Function sderivative 

pub fn sderivative(f: &impl Fn(f64) -> f64, x0: f64, h: Option<f64>) -> f64

Derivative of a univariate, scalar-valued function using the forward difference approximation.

Arguments

• f - Univariate, scalar-valued function, $f:\mathbb{R}\to\mathbb{R}$.
• x0 - Evaluation point, $x_{0}\in\mathbb{R}$.
• h - Relative step size, $h\in\mathbb{R}$. Defaults to SQRT_EPS.

Returns

Derivative of $f$ with respect to $x$, evaluated at $x=x_{0}$.

$$\frac{df}{dx}\bigg\rvert_{x=x_{0}}\in\mathbb{R}$$

Note

This function performs 2 evaluations of $f(x)$.

Examples

Basic Example

Approximate the derivative of

$$f(x)=x^{3}$$

at $x=2$, and compare the result to the true result of $f’(2)=12$.

use numtest::*;

use numdiff::forward_difference::sderivative;

// Define the function, f(x).
let f = |x: f64| x.powi(3);

// Approximate the derivative of f(x) at the evaluation point.
let df: f64 = sderivative(&f, 2.0, None);

// Check the accuracy of the derivative approximation.
assert_equal_to_decimal!(df, 12.0, 6);

We can also modify the relative step size. Choosing a coarser relative step size, we get a worse approximation.

use numtest::*;

use numdiff::forward_difference::sderivative;

let f = |x: f64| x.powi(3);
let df: f64 = sderivative(&f, 2.0, Some(0.001));
assert_equal_to_decimal!(df, 12.0, 1);

Example Passing Runtime Parameters

Approximate the derivative of a parameterized function

$$f(x)=ax^{2}+bx+c$$

where $a$, $b$, and $c$ are runtime parameters. Compare the result against the true derivative of

$$f’(x)=2ax+b$$

use numtest::*;

use numdiff::forward_difference::sderivative;

// Define the parameterized function.
fn f_param(x: f64, a: f64, b: f64, c:f64) -> f64 {
    a * x.powi(2) + b * x + c
}

// Runtime parameters.
let a = 2.5;
let b = -1.3;
let c = 4.7;

// Wrap the parameterized function with a closure that captures the parameters.
let f = |x: f64| f_param(x, a, b, c);

// True derivative function.
let df_true = |x: f64| 2.0 * a * x + b;

// Approximate the derivative at x = 1.0 and compare with true derivative.
let df_at_1: f64 = sderivative(&f, 1.0, None);
let df_at_1_true: f64 = df_true(1.0);
assert_equal_to_decimal!(df_at_1, df_at_1_true, 5);