2022-03-04 13:54:25 -05:00

690 lines
22 KiB
Rust

#![allow(clippy::too_many_arguments)] // Clippy, shut
#[allow(unused_imports)]
use crate::misc::{debug_log, BackingFunction, BoxFunction, SteppedVector, EPSILON};
use eframe::egui::{
plot::{BarChart, Line, Value, Values},
widgets::plot::Bar,
};
use meval::Expr;
use std::fmt::{self, Debug};
#[derive(PartialEq, Debug, Copy, Clone)]
pub enum RiemannSum {
Left,
Middle,
Right,
}
impl fmt::Display for RiemannSum {
fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result { write!(f, "{:?}", self) }
}
pub struct Function {
function: BackingFunction,
func_str: String,
min_x: f64,
max_x: f64,
pixel_width: usize,
back_cache: Option<Vec<Value>>,
front_cache: Option<(Vec<Bar>, Vec<Value>, f64)>,
derivative_cache: Option<Vec<Value>>,
pub(crate) integral: bool,
pub(crate) derivative: bool,
pub(crate) nth_derivative: u64,
integral_min_x: f64,
integral_max_x: f64,
integral_num: usize,
sum: RiemannSum,
}
// x^2 function, set here so we don't have to regenerate it every time a new function is made
fn default_function(x: f64) -> f64 { x.powi(2) }
impl Function {
// Creates Empty Function instance
pub fn empty() -> Self {
Self {
function: BackingFunction::new(Box::new(default_function)),
func_str: String::new(),
min_x: -1.0,
max_x: 1.0,
pixel_width: 100,
back_cache: None,
front_cache: None,
derivative_cache: None,
integral: false,
derivative: false,
nth_derivative: 1,
integral_min_x: f64::NAN,
integral_max_x: f64::NAN,
integral_num: 0,
sum: crate::egui_app::DEFAULT_RIEMANN,
}
}
// Runs the internal function to get values
fn run_func(&self, x: f64) -> f64 { self.function.get(x) }
pub fn update(
&mut self, func_str: String, integral: bool, derivative: bool, integral_min_x: Option<f64>,
integral_max_x: Option<f64>, integral_num: Option<usize>, sum: Option<RiemannSum>,
) {
// If the function string changes, just wipe and restart from scratch
if func_str != self.func_str {
self.func_str = func_str.clone();
self.function = BackingFunction::new(Box::new({
let expr: Expr = func_str.parse().unwrap();
expr.bind("x").unwrap()
}));
self.back_cache = None;
self.front_cache = None;
self.derivative_cache = None;
}
self.derivative = derivative;
self.integral = integral;
// Makes sure proper arguments are passed when integral is enabled
if integral
&& (integral_min_x != Some(self.integral_min_x))
| (integral_max_x != Some(self.integral_max_x))
| (integral_num != Some(self.integral_num))
| (sum != Some(self.sum))
{
self.front_cache = None;
self.integral_min_x = integral_min_x.expect("integral_min_x is None");
self.integral_max_x = integral_max_x.expect("integral_max_x is None");
self.integral_num = integral_num.expect("integral_num is None");
self.sum = sum.expect("sum is None");
}
}
pub fn update_bounds(&mut self, min_x: f64, max_x: f64, pixel_width: usize) {
if pixel_width != self.pixel_width {
self.back_cache = None;
self.derivative_cache = None;
self.min_x = min_x;
self.max_x = max_x;
self.pixel_width = pixel_width;
} else if ((min_x != self.min_x) | (max_x != self.max_x)) && self.back_cache.is_some() {
let resolution: f64 = self.pixel_width as f64 / (max_x.abs() + min_x.abs());
let back_cache = self.back_cache.as_ref().unwrap();
let x_data: SteppedVector = back_cache
.iter()
.map(|ele| ele.x)
.collect::<Vec<f64>>()
.into();
self.back_cache = Some(
(0..=self.pixel_width)
.map(|x| (x as f64 / resolution as f64) + min_x)
.map(|x| {
if let Some(i) = x_data.get_index(x) {
