Struct generic_newton::Newton

pub struct Newton<T> where
    T: Div<Output = T> + Sub<Output = T> + Copy,  { /* fields omitted */ }

An iterator that returns successive iterations of the Newton's method.

This iterator is generic over it's entry, and allows to freely use the Newton method on arbitrary types.

Example

use generic_newton::Newton;

fn main() {
    let mut n = Newton::<f64>::new(
        0.5, // Initial guess
        |x| x.cos() - x.powi(3), // The actual function
        |x| -(x.sin() + 3. * x.powi(2)), // Its derivative
    );

    assert!((n.nth(1000).unwrap() - 0.865474033102).abs() < 1E-11)
}

Implementations

impl<T> Newton<T> where
    T: Div<Output = T> + Sub<Output = T> + Copy, 

pub fn new(
    initial_guess: T,
    func: fn(_: T) -> T,
    derivative: fn(_: T) -> T
) -> Self

Creates a new Newton iterator.

• func is the actual function to find the root of
• derivative is it's derivative.

Trait Implementations

impl<T> Iterator for Newton<T> where
    T: Div<Output = T> + Sub<Output = T> + Copy, 

type Item = T

The type of the elements being iterated over.

fn next(&mut self) -> Option<Self::Item>

Advances the iterator and returns the next value.

fn size_hint(&self) -> (usize, Option<usize>)

Returns the bounds on the remaining length of the iterator.

fn count(self) -> usize

Consumes the iterator, counting the number of iterations and returning it.

fn last(self) -> Option<Self::Item>

Consumes the iterator, returning the last element.

fn advance_by(&mut self, n: usize) -> Result<(), usize>

🔬 This is a nightly-only experimental API. (iter_advance_by)

recently added

Advances the iterator by n elements.

fn nth(&mut self, n: usize) -> Option<Self::Item>

Returns the nth element of the iterator.

fn step_by(self, step: usize) -> StepBy<Self>

Creates an iterator starting at the same point, but stepping by the given amount at each iteration.

fn chain<U>(self, other: U) -> Chain<Self, <U as IntoIterator>::IntoIter> where
    U: IntoIterator<Item = Self::Item>, 

Takes two iterators and creates a new iterator over both in sequence.

fn zip<U>(self, other: U) -> Zip<Self, <U as IntoIterator>::IntoIter> where
    U: IntoIterator, 

'Zips up' two iterators into a single iterator of pairs.

fn map<B, F>(self, f: F) -> Map<Self, F> where
    F: FnMut(Self::Item) -> B, 

Takes a closure and creates an iterator which calls that closure on each element.

fn for_each<F>(self, f: F) where
    F: FnMut(Self::Item), 

Calls a closure on each element of an iterator.

fn filter<P>(self, predicate: P) -> Filter<Self, P> where
    P: FnMut(&Self::Item) -> bool, 

Creates an iterator which uses a closure to determine if an element should be yielded.

fn filter_map<B, F>(self, f: F) -> FilterMap<Self, F> where
    F: FnMut(Self::Item) -> Option<B>, 

Creates an iterator that both filters and maps.

fn enumerate(self) -> Enumerate<Self>

Creates an iterator which gives the current iteration count as well as the next value.

fn peekable(self) -> Peekable<Self>

Creates an iterator which can use peek to look at the next element of the iterator without consuming it.

fn skip_while<P>(self, predicate: P) -> SkipWhile<Self, P> where
    P: FnMut(&Self::Item) -> bool, 

Creates an iterator that skips elements based on a predicate.

fn take_while<P>(self, predicate: P) -> TakeWhile<Self, P> where
    P: FnMut(&Self::Item) -> bool, 

Creates an iterator that yields elements based on a predicate.

fn map_while<B, P>(self, predicate: P) -> MapWhile<Self, P> where
    P: FnMut(Self::Item) -> Option<B>, 

🔬 This is a nightly-only experimental API. (iter_map_while)

recently added

Creates an iterator that both yields elements based on a predicate and maps.

fn skip(self, n: usize) -> Skip<Self>

Creates an iterator that skips the first n elements.

fn take(self, n: usize) -> Take<Self>

Creates an iterator that yields its first n elements.

fn scan<St, B, F>(self, initial_state: St, f: F) -> Scan<Self, St, F> where
    F: FnMut(&mut St, Self::Item) -> Option<B>, 

An iterator adaptor similar to fold that holds internal state and produces a new iterator.

fn flat_map<U, F>(self, f: F) -> FlatMap<Self, U, F> where
    F: FnMut(Self::Item) -> U,
    U: IntoIterator, 

Creates an iterator that works like map, but flattens nested structure.

fn flatten(self) -> Flatten<Self> where
    Self::Item: IntoIterator, 

Creates an iterator that flattens nested structure.

fn fuse(self) -> Fuse<Self>

Creates an iterator which ends after the first None.

fn inspect<F>(self, f: F) -> Inspect<Self, F> where
    F: FnMut(&Self::Item), 

Does something with each element of an iterator, passing the value on.

fn by_ref(&mut self) -> &mut Self

Borrows an iterator, rather than consuming it.

