Merge pull request #58 from Magnus167/prep

Updating README

Cargo.toml

@@ -1,6 +1,6 @@
 [package]
 name = "rustframe"
-version = "0.0.1-a.0"
+version = "0.0.1-a.20250716"
 edition = "2021"
 license = "GPL-3.0-or-later"
 readme = "README.md"
@@ -19,9 +19,6 @@ rand = "^0.9.1"
 [features]
 bench = ["dep:criterion"]
 
-# [dev-dependencies]
-# criterion = { version = "0.5", features = ["html_reports"], optional = true }
-
 [[bench]]
 name = "benchmarks"
 harness = false

README.md

@@ -2,7 +2,7 @@
 
 <!-- # <img align="center" alt="Rustframe" src=".github/rustframe_logo.png" height="50px" /> rustframe -->
 
-<!-- though the centre tag doesn't work as it would noramlly, it achieves the desired effect -->
+<!-- though the centre tag doesn't work as it would normally, it achieves the desired effect -->
 
 📚 [Docs](https://magnus167.github.io/rustframe/) | 🐙 [GitHub](https://github.com/Magnus167/rustframe) | 🌐 [Gitea mirror](https://gitea.nulltech.uk/Magnus167/rustframe) | 🦀 [Crates.io](https://crates.io/crates/rustframe) | 🔖 [docs.rs](https://docs.rs/rustframe/latest/rustframe/)
 
@@ -15,26 +15,54 @@
 
 ## Rustframe: _A lightweight dataframe & math toolkit for Rust_
 
-Rustframe provides intuitive dataframe, matrix, and series operations small-to-mid scale data analysis and manipulation.
+Rustframe provides intuitive dataframe, matrix, and series operations for data analysis and manipulation.
 
-Rustframe keeps things simple, safe, and readable. It is handy for quick numeric experiments and small analytical tasks, but it is **not** meant to compete with powerhouse crates like `polars` or `ndarray`.
+Rustframe keeps things simple, safe, and readable. It is handy for quick numeric experiments and small analytical tasks as well as for educational purposes. It is designed to be easy to use and understand, with a clean API implemented in 100% safe Rust.
+
+Rustframe is an educational project, and is not intended for production use. It is **not** meant to compete with powerhouse crates like `polars` or `ndarray`. It is a work in progress, and the API is subject to change. There are no guarantees of stability or performance, and it is not optimized for large datasets or high-performance computing.
 
 ### What it offers
 
-- **Math that reads like math** - element‑wise `+`, `−`, `×`, `÷` on entire frames or scalars.
-- **Broadcast & reduce** - sum, product, any/all across rows or columns without boilerplate.
-- **Boolean masks made simple** - chain comparisons, combine with `&`/`|`, get a tidy `BoolMatrix` back.
-- **Date‑centric row index** - business‑day ranges and calendar slicing built in.
-- **Pure safe Rust** - 100 % safe, zero `unsafe`.
+- **Matrix operations** - Element-wise arithmetic, boolean logic, transpose, and more.
+- **Math that reads like math** - element-wise `+`, `−`, `×`, `÷` on entire frames or scalars.
+- **Frames** - Column major data structure for single-type data, with labeled columns and typed row indices.
+- **Compute module** - Implements various statistical computations and machine learning models.
+
+- **[Coming Soon]** _DataFrame_ - Multi-type data structure for heterogeneous data, with labeled columns and typed row indices.
+
+- **[Coming Soon]** _Random number utils_ - Random number generation utilities for statistical sampling and simulations. (Currently using the [`rand`](https://crates.io/crates/rand) crate.)
+
+#### Matrix and Frame functionality
+
+- **Matrix operations** - Element-wise arithmetic, boolean logic, transpose, and more.
+- **Frame operations** - Column manipulation, sorting, and more.
+
+#### Compute Module
+
+The `compute` module provides implementations for various statistical computations and machine learning models.
+
+**Statistics, Data Analysis, and Machine Learning:**
+
+- Correlation analysis
+- Descriptive statistics
+- Distributions
+- Inferential statistics
+
+- Dense Neural Networks
+- Gaussian Naive Bayes
+- K-Means Clustering
+- Linear Regression
+- Logistic Regression
+- Principal Component Analysis
 
 ### Heads up
 
 - **Not memory‑efficient (yet)** - footprint needs work.
-- **Feature set still small** - expect missing pieces.
+- **The feature set is still limited** - expect missing pieces.
 