back_cache[i]
} else {
Value::new(x, self.run_func(x))
}
})
.collect(),
);
if self.derivative_cache.is_some() {
let derivative_cache = self.derivative_cache.as_ref().unwrap();
self.derivative_cache = Some(
(0..=self.pixel_width)
.map(|x| (x as f64 / resolution as f64) + min_x)
.map(|x| {
if let Some(i) = x_data.get_index(x) {
derivative_cache[i]
} else {
Value::new(x, self.function.derivative(x, self.nth_derivative))
}
})
.collect(),
);
}
} else {
self.back_cache = None;
self.derivative_cache = None;
self.min_x = min_x;
self.max_x = max_x;
self.pixel_width = pixel_width;
}
}
pub fn run_back(
&mut self,
) -> (
Vec<Value>,
Option<(Vec<Bar>, Vec<Value>, f64)>,
Option<Vec<Value>>,
) {
let back_values: Vec<Value> = {
if self.back_cache.is_none() {
let resolution: f64 =
(self.pixel_width as f64 / (self.max_x - self.min_x).abs()) as f64;
self.back_cache = Some(
(0..self.pixel_width)
.map(|x| (x as f64 / resolution as f64) + self.min_x)
.map(|x| Value::new(x, self.run_func(x)))
.collect(),
);
}
self.back_cache.as_ref().unwrap().clone()
};
let derivative_values: Option<Vec<Value>> = match self.derivative {
true => {
if self.derivative_cache.is_none() {
let back_cache = self.back_cache.as_ref().unwrap().clone();
self.derivative_cache = Some(
back_cache
.iter()
.map(|ele| {
let x = ele.x;
let (x1, x2) = (x - EPSILON, x + EPSILON);
let (y1, y2) = (self.run_func(x1), self.run_func(x2));
let slope = (y2 - y1) / (EPSILON * 2.0);
Value::new(x, slope)
})
.collect(),
);
}
Some(self.derivative_cache.as_ref().unwrap().clone())
}
false => None,
};
let front_bars = match self.integral {
true => {
if self.front_cache.is_none() {
let (data, area) = self.integral_rectangles();
self.front_cache = Some((
data.iter().map(|(x, y, _)| Bar::new(*x, *y)).collect(),
data.iter().map(|(x, _, y)| Value::new(*x, *y)).collect(),
area,
));
}
let cache = self.front_cache.as_ref().unwrap();
Some((cache.0.clone(), cache.1.clone(), cache.2))
}
false => None,
};
(back_values, front_bars, derivative_values)
}
pub fn run(&mut self) -> (Line, Option<(BarChart, Line, f64)>, Option<Line>) {
let (back_values, front_data_option, derivative_option) = self.run_back();
(
Line::new(Values::from_values(back_values)),
if let Some(front_data1) = front_data_option {
Some((
BarChart::new(front_data1.0),
Line::new(Values::from_values(front_data1.1)),
front_data1.2,
))
} else {
None
},
derivative_option
.map(|derivative_data| Line::new(Values::from_values(derivative_data))),
)
}
// Creates and does the math for creating all the rectangles under the graph
fn integral_rectangles(&self) -> (Vec<(f64, f64, f64)>, f64) {
if self.integral_min_x.is_nan() {
panic!("integral_min_x is NaN")
} else if self.integral_max_x.is_nan() {
panic!("integral_max_x is NaN")
}
let step = (self.integral_min_x - self.integral_max_x).abs() / (self.integral_num as f64);
let mut area: f64 = 0.0;
let data2: Vec<(f64, f64, f64)> = (1..=self.integral_num)
.map(|e| {
let x: f64 = ((e as f64) * step) + self.integral_min_x;
let step_offset = step * x.signum(); // store the offset here so it doesn't have to be calculated multiple times
let x2: f64 = x + step_offset;
let (left_x, right_x) = match x.is_sign_positive() {
true => (x, x2),
false => (x2, x),
};
let y = match self.sum {
RiemannSum::Left => self.run_func(left_x),
RiemannSum::Right => self.run_func(right_x),
RiemannSum::Middle => (self.run_func(left_x) + self.run_func(right_x)) / 2.0,
};
if !y.is_nan() {
area += y * step;
}
