add rank-1 update of Cholesky decomposition

.gitignore

@@ -1,2 +1,3 @@
 /target
 Cargo.lock
+.idea

src/cholesky_update.rs

@@ -0,0 +1,69 @@
+use ndarray::{Array1, ArrayBase, DataMut, Ix2, NdFloat};
+
+
+pub trait CholeskyUpdate<F> {
+    fn cholesky_update_inplace(&mut self, update_vector: &Array1<F>);
+}
+
+impl<V,F> CholeskyUpdate<F> for ArrayBase<V,Ix2>
+where
+    F: NdFloat,
+    V: DataMut<Elem=F>,
+{
+    fn cholesky_update_inplace(&mut self, update_vector: &Array1<F>) {
+        let n = self.shape()[0];
+        if self.shape()[0] != update_vector.len() {
+            panic!("update_vector should be same size as self");
+        }
+        let mut w=update_vector.to_owned();
+        let mut b=F::from(1.0).unwrap();
+        for j in 0..n{
+            let ljj=self[(j,j)];
+            let ljj2=ljj*ljj;
+            let wj=w[j];
+            let wj2=wj*wj;
+            let nljj=(ljj2+wj2/b).sqrt();
+            let gamma=ljj2*b+wj2;
+            for k in j+1..n{
+                let lkj=self[(k,j)];
+                let wk=w[k]-wj*lkj/ljj;
+                self[(k,j)]=nljj*(lkj/ljj+wj*wk/gamma);
+                w[k]=wk;
+            }
+            b=b+wj2/ljj2;
+            self[(j,j)]=nljj;
+        }
+    }
+}
+
+
+
+#[cfg(test)]
+mod test{
+    use approx::assert_abs_diff_eq;
+    use super::*;
+    use ndarray::{array, Array};
+    use crate::cholesky::Cholesky;
+
+    #[test]
+    fn test_cholesky_update(){
+        let mut arr=array![[1.0, 0.0, 2.0, 3.0, 4.0],
+                                        [-2.0, 3.0, 10.0,5.0, 6.0],
+                                        [-1.0,-2.0,-7.0, 8.0, 9.0],
+                                        [11.0, 12.0, 3.0, 14.0, 5.0],
+                                        [8.0, 2.0, 13.0, 4.0, 5.0]];
+        arr=arr.t().dot(&arr);
+        let mut l_tri = arr.cholesky().unwrap();
+
+        let x = Array::from(vec![1.0, 2.0, 3.0,0.0, 1.0]);
+        let vt=x.clone().into_shape((1,x.shape()[0])).unwrap();
+        let v=x.clone().into_shape((x.shape()[0],1)).unwrap();
+
+        l_tri.cholesky_update_inplace(&x);
+
+        let restore=l_tri.dot(&l_tri.t());
+        let expected=arr+v.dot(&vt);
+
+        assert_abs_diff_eq!(restore, expected, epsilon=1e-7);
+    }
+}

src/lib.rs

@@ -25,6 +25,7 @@ pub mod reflection;
 pub mod svd;
 pub mod triangular;
 pub mod tridiagonal;
+pub mod cholesky_update;
 
 use ndarray::{ArrayBase, Ix2, RawData, ShapeError};
 use thiserror::Error;

tests/cholesky_update.rs

@@ -0,0 +1,32 @@
+use approx::assert_abs_diff_eq;
+use ndarray::prelude::*;
+use proptest::prelude::*;
+use linfa_linalg::{cholesky::*, cholesky_update::*};
+mod common;
+
+prop_compose! {
+    fn gram_arr()
+        (arr in common::square_arr()) -> (Array2<f64>,Array1<f64>){
+        let dim = arr.nrows();
+        let mut mul = arr.t().dot(&arr);
+        for i in 0..dim {
+            mul[(i, i)] += 1.0;
+        }
+
+        (mul,arr.slice(s![0,..]).to_owned())
+    }
+}
+
+fn run_cholesky_update_test(orig: (Array2<f64>, Array1<f64>)) {
+    let (arr, x) = orig;
+    let mut l_tri = arr.cholesky().unwrap();
+    l_tri.cholesky_update_inplace(&x);
+
+    let vt=x.clone().into_shape((1,x.shape()[0])).unwrap();
+    let v=x.clone().into_shape((x.shape()[0],1)).unwrap();
+
+    let restore = l_tri.dot(&l_tri.t());
+    let expected = arr + v.dot(&vt);
+    assert_abs_diff_eq!(restore, expected, epsilon = 1e-7);
+}
+