diff --git a/src/kernel.rs b/src/kernel.rs
index 20571b0..0ea844c 100644
--- a/src/kernel.rs
+++ b/src/kernel.rs
@@ -50,8 +50,14 @@ pub trait Kernel {
 }
 
 impl Kernel for Vec<Box<dyn Kernel>> {
-    fn k_mat(&self, _ts1: &[f64], _ts2: Option<&[f64]>) -> Array2<f64> {
-        unimplemented!();
+    fn k_mat(&self, ts1: &[f64], ts2: Option<&[f64]>) -> Array2<f64> {
+        let n = ts1.len();
+        let m = ts2.map_or(n, |ts| ts.len());
+
+        self.iter()
+            .fold(Array2::zeros((n, m)), |k_diag: Array2<f64>, kernel| {
+                k_diag + kernel.k_mat(ts1, ts2)
+            })
     }
 
     fn k_diag(&self, ts: &[f64]) -> Array1<f64> {
@@ -82,23 +88,23 @@ impl Kernel for Vec<Box<dyn Kernel>> {
 
         let dim = data
             .iter()
-            .fold((0, 0), |(w, h), m| (w + m.ncols(), h + m.nrows()));
+            .fold((0, 0), |(h, w), m| (h + m.nrows(), w + m.ncols()));
 
-        let mut cov = Array2::zeros(dim);
+        let mut block = Array2::zeros(dim);
 
         let mut r_d = 0;
         let mut c_d = 0;
 
         for m in data {
             for ((r, c), v) in m.indexed_iter() {
-                cov[(r + r_d, c + c_d)] = *v;
+                block[(r + r_d, c + c_d)] = *v;
             }
 
             r_d += m.nrows();
             c_d += m.ncols();
         }
 
-        cov
+        block
     }
 
     fn measurement_vector(&self) -> Array1<f64> {
@@ -118,23 +124,23 @@ impl Kernel for Vec<Box<dyn Kernel>> {
 
         let dim = data
             .iter()
-            .fold((0, 0), |(w, h), m| (w + m.ncols(), h + m.nrows()));
+            .fold((0, 0), |(h, w), m| (h + m.nrows(), w + m.ncols()));
 
-        let mut feedback = Array2::zeros(dim);
+        let mut block = Array2::zeros(dim);
 
         let mut r_d = 0;
         let mut c_d = 0;
 
         for m in data {
             for ((r, c), v) in m.indexed_iter() {
-                feedback[(r + r_d, c + c_d)] = *v;
+                block[(r + r_d, c + c_d)] = *v;
             }
 
             r_d += m.nrows();
             c_d += m.ncols();
         }
 
-        feedback
+        block
     }
 
     fn transition(&self, t0: f64, t1: f64) -> Array2<f64> {
@@ -145,23 +151,50 @@ impl Kernel for Vec<Box<dyn Kernel>> {
 
         let dim = data
             .iter()
-            .fold((0, 0), |(w, h), m| (w + m.ncols(), h + m.nrows()));
+            .fold((0, 0), |(h, w), m| (h + m.nrows(), w + m.ncols()));
 
-        let mut transition = Array2::zeros(dim);
+        let mut block = Array2::zeros(dim);
 
         let mut r_d = 0;
         let mut c_d = 0;
 
         for m in data {
             for ((r, c), v) in m.indexed_iter() {
-                transition[(r + r_d, c + c_d)] = *v;
+                block[(r + r_d, c + c_d)] = *v;
             }
 
             r_d += m.nrows();
             c_d += m.ncols();
         }
 
-        transition
+        block
+    }
+
+    fn noise_effect(&self) -> Array2<f64> {
+        let data = self
+            .iter()
+            .map(|kernel| kernel.noise_effect())
+            .collect::<Vec<_>>();
+
+        let dim = data
+            .iter()
+            .fold((0, 0), |(h, w), m| (h + m.nrows(), w + m.ncols()));
+
+        let mut block = Array2::zeros(dim);
+
+        let mut r_d = 0;
+        let mut c_d = 0;
+
+        for m in data {
+            for ((r, c), v) in m.indexed_iter() {
+                block[(r + r_d, c + c_d)] = *v;
+            }
+
+            r_d += m.nrows();
+            c_d += m.ncols();
+        }
+
+        block
     }
 
     fn noise_cov(&self, t0: f64, t1: f64) -> Array2<f64> {
@@ -172,22 +205,108 @@ impl Kernel for Vec<Box<dyn Kernel>> {
 
         let dim = data
             .iter()
-            .fold((0, 0), |(w, h), m| (w + m.ncols(), h + m.nrows()));
+            .fold((0, 0), |(h, w), m| (h + m.nrows(), w + m.ncols()));
 
