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use crate::{gamma_function, polygamma_function, Elementary::*, Factorial};
use std::{f64::consts::E, sync::Arc};
use crate::{Error, Func};
use super::series_expansions::SeriesExpansion;
// unit function f(x) -> x
fn f() -> Func {
Box::new(move |x| x)
}
#[derive(Debug, Clone, PartialEq)]
pub enum Elementary {
// Standard trig functions
Sin(Arc<Elementary>), // of the type sin(f(x))
Cos(Arc<Elementary>), // of the type cos(f(x))
Tan(Arc<Elementary>), // of the type tan(f(x))
Sec(Arc<Elementary>), // of the tyoe sec(f(x))
Csc(Arc<Elementary>), // of the type csc(f(x))
Cot(Arc<Elementary>), // of the type cot(f(x))
// Standard arcus functions
Asin(Arc<Elementary>), // of the type arcsin(f(x))
Acos(Arc<Elementary>), // of the type arccos(f(x))
Atan(Arc<Elementary>), // of the type arctan(f(x))
// hyperbolic trig functions
Sinh(Arc<Elementary>), // of the type sinh(f(x))
Cosh(Arc<Elementary>), // of the type cosh(f(x))
Tanh(Arc<Elementary>), // of the type tanh(f(x))
// Standard operations
Add(Arc<Elementary>, Arc<Elementary>), // of the type f(x) + g(x)
Sub(Arc<Elementary>, Arc<Elementary>), // of the type f(x) - g(x)
Mul(Arc<Elementary>, Arc<Elementary>), // of the type f(x) * g(x)
Div(Arc<Elementary>, Arc<Elementary>), // of the type f(x) / g(x)
Pow(Arc<Elementary>, Arc<Elementary>), // of the type f(x)^g(x)
Log(Arc<Elementary>, Arc<Elementary>), // of the type logb(f(x)) where b = g(x)
// special functions
Factorial(Arc<Elementary>),
// gamma function
Gamma(Arc<Elementary>), // of the type 𝜞(f(x))
Polygamma(Arc<Elementary>, usize), // Of the type 𝝍m(f(x))
// Absolute value function
Abs(Arc<Elementary>),
// Constant function
Con(f64), // of the type c
X, // unit function f(x) = x. Any function dependant on a variable must include this
// function as it returns a function of type Func which returns the input value.
// X will represent the independant variable in each function
}
impl Elementary {
pub fn call(self) -> Func {
Box::new(move |x| match self.clone() {
Sin(func) => (*func).clone().call()(x).sin(),
Cos(func) => (*func).clone().call()(x).cos(),
Tan(func) => (*func).clone().call()(x).tan(),
Sec(func) => 1. / (*func).clone().call()(x).cos(),
Csc(func) => 1. / (*func).clone().call()(x).sin(),
Cot(func) => 1. / (*func).clone().call()(x).tan(),
Asin(func) => (*func).clone().call()(x).asin(),
Acos(func) => (*func).clone().call()(x).acos(),
Atan(func) => (*func).clone().call()(x).atan(),
Sinh(func) => {
(E.powf((*func).clone().call()(x)) - E.powf(-(*func).clone().call()(x))) / 2.
}
Cosh(func) => {
(E.powf((*func).clone().call()(x)) + E.powf(-(*func).clone().call()(x))) / 2.
