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use crate::*;
use indxvec::Vecops;
use medians::{MedError, Medianf64};
use rayon::prelude::*;
impl<T> VecVec<T> for &[Vec<T>]
where
T: Clone + PartialOrd + Sync + Into<f64>,
Vec<Vec<T>>: IntoParallelIterator,
Vec<T>: IntoParallelIterator{
/// Linearly weighted approximate time series derivative at the last point (present time).
/// Weighted average (backwards half filter), minus the median.
fn dvdt(self, centre: &[f64]) -> Result<Vec<f64>, RE> {
let len = self.len();
if len < 2 {
return nodata_error(format!("dvdt time series is too short: {len}"));
};
let mut weight = 1_f64;
let mut sumwv:Vec<f64> = self[0].iter().map(|x| x.clone().into()).collect();
for v in self.iter().skip(1) {
weight += 1_f64;
sumwv.mutvadd(&v.smult(weight));
};
Ok(sumwv.smult(1.0/(sumn(len) as f64)).vsub(centre))
}
/// Maps scalar valued closure onto all vectors in self and collects
fn scalar_fn(self,f: impl Fn(&[T]) -> Result<f64,RE>) -> Result<Vec<f64>,RE> {
self.iter().map(|s|-> Result<f64,RE> {
f(s) }).collect::<Result<Vec<f64>,RE>>()
}
/// Maps vector 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> {
self.iter().map(|s|-> Result<Vec<f64>,RE> {
f(s) }).collect::<Result<Vec<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 radii(self, gm: &[f64]) -> Result<Vec<f64>, RE> {
self.scalar_fn(|s| Ok(gm.vdist(s)))
}
/// Selects a column by number
fn column(self, cnum: usize) -> Vec<f64> {
self.iter().map(|row| row[cnum].clone().into()).collect()
}
/// Multithreaded transpose of vec of vecs matrix
fn transpose(self) -> Vec<Vec<f64>> {
(0..self[0].len())
.into_par_iter()
.map(|cnum| self.column(cnum))
.collect()
}
/// Normalize columns of a matrix, so that they become unit row vectors
fn normalize(self) -> Result<Vec<Vec<f64>>, RE> {
(0..self[0].len())
.into_par_iter()
.map(|cnum| -> Result<Vec<f64>, RE> { self.column(cnum).vunit() })
.collect()
}
/// 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 house_ur(self) -> Result<(TriangMat, TriangMat),RE> {
let n = self.len();
let d = self[0].len();
let min = if d <= n { d } else { n }; // minimal dimension
let mut r = self.transpose(); // self.iter().map(|s| s.tof64()).collect::<Vec<Vec<f64>>>(); // //
let mut ures = vec![0.; sumn(min)];
let mut rres = Vec::with_capacity(sumn(min));
for j in 0..min {
let Some(slc) = r[j].get(j..d)
else { return data_error("house_ur: failed to extract uvec slice"); };
let uvec = slc.house_reflector();
for rlast in r.iter_mut().take(d).skip(j) {
let rvec = uvec.house_reflect::<f64>(&rlast.drain(j..d).collect::<Vec<f64>>());
rlast.extend(rvec);
// drained, reflected with this uvec, and rebuilt, all remaining rows of r
}
// these uvecs are columns, so they must be saved column-wise
for (row, &usave) in uvec.iter().enumerate() {
ures[sumn(row + j) + j] = usave; // using triangular index
}
// save completed `r[j]` components only up to and including the diagonal
// we are not even storing the rest, so no need to set those to zero
for &rsave in r[j].iter().take(j + 1) {
rres.push(rsave)
}
}
Ok((
TriangMat {
kind: 3,
data: ures,
}, // transposed, non symmetric kind
TriangMat {
kind: 3,
data: rres,
}, // transposed, non symmetric kind
))
}
/// Joint probability density function of n matched slices of the same length
fn jointpdfn(self) -> Result<Vec<f64>, RE> {
let d = self[0].len(); // their common dimensionality (length)
for v in self.iter().skip(1) {
if v.len() != d {
return data_error("jointpdfn: all vectors must be of equal length!");
};
}
let mut res: Vec<f64> = Vec::with_capacity(d);
let mut tuples = self.transpose();
let df = tuples.len() as f64; // for turning counts to probabilities
// lexical sort to group together occurrences of identical tuples
tuples.sort_unstable_by(
|a, b| a.partial_cmp(b)
.expect("jointpdfn: tuples comparison failed"));
let mut count = 1_usize; // running count
let mut lastindex = 0; // initial index of the last unique tuple
tuples.iter().enumerate().skip(1).for_each(|(i, ti)| {
if ti > &tuples[lastindex] {
// new tuple ti (Vec<T>) encountered
res.push((count as f64) / df); // save frequency count as probability
lastindex = i; // current index becomes the new one
count = 1_usize; // reset counter
} else {
count += 1;
}
});
res.push((count as f64) / df); // flush the rest!