#[must_use = "if you really need to exhaust the iterator, consider `.for_each(drop)` instead"]fn collect<B>(self) -> B where
    B: FromIterator<Self::Item>, 

Transforms an iterator into a collection.

fn partition<B, F>(self, f: F) -> (B, B) where
    B: Default + Extend<Self::Item>,
    F: FnMut(&Self::Item) -> bool, 

Consumes an iterator, creating two collections from it.

fn partition_in_place<'a, T, P>(self, predicate: P) -> usize where
    P: FnMut(&T) -> bool,
    Self: DoubleEndedIterator<Item = &'a mut T>,
    T: 'a, 

🔬 This is a nightly-only experimental API. (iter_partition_in_place)

new API

Reorders the elements of this iterator in-place according to the given predicate, such that all those that return true precede all those that return false. Returns the number of true elements found.

fn is_partitioned<P>(self, predicate: P) -> bool where
    P: FnMut(Self::Item) -> bool, 

🔬 This is a nightly-only experimental API. (iter_is_partitioned)

new API

Checks if the elements of this iterator are partitioned according to the given predicate, such that all those that return true precede all those that return false.

fn try_fold<B, F, R>(&mut self, init: B, f: F) -> R where
    F: FnMut(B, Self::Item) -> R,
    R: Try<Ok = B>, 

An iterator method that applies a function as long as it returns successfully, producing a single, final value.

fn try_for_each<F, R>(&mut self, f: F) -> R where
    F: FnMut(Self::Item) -> R,
    R: Try<Ok = ()>, 

An iterator method that applies a fallible function to each item in the iterator, stopping at the first error and returning that error.

fn fold<B, F>(self, init: B, f: F) -> B where
    F: FnMut(B, Self::Item) -> B, 

An iterator method that applies a function, producing a single, final value.

fn fold_first<F>(self, f: F) -> Option<Self::Item> where
    F: FnMut(Self::Item, Self::Item) -> Self::Item, 

🔬 This is a nightly-only experimental API. (iterator_fold_self)

The same as fold(), but uses the first element in the iterator as the initial value, folding every subsequent element into it. If the iterator is empty, return None; otherwise, return the result of the fold.

fn all<F>(&mut self, f: F) -> bool where
    F: FnMut(Self::Item) -> bool, 

Tests if every element of the iterator matches a predicate.

fn any<F>(&mut self, f: F) -> bool where
    F: FnMut(Self::Item) -> bool, 

Tests if any element of the iterator matches a predicate.

fn find<P>(&mut self, predicate: P) -> Option<Self::Item> where
    P: FnMut(&Self::Item) -> bool, 

Searches for an element of an iterator that satisfies a predicate.

fn find_map<B, F>(&mut self, f: F) -> Option<B> where
    F: FnMut(Self::Item) -> Option<B>, 

Applies function to the elements of iterator and returns the first non-none result.

fn try_find<F, R>(
    &mut self,
    f: F
) -> Result<Option<Self::Item>, <R as Try>::Error> where
    F: FnMut(&Self::Item) -> R,
    R: Try<Ok = bool>, 

🔬 This is a nightly-only experimental API. (try_find)

new API

Applies function to the elements of iterator and returns the first true result or the first error.

fn position<P>(&mut self, predicate: P) -> Option<usize> where
    P: FnMut(Self::Item) -> bool, 

Searches for an element in an iterator, returning its index.

fn rposition<P>(&mut self, predicate: P) -> Option<usize> where
    P: FnMut(Self::Item) -> bool,
    Self: ExactSizeIterator + DoubleEndedIterator, 

Searches for an element in an iterator from the right, returning its index.

fn max(self) -> Option<Self::Item> where
    Self::Item: Ord, 

Returns the maximum element of an iterator.

fn min(self) -> Option<Self::Item> where
    Self::Item: Ord, 

Returns the minimum element of an iterator.

fn max_by_key<B, F>(self, f: F) -> Option<Self::Item> where
    B: Ord,
    F: FnMut(&Self::Item) -> B, 

Returns the element that gives the maximum value from the specified function.

fn max_by<F>(self, compare: F) -> Option<Self::Item> where
    F: FnMut(&Self::Item, &Self::Item) -> Ordering, 

Returns the element that gives the maximum value with respect to the specified comparison function.

fn min_by_key<B, F>(self, f: F) -> Option<Self::Item> where
    B: Ord,
    F: FnMut(&Self::Item) -> B, 

Returns the element that gives the minimum value from the specified function.

fn min_by<F>(self, compare: F) -> Option<Self::Item> where
    F: FnMut(&Self::Item, &Self::Item) -> Ordering, 