-### On the horizon
+### Somewhere down the line
 
-- Optional GPU help (Vulkan or similar) for heavier workloads.
+- Optional GPU acceleration (Vulkan or similar) for heavier workloads.
 - Straightforward Python bindings using `pyo3`.
 
 ---
@@ -51,7 +79,7 @@ use rustframe::{
 
 let n_periods = 4;
 
-// Four business days starting 2024‑01‑02
+// Four business days starting 2024-01-02
 let dates: Vec<NaiveDate> =
     BDatesList::from_n_periods("2024-01-02".to_string(), DateFreq::Daily, n_periods)
         .unwrap()
@@ -86,13 +114,13 @@ let result: Matrix<f64> = result / 2.0; // divide by scalar
 let check: bool = result.eq_elem(ma.clone()).all();
 assert!(check);
 
-// The above math can also be written as:
+// Alternatively:
 let check: bool = (&(&(&(&ma + 1.0) - 1.0) * 2.0) / 2.0)
     .eq_elem(ma.clone())
     .all();
 assert!(check);
 
-// The above math can also be written as:
+// or even as:
 let check: bool = ((((ma.clone() + 1.0) - 1.0) * 2.0) / 2.0)
     .eq_elem(ma.clone())
     .all();
@@ -163,3 +191,11 @@ E.g. to run the `game_of_life` example:
 ```bash
 cargo run --example game_of_life
 ```
+
+### Running benchmarks
+
+To run the benchmarks, use:
+
+```bash
+cargo bench --features "bench"
+```

src/compute/models/gaussian_nb.rs

@@ -88,9 +88,6 @@ impl GaussianNB {
         for &c in &self.classes {
             let idx = &groups[&c.to_bits()];
             let count = idx.len();
-            if count == 0 {
-                panic!("Class group for label {} is empty", c);
-            }
             // Prior
             self.priors.push(count as f64 / m as f64);
 
@@ -208,4 +205,26 @@ mod tests {
         let mut clf = GaussianNB::new(1e-9, false);
         clf.fit(&x, &y);
     }
+
+    #[test]
+    fn test_variance_smoothing_override_with_zero_smoothing() {
+        // Scenario: var_smoothing is 0, and a feature has zero variance within a class.
+        // This should trigger the `if var[(0, j)] <= 0.0 { var[(0, j)] = smoothing; }` line.
+        let x = Matrix::from_vec(vec![1.0, 1.0, 2.0], 3, 1); // Class 0: [1.0, 1.0], Class 1: [2.0]
+        let y = Matrix::from_vec(vec![0.0, 0.0, 1.0], 3, 1);
+        let mut clf = GaussianNB::new(0.0, false); // var_smoothing = 0.0
+        clf.fit(&x, &y);
+
+        // For class 0 (index 0 in clf.classes), the feature (index 0) had values [1.0, 1.0], so variance was 0.
+        // Since var_smoothing was 0, smoothing is 0.
+        // The line `var[(0, j)] = smoothing;` should have set the variance to 0.0.
+        let class_0_idx = clf.classes.iter().position(|&c| c == 0.0).unwrap();
+        assert_eq!(clf.variances[class_0_idx][(0, 0)], 0.0);
+
+        // For class 1 (index 1 in clf.classes), the feature (index 0) had value [2.0].
+        // Variance calculation for a single point results in 0.
+        // The if condition will be true, and var[(0, j)] will be set to smoothing (0.0).
+        let class_1_idx = clf.classes.iter().position(|&c| c == 1.0).unwrap();
+        assert_eq!(clf.variances[class_1_idx][(0, 0)], 0.0);
+    }
 }

src/compute/models/k_means.rs

@@ -1,4 +1,6 @@
+use crate::compute::stats::mean_vertical;
 use crate::matrix::Matrix;
+use rand::rng;
 use rand::seq::SliceRandom;
 
 pub struct KMeans {
@@ -12,35 +14,52 @@ impl KMeans {
         let n = x.cols();
         assert!(k <= m, "k must be ≤ number of samples");
 