Ok(res)
}
/// Joint entropy of vectors of the same length
fn jointentropyn(self) -> Result<f64, RE> {
let jpdf = self.jointpdfn()?;
Ok(jpdf.iter().map(|&x| -x * (x.ln())).sum())
}
/// 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 dependencen(self) -> Result<f64, RE> {
Ok((0..self.len())
.into_par_iter()
.map(|i| self[i].entropy())
.sum::<f64>()
/ self.jointentropyn()?
- 1.0)
}
/// 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 crossfeatures(self, f: fn(&[T], &[T]) -> f64) -> Result<TriangMat, RE> {
Ok(TriangMat {
kind: 2, // symmetric, non transposed
data: (0..self.len())
.into_par_iter()
.flat_map(|i| {
(0..i+1)
.map(|j| f(&self[i], &self[j]))
.collect::<Vec<f64>>()
})
.collect::<Vec<f64>>(),
})
}
/// Sum of nd points (or vectors)
fn sumv(self) -> Vec<f64> {
let mut resvec = vec![0_f64; self[0].len()];
for v in self {
resvec.mutvadd(v)
}
resvec
}
/// acentroid = multidimensional arithmetic mean
fn acentroid(self) -> Vec<f64> {
self.sumv().smult(1. / (self.len() as f64))
}
/// multithreaded acentroid = multidimensional arithmetic mean
fn par_acentroid(self) -> Vec<f64> {
let sumvec = self
.par_iter()
.fold(
|| vec![0_f64; self[0].len()],
|mut vecsum: Vec<f64>, p| {
vecsum.mutvadd(p);
vecsum
},
)
.reduce(
|| vec![0_f64; self[0].len()],
|mut finalsum: Vec<f64>, partsum: Vec<f64>| {
finalsum.mutvadd(&partsum);
finalsum
},
);
sumvec.smult(1. / (self.len() as f64))
}
/// gcentroid = multidimensional geometric mean
fn gcentroid(self) -> Result<Vec<f64>,RE> {
let logvs = self.iter().map(|v|-> Result<Vec<f64>,RE> {
Ok(v.vunit()?.smult(v.vmag().ln())) })
.collect::<Result<Vec<Vec<f64>>,RE>>()?;
let logcentroid = logvs.acentroid();
Ok(logcentroid.vunit()?.smult(logcentroid.vmag().exp()))
}
/// hcentroid = multidimensional harmonic mean
fn hcentroid(self) -> Result<Vec<f64>,RE> {
let mut centre = vec![0_f64; self[0].len()];
for v in self {
centre.mutvadd(&v.vinverse()?)
}
Ok(centre
.vinverse()?.smult(self.len() as f64))
}
/// For each member point, gives its sum of distances to all other points and their MinMax
fn distsums(self) -> Vec<f64> {
let n = self.len();
let mut dists = vec![0_f64; n]; // distances accumulator for all points
// examine all unique pairings (lower triangular part of symmetric flat matrix)
self.iter().enumerate().for_each(|(i, thisp)| {
self.iter().take(i).enumerate().for_each(|(j, thatp)| {
let d = thisp.vdist(thatp); // calculate each distance relation just once
dists[i] += d;
dists[j] += d; // but add it to both points' sums
})
});
dists
}
/// Points nearest and furthest from the geometric median.
