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let area_target = 0.8800000000000001;
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do_test(Riemann::Right, area_target);
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}
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}
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