calculate autocorrelation stats_ineff and tau

src/correlation_analysis.rs

@@ -0,0 +1,75 @@
+use rgsl::statistics;
+
+// calculates the statistical inefficiency g of the given timeseries
+// the quantity g can be thought of: N/g is the number of uncorrelated
+// configurations in the timeseries, where samples are separated by
+// the a multiple of g 
+// For details, see "Chodera et al. (2007). Use of a Weighted Histogram Analysis
+// Method for the Analysis of Simulated and Parallel Tempering Simulations, JCTC"
+fn statistical_ineff(timeseries: &[f64]) -> f64 {
+    let n = timeseries.len();
+    let mean = statistics::mean(timeseries, 1, timeseries.len());
+    let d_mean = timeseries.iter().map(|x| x-mean).collect::<Vec<f64>>();
+    let cov = statistics::covariance(timeseries, 1, timeseries, 1, n);
+
+    let mut g = 1.0;
+    for t in 1..(n-1) {
+
+        // normalized autocorr C(t) = (<x_n*x_(n+t)> - <x_n>^2) / (<x_n^2> - <x_n>^2)
+        let tmp = d_mean[0..n-t].iter().zip(d_mean[t..n].iter()).map(|(x, y)| x*y);
+        let c: f64 = tmp.map(|x| x+x).sum::<f64>() / (2.0 * (n as f64-t as f64)*cov);
+
+        if c <= 0.0 {  // terminate at first 0 (autocorr gets noisy from here)
+            break;
+        }
+        g = g + (2.0*c*(1.0-t as f64/n as f64))
+    }
+    if g < 1.0 {
+        1.0
+    } else {
+        g
+    }
+}
+
+// The autocorrelation time of a timeseries can be deduced from the
+// `statistical_ineff` by (g-1)/2.0 
+fn autocorrelation_time(g: f64) -> f64 {
+    (g - 1.0) / 2.0
+}
+
+#[cfg(test)]
+mod tests {
+    use std::io::{BufRead, BufReader};
+    use std::fs::File;
+    
+    fn read_timeseries(filename: &str) -> Vec<f64> {
+        let mut timeseries: Vec<f64> = Vec::new();
+        let file = File::open(filename).unwrap();
+        let reader = BufReader::new(&file);
+        for line in reader.lines() {
+            let val = line.unwrap().split_whitespace()
+                .collect::<Vec<&str>>()[1].parse::<f64>().unwrap();
+            timeseries.push(val);
+        }
+        timeseries
+
+    }
+
+    #[test]
+    fn statistical_ineff() {
+        let timeseries = read_timeseries("example/1d_cyclic/COLVAR-2.5.xvg");
+        let g = super::statistical_ineff(&timeseries);
+        println!("{:?}", g);
+        assert!((g - 3.859).abs() < 0.001)
+    }
+
+    #[test]
+    fn autocorrelation_time() {
+        let timeseries = read_timeseries("example/1d_cyclic/COLVAR-2.5.xvg");
+        let g = super::statistical_ineff(&timeseries);
+        let tau = super::autocorrelation_time(g);
+        println!("{:?}", tau);
+        assert!((tau - 1.430).abs() < 0.001)
+    }
+
+}