(x + (step_offset / 2.0), y, area)
})
.filter(|(_, y, _)| !y.is_nan())
.collect();
(data2, area)
}
// Set func_str to an empty string
pub fn empty_func_str(&mut self) { self.func_str = String::new(); }
// Updates riemann value and invalidates front_cache if needed
pub fn update_riemann(mut self, riemann: RiemannSum) -> Self {
if self.sum != riemann {
self.sum = riemann;
self.front_cache = None;
}
self
}
// Toggles integral
pub fn integral(mut self, integral: bool) -> Self {
self.integral = integral;
self
}
// Toggles integral
pub fn integral_num(mut self, integral_num: usize) -> Self {
self.integral_num = integral_num;
self
}
pub fn pixel_width(mut self, pixel_width: usize) -> Self {
self.pixel_width = pixel_width;
self
}
pub fn integral_bounds(mut self, min_x: f64, max_x: f64) -> Self {
if min_x >= max_x {
panic!("integral_bounds: min_x is larger than max_x");
}
self.integral_min_x = min_x;
self.integral_max_x = max_x;
self
}
}
#[test]
fn left_function_test() {
let integral_num = 10;
let pixel_width = 10;
let mut function = Function::empty()
.update_riemann(RiemannSum::Left)
.pixel_width(pixel_width)
.integral_num(integral_num)
.integral_bounds(-1.0, 1.0);
let back_values_target = vec![
(-1.0, 1.0),
(-0.8, 0.6400000000000001),
(-0.6, 0.36),
(-0.4, 0.16000000000000003),
(-0.19999999999999996, 0.03999999999999998),
(0.0, 0.0),
(0.19999999999999996, 0.03999999999999998),
(0.3999999999999999, 0.15999999999999992),
(0.6000000000000001, 0.3600000000000001),
(0.8, 0.6400000000000001),
];
let derivative_target = vec![
(-1.0, -2.0000000000575113),
(-0.8, -1.5999999999349868),
(-0.6, -1.1999999998679733),
(-0.4, -0.8000000000230045),
(-0.19999999999999996, -0.3999999999906856),
(0.0, 0.0),
(0.19999999999999996, 0.3999999999906856),
(0.3999999999999999, 0.8000000000230045),
(0.6000000000000001, 1.1999999999234845),
(0.8, 1.5999999999349868),
];
let area_target = 0.8720000000000001;
let vec_bars_target = vec![
1.0,
0.6400000000000001,
0.3599999999999998,
0.15999999999999998,
0.0,
0.04000000000000007,
0.16000000000000011,
0.3600000000000001,
0.6400000000000001,
1.0,
];
let vec_integral_target = vec![
(-0.9, 0.2),
(-0.7, 0.32800000000000007),
(-0.4999999999999999, 0.4),
(-0.29999999999999993, 0.432),
(0.1, 0.432),
(0.30000000000000016, 0.44),
(0.5000000000000001, 0.47200000000000003),
(0.7000000000000001, 0.544),
(0.9, 0.672),
(1.1, 0.8720000000000001),
];
{
let (back_values, bars, derivative) = function.run_back();
assert!(derivative.is_none());
assert!(bars.is_none());
assert_eq!(back_values.len(), pixel_width);
let back_values_tuple: Vec<(f64, f64)> =
back_values.iter().map(|ele| (ele.x, ele.y)).collect();
assert_eq!(back_values_tuple, back_values_target);
}
{
function = function.integral(true);
let (back_values, bars, derivative) = function.run_back();
assert!(derivative.is_none());
assert!(bars.is_some());
assert_eq!(back_values.len(), pixel_width);
assert_eq!(bars.clone().unwrap().2, area_target);
let vec_bars = bars.unwrap().0;
assert_eq!(vec_bars.len(), integral_num);
let back_values_tuple: Vec<(f64, f64)> =
back_values.iter().map(|ele| (ele.x, ele.y)).collect();
assert_eq!(back_values_tuple, back_values_target);
}
{
function.derivative = true;
let (back_values, bars, derivative) = function.run_back();
assert!(derivative.is_some());
let derivative_vec: Vec<(f64, f64)> = derivative
.unwrap()
.iter()
.map(|ele| (ele.x, ele.y))
.collect();
assert_eq!(derivative_vec, derivative_target);
assert!(bars.is_some());
