Macro get_sderivative 

macro_rules! get_sderivative {
    ($f:ident, $func_name:ident) => { ... };
}

Get a function that returns the derivative of the provided univariate, scalar-valued function.

The derivative is computed using forward-mode automatic differentiation.

Arguments

• f - Univariate, scalar-valued function, $f:\mathbb{R}\to\mathbb{R}$.
• func_name - Name of the function that will return the derivative of $f(x)$ at any point $x\in\mathbb{R}$.

Warning

f cannot be defined as closure. It must be defined as a function.

Note

The function produced by this macro will perform 1 evaluation of $f(x)$ to evaluate its derivative.

Examples

Basic Example

Compute the derivative of

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

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

use linalg_traits::Scalar;
use numtest::*;

use numdiff::{get_sderivative, Dual};

// Define the function, f(x).
fn f<S: Scalar>(x: S, _p: &[f64]) -> S {
    x.powi(3)
}

// Parameter vector (empty for this example).
let p = [];

// Autogenerate the function "df" that can be used to compute the derivative of f(x) at any
// point x.
get_sderivative!(f, df);

// Compute the derivative of f(x) at the evaluation point, x = 2.
let df_at_2: f64 = df(2.0, &p);

// Check the accuracy of the derivative.
assert_equal_to_decimal!(df_at_2, 12.0, 16);

Example Passing Runtime Parameters

Compute 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 linalg_traits::Scalar;
use numtest::*;

use numdiff::{get_sderivative, Dual};

// Define the function, f(x).
fn f<S: Scalar>(x: S, p: &[f64]) -> S {
    let a = S::new(p[0]);
    let b = S::new(p[1]);
    let c = S::new(p[2]);
    a * x.powi(2) + b * x + c
}

// Parameter vector.
let a = 2.5;
let b = -1.3;
let c = 4.7;
let p = [a, b, c];

// Autogenerate the derivative function.
get_sderivative!(f, df);

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

// Compute the derivative at x = 1.0 using both the automatically generated derivative function
// and the true derivative function, and compare the results.
let df_at_1: f64 = df(1.0, &p);
let df_at_1_true: f64 = df_true(1.0);
assert_eq!(df_at_1, df_at_1_true);