/// Returns struct MinMax{min,minindex,max,maxindex}
fn medout(self, gm: &[f64]) -> Result<MinMax<f64>,RE> {
Ok(self.scalar_fn(|s| Ok(gm.vdist(s)))?.minmax())
}
/// Radius of a point specified by its subscript.
fn radius(self, i: usize, gm: &[f64]) -> Result<f64, RE> {
if i > self.len() {
return data_error("radius: invalid subscript");
}
Ok(self[i].vdist(gm))
}
/// 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 eccinfo(self, gm: &[f64]) -> Result<(Params, Params, MinMax<f64>), RE>
where
Vec<f64>: FromIterator<f64>,
{
let rads: Vec<f64> = self.radii(gm)?;
let radsmed = rads.medf_unchecked();
let radsmad = rads.madf(radsmed);
Ok((rads.ameanstd()?, Params{centre:radsmed,spread:radsmad}, rads.minmax()))
}
/// Quasi median, recommended only for comparison purposes
fn quasimedian(self) -> Result<Vec<f64>, RE> {
Ok((0..self[0].len())
.map(|colnum| self.column(colnum).medf_checked())
.collect::<Result<Vec<f64>, MedError<String>>>()?)
}
/// 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 sigvec(self, idx: &[usize]) -> Result<Vec<f64>, RE> {
let dims = self[0].len();
if self.is_empty() {
return nodata_error("sigvec given empty data");
};
let mut hemis = vec![0_f64; 2 * dims];
for &i in idx {
for (j, component) in self[i].iter().enumerate() {
let cf = component.clone().into();
if cf < 0. {
hemis[dims + j] -= cf;
continue;
};
hemis[j] += cf;
};
};
hemis.vunit()
}
/// madgm median of distances from gm: stable nd data spread measure
fn madgm(self, gm: &[f64]) -> Result<f64, RE> {
if self.is_empty() {
return nodata_error("madgm given empty vec!"); };
Ok(self.radii(gm)?.medf_unchecked())
}
/// stdgm mean of distances from gm: nd data spread measure, aka nd standard deviation
fn stdgm(self, gm: &[f64]) -> Result<f64,RE> {
if self.is_empty() {
return nodata_error("stdgm given empty vec!")?; };
Ok( self.iter()
.map(|s| s.vdist(gm)).sum::<f64>()/self.len() as f64 )
}
/// Outer hull subscripts from their square radii and their sort index
fn outer_hull(self, sqrads: &[f64], sindex: &[usize]) -> Vec<usize> {
let mut hullindex: Vec<usize> = Vec::new();
let len = sindex.len();
// test ipoints in descending sqrads order
'ploop: for i in (0..len).rev() {
let ipoint = &self[sindex[i]];
// against jpoints with greater radius
for j in (i+1..len).rev() {
// this jpoint lies outside the normal plane to ipoint => reject ipoint
if self[sindex[j]].dotp(ipoint) > sqrads[sindex[i]] { continue 'ploop; };
};
hullindex.push(sindex[i]); // passed
};
hullindex
}
/// Inner hull points from their square radii and their sort index
fn inner_hull(self, sqrads: &[f64], sindex: &[usize]) -> Vec<usize> {
let mut hullindex: Vec<usize> = Vec::new();
let len = sindex.len();
// test ipoints in ascending sqrads order
'ploop: for i in 0..len {
let ipoint = &self[sindex[i]];
// against jpoints with smaller radius
for j in 0..i {
// this jpoint lies inside ipoint => reject ipoint
if self[sindex[j]].dotp(ipoint) > sqrads[sindex[j]] { continue 'ploop; };
};
hullindex.push(sindex[i]); // ipoint passed
};
hullindex
}
/// 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(self, descending_index: &[usize], p: &[f64]) -> Result<f64,RE> {
let psq = p.vmagsq();
let mut sumvec = vec![0_f64;p.len()];
for &i in descending_index {
let s = &self[i];
let ssq = s.vmagsq();
if ssq <= psq { break; }; // no more outside points
if s.dotp(p) > psq { sumvec.mutvadd(&s.smult(1.0/(ssq.sqrt()))) };
};
Ok(sumvec.dotp(&p.vunit()?))
