lagrange interpolation

src/poly.rs

@@ -202,13 +202,48 @@ fn verify_point(p: Public, i: u32, m: u32, x: Scalar) -> bool {
     lhs == rhs
 }
 
+// Polynomial sum
+fn poly_sum(x: Vec<Scalar>, y: Vec<Scalar>) -> Vec<Scalar> {
+    let mut res = vec![Scalar::zero(); std::cmp::max(x.len(), y.len())];
+    for (i, xi) in x.iter().enumerate() {
+        res[i] += xi
+    }
+    for (i, yi) in y.iter().enumerate() {
+        res[i] += yi
+    }
+    res
+}
+
 // Polynomial product
 fn poly_prod(x: Vec<Scalar>, y: Vec<Scalar>) -> Vec<Scalar> {
     let mut res = vec![Scalar::zero(); x.len() + y.len() - 1];
     for (i, xi) in x.iter().enumerate() {
         for (j, yj) in y.iter().enumerate() {
-            res[i+j] += xi * yj
+            res[i + j] += xi * yj
         }
     }
     res
 }
+
+// lagrange basis polynomial L_n_j(x)
+fn lagrange_basis(j: usize, xs: &Vec<Scalar>) -> Vec<Scalar> {
+    let mut num = vec![Scalar::one()]; // numerator
+    let mut den = Scalar::one();
+    for (k, xk) in xs.iter().enumerate() {
+        if k != j {
+            num = poly_prod(num, vec![-xk, Scalar::one()]);
+            den *= xs[j] - xk
+        }
+    }
+    den = den.invert().unwrap();
+    num.iter().map(|v| v * den).collect()
+}
+
+fn lagrange_interpolate(points: Vec<(Scalar, Scalar)>) -> Vec<Scalar> {
+    let (xs, ys): (Vec<Scalar>, Vec<Scalar>) = points.iter().cloned().unzip();
+    let mut res = Vec::new();
+    for (j, yj) in ys.iter().enumerate() {
+        res = poly_sum(res, lagrange_basis(j, &xs).iter().map(|v| v * yj).collect())
+    }
+    res
+}