532 lines
14 KiB
Rust
532 lines
14 KiB
Rust
#![allow(clippy::too_many_arguments)] // Clippy, shut
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use crate::math_app::AppSettings;
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use crate::misc::*;
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use crate::parsing::{process_func_str, BackingFunction};
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use crate::widgets::AutoComplete;
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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(threading)]
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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)`, and `f''(x)`
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function: BackingFunction,
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/// Stores a function string (that hasn't been processed via `process_func_str`) to display to the user
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raw_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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/// 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 for other purposes)
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pub derivative: bool,
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back_data: Vec<Value>,
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integral_data: Option<(Vec<Bar>, f64)>,
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derivative_data: Vec<Value>,
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extrema_data: Vec<Value>,
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roots_data: Vec<Value>,
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autocomplete: AutoComplete<'static>,
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test_result: Option<String>,
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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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raw_func_str: String::new(),
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min_x: -1.0,
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max_x: 1.0,
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integral: false,
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derivative: false,
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back_data: Vec::new(),
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integral_data: None,
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derivative_data: Vec::new(),
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extrema_data: Vec::new(),
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roots_data: Vec::new(),
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autocomplete: AutoComplete::default(),
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test_result: None,
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}
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}
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}
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impl FunctionEntry {
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/// Create autocomplete ui and handle user input
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pub fn auto_complete(&mut self, ui: &mut egui::Ui, i: i32) -> (bool, bool, Option<String>) {
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let (output_string, in_focus) = self.autocomplete.ui(ui, self.raw_func_str.clone(), i);
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let changed = output_string != self.raw_func_str;
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if changed {
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self.update_string(&output_string);
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}
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(in_focus, changed, self.get_test_result())
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}
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/// Get function's cached test result
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pub fn get_test_result(&self) -> Option<String> { self.test_result.clone() }
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/// Update function string and test it
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fn update_string(&mut self, raw_func_str: &str) {
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let processed_func = process_func_str(raw_func_str);
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let output = crate::parsing::test_func(&processed_func);
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self.raw_func_str = raw_func_str.to_string();
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if output.is_some() {
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self.test_result = output;
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return;
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} else {
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self.test_result = None;
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}
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self.function = BackingFunction::new(&processed_func);
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self.invalidate_whole();
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}
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/// Get function that can be used to calculate integral based on Riemann Sum type
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fn get_sum_func(&self, sum: Riemann) -> FunctionHelper {
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match sum {
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Riemann::Left => {
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FunctionHelper::new(|left_x: f64, _: f64| -> f64 { self.function.get(left_x) })
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}
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Riemann::Right => {
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FunctionHelper::new(|_: f64, right_x: f64| -> f64 { self.function.get(right_x) })
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}
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Riemann::Middle => FunctionHelper::new(|left_x: f64, right_x: f64| -> f64 {
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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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}
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/// Creates and does the math for creating all the rectangles under the 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 sum_func = self.get_sum_func(*sum);
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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 = sum_func.get(left_x, right_x);
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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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/// 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) -> 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.back_data.as_slice(),
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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.derivative_data.as_slice(),
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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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dyn_iter(&newtons_method_output)
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.map(|x| Value::new(*x, self.function.get(*x)))
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.collect()
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}
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/// Does the calculations and stores results in `self`
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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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if self.test_result.is_some() {
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return;
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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.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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let derivative_required = settings.do_extrema | self.derivative;
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self.min_x = *min_x;
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self.max_x = *max_x;
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if width_changed {
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self.invalidate_back();
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self.invalidate_derivative();
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} else if min_max_changed && !self.back_data.is_empty() {
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partial_regen = true;
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let x_data: SteppedVector = self
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.back_data
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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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.map(|x| {
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if let Some(i) = x_data.get_index(x) {
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self.back_data[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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debug_assert_eq!(back_data.len(), settings.plot_width + 1);
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self.back_data = back_data;
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if derivative_required {
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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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self.derivative_data[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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debug_assert_eq!(new_derivative_data.len(), settings.plot_width + 1);
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self.derivative_data = new_derivative_data;
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} else {
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self.invalidate_derivative();
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}
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} else {
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self.invalidate_back();
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self.invalidate_derivative();
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}
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let threshold: f64 = resolution / 2.0;
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if !partial_regen {
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if self.back_data.is_empty() {
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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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debug_assert_eq!(data.len(), settings.plot_width + 1);
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self.back_data = data;
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}
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if derivative_required && self.derivative_data.is_empty() {
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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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debug_assert_eq!(data.len(), settings.plot_width + 1);
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self.derivative_data = data;
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}
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}
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if self.integral {
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if self.integral_data.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.integral_data =
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Some((data.iter().map(|(x, y)| Bar::new(*x, *y)).collect(), area));
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}
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} else {
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self.invalidate_integral();
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}
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// Calculates extrema
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if settings.do_extrema && (min_max_changed | self.extrema_data.is_empty()) {
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self.extrema_data = 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.roots_data.is_empty()) {
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self.roots_data = 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 `settings`.
