Trait rstats::VecVec

pub trait VecVec<T> {
    // Required methods
    fn dvdt(self, centre: &[f64]) -> Result<Vec<f64>, RE>;
    fn scalar_fn(
        self,
        f: impl Fn(&[T]) -> Result<f64, RE>
    ) -> Result<Vec<f64>, RE>;
    fn vector_fn(
        self,
        f: impl Fn(&[T]) -> Result<Vec<f64>, RE>
    ) -> Result<Vec<Vec<f64>>, RE>;
    fn radii(self, gm: &[f64]) -> Result<Vec<f64>, RE>;
    fn column(self, cnum: usize) -> Vec<f64>;
    fn transpose(self) -> Vec<Vec<f64>>;
    fn normalize(self) -> Result<Vec<Vec<f64>>, RE>;
    fn house_ur(self) -> Result<(TriangMat, TriangMat), RE>;
    fn jointpdfn(self) -> Result<Vec<f64>, RE>;
    fn jointentropyn(self) -> Result<f64, RE>;
    fn dependencen(self) -> Result<f64, RE>;
    fn crossfeatures(
        self,
        f: fn(_: &[T], _: &[T]) -> f64
    ) -> Result<TriangMat, RE>;
    fn sumv(self) -> Vec<f64>;
    fn acentroid(self) -> Vec<f64>;
    fn par_acentroid(self) -> Vec<f64>;
    fn gcentroid(self) -> Result<Vec<f64>, RE>;
    fn hcentroid(self) -> Result<Vec<f64>, RE>;
    fn distsums(self) -> Vec<f64>;
    fn medout(self, gm: &[f64]) -> Result<MinMax<f64>, RE>;
    fn radius(self, i: usize, gm: &[f64]) -> Result<f64, RE>;
    fn eccinfo(self, gm: &[f64]) -> Result<(Params, Params, MinMax<f64>), RE>
       where Vec<f64>: FromIterator<f64>;
    fn quasimedian(self) -> Result<Vec<f64>, RE>;
    fn sigvec(self, idx: &[usize]) -> Result<Vec<f64>, RE>;
    fn madgm(self, gm: &[f64]) -> Result<f64, RE>;
    fn stdgm(self, gm: &[f64]) -> Result<f64, RE>;
    fn outer_hull(self, sqrads: &[f64], sindex: &[usize]) -> Vec<usize>;
    fn inner_hull(self, sqrads: &[f64], sindex: &[usize]) -> Vec<usize>;
    fn depth(self, descending_index: &[usize], p: &[f64]) -> Result<f64, RE>;
    fn depth_ratio(self, descending_index: &[usize], p: &[f64]) -> f64;
    fn hulls(self) -> (Vec<usize>, Vec<usize>);
    fn gmerror(self, g: &[f64]) -> Result<f64, RE>;
    fn gmedian(self, eps: f64) -> Vec<f64>;
    fn par_gmedian(self, eps: f64) -> Vec<f64>;
    fn gmparts(self, eps: f64) -> (Vec<f64>, f64);
    fn covar(self, mid: &[f64]) -> Result<TriangMat, RE>;
    fn serial_covar(self, mid: &[f64]) -> Result<TriangMat, RE>;
}

Methods applicable to a slice of vectors of generic end type. Operations on a whole set of multidimensional vectors.

Required Methods

fn dvdt(self, centre: &[f64]) -> Result<Vec<f64>, RE>

Linearly weighted approximate time series derivative at the last point (present time).

fn scalar_fn(self, f: impl Fn(&[T]) -> Result<f64, RE>) -> Result<Vec<f64>, RE>

Maps a scalar valued closure onto all vectors in self

fn vector_fn( self, f: impl Fn(&[T]) -> Result<Vec<f64>, RE> ) -> Result<Vec<Vec<f64>>, RE>

Maps vector valued closure onto all vectors in self and collects

fn radii(self, gm: &[f64]) -> Result<Vec<f64>, RE>

Exact radii magnitudes to all member points from the Geometric Median.