}
/// 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 depth_ratio(self, descending_index: &[usize], p: &[f64]) -> f64 {
let psq = p.vmagsq();
let mut num = 0_f64;
for &i in descending_index {
let s = &self[i];
let ssq = s.vmagsq();
if ssq <= psq { break; }; // no more outside points
if s.dotp(p) > psq { num += 1.0; };
};
num/(self.len() as f64)
}
/// 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 hulls(self) -> (Vec<usize>, Vec<usize>) {
let sqradii = self.iter().map(|s| s.vmagsq()).collect::<Vec<f64>>();
let sindex = sqradii.mergesort_indexed();
let innerindex = self.inner_hull(&sqradii,&sindex);
let outerindex = self.outer_hull(&sqradii,&sindex);
(innerindex, outerindex)
}
/// Geometric median's residual error
fn gmerror(self, g: &[f64]) -> Result<f64, RE> {
let mut unitvecssum = vec![0_f64; self[0].len()];
for v in self { unitvecssum.mutvadd(&v.vsub(g).vunit()?); };
Ok(unitvecssum.vmag())
}
/// 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 gmedian(self, eps: f64) -> Vec<f64> {
let mut g = self.acentroid(); // start iterating from the mean or vec![0_f64; self[0].len()];
let mut recsum = 0f64;
loop {
// vector iteration till accuracy eps is exceeded
let mut nextg = vec![0_f64; self[0].len()];
let mut nextrecsum = 0_f64;
for p in self {
// |p-g| done in-place for speed. Could have simply called p.vdist(g)
let mag: f64 = p
.iter()
.zip(&g)
.map(|(vi, gi)| (vi.clone().into() - gi).powi(2))
.sum();
if mag > eps {
let rec = 1.0_f64 / (mag.sqrt()); // reciprocal of distance (scalar)
// vsum increment by components
for (vi, gi) in p.iter().zip(&mut nextg) {
*gi += vi.clone().into() * rec
}
nextrecsum += rec // add separately the reciprocals for final scaling
} // else simply ignore this point v, should its distance from g be <= eps
}
nextg.iter_mut().for_each(|gi| *gi /= nextrecsum);
// eprintln!("recsum {}, nextrecsum {} diff {}",recsum,nextrecsum,nextrecsum-recsum);
if nextrecsum - recsum < eps {
return nextg;
}; // termination test
g = nextg;
recsum = nextrecsum;
}
}
/// 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 par_gmedian(self, eps: f64) -> Vec<f64> {
let mut g = self.par_acentroid(); // start iterating from the mean or vec![0_f64; self[0].len()];
let mut recsum = 0_f64;
loop {
// vector iteration till accuracy eps is exceeded
let (mut nextg, nextrecsum) = self
.par_iter()
.fold(
|| (vec![0_f64; self[0].len()], 0_f64),
|mut pair: (Vec<f64>, f64), p: &Vec<T>| {
// |p-g| done in-place for speed. Could have simply called p.vdist(g)
let mag: f64 = p
.iter()
.zip(&g)
.map(|(vi, gi)| (vi.clone().into() - gi).powi(2))
.sum();
if mag > eps {
let rec = 1.0_f64 / (mag.sqrt()); // reciprocal of distance (scalar)
for (vi, gi) in p.iter().zip(&mut pair.0) {
*gi += vi.clone().into() * rec
}
pair.1 += rec; // add separately the reciprocals for the final scaling
} // else simply ignore this point should its distance from g be zero
pair
},
)
// must run reduce on the partial sums produced by fold
.reduce(
|| (vec![0_f64; self[0].len()], 0_f64),
|mut pairsum: (Vec<f64>, f64), pairin: (Vec<f64>, f64)| {
pairsum.0.mutvadd(&pairin.0);
pairsum.1 += pairin.1;
pairsum
},
);
nextg.iter_mut().for_each(|gi| *gi /= nextrecsum);
if nextrecsum - recsum < eps {
return nextg;
}; // termination test
g = nextg;
recsum = nextrecsum;
}
}
/// Like `gmedian` but returns also the sum of reciprocals.
