Indxvec

Author: Libor Spacek

Usage

The following will import everything:

rust use indxvec::{ here, MinMax, Search, Indices, Vecops, Mutops, Printing, printing::* };

Description

Vectors searching, indexing, ranking, sorting, merging, reversing, intersecting, printing, ..

Indxvec is lightweight and has no dependencies. The methods of all traits can be functionally chained to achieve numerous manipulations of Ranges, Vecs, and their indices, in compact form.

The facilities provided are:

• general binary search
• ranking, sorting (merge sort and hash sort), merging, indexing, selecting, partitioning
• many useful operations on generic vectors and their indices
• set operations
• serialising generic slices and slices of vectors to Strings: to_plainstr()
• printing and writing generic slices and slices of vectors: pvec(), wvec(&mut f)
• coloured pretty printing (ANSI terminal output, mainly for testing)
• macro here!() for more informative errors reporting

It is highly recommended to read and run tests/tests.rs to learn from examples of usage therein. Use a single thread to run them to keep the output in the right order. It is necessary to run the timing benchmark sorts() on its own for meaningful results.

bash cargo test --release -- --test-threads=1 --nocapture cargo test sorts --release -- --test --nocapture

Or just clicking the above test badge leads to the logs of the automated test run.

Glossary

• Sort Index - is obtained by stable merge sort sort_indexed or by hashsort_indexed. The original data is immutable (unchanged). The sort index produced is a list of subscripts to the data, such that the first subscript identifies the smallest item in the data, and so on (in ascending order). Suitable for bulky data that are not easily moved. It answers the question: 'what data item occupies a given sort position?'.

• K-Sort Index - allows more efficient sort implementation when only the first k items of the Sort Index are needed.

• Reversing an index - sort index can be reversed by generic reversal operation revs(), or mutrevs(). This has the effect of changing between ascending/descending sort orders without re-sorting or even reversing the (possibly bulky) actual data.

• Rank Index - corresponds to the given data order, listing the sort positions (ranks) for the data items, e.g.the third entry in the rank index gives the rank of the third data item. Some statistical measures require ranks of data. It answers the question: 'what is the sort position of a given data item?'.

• Inverting an index - sort index and rank index are mutually inverse. Thus they can be easily switched by invindex(). This is usually the easiest way to obtain a rank index. They will both be equal to 0..n for data that is already in ascending order.

• Complement of an index - beware that the standard reversal will not convert directly between ascending and descending ranks. This purpose is served by complindex(). Alternatively, descending ranks can be reconstructed by applying invindex() to a descending sort index.

• Unindexing - given a sort index and some data, unindex() will pick the data in the new order defined by the sort index. It can be used to efficiently transform lots of data vectors into the same (fixed) order. For example: Suppose we have vectors: keys and data_1,..data_n, not explicitly joined together in some bulky structure. The sort index obtained by:
  let indx = keys.sort_indexed();
  can then be efficiently applied to sort the data vectors individually, e.g. indx.unindex(data_n,true) (false to obtain a descending order at no extra cost).

Trait Search

binary_all

Binary Search for finding all the matches. This implementation is uniquely general. It is also very fast, especially over long ranges.

Searches within the given RangeInclusive<T> (self). It can be used in functionally chained 'builder style APIs', that select the subrange closer bracketing the target. The range values can be of any generic type T (satisfying the listed bounds), e.g. usize for indexing in-memory, u128 for searching whole disks or internet, f64 for solving equations which might not converge using other methods...

Comparator closure cmpr is comparing data against a target captured from its environment. Using closures enables custom comparisons of user's own data types. Also, this code is agnostic about the type of the target (and of the data)!

When the target is in order before self.start, empty self.start..self.start range is returned.
When the target is in order after self.end, self.end..self.end is returned.
When the target is not found, then ip..ip is returned, where ip is its insert position.

Otherwise the range of all consecutive values PartiallyEqual to the target is returned.

