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new 0.7.14  Jun 23, 2021 

0.7.5  May 28, 2021 
0.5.9  Oct 6, 2020 
#7 in Machine learning
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Used in tid2013stats
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Rstats  Rust Stats
Usage
Insert into your Cargo.toml file [dependencies] section:
rstats = "^0.7"
and import into your source file(s) any of these functions and/or traits that you want:
use rstats::{GI,GV,here,functions,Stats,Vecf64,Vecu8,VecVecf64,VecVecu8,Mutvectors};
Introduction
Rstats is primarily about characterising multidimensional sets of points, with applications to Machine Learning and Data Analysis. It begins with statistical measures and vector algebra, which provide some basic selfcontained tools for the more interesting algorithms but can also be used in their own right.
Our treatment of multidimensional sets of points is constructed from the first principles. Some original concepts, not found elsewhere, are introduced and implemented here. Specifically, the new multidimensional (geometric) median algorithm. Also, the comediance matrix
; a replacement for the covariance matrix. It is obtained simply by supplying covar
with the geometric median instead of the centroid.
Zero median vectors are generally preferable to the commonly used zero mean vectors.
Most authors 'cheat' by using quasi medians (1d medians along each axis). Quasi medians are a poor start to stable characterisation of multidimensional data. In a highly dimensional space, they are not even any easier to compute.
Specifically, all such 1d measures are sensitive to the choice of axis.
Our methods based on the True Geometric Median, computed here by gmedian
, are axis (rotation) independent from the first step.
Implementation
The constituent parts of Rstats are Rust traits grouping together functions applicable to vectors of data of relevant end types.End type f64 is most commonly used. Facilities for other end types are limited. For lots of data of other end types, it is always possible to clone to f64, see for example the included utility function vecu8asvecf64
.
Documentation
Follow the documentation link. Then select a trait of interest to see the skeletal comments on the prototype function declarations in lib.rs. To see more detailed comments, plus some examples from the implementation files, scroll to the bottom of the trait and unclick [+] to the left of the implementations
of the trait. To see the tests, consult tests.rs
.
To run the tests, use single thread. It will be slower but will produce the results in the right order:
cargo test release  testthreads=1 nocapture color always
Macro, structs and functions

macro
here!()
for easy diagnostics 
pub struct GI for printing in green any singular type that has display implemented

pub struct GV for printing in green any vector whose end type has display implemented

pub struct Med to hold median and quartiles

pub struct MStats to hold a mean and standard deviation

functions wsum, genvec, genvecu8 (see documentation for the module
functions
).
Traits
Stats
One dimensional statistical measures implemented for &[i64]
and &[f64]
.
All these methods operate on one vector of data and take no arguments.
For example, s.amean()
returns the arithmetic mean of slice s
of either type.
This is the only attempt at genericity.
This trait is carefully checked and will report all kinds of errors, such as empty input.
This means you have to call .unwrap()
or something similar on its results.
Included in this trait are:
 means (arithmetic, geometric and harmonic),
 standard deviations,
 linearly weighted means (useful for time dependent data analysis),
 median and quartiles.
Vecf64
Vector algebra implemented on one or two &[f64]
slices of any length (dimensionality):
 Autocorrelation, Pearson's, Spearman's and Kendall's correlations.
 Finding minimum and maximum, linear transformation to [0,1].
 Indirect merge sort, binary search.
This trait is sometimes unchecked (for speed), so some caution with data is advisable.
Vecu8
 Some vector algebra as above for vectors of u8 (bytes).
 Frequency count of bytes by their values (Histogram or Probability Density Function).
 Entropy measures in units of e (using natural logarithms).
MutVectors
Some of the above functions are for memory efficiency reasons reimplemented in this trait so that they mutate self
in place, instead of creating a new Vec. Clearly, they can only be applied to a mutable variable. They are useful in vector iterative methods. Beware that they work by sideeffect and do not return anything, so they can not be chained.
VecVec
Relationships of one vector to a set of vectors (of &[f64]
end types):
 sums of distances, eccentricity,
 centroid, medoid, true geometric median,
 transformation to zero (geometric) median data,
 relationship between sets of multidimensional vectors: trend.
Trait VecVec is entirely unchecked, so check your data upfront. This is the more sophisticated part of the library. The true geometric median is found iteratively.
VecVecu8
Some of the above for vectors of vectors of bytes.
Appendix I: Terminology (and some new definitions) for sets of nD points

