# [−][src]Crate autodiff

This crate provides a library for performing automatic differentiation.

# Examples

The following example differentiates a 1D function defined by a closure.

```    // Define a function `f(x) = e^{-0.5*x^2}`
let f = |x: F| (-x * x / F::cst(2.0)).exp();

// Differentiate `f` at zero.
println!("{}", diff(f, 0.0)); // prints `0````

To compute the gradient of a function, use the function `grad` as follows:

```    // Define a function `f(x,y) = x*y^2`
let f = |x: &[F]| x[0] * x[1] * x[1];

// Differentiate `f` at `(1,2)`.
let g = grad(f, &vec![1.0, 2.0]);
println!("({}, {})", g[0], g[1]); // prints `(4, 4)````

Compute a specific derivative of a multi-variable function:

```    // Define a function `f(x,y) = x*y^2`.
let f = |v: &[F]| v[0] * v[1] * v[1];

// Differentiate `f` at `(1,2)` with respect to `x` (the first unknown) only.
let v = vec![
F::var(1.0), // Create a variable.
F::cst(2.0), // Create a constant.
];
println!("{}", f(&v).deriv()); // prints `4````

## Re-exports

 `pub use crate::forward_autodiff::*;`

## Traits

 Float Generic trait for floating point numbers FloatConst NumCast An interface for casting between machine scalars. One Defines a multiplicative identity element for `Self`. ToPrimitive A generic trait for converting a value to a number. Zero Defines an additive identity element for `Self`.