The first hit encountered will be anywhere within some unknown number of matching items. The algorithm then conducts two more binary searches in both directions away from the first hit. These secondary searches are applied only within the last (narrowest) range found during the main search. First non-matching items in both directions are found, giving the full enclosed matching range.

binary_any

finds and returns only the first hit and its last enclosing range. It is used by binary_all for its three searches. It can also be used on its own when just one found item will do. For example, to solve non-linear equations, using range values of f64 type.

rust /// Binary search algoritms implemented on RangeInclusive<T> pub trait Search<T> { /// General Binary Search using a closure to sample and compare data fn binary_all(&self, cmpr: &mut impl FnMut(&T) -> Ordering) -> Range<T>; /// First hit and the last search range fn binary_any(&self, cmpr: &mut impl FnMut(&T) -> Ordering) -> (T, Range<T>); }

Trait Indices

rust use indxvec::{Indices};

The methods of this trait are implemented for slices of subscripts, i.e. they take the type &[usize] as input (self) and produce new index Vec<usize>, new data vector Vec<T> or Vec<f64>, or other results, as appropriate. Please see the Glossary below for descriptions of the indices and operations on them.

rust /// Methods to manipulate indices of `Vec<usize>` type. pub trait Indices { /// Reverse an index slice by simple reverse iteration. fn revindex(self) -> Vec<usize>; /// Invert an index - turns a sort index into rank index and vice-versa fn invindex(self) -> Vec<usize>; /// Complement of an index - reverses the ranking order fn complindex(self) -> Vec<usize>; /// Collect values from `v` in the order of index in self. Or opposite order. fn unindex<T: Clone>(self, v:&[T], ascending:bool) -> Vec<T>; /// Pearson's correlation coefficient of two slices, typically ranks. fn ucorrelation(self, v: &[usize]) -> f64; /// Potentially useful clone-recast of &[usize] to Vec<f64> fn indx_to_f64 (self) -> Vec<f64>; }

Trait Vecops

rust use indxvec::{Vecops};

The methods of this trait are applicable to all generic slices &[T] (the data). Thus they will work on all Rust primitive numeric end types, such as f64. They can also work on slices holding any arbitrarily complex end type T, as long as the required traits, PartialOrd and/or Clone, are implemented for T. The methods are too numerous to list here, please see the documentation.

Trait Mutops

rust use indxvec::{Mutops};

This trait contains muthashsort, which overwrites self with sorted data. When we do not need to keep the original order, this is the most efficient way to sort. A non-destructive version sorth in in trait Vecops.

Nota bene: muthashsort really wins on longer Vecs. For about one thousand items upwards, it is on average about 25%-30% faster than the default Rust (Quicksort) sort_unstable.

``rust /// Mutable Operators on&mut[T] pub trait Mutops<T> { /// Sorts a mutable slice in place. fn mutquicksort(self) where T: PartialOrd; /// mutable reversal, general utility fn mutrevs(self); /// utility that mutably swaps two indexed items into ascending order fn mutsorttwo(self, i0: usize, i1: usize) -> bool where T: PartialOrd; /// utility that mutably bubble sorts three indexed items into ascending order fn mutsortthree(self, i0: usize, i1: usize, i2: usize) where T: PartialOrd; /// Possibly the fastest sort for long lists. Wrapper formuthashsortslice`. fn muthashsort(self, quantify: &mut impl FnMut(&T) -> f64) where T: PartialOrd + Clone;

/// Sorts n items from i in self. Used by muthashsort.
fn muthashsortslice(
    self,
    i: usize,
    n: usize,
    min: f64,
    max: f64,
    quantify: &mut impl FnMut(&T) -> f64,
) where
    T: PartialOrd + Clone;

} ```

Trait Printing

rust use indxvec::Printing; // the trait methods use indxvec::printing::*; // the ANSI colour constants

See tests/tests.rs for examples of usage.

Suitable for printing or writing to files up to 4-tuples of differing type items, all kinds of Vecs and slices and irregularly shaped 2D matrices.

Serializes tuples: &(T,U), &(T,U,V), &(T,U,V,W)
and slices: &[T], &[&[T]], &[Vec<T>].

Additionally, wvec writes contents of self as plain space separated values (.ssv) to File, possibly raising io::Error(s):

rust fn wvec(self,f:&mut File) -> Result<(), io::Error> where Self: Sized;

Similarly, pvec prints to stdout:

rust fn pvec(self) where Self: Sized;

All above listed types are converted to Strings and optionally decorated and coloured. Included are methods and constants to render the resulting String in six primary bold ANSI terminal colours.

Note that all these types are unprintable in standard Rust (they do not have Display implemented). Which is a big stumbling block for beginners. The methods of this trait convert all these types to printable (writeable) strings.