Centroid\Centre\Mean
is the (generally non member) point that minimises the sum of squares of distances to all member points. Thus it is susceptible to outliers. Specifically, it is the ndimensional arithmetic mean. By drawing physical analogy with gravity, it is sometimes called 'the centre of mass'. Centroid can also sometimes mean the member of the set which is the nearest to the Centre. Here we follow the common (if somewhat confusing) usage: Centroid = Centre = Arithmetic Mean. 
Quasi\Marginal Median
is the point minimising sums of distances separately in each dimension (its coordinates are 1d medians along each axis). It is a mistaken concept which we do not use here. 
Tukey Median
is the point maximisingTukey's Depth
, which is the minimum number of (outlying) points found in a hemisphere in any direction. Potentially useful concept but not yet implemented here, as its advantages over GM are not clear. 
Medoid
is the member of the set with the least sum of distances to all other members. 
Outlier
is the member of the set with the greatest sum of distances to all other members. 
Median or the true geometric median (gm)
, is the point (generally non member), which minimises the sum of distances to all members. This is the one we want. It is much less susceptible to outliers and is rotation independent. 
Zero median vector
is obtained by subtracting the geometric median. This is a proposed alternative to the commonly usedzero mean vector
, obtained by subtracting the centroid. 
Comediance
is similar to covariance, except zero median vectors are used to compute it instead of zero mean vectors.
Appendix II: Recent Releases

Version 0.7.14 Added weighted centroid
wacentroid
. Updated weighted geometric medianwgmedian
. Updatedgmedian
andwgmedian
invecvecu8
to include the optimisations of v. 0.7.11. Ensured compatibility with the latest release of crateindxvec
. 
Version 0.7.12 Split off Index trait and associated functions into a new crate
indxvec
. 
Version 0.7.11 Removed Kazutsugi (too specialised). Added
gcentroid
(geometric centroid). Further optimisations togmedian
. 
Version 0.7.10 Added
symmatrix
to reconstruct full symmetric matrix from its lower triangular part (for compatibility with crates which duplicate data). Renamed mergerank to plainrank
and added boolean argument to facilitate ranking in ascending or descending order. Expanded vecf64() tests (see it for instructive example usage). 
Version 0.7.9 Added
wcovar
of weighted points. Improved struct GV and tests. Replacedemsg
with macrohere!()
for easier diagnostics. Moved all structs into lib.rs. 
Version 0.7.8 Added
covar
= covariance or comediance matrix computations. Some changes to this text (Readme.md). 
Version 0.7.7 Fixed
merge_immutable
and added a test. Addedcityblockd
andvaddu8
. 
Version 0.7.6 Added
merge_immutable
andmerge_indices
. Simplifiedmergesort
. 
Version 0.7.5 Renamed VecVec trait to VecVecf64 to make the naming consistent. Added
unindexu8
. Removedwsortedeccs
andwsortedcos
for being too application specific. 
Version 0.7.4 Added merge of two sorted &[f64]. Added
ascending
boolean flag tounindex
,sortm
and functions that call them, to facilitate easy sorting in ascending or descending order. Addedgenvecu8
tofunctions
to generate sets of random u8 vectors. Normalised cummulative probability density functions to [0,1]. 
Version 0.7.3 Replaced varc with vector similarity and dissimilarity in [0,1] in terms of their cosines. Similar to unstandardised Pearson's correlation.

Version 0.7.2 Added weighted
wgmedian
andwsortedeccs
to VecVecu8. Created new source file for VecVecu8 trait. 
Version 0.7.1 Ported the improved gmedian also to VecVecu8.

Version 0.7.0 Made gmedian slightly more accurate. Added Weighted Geometric Median and supporing functions. Added vecu8asvecf64 utility conversion.
Dependencies
~110KB