-        let mut cov = Array2::zeros(dim);
+        let mut block = Array2::zeros(dim);
 
         let mut r_d = 0;
         let mut c_d = 0;
 
         for m in data {
             for ((r, c), v) in m.indexed_iter() {
-                cov[(r + r_d, c + c_d)] = *v;
+                block[(r + r_d, c + c_d)] = *v;
             }
 
             r_d += m.nrows();
             c_d += m.ncols();
         }
 
-        cov
+        block
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    extern crate intel_mkl_src;
+
+    use approx::assert_abs_diff_eq;
+    use rand::{distributions::Standard, thread_rng, Rng};
+
+    use super::*;
+
+    #[test]
+    fn test_kernel_matrix() {
+        let kernel: Vec<Box<dyn Kernel>> = vec![
+            Box::new(Matern32::new(1.5, 0.7)),
+            Box::new(Matern52::new(0.2, 5.0)),
+        ];
+
+        let ts = [1.26, 1.46, 2.67];
+
+        assert_abs_diff_eq!(
+            kernel.k_mat(&ts, None),
+            array![
+                [1.7, 1.5667546855502472, 0.3933043131476467],
+                [1.5667546855502472, 1.7, 0.4908539038626858],
+                [0.3933043131476467, 0.4908539038626858, 1.7]
+            ]
+        );
+    }
+
+    #[test]
+    fn test_kernel_diag() {
+        let kernel: Vec<Box<dyn Kernel>> = vec![
+            Box::new(Matern32::new(1.5, 0.7)),
+            Box::new(Matern52::new(0.2, 5.0)),
+        ];
+
+        let ts: Vec<_> = thread_rng()
+            .sample_iter::<f64, _>(Standard)
+            .take(10)
+            .map(|x| x * 10.0)
+            .collect();
+
+        assert_eq!(kernel.k_mat(&ts, None).diag(), kernel.k_diag(&ts));
+    }
+
+    #[test]
+    fn test_kernel_order() {
+        let kernel: Vec<Box<dyn Kernel>> = vec![
+            Box::new(Matern32::new(1.5, 0.7)),
+            Box::new(Matern52::new(0.2, 5.0)),
+        ];
+
+        let m = kernel.order();
+
+        assert_eq!(kernel.state_mean(0.0).shape(), &[m]);
+        assert_eq!(kernel.state_cov(0.0).shape(), &[m, m]);
+        assert_eq!(kernel.measurement_vector().shape(), &[m]);
+        assert_eq!(kernel.feedback().shape(), &[m, m]);
+        assert_eq!(kernel.noise_effect().shape()[0], m);
+        assert_eq!(kernel.transition(0.0, 1.0).shape(), &[m, m]);
+        assert_eq!(kernel.noise_cov(0.0, 1.0).shape(), &[m, m]);
+    }
+
+    #[test]
+    fn test_ssm_variance() {
+        let kernel: Vec<Box<dyn Kernel>> = vec![
+            Box::new(Matern32::new(1.5, 0.7)),
+            Box::new(Matern52::new(0.2, 5.0)),
+        ];
+
+        let ts: Vec<_> = thread_rng()
+            .sample_iter::<f64, _>(Standard)
+            .take(10)
+            .map(|x| x * 10.0)
+            .collect();
+
+        let h = kernel.measurement_vector();
+
+        let vars = ts
+            .iter()
+            .map(|t| h.dot(&kernel.state_cov(*t)).dot(&h))
+            .collect::<Vec<_>>();
+
+        assert_abs_diff_eq!(Array::from(vars), kernel.k_diag(&ts));
     }
 }