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/// Returns an `Option<f64>` of the calculated integral.
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pub fn display(
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&self, plot_ui: &mut PlotUi, settings: &AppSettings, main_plot_color: Color32,
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) -> Option<f64> {
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if self.test_result.is_some() {
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return None;
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}
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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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if !self.back_data.is_empty() {
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plot_ui.line(
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self.back_data
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.to_line()
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.color(main_plot_color)
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.name(&self.raw_func_str),
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);
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}
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// Plot derivative data
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if self.derivative && !self.derivative_data.is_empty() {
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plot_ui.line(
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self.derivative_data
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.to_line()
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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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// Plot extrema points
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if settings.do_extrema {
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plot_ui.points(
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self.extrema_data
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.to_points()
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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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// Plot roots points
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if settings.do_roots {
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plot_ui.points(
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self.roots_data
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.to_points()
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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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// Plot integral data
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match &self.integral_data {
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Some(integral_data) => {
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plot_ui.bar_chart(
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BarChart::new(integral_data.0.clone())
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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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}
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_ => None,
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}
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}
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/// Invalidate entire cache
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pub fn invalidate_whole(&mut self) {
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self.invalidate_back();
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self.invalidate_integral();
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self.invalidate_derivative();
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self.extrema_data.clear();
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self.roots_data.clear();
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}
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/// Invalidate `back` data
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pub fn invalidate_back(&mut self) { self.back_data.clear(); }
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/// Invalidate Integral data
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pub fn invalidate_integral(&mut self) { self.integral_data = None; }
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/// Invalidate Derivative data
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pub fn invalidate_derivative(&mut self) { self.derivative_data.clear(); }
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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 back_target = back_target;
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assert!(!self.back_data.is_empty());
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assert_eq!(self.back_data.len(), settings.plot_width + 1);
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let back_vec_tuple = self.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.roots_data.is_empty(), settings.do_roots);
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assert_eq!(!self.extrema_data.is_empty(), settings.do_extrema);
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assert!(!self.derivative_data.is_empty());
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assert!(self.integral_data.is_some());
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assert_eq!(self.derivative_data.to_tuple(), derivative_target);
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assert_eq!(self.integral_data.clone().unwrap().1, area_target);
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}
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{
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self.update_string("sin(x)");
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assert!(self.get_test_result().is_none());
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assert_eq!(&self.raw_func_str, "sin(x)");
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self.integral = false;
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self.derivative = false;
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assert!(!self.integral);
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assert!(!self.derivative);
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assert!(self.back_data.is_empty());
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assert!(self.integral_data.is_none());
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assert!(self.roots_data.is_empty());
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assert!(self.extrema_data.is_empty());
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assert!(self.derivative_data.is_empty());
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self.calculate(&min_x, &max_x, true, &settings);
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assert!(!self.back_data.is_empty());
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assert!(self.integral_data.is_none());
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assert!(self.roots_data.is_empty());
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assert!(self.extrema_data.is_empty());
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assert!(self.derivative_data.is_empty());
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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::math_app::AppSettings {
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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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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_string("x^2");
|
|
function.integral = true;
|
|
function.derivative = true;
|
|
|
|
function.tests(
|
|
settings,
|
|
BACK_TARGET.to_vec(),
|
|
DERIVATIVE_TARGET.to_vec(),
|
|
area_target,
|
|
-1.0,
|
|
1.0,
|
|
);
|
|
}
|
|
|
|
#[test]
|
|
fn function_entry_test() {
|
|
do_test(Riemann::Left, 0.9600000000000001);
|
|
do_test(Riemann::Middle, 0.92);
|
|
do_test(Riemann::Right, 0.8800000000000001);
|
|
}
|
|
}
|