[−][src]Trait rstats::Vectors
Implementing basic vector algebra and safe geometric median.
Required methods
fn dotp(self, v: &[f64]) -> f64
Scalar product of two vectors
fn vsub(self, v: &[f64]) -> Vec<f64>
Vector subtraction
fn vadd(self, v: &[f64]) -> Vec<f64>
Vector addition
fn vmag(self) -> f64
Vector magnitude
fn vdist(self, v: &[f64]) -> f64
Euclidian distance between two points
fn smult(self, s: f64) -> Vec<f64>
Scalar multiplication
fn vunit(self) -> Vec<f64>
Unit vector
fn correlation(self, v: &[f64]) -> Result<f64>
Correlation
fn kendalcorr(self, v: &[f64]) -> Result<f64>
Kendall's tau-b (rank order) correlation
fn spearmancorr(self, v: &[f64]) -> Result<f64>
Spearman's rho (rank differences) correlation
fn autocorr(self) -> Result<f64>
Autocorrelation
fn minmax(self) -> (f64, usize, f64, usize)
Minimum, minimum's index, maximum, maximum's index.
fn acentroid(self, d: usize) -> Vec<f64>
Centroid = euclidian mean of a set of points
fn distances(self, d: usize) -> Result<Vec<f64>>
Sums of distances from each point to all other points
fn distsuminset(self, d: usize, indx: usize) -> f64
Sum of distances from one point given by indx
fn distsum(self, d: usize, v: &[f64]) -> f64
Sum of distances from arbitrary point (v) to all the points in self
fn medoid(self, d: usize) -> (f64, usize, f64, usize)
Medoid and Outlier (by distance) of a set of points
fn eccentricities(self, d: usize) -> Result<Vec<Vec<f64>>>
Eccentricity vectors from each point
fn eccentr(self, d: usize, indx: usize) -> f64
Ecentricity measure (0,1) of an internal point given by indx
fn veccentr(self, d: usize, thisp: &[f64]) -> Result<(f64, Vec<f64>)>
Eccentricity measure and vector of any point
fn ecc(self, d: usize, v: &[f64]) -> f64
Eccentricity measure only, of any point
fn moe(self, d: usize) -> Med
Median of eccentricities (measure of spread of multivariate sample)
fn emedoid(self, d: usize) -> (f64, usize, f64, usize)
Medoid and Outlier defined by eccentricities
fn nmedian(self, d: usize, eps: f64) -> Result<Vec<f64>>
Geometric median of the set
Implementations on Foreign Types
impl<'_> Vectors for &'_ [f64][src]
fn smult(self, s: f64) -> Vec<f64>[src]
Scalar multiplication of a vector, creates new vec
fn dotp(self, v: &[f64]) -> f64[src]
Scalar product of two f64 slices.
Must be of the same length - no error checking for speed
fn vsub(self, v: &[f64]) -> Vec<f64>[src]
Vector subtraction, creates a new Vec result
fn vadd(self, v: &[f64]) -> Vec<f64>[src]
Vector addition, creates a new Vec result
fn vdist(self, v: &[f64]) -> f64[src]
Euclidian distance between two n dimensional points (vectors).
Slightly faster than vsub followed by vmag, as both are done in one loop
fn vmag(self) -> f64[src]
Vector magnitude
fn vunit(self) -> Vec<f64>[src]
Unit vector - creates a new one
fn correlation(self, v: &[f64]) -> Result<f64>[src]
Correlation coefficient of a sample of two f64 variables.
Example
use rstats::Vectors; let v1 = vec![1_f64,2.,3.,4.,5.,6.,7.,8.,9.,10.,11.,12.,13.,14.]; let v2 = vec![14_f64,13.,12.,11.,10.,9.,8.,7.,6.,5.,4.,3.,2.,1.]; assert_eq!(v1.correlation(&v2).unwrap(),-1_f64);
fn kendalcorr(self, v: &[f64]) -> Result<f64>[src]
Kendall Tau-B correlation coefficient of a sample of two f64 variables. Defined by: tau = (conc - disc) / sqrt((conc + disc + tiesx) * (conc + disc + tiesy)) This is the simplest implementation with no sorting.
Example
use rstats::Vectors; let v1 = vec![1_f64,2.,3.,4.,5.,6.,7.,8.,9.,10.,11.,12.,13.,14.]; let v2 = vec![14_f64,13.,12.,11.,10.,9.,8.,7.,6.,5.,4.,3.,2.,1.]; assert_eq!(v1.kendalcorr(&v2).unwrap(),-1_f64);
fn spearmancorr(self, v: &[f64]) -> Result<f64>[src]
Spearman rho correlation coefficient of a sample of two f64 variables. This is the simplest implementation with no sorting.
