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� � � � � � � � G � � i � � � P O M 8 7 � � � K G ? ' # � � � o g c U Q � v M � � � 9 � � � � � � h ; : � � } assert_eq!(argsort(&arr).as_slice(), &idcs); let idcs = [2, 7, 1, 5, 0, 4, 6, 3]; let arr = [2, -2, -9, 8, 4, 1, 6, -3]; fn test_argsort() { #[test] } assert_eq!(xicorf(&y, &x), 0.06099306099306101); // function of y - this is a one-to-many relationship // There is /// ``` /// assert_eq!(xi, 0.9375); /// //// ``` /// assert_eq!(xi, 0.9375); /// /// let xi = xicor(&x, &y); /// let y: /// ``` /// assert_eq!(xi, 0.9375); /// /// let xi = xicor(&x, &y); /// /// ``` /// assert_eq!(xi, 0.9375); /// /// let xi = xicor(&x, &y); /// /// ``` /// assert_eq!(xi, 0.9375); /// /// let xi = xicor(&x, &y); /// let y:/// ``` //// ``` /// assert_eq!(xi, 0.93/// ``` /// assert_eq!(xi, 0.9375); /// /// let xi = xicor(&x, &y); /// let y/// /// ``` /// assert_eq!(xi, 0.9375); /// /// let xi = /// /// ``` /// as/// /// ``` /// ``` /// assert_eq!(xi, 0/// /// ``` /// assert_eq!(xi, 0.9375); /// /// let xi = xicor(/// ``` /// assert_eq!(xi, 0.9375); /// /// let xi = xi/// ``` /// assert_eq!(xi, 0.9375)/// /// ``` /// assert_eq!(x/// ``` /// /// ``` /// assert_eq!(xi, 0.9375); /// /// let xi = xicor(&x, &y); /// let y: V/// ``` /// assert_eq!(xi, 0.9375); ////// ``` /// assert_eq!(xi, 0.9375); /// /// let xi = xicor(&/// ``` /// assert_eq!(xi, 0/// ``` /// assert_eq!(xi, 0.//// ``` /// assert_eq////// ``` /// assert_eq!(xi, 0.9375); /// /// let xi = xicor(&x, &y); /// let y:/// ``` /// assert_eq!(xi, 0.9375); /// /// /// ``` /// assert_eq!(xi, 0.9375); /// /// let xi = xicor(&x, &y); /// let y: V/// ``` /// assert_eq!(xi, 0.9375); /// /// let xi = xicor(&x, &y); /// let y: /// ``` /// assert_eq!(xi, 0.9375); /// /// let xi = xicor(&x, &y); /// /// ``` /// assert_eq!(xi, 0.9375); /// /// let xi = xicor(&x, &y); ///pub use xicor::*; mod xicor; mod tests; #[cfg(test)] //! xi (given certain repub use xicor::*; mod xicor; mod tests; #[cfg(test)] //! xi (given certain rpub use xicor::*; mod xicor; mod tests; #[cfg(test)] //! xi (given certain reqpub use xicor::*; mod xicor; mod tests; #[cfg(test)] //! - [ ] P-values for testing independence //! - [x] Calculation of the xi coefficient itself //! //! ## Progress //! //! sorting routines. //! revealed that 80% of this calculation lay in the standard library's //! [`xicorf`] was able to process 1,000,000 pairs in 0.33 seconds. Profiling //! - Quite fast. In release mode on a 12-year-old machine (Dell M4700), //! could be correlated in this manner (lexicographically), for example. //! themselves, only the ability to compare them. In principle even strings //! - Generic over `Ord`, as xi does not require calculations on the elements //! two slices containing the data) //! - Extremely simple to use (just call [`xicor()`], [`xicorf()`], etc, with //! //! ## Highlights //! //! of what function that may be. //! close to 1, representing that `y` is strongly a function of `x`, regardless //! measures _linear_ dependence. On the other hand, Chatterjee's xi will be //! Pearson's correlation coefficient will be roughly zero for this data, as it //! distributed from zero to tau. For each one, we compute `y = sin(x)`. //! coefficient. Suppose we have some sequence of random `x` values uniformly //! in a much more general sense than, for example, Pearson's correlation //! Chatterjee's xi provides a measure of one variable's dependence on another //! //! [the original paper](https://arxiv.org/pdf/1909.10140). //! Chatterjee's xi-correlation coefficient, based on //! This crate provides a reasonably efficient implementation of Sourav ad �
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} } assert_eq!(cumulative_gte(&arr).as_slice(), &counts); let counts = [11, 11, 9, 9, 9, 6, 5, 4, 4, 2, 1]; let arr = [1.1, 1.1, 2.5, 2.5, 2.5, 3., 8., 19., 19., 51.7, 100.]; fn test_cumulative_gte() { #[test] } assert_eq!(cumulative_lte(&arr).as_slice(), &counts); let counts = [2, 2, 5, 5, 5, 6, 7, 9, 9, 11, 11]; let arr = [1.1, 1.1, 2.5, 2.5, 2.5, 3., 8., 19., 19., 51.7, 51.7]; fn test_cumulative_lte() { #[test] } assert_eq!(permute(&arr, &idcs).as_slice(), &permuted); let permuted = [-9, -3, -2, 1, 2, 4, 6, 8]; let idcs = [2, 7, 1, 5, 0, 4, 6, 3]; let arr = [2, -2, -9, 8, 4, 1, 6, -3]; fn test_permute() { #[test] ad � � E � � � g D C # � � � j G F �
