| 1234567891011121314151617181920212223242526272829303132333435 |
- use numerics::solve
- use numerics::diff
- use numerics::fixed_point
- # Root finding
- fn f1(x) = x³ - x - 2
- assert_eq(root_bisect(f1, 1, 2, 1e-10, 1e-10), 1.52137970680, 1e-8)
- fn f1_prime(x) = 3 x² - 1
- assert_eq(root_newton(f1, f1_prime, 1, 1e-10), 1.52137970680, 1e-8)
- assert_eq(root_newton(f1, f1_prime, 2, 1e-10), 1.52137970680, 1e-8)
- # Fixed point iteration
- let a = 3
- fn f_sqrt3(x: Scalar) = 0.5 * (a / x + x)
- assert_eq(fixed_point(f_sqrt3, 1, 1e-10), sqrt(3), 1e-10)
- # Differentiation
- assert_eq(diff(log, 2.0, 1e-10), 0.5, 1e-5)
- assert_eq(diff(sin, 0.0, 1e-10), 1.0, 1e-5)
- assert_eq(diff(sqrt, 1.0, 1e-10), 0.5, 1e-5)
- fn f2(x: Scalar) -> Scalar = x² + 4 x + 1
- assert_eq(diff(f2, 2.0, 1e-10), 8.0, 1e-5)
- fn dist(t: Time) -> Length = 0.5 g0 t^2
- fn velocity(t: Time) -> Velocity = diff(dist, t, 1e-10 s)
- assert_eq(velocity(2.0 s), 2.0 s × g0, 1e-3 m/s)
|
