feat: + ridge regression

src/linalg/stats.rs

@@ -0,0 +1,139 @@
+//! # Various Statistical Methods
+//!
+//!
+
+use crate::linalg::BaseMatrix;
+use crate::math::num::RealNumber;
+
+/// Defines baseline implementations for various statistical functions
+pub trait MatrixStats<T: RealNumber>: BaseMatrix<T> {
+    /// Compute the arithmetic mean along the specified axis.
+    fn mean(&self, axis: u8) -> Vec<T> {
+        let (n, m) = match axis {
+            0 => {
+                let (n, m) = self.shape();
+                (m, n)
+            }
+            _ => self.shape(),
+        };
+
+        let mut x: Vec<T> = vec![T::zero(); n];
+
+        let div = T::from_usize(m).unwrap();
+
+        for i in 0..n {
+            for j in 0..m {
+                x[i] += match axis {
+                    0 => self.get(j, i),
+                    _ => self.get(i, j),
+                };
+            }
+            x[i] /= div;
+        }
+
+        x
+    }
+
+    /// Compute the standard deviation along the specified axis.
+    fn std(&self, axis: u8) -> Vec<T> {
+        let (n, m) = match axis {
+            0 => {
+                let (n, m) = self.shape();
+                (m, n)
+            }
+            _ => self.shape(),
+        };
+
+        let mut x: Vec<T> = vec![T::zero(); n];
+
+        let div = T::from_usize(m).unwrap();
+
+        for i in 0..n {
+            let mut mu = T::zero();
+            let mut sum = T::zero();
+            for j in 0..m {
+                let a = match axis {
+                    0 => self.get(j, i),
+                    _ => self.get(i, j),
+                };
+                mu += a;
+                sum += a * a;
+            }
+            mu /= div;
+            x[i] = (sum / div - mu * mu).sqrt();
+        }
+
+        x
+    }
+
+    /// standardize values by removing the mean and scaling to unit variance
+    fn scale_mut(&mut self, mean: &Vec<T>, std: &Vec<T>, axis: u8) {
+        let (n, m) = match axis {
+            0 => {
+                let (n, m) = self.shape();
+                (m, n)
+            }
+            _ => self.shape(),
+        };
+
+        for i in 0..n {
+            for j in 0..m {
+                match axis {
+                    0 => self.set(j, i, (self.get(j, i) - mean[i]) / std[i]),
+                    _ => self.set(i, j, (self.get(i, j) - mean[i]) / std[i]),
+                }
+            }
+        }
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+    use crate::linalg::naive::dense_matrix::DenseMatrix;
+    use crate::linalg::BaseVector;
+
+    #[test]
+    fn mean() {
+        let m = DenseMatrix::from_2d_array(&[
+            &[1., 2., 3., 1., 2.],
+            &[4., 5., 6., 3., 4.],
+            &[7., 8., 9., 5., 6.],
+        ]);
+        let expected_0 = vec![4., 5., 6., 3., 4.];
+        let expected_1 = vec![1.8, 4.4, 7.];
+
+        assert_eq!(m.mean(0), expected_0);
+        assert_eq!(m.mean(1), expected_1);
+    }
+
+    #[test]
+    fn std() {
+        let m = DenseMatrix::from_2d_array(&[
+            &[1., 2., 3., 1., 2.],
+            &[4., 5., 6., 3., 4.],
+            &[7., 8., 9., 5., 6.],
+        ]);
+        let expected_0 = vec![2.44, 2.44, 2.44, 1.63, 1.63];
+        let expected_1 = vec![0.74, 1.01, 1.41];
+
+        assert!(m.std(0).approximate_eq(&expected_0, 1e-2));
+        assert!(m.std(1).approximate_eq(&expected_1, 1e-2));
+    }
+
+    #[test]
+    fn scale() {
+        let mut m = DenseMatrix::from_2d_array(&[&[1., 2., 3.], &[4., 5., 6.]]);
+        let expected_0 = DenseMatrix::from_2d_array(&[&[-1., -1., -1.], &[1., 1., 1.]]);
+        let expected_1 = DenseMatrix::from_2d_array(&[&[-1.22, 0.0, 1.22], &[-1.22, 0.0, 1.22]]);
+
+        {
+            let mut m = m.clone();
+            m.scale_mut(&m.mean(0), &m.std(0), 0);
+            assert!(m.approximate_eq(&expected_0, std::f32::EPSILON));
+        }
+
+        m.scale_mut(&m.mean(1), &m.std(1), 1);
+        assert!(m.approximate_eq(&expected_1, 1e-2));
+    }
+}