assert_eq!(back_values.len(), pixel_width);
assert_eq!(bars.clone().unwrap().2, area_target);
let bars_unwrapped = bars.unwrap();
let vec_bars: Vec<f64> = bars_unwrapped.0.iter().map(|bar| bar.value).collect();
assert_eq!(vec_bars.len(), integral_num);
assert_eq!(vec_bars, vec_bars_target);
let integral_line = bars_unwrapped.1;
let vec_integral: Vec<(f64, f64)> =
integral_line.iter().map(|ele| (ele.x, ele.y)).collect();
assert_eq!(vec_integral.len(), integral_num);
assert_eq!(vec_integral, vec_integral_target);
assert_eq!(vec_integral[vec_integral.len() - 1].1, area_target);
}
}
#[test]
fn middle_function_test() {
let integral_num = 10;
let pixel_width = 10;
let mut function = Function::empty()
.update_riemann(RiemannSum::Middle)
.pixel_width(pixel_width)
.integral_num(integral_num)
.integral_bounds(-1.0, 1.0);
let back_values_target = vec![
(-1.0, 1.0),
(-0.8, 0.6400000000000001),
(-0.6, 0.36),
(-0.4, 0.16000000000000003),
(-0.19999999999999996, 0.03999999999999998),
(0.0, 0.0),
(0.19999999999999996, 0.03999999999999998),
(0.3999999999999999, 0.15999999999999992),
(0.6000000000000001, 0.3600000000000001),
(0.8, 0.6400000000000001),
];
let derivative_target = vec![
(-1.0, -2.0000000000575113),
(-0.8, -1.5999999999349868),
(-0.6, -1.1999999998679733),
(-0.4, -0.8000000000230045),
(-0.19999999999999996, -0.3999999999906856),
(0.0, 0.0),
(0.19999999999999996, 0.3999999999906856),
(0.3999999999999999, 0.8000000000230045),
(0.6000000000000001, 1.1999999999234845),
(0.8, 1.5999999999349868),
];
let area_target = 0.9200000000000002;
let vec_bars_target = vec![
0.8200000000000001,
0.5,
0.2599999999999999,
0.09999999999999998,
0.020000000000000004,
0.1000000000000001,
0.2600000000000001,
0.5000000000000001,
0.8200000000000001,
1.22,
];
let vec_integral_target = vec![
(-0.9, 0.16400000000000003),
(-0.7, 0.264),
(-0.4999999999999999, 0.316),
(-0.29999999999999993, 0.336),
(0.1, 0.34),
(0.30000000000000016, 0.36000000000000004),
(0.5000000000000001, 0.4120000000000001),
(0.7000000000000001, 0.5120000000000001),
(0.9, 0.6760000000000002),
(1.1, 0.9200000000000002),
];
{
let (back_values, bars, derivative) = function.run_back();
assert!(derivative.is_none());
assert!(bars.is_none());
assert_eq!(back_values.len(), pixel_width);
let back_values_tuple: Vec<(f64, f64)> =
back_values.iter().map(|ele| (ele.x, ele.y)).collect();
assert_eq!(back_values_tuple, back_values_target);
}
{
function = function.integral(true);
let (back_values, bars, derivative) = function.run_back();
assert!(derivative.is_none());
assert!(bars.is_some());
assert_eq!(back_values.len(), pixel_width);
assert_eq!(bars.clone().unwrap().2, area_target);
let vec_bars = bars.unwrap().0;
assert_eq!(vec_bars.len(), integral_num);
let back_values_tuple: Vec<(f64, f64)> =
back_values.iter().map(|ele| (ele.x, ele.y)).collect();
assert_eq!(back_values_tuple, back_values_target);
}
{
function.derivative = true;
let (back_values, bars, derivative) = function.run_back();
assert!(derivative.is_some());
let derivative_vec: Vec<(f64, f64)> = derivative
.unwrap()
.iter()
.map(|ele| (ele.x, ele.y))
.collect();
assert_eq!(derivative_vec, derivative_target);
assert!(bars.is_some());
assert_eq!(back_values.len(), pixel_width);
assert_eq!(bars.clone().unwrap().2, area_target);
let bars_unwrapped = bars.unwrap();
let vec_bars: Vec<f64> = bars_unwrapped.0.iter().map(|bar| bar.value).collect();
assert_eq!(vec_bars.len(), integral_num);
assert_eq!(vec_bars, vec_bars_target);