}
Tanh(func) => Sinh(func.clone()).call()(x) / Cosh(func).call()(x),
Add(func1, func2) => (*func1).clone().call()(x) + (*func2).clone().call()(x),
Sub(func1, func2) => (*func1).clone().call()(x) - (*func2).clone().call()(x),
Mul(func1, func2) => (*func1).clone().call()(x) * (*func2).clone().call()(x),
Div(func1, func2) => (*func1).clone().call()(x) / (*func2).clone().call()(x),
Pow(func1, func2) => (*func1).clone().call()(x).powf((*func2).clone().call()(x)),
Log(func1, func2) => (*func2).clone().call()(x).log((*func1).clone().call()(x)),
Factorial(func) => (*func).clone().call()(x).factorial(),
Gamma(func) => gamma_function((*func).clone().call()(x)),
Polygamma(func, order) => polygamma_function((*func).clone().call()(x), order),
Abs(func) => (*func).clone().call()(x).abs(),
Con(numb) => numb,
X => f()(x),
})
}
}
// returns the inner Elementary value of the Arc or returns a clone
pub fn force_unwrap(element: &Arc<Elementary>) -> Elementary {
if let Ok(inner) = Arc::try_unwrap(element.clone()) {
inner
} else {
(**element).clone()
}
}
// basic trig functions
/// Creates a [Function](crate::Function) equal to the sine of the passed [Function](crate::Function)
///
/// i.e f(x) ⟹ sin(f(x))
///
/// Example:
/// ```rust
/// let x = Function::default();
/// let sin_of_x = sin(x);
/// assert_eq!(sin_of_x.call(PI / 2.), 1.);
/// ```
pub fn sin(func: Function) -> Function {
let new_function = Sin(Arc::new(func.elementary()));
Function::from(new_function)
}
/// Creates a [Function](crate::Function) equal to the cosine of the passed [Function](crate::Function)
///
/// i.e f(x) ⟹ cos(f(x))
///
/// Example:
/// ```rust
/// let x = Function::default();
/// let cos_of_x = cos(x);
/// assert_eq!(cos_of_x.call(0.), 1.);
/// ```
pub fn cos(func: Function) -> Function {
let new_function = Cos(Arc::new(func.elementary()));
Function::from(new_function)
}
/// Creates a [Function](crate::Function) equal to the tangent of the passed [Function](crate::Function)
///
/// i.e f(x) ⟹ tan(f(x))
///
/// Example:
/// ```rust
/// let x = Function::default();
/// let tan_of_x = tan(x);
/// assert_eq!(tan_of_x.call(PI / 4.), 1.);
/// ```
pub fn tan(func: Function) -> Function {
let new_function = Tan(Arc::new(func.elementary()));
Function::from(new_function)
}
/// Creates a [Function](crate::Function) equal to the secant of the passed [Function](crate::Function)
///
/// i.e f(x) ⟹ sec(f(x))
///
/// Example:
/// ```rust
/// let x = Function::default();
/// let sec_of_x = sec(x);
/// assert_eq!(sec_of_x.call(PI), -1.);
/// ```
pub fn sec(func: Function) -> Function {
let new_function = Sec(Arc::new(func.elementary()));
Function::from(new_function)
}
/// Creates a [Function](crate::Function) equal to the cosecant of the passed [Function](crate::Function)
///
/// i.e f(x) ⟹ csc(f(x))
///
/// Example:
/// ```rust
/// let x = Function::default();
/// let csc_of_x = csc(x);
/// assert_eq!(csc_of_x.call(3./2. * PI), -1.);
/// ```
pub fn csc(func: Function) -> Function {
let new_function = Csc(Arc::new(func.elementary()));
Function::from(new_function)
}
/// Creates a [Function](crate::Function) equal to the cotangent of the passed [Function](crate::Function)
///
/// i.e f(x) ⟹ cot(f(x))
///
/// Example:
/// ```rust
/// let x = Function::default();
/// let cot_of_x = cot(x);
/// assert_eq!(cot_of_x.call(PI/2.), 0.);
/// ```
pub fn cot(func: Function) -> Function {
let new_function = Cot(Arc::new(func.elementary()));
Function::from(new_function)
}
// basic arcus functions
/// Creates a [Function](crate::Function) equal to the arcsine of the passed [Function](crate::Function)
///
/// i.e f(x) ⟹ asin(f(x))
///
/// Example:
/// ```rust
/// let x = function::default();