The colouring methods add the relevant colouring to the string output. This makes testing output much prettier and avoids reliance on Debug mode in production code. For finer control of the colouring, import the colour constants from printing::* and use them in formatting strings manually. For example, switching colours:

rust use indxvec::printing::*; // ANSI colours constants println!("{GR}green text, {RD}red warning, {BL}feeling blue{UN}");

Note that all of these colouring interpolations set their own new colour regardless of the previous settings. Interpolating {UN} resets the terminal to its default foreground rendering. UN is automatically appended at the end of strings produced by the colouring methods rd()..cy(). Be careful to always close with one of these, or explicit {UN}. Otherwise all the following output will continue with the last selected colour foreground rendering!

Example from tests/tests.rs:

rust println!("Memsearch for {BL}{midval}{UN}, found at: {}", vm.memsearch(midval) .map_or_else(||"None".rd(),|x| x.gr()) );

memsearch returns Option(None), when midval is not found in vm. Here, None will be printed in red, while any found item will be printed in green. Since x has been 'stringified' by .gr(), both closures return the same types, as required by map_or_else.

Struct and Utility Functions

rust use indxvec::{MinMax,here};

• pub struct Minmax holds minimum and maximum values of a Vec and their indices.
• here!() is a macro giving the filename, line number and function name of the place from where it was invoked. It can be interpolated into any error/tracing messages and reports.

Release Notes (Latest First)

Version 1.7.0 More simplification. Removed trait BinarySearch, which was just a couple of wrappers for Search methods.

Version 1.6.0 Simplified the binary search code.

Version 1.5.1 Made biggest_k and smallest_k even more efficient. Upped ran dependency to 1.1.

Version 1.5.0 Bumped up version because of some minor breaking changes.

Version 1.4.16 Added: biggest_k to complement smallest_k. Returns BinaryHeap<Reverse<&T>> of k biggest items.

Version 1.4.15 Tuples with items of different types now also print.

Version 1.4.14 Pruning: removed max_1_min_k and max_2_min_k, specific to medians, to medians crate code.

Version 1.4.13 Added to trait Printing the capability to print pairs &(T,T) and triples &(T,T,T), to avoid reliance on Debug mode in common situations (passing simple uniform tuple results).

Version 1.4.11 - Added to Vecops smallest_k method, similar to smallest_k_heap, except it avoids unnecessary copying (is suitable for complex types T). It returns just the final Vec of k smallest items. Also added max_1_min_k and max_2_min_k, to be used in crate medians. The point of these methods is that they find these values in the most efficient manner, using BinaryHeap. Added here because there may be also other uses for them. Typically picking a group to qualify to 'the final' and some overall winners.

Version 1.4.10 - Added method
smallest_k_heap(self, k: usize) -> BinaryHeap<T>
to Vecops. It efficiently returns max heap of k smallest items.

Version 1.4.9 - Breaking change of hash sort methods. They now require a closure quantify for converting any user type T to f64 (it defines how to build an f64 sort key from any type). This makes prerequisite for sorth explicit and gives more power to the user. It is no longer necessary to implement From trait for every such user type and its methods of quantification, of which there could be many. It is not reasonable to expect the users to have to do that. This new capability is demonstrated at the beginning of test text() (fast sorting of words by their length with a simple closure).

Version 1.4.8 - Added trait Binarysearch with two convenient and safer wrapper methods for the previously introduced methods in Search. Now using RangeInclusive<T> for safe input range.

Version 1.4.7 - General tidying up, mostly just of the documentation.

Version 1.4.6 - Added function search_all which is a kind of easier wrapper for binary_all, without the need to specify the sort order.

Version 1.4.5 - Improved binary_all usage. Added solve to trait Search for solving equations (with guaranteed convergence, unlike secant methods). Added demonstration to tests.rs.

Version 1.4.4 - No change to functionality. Added fully automated github action testing, outputs can be found by clicking the test badge at the top of this document.

Version 1.4.3 - Updated dev dependency ran. Added github action.

Version 1.4.2 - Introduced automatic sort order detection in binary_all, thus allowing more code simplification in methods binsearch and binsearch_indexed that depend on it.

Version 1.4.1 - Rewritten binsearch and binsearch_indexed from trait Vecops as encapsulations of the general purpose binary_all from trait Sort. Reduced the code size.

Version 1.4.0 - Introduced new trait Search: impl<T> Search<T> for Range<T>. The search algorithms can now be applied in 'builder style chained API's', filtering the ranges.