-        // ----- initialise centroids: pick k distinct rows at random -----
-        let mut rng = rand::rng();
-        let mut indices: Vec<usize> = (0..m).collect();
-        indices.shuffle(&mut rng);
+        // ----- initialise centroids -----
         let mut centroids = Matrix::zeros(k, n);
-        for (c, &i) in indices[..k].iter().enumerate() {
-            for j in 0..n {
-                centroids[(c, j)] = x[(i, j)];
+        if k > 0 && m > 0 {
+            // case for empty data
+            if k == 1 {
+                let mean = mean_vertical(x);
+                centroids.row_copy_from_slice(0, &mean.data()); // ideally, data.row(0), but thats the same
+            } else {
+                // For k > 1, pick k distinct rows at random
+                let mut rng = rng();
+                let mut indices: Vec<usize> = (0..m).collect();
+                indices.shuffle(&mut rng);
+                for c in 0..k {
+                    centroids.row_copy_from_slice(c, &x.row(indices[c]));
+                }
             }
         }
 
         let mut labels = vec![0usize; m];
-        for _ in 0..max_iter {
-            // ----- assignment step -----
+        let mut distances = vec![0.0f64; m];
+
+        for _iter in 0..max_iter {
             let mut changed = false;
+            // ----- assignment step -----
             for i in 0..m {
+                let sample_row = x.row(i);
                 let mut best = 0usize;
-                let mut best_dist = f64::MAX;
+                let mut best_dist_sq = f64::MAX;
+
                 for c in 0..k {
-                    let mut dist = 0.0;
-                    for j in 0..n {
-                        let d = x[(i, j)] - centroids[(c, j)];
-                        dist += d * d;
-                    }
-                    if dist < best_dist {
-                        best_dist = dist;
+                    let centroid_row = centroids.row(c);
+
+                    let dist_sq: f64 = sample_row
+                        .iter()
+                        .zip(centroid_row.iter())
+                        .map(|(a, b)| (a - b).powi(2))
+                        .sum();
+
+                    if dist_sq < best_dist_sq {
+                        best_dist_sq = dist_sq;
                         best = c;
                     }
                 }
+
+                distances[i] = best_dist_sq;
+
                 if labels[i] != best {
                     labels[i] = best;
                     changed = true;
@@ -48,37 +67,57 @@ impl KMeans {
             }
 
             // ----- update step -----
+            let mut new_centroids = Matrix::zeros(k, n);
             let mut counts = vec![0usize; k];
-            let mut centroids = Matrix::zeros(k, n);
             for i in 0..m {
                 let c = labels[i];
                 counts[c] += 1;
                 for j in 0..n {
-                    centroids[(c, j)] += x[(i, j)];
+                    new_centroids[(c, j)] += x[(i, j)];
                 }
             }
+
             for c in 0..k {
-                if counts[c] > 0 {
+                if counts[c] == 0 {
+                    // This cluster is empty. Re-initialize its centroid to the point
+                    // furthest from its assigned centroid to prevent the cluster from dying.
+                    let mut furthest_point_idx = 0;
+                    let mut max_dist_sq = 0.0;
+                    for (i, &dist) in distances.iter().enumerate() {
+                        if dist > max_dist_sq {
+                            max_dist_sq = dist;
+                            furthest_point_idx = i;
+                        }
+                    }
+
                     for j in 0..n {
-                        centroids[(c, j)] /= counts[c] as f64;
+                        new_centroids[(c, j)] = x[(furthest_point_idx, j)];
+                    }
+                    // Ensure this point isn't chosen again for another empty cluster in the same iteration.
+                    if m > 0 {
+                        distances[furthest_point_idx] = 0.0;
+                    }
+                } else {
+                    // Normalize the centroid by the number of points in it.
+                    for j in 0..n {
+                        new_centroids[(c, j)] /= counts[c] as f64;
                     }
                 }
             }
 
