# Crate iterative_methods[−][src]

Expand description

# Iterative methods

Implements iterative methods and utilities for using and developing them as StreamingIterators. A series of blog posts provide a gentle introduction.

… but ok fine, here is a really quick example:

```// Problem: minimize the convex parabola f(x) = x^2 + x
let function = |x| x * x + x;

// An iterative solution by gradient descent
let derivative = |x| 2.0 * x + 1.0;
let step_size = 0.2;
let x_0 = 2.0;

// Au naturale:
let mut x = x_0;
for i in 0..10 {
x -= step_size * derivative(x);
println!("x_{} = {:.2}; f(x_{}) = {:.4}", i, x, i, x * x + x);
}

// Using replaceable components:
let dd = DerivativeDescent::new(function, derivative, step_size, x_0);
let dd = enumerate(dd);
let mut dd = dd.take(10);
while let Some(&Numbered{item: Some(ref curr), count}) = dd.next() {
println!("x_{} = {:.2}; f(x_{}) = {:.4}", count, curr.x, count, curr.value());
}```

Both produce the exact same output (below), and the first common approach is much easier to look at, the descent step is right there. The second separates the algorithm and every other concern into an easily reusable and composable components. If that sounds useful, have fun exploring.

``` x_0 = 1.00; f(x_0) = 2.0000
x_1 = 0.40; f(x_1) = 0.5600
x_2 = 0.04; f(x_2) = 0.0416
x_3 = -0.18; f(x_3) = -0.1450
x_4 = -0.31; f(x_4) = -0.2122
x_5 = -0.38; f(x_5) = -0.2364
x_6 = -0.43; f(x_6) = -0.2451
x_7 = -0.46; f(x_7) = -0.2482
x_8 = -0.47; f(x_8) = -0.2494
x_9 = -0.48; f(x_9) = -0.2498```

## Modules

 algorithms conjugate_gradient Implementation of conjugate gradient following lecture notes by Shen. Thanks Shen! derivative_descent Library code for example from crate top-level documentation utils

## Structs

 Annotate An adaptor that annotates every underlying item `x` with `f(x)`. AnnotatedResult Store a generic annotation next to the state. Enumerate An adaptor that enumerates items. ExtractValue An adaptor that converts items from `WeightedDatum` to `T`. Numbered A struct that wraps an `Item` as `Option` and annotates it with an `i64`. Used by `Enumerate`. ReservoirSample Adaptor to reservoir sample. StepBy An iterator for stepping iterators by a custom amount. TakeUntil An adaptor that returns initial elements until and including the first satisfying a predicate. Time Adaptor that times every call to `advance` on adaptee. Stores start time and duration. TimedResult Wrapper for Time. Weight Adaptor wrapping items with a computed weight. WeightedDatum Wrapper for Weight. WeightedReservoirSample Adaptor that reservoir samples with weights WriteYamlDocuments Write items of StreamingIterator to a Yaml file.

## Enums

 UntilState

## Traits

 YamlDataType Define a trait object for converting to YAML objects.

## Functions

 assess Annotate every underlying item with its score, as defined by `f`. enumerate A constructor for Enumerate. extract_value The constructor for ExtractValue. Apply it to a StreamingIterator with `Item = WeightedDatum` and it returns a StreamingIterator with `Item = T`. inspect Apply `f(_)->()` to every underlying item (for side-effects). last Get the item before the first None, assuming any exist. new_datum Constructor for WeightedDatum. reservoir_sample An adaptor for which the items are random samples of the underlying iterator up to the item processed. The constructor for ReservoirSample. step_by Creates an iterator starting at the same point, but stepping by the given amount at each iteration. take_until Creates an iterator which returns initial elements until and including the first satisfying a predicate. time Wrap each value of a streaming iterator with the durations: wd_iterable Annotates items of an iterable with a weight using a function `f`. weighted_reservoir_sample Create a random sample of the underlying weighted stream. write_yaml_documents Adaptor that writes each item to a YAML document. write_yaml_object Function used by WriteYamlDocuments to specify how to write each item to file.