fn gmparts(self, eps: f64) -> (Vec<f64>, f64) {
let mut g = self.acentroid(); // start iterating from the Centre
let mut recsum = 0f64;
loop {
// vector iteration till accuracy eps is exceeded
let mut nextg = vec![0_f64; self[0].len()];
let mut nextrecsum = 0f64;
for x in self {
let mag = g
.iter()
.zip(x)
.map(|(&gi, xi)| (xi.clone().into() - gi).powi(2))
.sum::<f64>();
if mag.is_normal() {
let rec = 1.0_f64 / (mag.sqrt()); // reciprocal of distance (scalar)
// vsum increments by components
nextg
.iter_mut()
.zip(x)
.for_each(|(vi, xi)| *vi += xi.clone().into() * rec);
nextrecsum += rec // add separately the reciprocals for final scaling
} // else simply ignore this point should its distance from g be zero
}
if nextrecsum - recsum < eps {
return (
nextg
.iter()
.map(|&gi| gi / nextrecsum)
.collect::<Vec<f64>>(),
nextrecsum,
);
}; // termination
nextg.iter_mut().for_each(|gi| *gi /= nextrecsum);
g = nextg;
recsum = nextrecsum;
}
}
/// 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 covar(self, mid:&[f64]) -> Result<TriangMat,RE> {
let d = self[0].len(); // dimension of the vector(s)
if d != mid.len() {
return data_error("covar self and mid dimensions mismatch"); };
let mut covsum = self
.par_iter()
.fold(
|| vec![0_f64; (d+1)*d/2],
| mut cov: Vec<f64>, p | {
let mut covsub = 0_usize; // subscript into the flattened array cov
let vm = p.vsub(mid); // zero mean vector
vm.iter().enumerate().for_each(|(i,thisc)|
// its products up to and including the diagonal (itself)
vm.iter().take(i+1).for_each(|vmi| {
cov[covsub] += thisc*vmi;
covsub += 1;
}));
cov
}
)
.reduce(
|| vec![0_f64; (d+1)*d/2],
| mut covout: Vec<f64>, covin: Vec<f64> | {
covout.mutvadd(&covin);
covout
}
);
// now compute the means and return
let lf = self.len() as f64;
covsum.iter_mut().for_each(|c| *c /= lf);
Ok(TriangMat{ kind:2,data:covsum }) // symmetric, non transposed
}
/// 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).
fn serial_covar(self, mid:&[f64]) -> Result<TriangMat,RE> {
let d = self[0].len(); // dimension of the vector(s)
if d != mid.len() {
return data_error("serial_covar self and mid dimensions mismatch")?; };
let mut covsums = vec![0_f64; (d+1)*d/2];
for p in self {
let mut covsub = 0_usize; // subscript into the flattened array cov
let zp = p.vsub(mid); // zero mean/median vector
zp.iter().enumerate().for_each(|(i,thisc)|
// its products up to and including the diagonal
zp.iter().take(i+1).for_each(|otherc| {
covsums[covsub] += thisc*otherc;
covsub += 1;
}) )
};
// now compute the means and return
let lf = self.len() as f64;
for c in covsums.iter_mut() { *c /= lf };
Ok(TriangMat{ kind:2,data:covsums }) // kind 2 = symmetric, non transposed
}
/// Projects self onto a given basis, e.g. PCA dimensional reduction
/// The returned vectors will have lengths equal to the number of supplied basis vectors.
fn projection(self, basis: &[Vec<f64>]) -> Result<Vec<Vec<f64>>, RE>
{
if self.is_empty() {
return nodata_error("projection: empty data");
};
let olddims = self[0].len();
if basis.len() > olddims {
return data_error("projection: given too many basis vectors");
};
if olddims != basis[0].len() {
return data_error("projection: lengths of data vectors and basis vectors differ!");
};
let mut res = Vec::with_capacity(self.len());
for dvec in self {
res.push(
basis
.iter()
.map(|ev| dvec.dotp(ev))
.collect::<Vec<f64>>(),
)
};
Ok(res)
}
}