fn column(self, cnum: usize) -> Vec<f64>

Selects a column by number

fn transpose(self) -> Vec<Vec<f64>>

Transpose slice of vecs matrix

fn normalize(self) -> Result<Vec<Vec<f64>>, RE>

Normalize columns, so that they are all unit vectors

fn house_ur(self) -> Result<(TriangMat, TriangMat), RE>

Householder’s method returning matrices (U,R)

fn jointpdfn(self) -> Result<Vec<f64>, RE>

Joint probability density function of n matched slices of the same length

fn jointentropyn(self) -> Result<f64, RE>

Joint entropy between a set of vectors of the same length

fn dependencen(self) -> Result<f64, RE>

Dependence (component wise) of a set of vectors.

fn crossfeatures(self, f: fn(_: &[T], _: &[T]) -> f64) -> Result<TriangMat, RE>

Binary relations between columns of self

fn sumv(self) -> Vec<f64>

Sum of nd points (or vectors)

fn acentroid(self) -> Vec<f64>

Arithmetic Centre = euclidian mean of a set of points

fn par_acentroid(self) -> Vec<f64>

Multithreaded Arithmetic Centre = euclidian mean of a set of points

fn gcentroid(self) -> Result<Vec<f64>, RE>

Geometric Centroid

fn hcentroid(self) -> Result<Vec<f64>, RE>

Harmonic Centroid = harmonic mean of a set of points

fn distsums(self) -> Vec<f64>

Sums of distances from each point to all other points

fn medout(self, gm: &[f64]) -> Result<MinMax<f64>, RE>

Medoid distance, its index, outlier distance, its index

fn radius(self, i: usize, gm: &[f64]) -> Result<f64, RE>

Radius of a point specified by its subscript.

fn eccinfo(self, gm: &[f64]) -> Result<(Params, Params, MinMax<f64>), RE>

where Vec<f64>: FromIterator<f64>,

Arith mean and std (in Params struct), Median and mad, Medoid and Outlier (in MinMax struct)

fn quasimedian(self) -> Result<Vec<f64>, RE>

Quasi median, recommended only for comparison purposes

fn sigvec(self, idx: &[usize]) -> Result<Vec<f64>, RE>

Proportional projections on each +/- axis (by hemispheres)

fn madgm(self, gm: &[f64]) -> Result<f64, RE>

madgm, median of radii from geometric median: stable nd data spread estimator

fn stdgm(self, gm: &[f64]) -> Result<f64, RE>

stdgm mean of radii from gm: nd data spread estimator

fn outer_hull(self, sqrads: &[f64], sindex: &[usize]) -> Vec<usize>

Outer hull subscripts from their square radii and their sort index.

fn inner_hull(self, sqrads: &[f64], sindex: &[usize]) -> Vec<usize>

Inner hull subscripts from their square radii and their sort index.

fn depth(self, descending_index: &[usize], p: &[f64]) -> Result<f64, RE>

Measure of likelihood of zero median point p belonging to zero median data cloud self.

fn depth_ratio(self, descending_index: &[usize], p: &[f64]) -> f64

The proportion of points outside of the normal plane through p

fn hulls(self) -> (Vec<usize>, Vec<usize>)

Collects indices of outer and inner hull points, from zero median data

fn gmerror(self, g: &[f64]) -> Result<f64, RE>

Geometric median’s residual error

fn gmedian(self, eps: f64) -> Vec<f64>

New algorithm for geometric median, to accuracy eps

fn par_gmedian(self, eps: f64) -> Vec<f64>

Parallel (multithreaded) implementation of Geometric Median. Possibly the fastest you will find.

fn gmparts(self, eps: f64) -> (Vec<f64>, f64)

Like gmedian but returns also the sum of reciprocals of distances

fn covar(self, mid: &[f64]) -> Result<TriangMat, RE>

Flattened lower triangular part of a covariance matrix of a Vec of f64 vectors.

fn serial_covar(self, mid: &[f64]) -> Result<TriangMat, RE>

Flattened lower triangular part of a covariance matrix of a Vec of f64 vectors.