Example
use rstats::Vectors; let v1 = vec![1_f64,2.,3.,4.,5.,6.,7.,8.,9.,10.,11.,12.,13.,14.]; let v2 = vec![14_f64,13.,12.,11.,10.,9.,8.,7.,6.,5.,4.,3.,2.,1.]; assert_eq!(v1.spearmancorr(&v2).unwrap(),-1_f64);
fn autocorr(self) -> Result<f64>[src]
(Auto)correlation coefficient of pairs of successive values of (time series) f64 variable.
Example
use rstats::Vectors; let v1 = vec![1_f64,2.,3.,4.,5.,6.,7.,8.,9.,10.,11.,12.,13.,14.]; assert_eq!(v1.autocorr().unwrap(),0.9984603532054123_f64);
fn acentroid(self, d: usize) -> Vec<f64>[src]
Centroid = simple multidimensional arithmetic mean
Example
use rstats::{Vectors,vimpls::genvec}; let pts = genvec(15,15,255,30); let centre = pts.acentroid(15); let dist = pts.distsum(15,¢re); assert_eq!(dist, 4.14556218326653_f64);
fn minmax(self) -> (f64, usize, f64, usize)[src]
Finds minimum, minimum's index, maximum, maximum's index of &f64 Here self is usually some data, rather than a vector
fn distances(self, d: usize) -> Result<Vec<f64>>[src]
For each point, gives its sum of distances to all other points This is the efficient workhorse of distances based analysis
fn distsuminset(self, d: usize, indx: usize) -> f64[src]
The sum of distances from within-set point given by indx to all points in self.
Geometric Median is defined as v which minimises this function.
fn distsum(self, d: usize, v: &[f64]) -> f64[src]
The sum of distances from any point v to all points in self.
Geometric Median is defined as v which minimises this function.
fn medoid(self, d: usize) -> (f64, usize, f64, usize)[src]
Medoid is the point belonging to set of points self,
which has the least sum of distances to all other points.
Outlier is the point with the greatest sum of distances.
This function returns a four-tuple:
(medoid_distance, medoid_index, outlier_distance, outlier_index).
d is the number of dimensions = length of the point sub-slices.
The entire set of points is held in one flat &[f64].
This is faster than vec of vecs but we have to handle the indices.
Example
use rstats::{Vectors,vimpls::genvec}; let pts = genvec(15,15,255,30); let (dm,_,_,_) = pts.medoid(15); assert_eq!(dm,4.812334638782327_f64);
fn eccentricities(self, d: usize) -> Result<Vec<Vec<f64>>>[src]
Eccentricity vector for each point This is the efficient workhorse of eccentrities analysis
fn eccentr(self, d: usize, indx: usize) -> f64[src]
Eccentricity of a d-dimensional point belonging to the set self, specified by its indx.
Eccentricity is a scalar measure between 0.0 and 1.0 of a point not being a median of the given set.
It does not need the median. The perfect median has eccentricity zero.
fn veccentr(self, d: usize, thisp: &[f64]) -> Result<(f64, Vec<f64>)>[src]
Ecentricity measure and the eccentricity vector of any point (typically one not belonging to the set).
It is a measure between 0.0 and 1.0 of not being a median but it does not need the median.
The eccentricity vector points towards the median and has the maximum possible magnitude of n, by
which the scalar measure is normalised.
fn ecc(self, d: usize, v: &[f64]) -> f64[src]
This convenience wrapper calls veccentr and extracts just the eccentricity (residual error for median).
fn moe(self, d: usize) -> Med[src]
We now define MOE (median of ecentricities), a new measure of spread of multidimensional points (or multivariate sample)
fn emedoid(self, d: usize) -> (f64, usize, f64, usize)[src]
fn nmedian(self, d: usize, eps: f64) -> Result<Vec<f64>>[src]
Geometric Median (gm) is the point that minimises the sum of distances to a given set of points.
It has (provably) only vector iterative solutions.
Searching methods are slow and difficult in highly dimensional space.
Weiszfeld's fixed point iteration formula had known problems with sometimes failing to converge.
Especially, when the points are dense in the close proximity of the gm,
or it coincides with one of them.
However, these problems are fixed in my improved algorithm here.
There is eventually going to be a multithreaded version of nmedian.
Example
use rstats::{Vectors,vimpls::genvec}; let pt = genvec(15,15,255,30); let gm = pt.nmedian(15, 1e-5).unwrap(); let error = pt.ecc(15,&gm); assert_eq!(error,0.000004826966175302838_f64);