Fix Solve and add unit tests on an identity matrix

tests/ops.rs

@@ -1,10 +1,9 @@
 use generic_parameterize::parameterize;
-use std::convert::identity;
+use num_traits::real::Real;
 use std::fmt::Debug;
+use std::iter::{Product, Sum};
 use std::ops;
-use std::thread::sleep;
-use std::time::Duration;
-use vector_victor::Matrix;
+use vector_victor::{Matrix, Vector};
 
 #[parameterize(S = (i32, f32, u32), M = [1,4], N = [1,4])]
 #[test]
@@ -20,10 +19,46 @@ where
     }
 }
 
+#[parameterize(S = (f32, f64), M = [1,2,3,4])]
 #[test]
-fn test_lu() {
+fn test_lu_identity<S: Default + Real + Debug + Product + Sum, const M: usize>() {
     // let a: Matrix<f32, 3, 3> = Matrix::<f32, 3, 3>::identity();
-    let a = Matrix::new([[1.0, 2.0], [3.0, 4.0]]);
-    let (lu, _idx, _d) = a.lu().expect("What");
-    println!("{:?}", lu);
+    let i = Matrix::<S, M, M>::identity();
+    let ones = Vector::<S, M>::fill(S::one());
+    let (lu, idx, d) = i.lu().expect("Singular matrix encountered");
+    assert_eq!(
+        lu,
+        i,
+        "Incorrect LU decomposition matrix for {m}x{m} identity matrix",
+        m = M
+    );
+    assert!(
+        (0..M).eq(idx.elements().cloned()),
+        "Incorrect permutation matrix result for {m}x{m} identity matrix",
+        m = M
+    );
+    assert_eq!(
+        d,
+        S::one(),
+        "Incorrect permutation parity for {m}x{m} identity matrix",
+        m = M
+    );
+    assert_eq!(
+        i.det(),
+        S::one(),
+        "Incorrect determinant for {m}x{m} identity matrix",
+        m = M
+    );
+    assert_eq!(
+        i.inverse(),
+        Some(i),
+        "Incorrect inverse for {m}x{m} identity matrix",
+        m = M
+    );
+    assert_eq!(
+        i.solve(&ones),
+        Some(ones),
+        "Incorrect solve result for {m}x{m} identity matrix",
+        m = M
+    )
 }