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use anyhow::{Result,Context,ensure}; use crate::{RStats,MutVectors,Vectors,Med}; use crate::f64impls::{emsg}; use std::cmp::Ordering::Equal; use std::fmt; impl MutVectors for &mut[f64] { /// Scalar multiplication of a vector, mutates self fn mutsmult(self, s:f64) { self.iter_mut().for_each(|x|{ *x*=s }); } /// Vector subtraction, mutates self fn mutvsub(self, v: &[f64]) { self.iter_mut().enumerate().for_each(|(i,x)|*x-=v[i]) } /// Vector addition, mutates self fn mutvadd(self, v: &[f64]) { self.iter_mut().enumerate().for_each(|(i,x)|*x+=v[i]) } /// Mutate to unit vector fn mutvunit(self) { self.mutsmult(1_f64/self.iter().map(|x|x.powi(2)).sum::<f64>().sqrt()) } /// Vector magnitude duplicated for mutable type fn mutvmag(self) -> f64 { self.iter().map(|x|x.powi(2)).sum::<f64>().sqrt() } } impl Vectors for &[f64] { /// Scalar multiplication of a vector, creates new vec fn smult(self, s:f64) -> Vec<f64> { self.iter().map(|&x|s*x).collect() } /// Scalar product of two f64 slices. /// Must be of the same length - no error checking for speed fn dotp(self, v: &[f64]) -> f64 { self.iter().enumerate().map(|(i,&x)| x*v[i]).sum::<f64>() } /// Vector subtraction, creates a new Vec result fn vsub(self, v: &[f64]) -> Vec<f64> { self.iter().enumerate().map(|(i,&x)|x-v[i]).collect() } /// Vector addition, creates a new Vec result fn vadd(self, v: &[f64]) -> Vec<f64> { self.iter().enumerate().map(|(i,&x)|x+v[i]).collect() } /// Euclidian distance between two n dimensional points (vectors). /// Slightly faster than vsub followed by vmag, as both are done in one loop fn vdist(self, v: &[f64]) -> f64 { self.iter().enumerate().map(|(i,&x)|(x-v[i]).powi(2)).sum::<f64>().sqrt() } /// Vector magnitude fn vmag(self) -> f64 { self.iter().map(|&x|x.powi(2)).sum::<f64>().sqrt() } /// Unit vector - creates a new one fn vunit(self) ->Vec<f64> { self.smult(1./self.iter().map(|x|x.powi(2)).sum::<f64>().sqrt()) } /// 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 correlation(self,v:&[f64]) -> Result<f64> { let n = self.len(); ensure!(n>0,emsg(file!(),line!(),"correlation - first sample is empty")); ensure!(n==v.len(),emsg(file!(),line!(),"correlation - samples are not of the same size")); let (mut sy,mut sxy,mut sx2,mut sy2) = (0_f64,0_f64,0_f64,0_f64); let sx:f64 = self.iter().enumerate().map(|(i,&x)| { let y = v[i]; sy += y; sxy += x*y; sx2 += x*x; sy2 += y*y; x }).sum(); let nf = n as f64; Ok( (sxy-sx/nf*sy)/(((sx2-sx/nf*sx)*(sy2-sy/nf*sy)).sqrt()) ) } /// 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 kendalcorr(self,v:&[f64]) -> Result<f64> { let n = self.len(); ensure!(n>0,emsg(file!(),line!(),"kendalcorr - first sample is empty")); ensure!(n==v.len(),emsg(file!(),line!(),"kendalcorr - samples are not of the same size")); let (mut conc, mut disc, mut tiesx, mut tiesy) = (0_i64,0_i64,0_i64,0_i64); for i in 1..n { let x = self[i]; let y = v[i]; for j in 0..i { let xd = x - self[j]; let yd = y - v[j]; if !xd.is_normal() { if !yd.is_normal() { continue } else { tiesx += 1; continue } }; if !yd.is_normal() { tiesy += 1; continue }; if (xd*yd).signum() > 0_f64 { conc += 1 } else { disc += 1 } } } Ok((conc-disc) as f64/(((conc+disc+tiesx)*(conc+disc+tiesy)) as f64).sqrt()) } /// 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 spearmancorr(self,v:&[f64]) -> Result<f64> { let n = self.len(); ensure!(n>0,emsg(file!(),line!(),"spearmancorr - first sample is empty")); ensure!(n==v.len(),emsg(file!(),line!(),"spearmancorr - samples are not of the same size")); let xvec = self.ranks().unwrap(); let yvec = v.ranks().unwrap(); let mx = xvec.ameanstd().unwrap(); let my = yvec.ameanstd().unwrap(); let mut covar = 0_f64; for i in 0..n { covar += (xvec[i]-mx.mean)*(yvec[i]-my.mean); } covar /= mx.std*my.std*(n as f64); // remove small truncation errors if covar > 1.0 { covar=1_f64 } else if covar < -1_f64 { covar=-1.0 }; Ok(covar) } /// (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 autocorr(self) -> Result<f64> { let n = self.len(); ensure!(n>=2,emsg(file!(),line!