feat: adds PCA

2020-03-06 09:13:54 -08:00
parent 619560a1cd
commit 7b3fa982be
9 changed files with 1422 additions and 20 deletions
@@ -0,0 +1,112 @@
+use crate::linalg::{Matrix};
+
+#[derive(Debug, Clone)]
+pub struct EVD<M: Matrix> {        
+    pub d: Vec<f64>,
+    pub e: Vec<f64>,
+    pub V: M
+}
+
+impl<M: Matrix> EVD<M> {
+    pub fn new(V: M, d: Vec<f64>, e: Vec<f64>) -> EVD<M> {
+        EVD {
+            d: d,
+            e: e,
+            V: V
+        }
+    }
+}
+
+#[cfg(test)]
+mod tests {    
+    use super::*; 
+    use crate::linalg::naive::dense_matrix::DenseMatrix;
+
+    #[test]
+    fn decompose_symmetric() { 
+
+        let A = DenseMatrix::from_array(&[
+            &[0.9000, 0.4000, 0.7000],
+            &[0.4000, 0.5000, 0.3000],
+            &[0.7000, 0.3000, 0.8000]]);
+
+        let eigen_values = vec![1.7498382, 0.3165784, 0.1335834];
+
+        let eigen_vectors = DenseMatrix::from_array(&[
+            &[0.6881997, -0.07121225, 0.7220180],
+            &[0.3700456, 0.89044952, -0.2648886],
+            &[0.6240573, -0.44947578, -0.6391588]
+        ]);
+
+        let evd = A.evd(true);        
+
+        assert!(eigen_vectors.abs().approximate_eq(&evd.V.abs(), 1e-4));        
+        for i in 0..eigen_values.len() {
+            assert!((eigen_values[i] - evd.d[i]).abs() < 1e-4);
+        }
+        for i in 0..eigen_values.len() {
+            assert!((0f64 - evd.e[i]).abs() < std::f64::EPSILON);
+        }
+
+    }
+
+    #[test]
+    fn decompose_asymmetric() { 
+
+        let A = DenseMatrix::from_array(&[
+            &[0.9000, 0.4000, 0.7000],
+            &[0.4000, 0.5000, 0.3000],
+            &[0.8000, 0.3000, 0.8000]]);
+
+        let eigen_values = vec![1.79171122, 0.31908143, 0.08920735];
+
+        let eigen_vectors = DenseMatrix::from_array(&[
+            &[0.7178958,  0.05322098,  0.6812010],
+            &[0.3837711, -0.84702111, -0.1494582],
+            &[0.6952105,  0.43984484, -0.7036135]
+        ]);
+
+        let evd = A.evd(false);   
+        
+        assert!(eigen_vectors.abs().approximate_eq(&evd.V.abs(), 1e-4));        
+        for i in 0..eigen_values.len() {
+            assert!((eigen_values[i] - evd.d[i]).abs() < 1e-4);
+        }
+        for i in 0..eigen_values.len() {
+            assert!((0f64 - evd.e[i]).abs() < std::f64::EPSILON);
+        }
+
+    }
+
+    #[test]
+    fn decompose_complex() { 
+
+        let A = DenseMatrix::from_array(&[
+            &[3.0, -2.0, 1.0, 1.0],
+            &[4.0, -1.0, 1.0, 1.0],
+            &[1.0, 1.0, 3.0, -2.0],
+            &[1.0, 1.0, 4.0, -1.0]]);
+
+        let eigen_values_d = vec![0.0, 2.0, 2.0, 0.0];
+        let eigen_values_e = vec![2.2361, 0.9999, -0.9999, -2.2361];
+
+        let eigen_vectors = DenseMatrix::from_array(&[
+            &[-0.9159, -0.1378, 0.3816, -0.0806],
+            &[-0.6707, 0.1059, 0.901, 0.6289],
+            &[0.9159, -0.1378, 0.3816, 0.0806],
+            &[0.6707, 0.1059, 0.901, -0.6289]
+        ]);
+
+        let evd = A.evd(false);   
+        
+        assert!(eigen_vectors.abs().approximate_eq(&evd.V.abs(), 1e-4));        
+        for i in 0..eigen_values_d.len() {
+            assert!((eigen_values_d[i] - evd.d[i]).abs() < 1e-4);
+        }
+        for i in 0..eigen_values_e.len() {
+            assert!((eigen_values_e[i] - evd.e[i]).abs() < 1e-4);
+        }
+
+    }
+    
+}