Object Safety

This trait is not object safe.

Implementations on Foreign Types

impl<T> VecVec<T> for &[Vec<T>]

where T: Clone + PartialOrd + Sync + Into<f64>, Vec<Vec<T>>: IntoParallelIterator, Vec<T>: IntoParallelIterator,

fn dvdt(self, centre: &[f64]) -> Result<Vec<f64>, RE>

Linearly weighted approximate time series derivative at the last point (present time). Weighted average (backwards half filter), minus the median.

fn scalar_fn(self, f: impl Fn(&[T]) -> Result<f64, RE>) -> Result<Vec<f64>, RE>

Maps scalar valued closure onto all vectors in self and collects

fn vector_fn( self, f: impl Fn(&[T]) -> Result<Vec<f64>, RE> ) -> Result<Vec<Vec<f64>>, RE>

Maps vector valued closure onto all vectors in self and collects

fn radii(self, gm: &[f64]) -> Result<Vec<f64>, RE>

Exact radii magnitudes to all member points from the Geometric Median. More accurate and usually faster as well than the approximate eccentricities above, especially when there are many points.

fn column(self, cnum: usize) -> Vec<f64>

Selects a column by number

fn transpose(self) -> Vec<Vec<f64>>

Multithreaded transpose of vec of vecs matrix

fn normalize(self) -> Result<Vec<Vec<f64>>, RE>

Normalize columns, so that they become unit row vectors

fn house_ur(self) -> Result<(TriangMat, TriangMat), RE>

Householder’s method returning triangular matrices (U’,R), where U are the reflector generators for use by house_uapply(m). R is the upper triangular decomposition factor. Here both U and R are returned for convenience in their transposed lower triangular forms. Transposed input self for convenience, so that original columns get accessed easily as rows.

fn jointpdfn(self) -> Result<Vec<f64>, RE>

Joint probability density function of n matched slices of the same length

fn jointentropyn(self) -> Result<f64, RE>

Joint entropy of vectors of the same length

fn dependencen(self) -> Result<f64, RE>

Dependence (component wise) of a set of vectors. i.e. dependencen returns 0 iff they are statistically independent bigger values when they are dependentent

fn crossfeatures(self, f: fn(_: &[T], _: &[T]) -> f64) -> Result<TriangMat, RE>

Flattened lower triangular part of a symmetric matrix for vectors in self. The upper triangular part can be trivially generated for all j>i by: c(j,i) = c(i,j). Applies closure f to compute a scalar binary relation between all pairs of vector components of self.
The closure typically invokes one of the methods from Vecg trait (in vecg.rs), such as dependencies.
Example call: pts.transpose().crossfeatures(|v1,v2| v1.mediancorrf64(v2)?)? computes median correlations between all column vectors (features) in pts.

fn sumv(self) -> Vec<f64>

Sum of nd points (or vectors)

fn acentroid(self) -> Vec<f64>

acentroid = multidimensional arithmetic mean

fn par_acentroid(self) -> Vec<f64>

multithreaded acentroid = multidimensional arithmetic mean

fn gcentroid(self) -> Result<Vec<f64>, RE>

gcentroid = multidimensional geometric mean

fn hcentroid(self) -> Result<Vec<f64>, RE>

hcentroid = multidimensional harmonic mean

fn distsums(self) -> Vec<f64>

For each member point, gives its sum of distances to all other points and their MinMax

fn medout(self, gm: &[f64]) -> Result<MinMax<f64>, RE>

Points nearest and furthest from the geometric median. Returns struct MinMax{min,minindex,max,maxindex}

fn radius(self, i: usize, gm: &[f64]) -> Result<f64, RE>

Radius of a point specified by its subscript.

fn eccinfo(self, gm: &[f64]) -> Result<(Params, Params, MinMax<f64>), RE>

where Vec<f64>: FromIterator<f64>,

Arith mean and std (in Params struct), Median and MAD (in another Params struct), Medoid and Outlier (in MinMax struct) of scalar radii of points in self. These are new robust measures of a cloud of multidimensional points (or multivariate sample).