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� � � c ] \ Q O N � � w 5 4 � � � � � � � � � � n m $ � � � � � y x C � � � � � h � � � J � � � � � � l 5 � � � � { Z 7 6 A @ } assert_eq!(argsort(&arr).as_slice() if a == b { return true; } fn eq_within(a: f6 assert_req assert_req(xicorf_norm(&x, &y), 0.9910030989, RTOL); l assert_req(xicorf_no asse assert_req(xic assert_req(xicorf_norm(&x, &y), 0.9910030989, R assert_req(xicorf_norm(&x, &y), 0.9910030989, assert_req(xicorf_norm(&x, &y), 0.9910030989, R asse assert_req(xico assert_req(xicorf_norm(&x, &y), 0.9910030989, RTOL); l assert_req(xicorf_norm(&x, &y), 0.9910030989, RTOL); let assert_req(xicorf_norm(&x, &y), 0.9910030989, RTOL); let y: V assert_req(xicorf_norm(&x, &y), 0.9910030989, RT assert_req(xicorf_norm(&x, &y), 0.9910030989, RTOL); let y: assert_req(xicorf_norm(&x, &y), 0.9910030989, RTOL); assert_req(xicorf_norm(&x, &y), 0.9910030989, RT asse assert_req(xicorf_n assert_req(xicorf_norm(&x, &y), 0.9910030989, R assert_req(xicorf_norm(&x, &y), 0.9910030989, assert_req(xicorf_norm(&x, &y), 0.9910030989, asse assert_req(xicorf_no assert_req(xicorf_norm(&x, &y), 0.9910030989, RTOL); l assert_req(xicorf_norm(&x, &y), 0.9910030989, RTOL); let assert_req(xicorf_norm(&x, &y), 0.9910030989, RTOL); mmod tests; #[mod tests; } counts } if arr[i+1] == arr[i] { counts[i+1] = counts[i]; } for i in 0..arr.len()-1 { let mut counts: Vec<usize> = (1..=arr.len()).rev().collect(); fn cumulative_gte<T: PartialEq<T> + Copy>(arr: &[T]) -> Vec<usize> { // equal to it. The array should be sorted before it is passed in. // For every element in the array, count how many elements are greater than or } counts } if arr[i] == arr[i+1] { counts[i] = counts[i+1]; } for i in (0..arr.len()-1).rev() { let mut counts: Vec<usize> = (1..=arr.len()).collect(); fn cumulative_lte<T: PartialEq<T> + Copy>(arr: &[T]) -> Vec<usize> { // equal to it. The array should be sorted before it is passed in. // For every element in the array, count how many elements are less than or } .collect() .map(|&i| arr[i]) idcs.iter() fn permute<T: Copy>(arr: &[T], idcs: &[usize]) -> Vec<T> { // Permute the given array such that arr[n] ends up at idcs[n]. } idcs idcs.sort_unstable_by_key(|&i| &arr[i]); let mut idcs: Vec<usize> = (0..arr.len()).collect(); fn argsort<T: Ord>(arr: &[T]) -> Vec<usize> { // returned sequence of indices i -> arr[i], the resulting sequence is sorted. // Return the indices that would sort the given array. That is, if you map the } 1.-(n as f64)*(rsum as f64)/(2.*lsum as f64) .sum::<usize>(); .map(|l| l*(n-l)) let lsum = ls.into_iter() let n = x.len(); .sum::<usize>(); .map(|win| win[0].abs_diff(win[1])) let rsum = rs.windows(2) } ls[i] = l; rs[i] = r; for ((i, r), l) in idcs.into_iter().zip(r_ascending).zip(l_ascending) { let mut ls = vec![0; x.len()]; let mut rs = vec![0; x.len()]; let l_ascending = cumulative_gte(&y_ascending); let r_ascending = cumulative_lte(&y_ascending); let y_ascending = permute(&y_ord, &idcs); let idcs = argsort(&y_ord); let y_ord = permute(y, &idcs); let idcs = argsort(x); assert!(x.len() == y.len(), "x and y must have the same length"); pub fn xicor<T: Ord + Copy>(x: &[T], y: &[T]) -> f64 { ad �
� � � x d / � � � � � � � | O N } } assert_eq!(argsort(&arr).as_slice(), &idcs); let idcs = [2, 7, 1, 5, 0, 4, 6, 3]; let arr = [2, -2, -9, 8, 4, 1, 6, -3]; fn test_argsort() { #[test] } } ); right: {right}" left: {left}\n\ "assertion `left ~= right` failed\n\ panic!( if diff/mean_size > rtol { let diff = (left-right).abs(); let mean_size = (left.abs()+right.abs())/2.; ad + W � � � � W ] ; if a == b { return fn assert_req(left: f64, right: f64, rtol: f64) { // tolerance of eachother. // Check whether 2 floating-point values are within the given fractional }