/// let asin_of_x = asin(x);
/// assert_eq!(asin_of_x.call(1.), PI/2.);
/// ```
pub fn asin(func: Function) -> Function {
let new_function = Asin(Arc::new(func.elementary()));
Function::from(new_function)
}
/// Creates a [Function](crate::Function) equal to the arccosine of the passed [Function](crate::Function)
///
/// i.e f(x) ⟹ acos(f(x))
///
/// Example:
/// ```rust
/// let x = function::default();
/// let acos_of_x = acos(x);
/// assert_eq!(acos_of_x.call(1.), 0.);
/// ```
pub fn acos(func: Function) -> Function {
let new_function = Acos(Arc::new(func.elementary()));
Function::from(new_function)
}
/// Creates a [Function](crate::Function) equal to the arctangent of the passed [Function](crate::Function)
///
/// i.e f(x) ⟹ atan(f(x))
///
/// Example:
/// ```rust
/// let x = function::default();
/// let atan_of_x = atan(x);
/// assert_eq!(atan_of_x.call(1.), PI/4.);
/// ```
pub fn atan(func: Function) -> Function {
let new_function = Atan(Arc::new(func.elementary()));
Function::from(new_function)
}
// hyperbolic functions
/// Creates a [Function](crate::Function) equal to the hyperbolic sine of the passed [Function](crate::Function)
///
/// i.e f(x) ⟹ sinh(f(x))
///
/// Example:
/// ```rust
/// let x = function::default();
/// let sinh_of_x = sinh(x);
/// assert_eq!(sinh_of_x.call(0.), 0.);
/// ```
pub fn sinh(func: Function) -> Function {
let new_function = Sinh(Arc::new(func.elementary()));
Function::from(new_function)
}
/// Creates a [Function](crate::Function) equal to the hyperbolic cosine of the passed [Function](crate::Function)
///
/// i.e f(x) ⟹ cosh(f(x))
///
/// Example:
/// ```rust
/// let x = function::default();
/// let cosh_of_x = cosh(x);
/// assert_eq!(cosh_of_x.call(0.), 1.);
/// ```
pub fn cosh(func: Function) -> Function {
let new_function = Cosh(Arc::new(func.elementary()));
Function::from(new_function)
}
/// Creates a [Function](crate::Function) equal to the hyperbolic tangent of the passed [Function](crate::Function)
///
/// i.e f(x) ⟹ tanh(f(x))
///
/// Example:
/// ```rust
/// let x = function::default();
/// let tanh_of_x = tanh(x);
/// assert_eq!(tanh_of_x.call(0.), 0.);
/// ```
pub fn tanh(func: Function) -> Function {
let new_function = Tanh(Arc::new(func.elementary()));
Function::from(new_function)
}
// abs function
/// Creates a [Function](crate::Function) equal to the absolute value of the passed [Function](crate::Function)
///
/// i.e f(x) ⟹ |f(x)|
///
/// Example:
/// ```rust
/// let x = function::default();
/// let abs_of_x = abs(x);
/// assert_eq!(abs_of_x.call(-1.), 1.);
/// ```
pub fn abs(func: Function) -> Function {
let new_function = Abs(Arc::new(func.elementary()));
Function::from(new_function)
}
// ln function
/// Creates a [Function](crate::Function) equal to the natural logarithm (base e) of the passed [Function](crate::Function)
///
/// i.e f(x) ⟹ ln(f(x))
///
/// Example:
/// ```rust
/// let x = function::default();
/// let ln_of_x = ln(x);
/// assert_eq!(ln_of_x.call(E), 1.);
/// ```
pub fn ln(func: Function) -> Function {
let new_function = Log(Con(E).into(), func.elementary().into());
Function::from(new_function)
}
/// Creates a [Function](crate::Function) equal to the square root of the passed [Function](crate::Function)
///
/// i.e f(x) ⟹ √f(x)
///
/// Example:
/// ```rust
/// let x = function::default();
/// let sqrt_of_x = sqrt(x);
/// assert_eq!(sqrt_of_x.call(4.), 2.);
/// ```
pub fn sqrt(func: Function) -> Function {
let new_function = Pow(Arc::new(func.elementary()), Arc::new(Con(0.5)));
Function::from(new_function)
}
/// Creates a [Function](crate::Function) equal to the factorial of the passed [Function](crate::Function)
///
/// i.e f(x) ⟹ f(x)!