let integral_line = bars_unwrapped.1;
let vec_integral: Vec<(f64, f64)> =
integral_line.iter().map(|ele| (ele.x, ele.y)).collect();
assert_eq!(vec_integral.len(), integral_num);
assert_eq!(vec_integral, vec_integral_target);
assert_eq!(vec_integral[vec_integral.len() - 1].1, area_target);
}
}
#[test]
fn right_function_test() {
let integral_num = 10;
let pixel_width = 10;
let mut function = Function::empty()
.update_riemann(RiemannSum::Right)
.pixel_width(pixel_width)
.integral_num(integral_num)
.integral_bounds(-1.0, 1.0);
let back_values_target = vec![
(-1.0, 1.0),
(-0.8, 0.6400000000000001),
(-0.6, 0.36),
(-0.4, 0.16000000000000003),
(-0.19999999999999996, 0.03999999999999998),
(0.0, 0.0),
(0.19999999999999996, 0.03999999999999998),
(0.3999999999999999, 0.15999999999999992),
(0.6000000000000001, 0.3600000000000001),
(0.8, 0.6400000000000001),
];
let derivative_target = vec![
(-1.0, -2.0000000000575113),
(-0.8, -1.5999999999349868),
(-0.6, -1.1999999998679733),
(-0.4, -0.8000000000230045),
(-0.19999999999999996, -0.3999999999906856),
(0.0, 0.0),
(0.19999999999999996, 0.3999999999906856),
(0.3999999999999999, 0.8000000000230045),
(0.6000000000000001, 1.1999999999234845),
(0.8, 1.5999999999349868),
];
let area_target = 0.9680000000000002;
let vec_bars_target = vec![
0.6400000000000001,
0.36,
0.15999999999999992,
0.03999999999999998,
0.04000000000000001,
0.16000000000000014,
0.3600000000000001,
0.6400000000000001,
1.0,
1.44,
];
let vec_integral_target = vec![
(-0.9, 0.12800000000000003),
(-0.7, 0.2),
(-0.4999999999999999, 0.23199999999999998),
(-0.29999999999999993, 0.24),
(0.1, 0.248),
(0.30000000000000016, 0.28),
(0.5000000000000001, 0.35200000000000004),
(0.7000000000000001, 0.4800000000000001),
(0.9, 0.6800000000000002),
(1.1, 0.9680000000000002),
];
{
let (back_values, bars, derivative) = function.run_back();
assert!(derivative.is_none());
assert!(bars.is_none());
assert_eq!(back_values.len(), pixel_width);
let back_values_tuple: Vec<(f64, f64)> =
back_values.iter().map(|ele| (ele.x, ele.y)).collect();
assert_eq!(back_values_tuple, back_values_target);
}
{
function = function.integral(true);
let (back_values, bars, derivative) = function.run_back();
assert!(derivative.is_none());
assert!(bars.is_some());
assert_eq!(back_values.len(), pixel_width);
assert_eq!(bars.clone().unwrap().2, area_target);
let vec_bars = bars.unwrap().0;
assert_eq!(vec_bars.len(), integral_num);
let back_values_tuple: Vec<(f64, f64)> =
back_values.iter().map(|ele| (ele.x, ele.y)).collect();
assert_eq!(back_values_tuple, back_values_target);
}
{
function.derivative = true;
let (back_values, bars, derivative) = function.run_back();
assert!(derivative.is_some());
let derivative_vec: Vec<(f64, f64)> = derivative
.unwrap()
.iter()
.map(|ele| (ele.x, ele.y))
.collect();
assert_eq!(derivative_vec, derivative_target);
assert!(bars.is_some());
assert_eq!(back_values.len(), pixel_width);
assert_eq!(bars.clone().unwrap().2, area_target);
let bars_unwrapped = bars.unwrap();
let vec_bars: Vec<f64> = bars_unwrapped.0.iter().map(|bar| bar.value).collect();
assert_eq!(vec_bars.len(), integral_num);
assert_eq!(vec_bars, vec_bars_target);
let integral_line = bars_unwrapped.1;
let vec_integral: Vec<(f64, f64)> =
integral_line.iter().map(|ele| (ele.x, ele.y)).collect();
assert_eq!(vec_integral.len(), integral_num);
assert_eq!(vec_integral, vec_integral_target);
assert_eq!(vec_integral[vec_integral.len() - 1].1, area_target);
}
}