fn quasimedian(self) -> Result<Vec<f64>, RE>

Quasi median, recommended only for comparison purposes

fn sigvec(self, idx: &[usize]) -> Result<Vec<f64>, RE>

Proportional projections on each +/- axis (by hemispheres). Adds only points that are specified in idx. Self should be zero median vectors, previously obtained by self.translate(&gm). The result is normalized to unit vector.

fn madgm(self, gm: &[f64]) -> Result<f64, RE>

madgm median of distances from gm: stable nd data spread measure

fn stdgm(self, gm: &[f64]) -> Result<f64, RE>

stdgm mean of distances from gm: nd data spread measure, aka nd standard deviation

fn outer_hull(self, sqrads: &[f64], sindex: &[usize]) -> Vec<usize>

Outer hull subscripts from their square radii and their sort index

fn inner_hull(self, sqrads: &[f64], sindex: &[usize]) -> Vec<usize>

Inner hull points from their square radii and their sort index

fn depth(self, descending_index: &[usize], p: &[f64]) -> Result<f64, RE>

Likelihood of zero median point p belonging to zero median data cloud self, based on the points outside of the normal plane through p. Returns the sum of unit vectors of its outside points, projected onto unit p. Index should be in the descending order of magnitudes of self points (for efficiency).

fn depth_ratio(self, descending_index: &[usize], p: &[f64]) -> f64

Likelihood of zero median point p belonging to zero median data cloud self, based on the proportion of points outside of the normal plane through p. Index should be in the descending order of magnitudes of self points (for efficiency).

fn hulls(self) -> (Vec<usize>, Vec<usize>)

Collects indices of inner hull and outer hull, from zero median points in self. We put a plane trough data point A, normal to its zero median vector a.
B is an inner hull point, when it lies inside all other points’ normal planes.
C is an outer hull point, when there is no other point outside its own normal plane. B can belong to both hulls, as when all the points lie on a hyper-sphere around gm.
The testing is done in increasing (decreasing) radius order.
B lies outside the normal plane of a, when its projection onto unit a exceeds |a|: |b|cos(θ) > |a| => a*b > |a|^2,
such B immediately fails as a candidate for the inner hull. Using square magnitudes, |a|^2 saves taking square roots and dividing the dot product by |a|.
Similarly for the outer hull, where A and B simply swap roles.

fn gmerror(self, g: &[f64]) -> Result<f64, RE>

Geometric median’s residual error

fn gmedian(self, eps: f64) -> Vec<f64>

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. Search methods are slow and difficult in highly dimensional space. Weiszfeld’s fixed point iteration formula has known problems with sometimes failing to converge. Especially, when the points are dense in the close proximity of the gm, or gm coincides with one of them.
However, these problems are fixed in my new algorithm here. The sum of reciprocals is strictly increasing and so is used here as easy to evaluate termination condition.

fn par_gmedian(self, eps: f64) -> Vec<f64>

Parallel (multithreaded) implementation of Geometric Median. Possibly the fastest you will find.
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.
Search methods are slow and difficult in hyper space.
Weiszfeld’s fixed point iteration formula has known problems and sometimes fails to converge.
Specifically, when the points are dense in the close proximity of the gm, or gm coincides with one of them.
However, these problems are solved in my new algorithm here.
The sum of reciprocals is strictly increasing and so is used to easily evaluate the termination condition.

fn gmparts(self, eps: f64) -> (Vec<f64>, f64)

Like gmedian but returns also the sum of reciprocals.

fn covar(self, mid: &[f64]) -> Result<TriangMat, RE>

Symmetric covariance matrix. Becomes comediance when argument mid
is the geometric median instead of the centroid. The indexing is always in this order: (row,column) (left to right, top to bottom). The items are flattened into a single vector in this order.

fn serial_covar(self, mid: &[f64]) -> Result<TriangMat, RE>

Symmetric covariance matrix. Becomes comediance when supplied argument mid
is the geometric median instead of the centroid. Indexing is always in this order: (row,column) (left to right, top to bottom).

Implementors