Returns the element that gives the minimum value with respect to the specified comparison function.

fn rev(self) -> Rev<Self> where
    Self: DoubleEndedIterator, 

Reverses an iterator's direction.

fn unzip<A, B, FromA, FromB>(self) -> (FromA, FromB) where
    FromA: Default + Extend<A>,
    FromB: Default + Extend<B>,
    Self: Iterator<Item = (A, B)>, 

Converts an iterator of pairs into a pair of containers.

fn copied<'a, T>(self) -> Copied<Self> where
    Self: Iterator<Item = &'a T>,
    T: 'a + Copy, 

Creates an iterator which copies all of its elements.

fn cloned<'a, T>(self) -> Cloned<Self> where
    Self: Iterator<Item = &'a T>,
    T: 'a + Clone, 

Creates an iterator which clones all of its elements.

fn cycle(self) -> Cycle<Self> where
    Self: Clone, 

Repeats an iterator endlessly.

fn sum<S>(self) -> S where
    S: Sum<Self::Item>, 

Sums the elements of an iterator.

fn product<P>(self) -> P where
    P: Product<Self::Item>, 

Iterates over the entire iterator, multiplying all the elements

fn cmp<I>(self, other: I) -> Ordering where
    I: IntoIterator<Item = Self::Item>,
    Self::Item: Ord, 

Lexicographically compares the elements of this Iterator with those of another.

fn cmp_by<I, F>(self, other: I, cmp: F) -> Ordering where
    F: FnMut(Self::Item, <I as IntoIterator>::Item) -> Ordering,
    I: IntoIterator, 

🔬 This is a nightly-only experimental API. (iter_order_by)

Lexicographically compares the elements of this Iterator with those of another with respect to the specified comparison function.

fn partial_cmp<I>(self, other: I) -> Option<Ordering> where
    I: IntoIterator,
    Self::Item: PartialOrd<<I as IntoIterator>::Item>, 

Lexicographically compares the elements of this Iterator with those of another.

fn partial_cmp_by<I, F>(self, other: I, partial_cmp: F) -> Option<Ordering> where
    F: FnMut(Self::Item, <I as IntoIterator>::Item) -> Option<Ordering>,
    I: IntoIterator, 

🔬 This is a nightly-only experimental API. (iter_order_by)

Lexicographically compares the elements of this Iterator with those of another with respect to the specified comparison function.

fn eq<I>(self, other: I) -> bool where
    I: IntoIterator,
    Self::Item: PartialEq<<I as IntoIterator>::Item>, 

Determines if the elements of this Iterator are equal to those of another.

fn eq_by<I, F>(self, other: I, eq: F) -> bool where
    F: FnMut(Self::Item, <I as IntoIterator>::Item) -> bool,
    I: IntoIterator, 

🔬 This is a nightly-only experimental API. (iter_order_by)

Determines if the elements of this Iterator are equal to those of another with respect to the specified equality function.

fn ne<I>(self, other: I) -> bool where
    I: IntoIterator,
    Self::Item: PartialEq<<I as IntoIterator>::Item>, 

Determines if the elements of this Iterator are unequal to those of another.

fn lt<I>(self, other: I) -> bool where
    I: IntoIterator,
    Self::Item: PartialOrd<<I as IntoIterator>::Item>, 

Determines if the elements of this Iterator are lexicographically less than those of another.

fn le<I>(self, other: I) -> bool where
    I: IntoIterator,
    Self::Item: PartialOrd<<I as IntoIterator>::Item>, 

Determines if the elements of this Iterator are lexicographically less or equal to those of another.

fn gt<I>(self, other: I) -> bool where
    I: IntoIterator,
    Self::Item: PartialOrd<<I as IntoIterator>::Item>, 

Determines if the elements of this Iterator are lexicographically greater than those of another.

fn ge<I>(self, other: I) -> bool where
    I: IntoIterator,
    Self::Item: PartialOrd<<I as IntoIterator>::Item>, 

Determines if the elements of this Iterator are lexicographically greater than or equal to those of another.

fn is_sorted(self) -> bool where
    Self::Item: PartialOrd<Self::Item>, 

🔬 This is a nightly-only experimental API. (is_sorted)

new API

Checks if the elements of this iterator are sorted.

fn is_sorted_by<F>(self, compare: F) -> bool where
    F: FnMut(&Self::Item, &Self::Item) -> Option<Ordering>, 

🔬 This is a nightly-only experimental API. (is_sorted)

new API

Checks if the elements of this iterator are sorted using the given comparator function.

fn is_sorted_by_key<F, K>(self, f: F) -> bool where
    F: FnMut(Self::Item) -> K,
    K: PartialOrd<K>, 

🔬 This is a nightly-only experimental API. (is_sorted)

new API

Checks if the elements of this iterator are sorted using the given key extraction function.