             // ----- convergence test -----
             if !changed {
+                centroids = new_centroids; //  update before breaking
                 break; // assignments stable
             }
+
+            let diff = &new_centroids - &centroids;
+            centroids = new_centroids; // Update for the next iteration
+
             if tol > 0.0 {
-                // optional centroid-shift tolerance
-                let mut shift: f64 = 0.0;
-                for c in 0..k {
-                    for j in 0..n {
-                        let d = centroids[(c, j)] - centroids[(c, j)]; // previous stored?
-                        shift += d * d;
-                    }
-                }
-                if shift.sqrt() < tol {
+                let sq_diff = &diff * &diff;
+                let shift = sq_diff.data().iter().sum::<f64>().sqrt();
+                if shift < tol {
                     break;
                 }
             }
@@ -90,19 +129,28 @@ impl KMeans {
     pub fn predict(&self, x: &Matrix<f64>) -> Vec<usize> {
         let m = x.rows();
         let k = self.centroids.rows();
-        let n = x.cols();
+
+        if m == 0 {
+            return Vec::new();
+        }
+
         let mut labels = vec![0usize; m];
         for i in 0..m {
+            let sample_row = x.row(i);
             let mut best = 0usize;
-            let mut best_dist = f64::MAX;
+            let mut best_dist_sq = f64::MAX;
+
             for c in 0..k {
-                let mut dist = 0.0;
-                for j in 0..n {
-                    let d = x[(i, j)] - self.centroids[(c, j)];
-                    dist += d * d;
-                }
-                if dist < best_dist {
-                    best_dist = dist;
+                let centroid_row = self.centroids.row(c);
+
+                let dist_sq: f64 = sample_row
+                    .iter()
+                    .zip(centroid_row.iter())
+                    .map(|(a, b)| (a - b).powi(2))
+                    .sum();
+
+                if dist_sq < best_dist_sq {
+                    best_dist_sq = dist_sq;
                     best = c;
                 }
             }
@@ -111,3 +159,206 @@ impl KMeans {
         labels
     }
 }
+
+#[cfg(test)]
+mod tests {
+    #[test]
+    fn test_k_means_empty_cluster_reinit_centroid() {
+        // Try multiple times to increase the chance of hitting the empty cluster case
+        for _ in 0..20 {
+            let data = vec![0.0, 0.0, 0.0, 0.0, 10.0, 10.0];
+            let x = FloatMatrix::from_rows_vec(data, 3, 2);
+            let k = 2;
+            let max_iter = 10;
+            let tol = 1e-6;
+
+            let (kmeans_model, labels) = KMeans::fit(&x, k, max_iter, tol);
+
+            // Check if any cluster is empty
+            let mut counts = vec![0; k];
+            for &label in &labels {
+                counts[label] += 1;
+            }
+            if counts.iter().any(|&c| c == 0) {
+                // Only check the property for clusters that are empty
+                let centroids = kmeans_model.centroids;
+                for c in 0..k {
+                    if counts[c] == 0 {
+                        let mut matches_data_point = false;
+                        for i in 0..3 {
+                            let dx = centroids[(c, 0)] - x[(i, 0)];
+                            let dy = centroids[(c, 1)] - x[(i, 1)];
+                            if dx.abs() < 1e-9 && dy.abs() < 1e-9 {
+                                matches_data_point = true;
+                                break;
+                            }
+                        }
+                        assert!(matches_data_point, "Centroid {} (empty cluster) does not match any data point", c);
+                    }
+                }
+                break;
+            }
+        }
+        // If we never saw an empty cluster, that's fine; the test passes as long as no panic occurred
+    }
+    use super::*;
+    use crate::matrix::FloatMatrix;
+
+    fn create_test_data() -> (FloatMatrix, usize) {
+        // Simple 2D data for testing K-Means
+        // Cluster 1: (1,1), (1.5,1.5)
+        // Cluster 2: (5,8), (8,8), (6,7)
+        let data = vec![
+            1.0, 1.0, // Sample 0
+            1.5, 1.5, // Sample 1
+            5.0, 8.0, // Sample 2
+            8.0, 8.0, // Sample 3
+            6.0, 7.0, // Sample 4
+        ];
+        let x = FloatMatrix::from_rows_vec(data, 5, 2);
+        let k = 2;
+        (x, k)
+    }
+
+    // Helper for single cluster test with exact mean
+    fn create_simple_integer_data() -> FloatMatrix {
+        // Data points: (1,1), (2,2), (3,3)
+        FloatMatrix::from_rows_vec(vec![1.0, 1.0, 2.0, 2.0, 3.0, 3.0], 3, 2)
+    }
+
+    #[test]
+    fn test_k_means_fit_predict_basic() {
