utils: matrix-vector products & Hadamard product

src/utils.rs

@@ -0,0 +1,134 @@
+use ark_ff::fields::PrimeField;
+use core::ops::Add;
+
+pub fn vector_elem_product<F: PrimeField>(a: &Vec<F>, e: &F) -> Vec<F> {
+    // maybe move this method to operator a * e
+    let mut r: Vec<F> = vec![F::zero(); a.len()];
+    for i in 0..a.len() {
+        r[i] = a[i] * e;
+    }
+    r
+}
+pub fn matrix_vector_product<F: PrimeField>(M: &Vec<Vec<F>>, z: &Vec<F>) -> Vec<F> {
+    // TODO assert len
+    let mut r: Vec<F> = vec![F::zero(); M.len()];
+    for i in 0..M.len() {
+        for j in 0..M[i].len() {
+            r[i] += M[i][j] * z[j];
+        }
+    }
+    r
+}
+pub fn hadamard_product<F: PrimeField>(a: Vec<F>, b: Vec<F>) -> Vec<F> {
+    // maybe move this method to operator a * b
+    // TODO assert equals len
+    let mut r: Vec<F> = vec![F::zero(); a.len()];
+    for i in 0..a.len() {
+        r[i] = a[i] * b[i];
+    }
+    r
+}
+
+pub fn vec_add<F: PrimeField>(a: Vec<F>, b: Vec<F>) -> Vec<F> {
+    let mut r: Vec<F> = vec![F::zero(); a.len()];
+    for i in 0..a.len() {
+        r[i] = a[i] + b[i];
+    }
+    r
+}
+// TODO instead of vec_add do:
+// impl<'a, 'b, F> Add<&'b Vec<F>> for &'a Vec<F> {
+//     type Output = Vec<F>;
+//     fn add(self, rhs: &'b Vec<F>) -> Vec<F> {
+//         let mut r: Vec<F> = vec![F::zero(); self.len()];
+//         for i in 0..self.len() {
+//             r[i] = self[i] + rhs[i];
+//         }
+//         r
+//     }
+// }
+pub fn vec_sub<F: PrimeField>(a: Vec<F>, b: Vec<F>) -> Vec<F> {
+    let mut r: Vec<F> = vec![F::zero(); a.len()];
+    for i in 0..a.len() {
+        r[i] = a[i] - b[i];
+    }
+    r
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+    use ark_bn254::{g1::G1Affine, Fr};
+    use ark_ec::CurveGroup;
+    use ark_std::{One, Zero};
+    use std::ops::Mul;
+
+    fn to_F_matrix<F: PrimeField>(M: Vec<Vec<usize>>) -> Vec<Vec<F>> {
+        let mut R: Vec<Vec<F>> = vec![Vec::new(); M.len()];
+        for i in 0..M.len() {
+            R[i] = vec![F::zero(); M[i].len()];
+            for j in 0..M[i].len() {
+                R[i][j] = F::from(M[i][j] as u64);
+            }
+        }
+        R
+    }
+    fn to_F_vec<F: PrimeField>(z: Vec<usize>) -> Vec<F> {
+        let mut r: Vec<F> = vec![F::zero(); z.len()];
+        for i in 0..z.len() {
+            r[i] = F::from(z[i] as u64);
+        }
+        r
+    }
+
+    #[test]
+    fn test_matrix_vector_product() {
+        let A = to_F_matrix::<Fr>(vec![
+            vec![0, 1, 0, 0, 0, 0],
+            vec![0, 0, 0, 1, 0, 0],
+            vec![0, 1, 0, 0, 1, 0],
+            vec![5, 0, 0, 0, 0, 1],
+        ]);
+        let z = to_F_vec(vec![1, 3, 35, 9, 27, 30]);
+        let Az = matrix_vector_product(&A, &z);
+        assert_eq!(Az, to_F_vec(vec![3, 9, 30, 35]));
+    }
+
+    #[test]
+    fn test_hadamard_product() {
+        let a = to_F_vec::<Fr>(vec![1, 2, 3, 4, 5, 6]);
+        let b = to_F_vec(vec![7, 8, 9, 10, 11, 12]);
+        assert_eq!(
+            hadamard_product(a, b),
+            to_F_vec(vec![7, 16, 27, 40, 55, 72])
+        );
+    }
+
+    #[test]
+    fn test_ABC_hadamard() {
+        let A = to_F_matrix::<Fr>(vec![
+            vec![0, 1, 0, 0, 0, 0],
+            vec![0, 0, 0, 1, 0, 0],
+            vec![0, 1, 0, 0, 1, 0],
+            vec![5, 0, 0, 0, 0, 1],
+        ]);
+        let B = to_F_matrix(vec![
+            vec![0, 1, 0, 0, 0, 0],
+            vec![0, 1, 0, 0, 0, 0],
+            vec![1, 0, 0, 0, 0, 0],
+            vec![1, 0, 0, 0, 0, 0],
+        ]);
+        let C = to_F_matrix(vec![
+            vec![0, 0, 0, 1, 0, 0],
+            vec![0, 0, 0, 0, 1, 0],
+            vec![0, 0, 0, 0, 0, 1],
+            vec![0, 0, 1, 0, 0, 0],
+        ]);
+        let z = to_F_vec(vec![1, 3, 35, 9, 27, 30]);
+
+        let Az = matrix_vector_product(&A, &z);
+        let Bz = matrix_vector_product(&B, &z);
+        let Cz = matrix_vector_product(&C, &z);
+        assert_eq!(hadamard_product(Az, Bz), Cz);
+    }
+}