(),"autocorr - sample is too small")); let (mut sx,mut sy,mut sxy,mut sx2,mut sy2) = (0_f64,0_f64,0_f64,0_f64,0_f64); for i in 0..n-1 { let x = self[i]; let y = self[i+1]; sx += x; sy += y; sxy += x*y; sx2 += x*x; sy2 += y*y } let nf = n as f64; Ok( (sxy-sx/nf*sy)/(((sx2-sx/nf*sx)*(sy2-sy/nf*sy)).sqrt()) ) } /// 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 acentroid(self, d:usize) -> Vec<f64> { let n = self.len()/d; let mut centre = vec![0_f64;d]; for i in 0..n { centre.as_mut_slice().mutvadd(self.get(i*d .. (i+1)*d).unwrap()) } centre.as_mut_slice().mutsmult(1.0/n as f64); centre } /// Finds minimum, minimum's index, maximum, maximum's index of &[f64] /// Here self is usually some data, rather than a vector fn minmax(self) -> (f64,usize,f64,usize) { let mut min = self[0]; // initialise to the first value let mut mini = 0; let mut max = self[0]; // initialised as min, allowing 'else' below let mut maxi = 0; for i in 1..self.len() { let x = self[i]; if x < min { min = x; mini = i } else if x > max { max = x; maxi = i } } (min,mini,max,maxi) } /// For each point, gives its sum of distances to all other points /// This is the efficient workhorse of distances based analysis fn distances(self, d:usize) -> Result<Vec <f64>> { let n = self.len()/d; ensure!(n*d == self.len(),emsg(file!(),line!(),"distances - d must divide vector length")); let mut dists = vec![0_f64;n]; // distances accumulator for all points // examine all unique pairings (lower triangular part of symmetric flat matrix) for i in 1..n { let thisp = self.get(i*d .. (i+1)*d) .with_context(||emsg(file!(),line!(),"distances failed to get this slice"))?; for j in 0..i { let thatp = self.get(j*d .. (j+1)*d) .with_context(||emsg(file!(),line!(),"distances failed to get that slice"))?; let d = thisp.vdist(&thatp); // calculate each distance relation just once dists[i] += d; dists[j] += d; // but add it to both points } } Ok(dists) } /// 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 distsuminset(self, d:usize, indx:usize) -> f64 { let n = self.len()/d; let mut sum = 0_f64; let thisp = self.get( indx*d .. (indx+1)*d).unwrap(); for i in 0..n { if i == indx { continue }; let thatp = self.get(i*d .. (i+1)*d).unwrap(); sum += thatp.vdist(&thisp) } sum } /// The sum of distances from any point v to all points in self. /// Geometric Median is defined as v which minimises this function. fn distsum(self, d:usize, v:&[f64]) -> f64 { let n = self.len()/v.len(); let mut sum = 0_f64; for i in 0..n { let thisp = self.get(i*d .. (i+1)*d).unwrap(); sum += v.vdist(&thisp) } sum } /// 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 medoid(self, d:usize) -> (f64,usize,f64,usize) { self.distances(d).unwrap().minmax() } /// Eccentricity vector for each point /// This is the efficient workhorse of eccentrities analysis fn eccentricities(self, d:usize) -> Result<Vec<Vec<f64>>> { let n = self.len()/d; ensure!(n*d == self.len(),emsg(file!(),line!(),"distances - d must divide vector length")); // allocate vectors for the results let mut eccs = vec![vec![0_f64;d];n]; // ecentricities vectors accumulator for all points // examine all unique pairings (lower triangular part of symmetric flat matrix) for i in 1..n { let thisp = self.get(i*d .. (i+1)*d).unwrap(); for j in 0..i { let thatp = self.get(j*d .. (j+1)*d).unwrap(); let e = thatp.vsub(&thisp).vunit(); // calculate each vector just once eccs[i].as_mut_slice().mutvadd(&e); eccs[j].as_mut_slice().mutvsub(&e); // mind the vector's orientation! } } Ok(eccs) } /// 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 eccentr(self, d:usize, indx:usize) -> f64 { let n = self.len()/d; let mut vsum = vec![0_f64;d]; let thisp = self.get(indx*d .. (indx+1)*d).unwrap(); for i in 0..n { if i == indx { continue }; // exclude this point let thatp = self.get(i*d .. (i+1)*d).unwrap(); let unitdv = thatp.vsub(thisp).vunit(); vsum.as_mut_slice().mutvadd(&unitdv); // add it to their sum } vsum.vmag()/n as f64 } /// 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 veccentr(self, d:usize, thisp:&[f64]) -> Result<(f64,Vec<f64>)> { let n = self.len()/d; let mut vsum = vec![0_f64;d]; for i in 0..n { let thatp = self.get(i*d .. (i+1)*d) .with_context(||emsg(file!(),line!