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jungin.rhee
2023-08-18 16:07:30 +00:00
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commit b1f1f1a5fc
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src/assignments/assignment06/symbolic_differentiation_grade.rs Normal file
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#[cfg(test)]
mod test {
use super::super::symbolic_differentiation::*;
use ntest::assert_about_eq;
// Constant rationals to use
const TWO: Rational = Rational::new(2, 1);
const FOUR: Rational = Rational::new(4, 1);
const THIRD: Rational = Rational::new(1, 3);
const FIVE_THIRD: Rational = Rational::new(5, 3);
const TWO_SEVENTH: Rational = Rational::new(2, 7);
#[test]
fn test_rational_simpl() {
assert_eq!(format!("{}", Rational::new(1, 2)), "1/2".to_string());
assert_eq!(format!("{}", Rational::new(0, 0)), "0".to_string());
assert_eq!(format!("{}", Rational::new(1, 1)), "1".to_string());
assert_eq!(format!("{}", Rational::new(-3, 7)), "-3/7".to_string());
}
#[test]
fn test_rational_arithmetic() {
assert_eq!(
format!("{}", Rational::new(1, 4) + Rational::new(3, 4)),
"1".to_string()
);
assert_eq!(
format!("{}", Rational::new(1, 3) + Rational::new(1, 6)),
"1/2".to_string()
);
assert_eq!(
format!("{}", Rational::new(1, 5) - Rational::new(1, 2)),
"-3/10".to_string()
);
assert_eq!(
format!("{}", Rational::new(-5, 12) * Rational::new(6, 125)),
"-1/50".to_string()
);
assert_eq!(
format!("{}", Rational::new(-3, 4) / Rational::new(-7, 13)),
"39/28".to_string()
);
}
#[test]
fn test_rational_arithmetic_long() {
assert_eq!(
format!(
"{}",
Rational::new(1, 2) + Rational::new(1, 2) + Rational::new(1, 2)
),
"3/2".to_string()
);
assert_eq!(
format!(
"{}",
Rational::new(1, 2) - Rational::new(1, 4) + Rational::new(1, 5)
),
"9/20".to_string()
);
assert_eq!(
format!(
"{}",
Rational::new(1, 2)
* Rational::new(1, 4)
* Rational::new(1, 8)
* Rational::new(1, 16)
/ Rational::new(1, 1024)
),
"1".to_string()
);
assert_eq!(
format!(
"{}",
Rational::new(123, 798)
+ Rational::new(684, 32) / (Rational::new(13, 44) - Rational::new(123, 4472))
* Rational::new(1237, 2)
),
"12356494070/250439".to_string()
);
}
#[test]
fn test_differentiate_simple() {
// Constant
assert_eq!(format!("{}", Rational::new(3, 2).diff()), "0".to_string());
// Polynomials
assert_eq!(
format!("{}", SingletonPolynomial::new_c(Rational::new(3, 1)).diff()),
"0".to_string()
);
assert_eq!(
format!("{}", SingletonPolynomial::new_poly(TWO, FOUR).diff()),
"(8)x^(3)".to_string()
);
assert_eq!(
format!(
"{}",
SingletonPolynomial::new_poly(FIVE_THIRD, THIRD).diff()
),
"(5/9)x^(-2/3)".to_string()
);
// Exponential
assert_eq!(format!("{}", Exp::new().diff()), "exp(x)".to_string());
// Trigonometric
assert_eq!(
format!("{}", Trignometric::new_sine(ONE).diff()),
"cos(x)".to_string()
);
assert_eq!(
format!("{}", Trignometric::new_cosine(ONE).diff()),
"-sin(x)".to_string()
);
assert_eq!(
format!("{}", Trignometric::new_sine(FIVE_THIRD).diff()),
"(5/3)cos(x)".to_string()
);
assert_eq!(
format!("{}", Trignometric::new_cosine(TWO_SEVENTH).diff()),
"(-2/7)sin(x)".to_string()
);
}
#[test]
fn test_differentiate_complex() {
type BF = BaseFuncs;
type CF = ComplexFuncs<BF>;
// Unlike the above simple test, it is hard to state a canonical
// form for derivative of more complex functions. Thus, we only test that the
// derivative is correct at certain points.
// Add
//
// d/dx (2x^4 + exp(x)) = 8x^3 + exp(x)
let f1 = SingletonPolynomial::new_poly(TWO, FOUR);
let f2 = Exp::new();
let deriv = CF::Add(
Box::new(CF::Func(BF::Poly(f1))),
Box::new(CF::Func(BF::Exp(f2))),
)
.diff();
assert_about_eq!(deriv.evaluate(2.2), 94.2090134994f64);
assert_about_eq!(deriv.evaluate(4.5), 819.017131301);
// Sub
//
// d/dx ((5/3)cos(x) - sin(x)) = (-5/3)sin(x) - cos(x)
let f1 = Trignometric::new_cosine(FIVE_THIRD);
let f2 = Trignometric::new_sine(ONE);
let deriv = CF::Sub(
Box::new(CF::Func(BF::Trig(f1))),
Box::new(CF::Func(BF::Trig(f2))),
)
.diff();
assert_about_eq!(deriv.evaluate(2.7), 0.191772341627);
assert_about_eq!(deriv.evaluate(0.01), -1.01661638931);
// Mult
//
// d/dx (2x^4 * cos(x) * exp(x)) =
// 8x^2 * cos(x) * exp(x) - 2x^4 * sin(x) * exp(x) + 2x^4 * cos(x) * exp(x)
let f1 = SingletonPolynomial::new_poly(TWO, FOUR);
let f2 = Trignometric::new_cosine(ONE);
let f3 = Exp::new();
let deriv = CF::Mul(
Box::new(CF::Func(BF::Poly(f1))),
Box::new(CF::Mul(
Box::new(CF::Func(BF::Trig(f2))),
Box::new(CF::Func(BF::Exp(f3))),
)),
)
.diff();
assert_about_eq!(deriv.evaluate(3.4), -14804.9016757);
assert_about_eq!(deriv.evaluate(0.07), 0.00298352866);
// Div
//
// (d/dx) (sin(x)/cos(x)) = (cos(x)*cos(x) + sin(x)*sin(x)) / cos(x)*cos(x)
let f1 = Trignometric::new_sine(ONE);
let f2 = Trignometric::new_cosine(ONE);
let deriv = CF::Div(
Box::new(CF::Func(BF::Trig(f1))),
Box::new(CF::Func(BF::Trig(f2))),
)
.diff();
assert_about_eq!(deriv.evaluate(core::f64::consts::PI), 1f64);
assert_about_eq!(deriv.evaluate(0f64), 1f64);
// Comp
//
// d/dx (cos(x^2)) = -2x * sin(x^2)
let f1 = Trignometric::new_cosine(ONE);
let f2 = SingletonPolynomial::new_poly(ONE, TWO);
let deriv = CF::Comp(
Box::new(CF::Func(BF::Trig(f1))),
Box::new(CF::Func(BF::Poly(f2))),
)
.diff();
assert_about_eq!(deriv.evaluate(2.714), -4.79392977);
assert_about_eq!(deriv.evaluate(3.9), -3.72556973);
}
}