///
/// Example:
/// ```rust
/// let x = function::default();
/// let factorial_of_x = factorial(x);
/// assert_eq!(factorial_of_x.call(4.), 2.);
/// ```
pub fn factorial(func: Function) -> Function {
let new_function = Factorial(func.elementary().into());
Function::from(new_function)
}
/// Creates a [Function](crate::Function) equal to the nth root of the passed [Function](crate::Function)
///
/// i.e f(x) ⟹ √f(x)
///
/// Example:
/// ```rust
/// let x = function::default();
/// let nth_root_of_x = nth_root(x, 3);
/// assert_eq!(nth_root_of_x.call(8.), 2.);
/// ```
pub fn nth_root(func: Function, n: f64) -> Function {
let new_function = Pow(Arc::new(func.elementary()), Arc::new(Con(1.) / n));
Function::from(new_function)
}
pub struct Function {
func: Elementary,
}
impl Function {
/// Returns the Elementary absraction of the Function instance
pub fn elementary(&self) -> Elementary {
self.func.clone()
}
/// Sets the function to represent the provided Elementary abstraction
pub fn set_function(&mut self, element: Elementary) {
self.func = element;
}
/// Turns self into the derivative of self
///
/// i.e. f(x) ⟹ f'(x)
///
/// Example:
/// ```rust
/// let mut function = Function::from("cosh(x)");
///
/// // take derivative
/// function.differentiate();
/// // cosh(x)' = sinh(x)
/// // sinh(0) = 0
/// assert_eq!(function.call(0.), 0.);
/// ```
///
/// Do also note that differentiating a function will not simplify the result. This is to make
/// sure that this method can never fail, but it does also mean that there are instances where
/// the resulting derivative will return [NaN](f64::NAN) for certain values.
pub fn differentiate(&mut self) {
self.func = self.elementary().to_owned().derivative_unsimplified();
}
/// Turns the given [Function](crate::Function) instance into a Taylor series expansion centered around the value
/// of a.
///
/// If the conversion fails, an [Error::ExpansionError](Error) is returned.
pub fn as_taylor_expansion(&mut self, order: u8, a: f64) -> Result<(), Error> {
self.func = self.func.expand_taylor(order, a)?.get_elementary();
Ok(())
}
/// Returns a Taylor expansion of the provided order of the function centered around the provided value a.
pub fn get_taylor_expansion(&self, order: u8, a: f64) -> Result<SeriesExpansion, Error> {
self.func.expand_taylor(order, a)
}
/// Returns a Maclaurin expansion of the provided order.
pub fn get_maclaurin_expansion(&self, order: u8) -> Result<SeriesExpansion, Error> {
self.func.expand_maclaurin(order)
}
}
impl Default for Function {
/// The default() method returns the unit function f(x) = x, returning the independant variable
/// for each input value.
fn default() -> Self {
Self { func: X }
}
}
/// A [Function](crate::Function) instance can be parsed from any string type using the from method.
///
/// Example:
/// ```rust
/// let func = Function::from("sin(ln(x))");
///
/// assert_eq!(func.call(1.), 0.);
/// // ...or using the nightly feature
/// // assert_eq!(func(1.), 0.);
/// ```
impl<'a> From<&'a str> for Function {
fn from(value: &'a str) -> Self {
let func = Elementary::from(value);
Self { func }
}
}
impl From<String> for Function {
fn from(value: String) -> Self {
let func = Elementary::from(&value[..]);
Self { func }
}
}
impl<'a> From<&'a String> for Function {
fn from(value: &'a String) -> Self {
let func = Elementary::from(&value[..]);
Self { func }
}
}
impl From<Elementary> for Function {
fn from(value: Elementary) -> Self {
Self { func: value }
}
}
/// A [Function](crate::Function) instance can be obtained from a SeriesExpansion instance using the from method.
///
/// Example:
/// ```rust
/// // create the Function instance
/// let func = Function::from("sin(x)");
///
/// // Get the SeriesExpansion
/// // In this instance we're creating a Taylor expansion of order 5 centered around 0
/// let expansion = func.get_taylor_expansion(5, 0.);
///
/// // Convert the SeriesExpansion into a Function using the from method
/// let func_expansion = Function::from(expansion);
/// // Note that this could also be done using the get_function method:
/// // let func_expansion = expansion.get_function()
/// //
/// // ... or using the as_taylor_expansion method to convert the original Function instance into a
/// // Taylor expansion without creating the SeriesExpansion instance seperatly:
/// // func.as_taylor_expansion()
///
/// ```
impl From<SeriesExpansion> for Function {
fn from(value: SeriesExpansion) -> Self {
value.get_function()
}
}
impl From<&SeriesExpansion> for Function {
fn from(value: &SeriesExpansion) -> Self {
(*value).clone().get_function()
}
}