(),"veccentr failed to extract that point"))?; let mut vdif = thatp.vsub(thisp); let mag = vdif.vmag(); if !mag.is_normal() { continue }; // thisp belongs to the set // make vdif into a unit vector with its already known magnitude vdif.as_mut_slice().mutsmult(1./mag); vsum.as_mut_slice().mutvadd(&vdif); // add it to their sum } Ok((vsum.vmag()/n as f64, vsum)) } /// This convenience wrapper calls `veccentr` and extracts just the eccentricity (residual error for median). fn ecc(self, d:usize, v:&[f64]) -> f64 { let (eccentricity,_) = self.veccentr(d,v).unwrap(); eccentricity } /// We now define MOE (median of ecentricities), a new measure of spread of multidimensional points /// (or multivariate sample) fn moe(self, d:usize) -> Med { scalarecc(self.eccentricities(d).unwrap()) .median().unwrap() } fn emedoid(self, d:usize) -> (f64,usize,f64,usize) { scalarecc(self.eccentricities(d).unwrap()).minmax() } /// 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); /// ``` fn nmedian(self, d:usize, eps:f64) -> Result<Vec<f64>> { let n = self.len()/d; ensure!(n*d == self.len(),emsg(file!(),line!(),"gmedian d must divide vector length")); let mut oldpoint = self.acentroid(d); // start with the centroid loop { let (rsum,mut newv) = betterpoint(self,d,&oldpoint) .with_context(||emsg(file!(),line!(),"nmedian betterpoint call failed"))?; // find new point newv.as_mut_slice().mutsmult(1.0/rsum); // adding unit vectors if newv.vdist(&oldpoint) < eps { oldpoint = newv; break // use the last iteration anyway }; oldpoint = newv } Ok(oldpoint) } } /// betterpoint is called by nmedian. /// Scaling by rsum is left as the final step at calling level, /// in order to facilitate data parallelism. fn betterpoint(set:&[f64], d:usize, v:&[f64]) -> Result<(f64,Vec<f64>)> { let n = set.len()/d; let mut rsum = 0_f64; let mut vsum = vec![0_f64;d]; for i in 0..n { let thatp = set.get(i*d .. (i+1)*d) .with_context(||emsg(file!(),line!(),"betterpoint failed to extract that point"))?; let dist = v.vdist(&thatp); if !dist.is_normal() { continue }; let recip = 1.0/dist; rsum += recip; vsum.as_mut_slice().mutvadd(&thatp.smult(recip)); } Ok((rsum,vsum)) } /// Converts the set of vectors produced by `eccentricities` /// to their magnitudes normalised by n. /// the output can be typically passed to `median` /// or `minmax` to find the Outlier and the Medoid pub fn scalarecc(ev:Vec<Vec<f64>>) -> Vec<f64> { let mut scalars = Vec::new(); let n = ev.len(); let nf = n as f64; for i in 0..n { scalars.push(ev[i].vmag()/nf) }; scalars } /// Sorts a mutable `Vec<f64>` in place. /// It is the responsibility of the user to ensure that there are no NaNs etc. pub fn sortf(v: &mut [f64]) { v.sort_by(|a, b| a.partial_cmp(b).unwrap_or(Equal)) } /// Generates a random f64 vector of size d x n suitable for testing. It needs two seeds. /// Uses local closure `rand` to generate random numbers (avoids dependencies). /// Random numbers are in the open interval 0..1 with uniform distribution. pub fn genvec(d:usize, n:usize, s1:u32, s2:u32 ) -> Vec<f64> { let size = d*n; // change the seeds as desired let mut m_z = s1 as u32; let mut m_w = s2 as u32; let mut rand = || { m_z = 36969 * (m_z & 65535) + (m_z >> 16); m_w = 18000 * (m_w & 65535) + (m_w >> 16); (((m_z << 16) & m_w) as f64 + 1.0)*2.328306435454494e-10 }; let mut v = Vec::with_capacity(size); for _i in 0..size { v.push(rand()) }; // fills the lot with random numbers return v } /// GreenIt struct facilitates printing (in green) any type /// that has Display implemented. pub struct GreenIt<T: fmt::Display>(pub T); impl<T: fmt::Display> fmt::Display for GreenIt<T> { fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result { write!(f,"\x1B[01;92m{}\x1B[0m",self.0.to_string()) } } /// GreenVec struct facilitates printing (in green) of vectors of any type /// that has Display implemented. pub struct GreenVec<T: fmt::Display>(pub Vec<T>); impl<T: fmt::Display> fmt::Display for GreenVec<T> { fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result { let mut s = String::from("\x1B[01;92m["); let n = self.0.len(); if n > 0 { s.push_str(&self.0[0].to_string()); // first item for i in 1..n { s.push_str(", "); s.push_str(&self.0[i].to_string()); } } write!(f,"{}]\x1B[0m", s) } }