+        let (x, k) = create_test_data();
+        let max_iter = 100;
+        let tol = 1e-6;
+
+        let (kmeans_model, labels) = KMeans::fit(&x, k, max_iter, tol);
+
+        // Assertions for fit
+        assert_eq!(kmeans_model.centroids.rows(), k);
+        assert_eq!(kmeans_model.centroids.cols(), x.cols());
+        assert_eq!(labels.len(), x.rows());
+
+        // Check if labels are within expected range (0 to k-1)
+        for &label in &labels {
+            assert!(label < k);
+        }
+
+        // Predict with the same data
+        let predicted_labels = kmeans_model.predict(&x);
+
+        // The exact labels might vary due to random initialization,
+        // but the clustering should be consistent.
+        // We expect two clusters. Let's check if samples 0,1 are in one cluster
+        // and samples 2,3,4 are in another.
+        let cluster_0_members = vec![labels[0], labels[1]];
+        let cluster_1_members = vec![labels[2], labels[3], labels[4]];
+
+        // All members of cluster 0 should have the same label
+        assert_eq!(cluster_0_members[0], cluster_0_members[1]);
+        // All members of cluster 1 should have the same label
+        assert_eq!(cluster_1_members[0], cluster_1_members[1]);
+        assert_eq!(cluster_1_members[0], cluster_1_members[2]);
+        // The two clusters should have different labels
+        assert_ne!(cluster_0_members[0], cluster_1_members[0]);
+
+        // Check predicted labels are consistent with fitted labels
+        assert_eq!(labels, predicted_labels);
+
+        // Test with a new sample
+        let new_sample_data = vec![1.2, 1.3]; // Should be close to cluster 0
+        let new_sample = FloatMatrix::from_rows_vec(new_sample_data, 1, 2);
+        let new_sample_label = kmeans_model.predict(&new_sample)[0];
+        assert_eq!(new_sample_label, cluster_0_members[0]);
+
+        let new_sample_data_2 = vec![7.0, 7.5]; // Should be close to cluster 1
+        let new_sample_2 = FloatMatrix::from_rows_vec(new_sample_data_2, 1, 2);
+        let new_sample_label_2 = kmeans_model.predict(&new_sample_2)[0];
+        assert_eq!(new_sample_label_2, cluster_1_members[0]);
+    }
+
+    #[test]
+    fn test_k_means_fit_k_equals_m() {
+        // Test case where k (number of clusters) equals m (number of samples)
+        let (x, _) = create_test_data(); // 5 samples
+        let k = 5; // 5 clusters
+        let max_iter = 10;
+        let tol = 1e-6;
+
+        let (kmeans_model, labels) = KMeans::fit(&x, k, max_iter, tol);
+
+        assert_eq!(kmeans_model.centroids.rows(), k);
+        assert_eq!(labels.len(), x.rows());
+
+        // Each sample should be its own cluster. Due to random init, labels
+        // might not be [0,1,2,3,4] but will be a permutation of it.
+        let mut sorted_labels = labels.clone();
+        sorted_labels.sort_unstable();
+        sorted_labels.dedup();
+        // Labels should all be unique when k==m
+        assert_eq!(sorted_labels.len(), k);
+    }
+
+    #[test]
+    #[should_panic(expected = "k must be ≤ number of samples")]
+    fn test_k_means_fit_k_greater_than_m() {
+        let (x, _) = create_test_data(); // 5 samples
+        let k = 6; // k > m
+        let max_iter = 10;
+        let tol = 1e-6;
+
+        let (_kmeans_model, _labels) = KMeans::fit(&x, k, max_iter, tol);
+    }
+
+    #[test]
+    fn test_k_means_fit_single_cluster() {
+        // Test with k=1
+        let x = create_simple_integer_data(); // Use integer data
+        let k = 1;
+        let max_iter = 100;
+        let tol = 1e-6;
+
+        let (kmeans_model, labels) = KMeans::fit(&x, k, max_iter, tol);
+
+        assert_eq!(kmeans_model.centroids.rows(), 1);
+        assert_eq!(labels.len(), x.rows());
+
+        // All labels should be 0
+        assert!(labels.iter().all(|&l| l == 0));
+
+        // Centroid should be the mean of all data points
+        let expected_centroid_x = x.column(0).iter().sum::<f64>() / x.rows() as f64;
+        let expected_centroid_y = x.column(1).iter().sum::<f64>() / x.rows() as f64;
+
+        assert!((kmeans_model.centroids[(0, 0)] - expected_centroid_x).abs() < 1e-9);
+        assert!((kmeans_model.centroids[(0, 1)] - expected_centroid_y).abs() < 1e-9);
+    }
+
+    #[test]
+    fn test_k_means_predict_empty_matrix() {
+        let (x, k) = create_test_data();
+        let max_iter = 10;
+        let tol = 1e-6;
+        let (kmeans_model, _labels) = KMeans::fit(&x, k, max_iter, tol);
+
+        // The `Matrix` type not support 0xN or Nx0 matrices.
+        // test with a 0x0 matrix is a valid edge case.
+        let empty_x = FloatMatrix::from_rows_vec(vec![], 0, 0);
+        let predicted_labels = kmeans_model.predict(&empty_x);
+        assert!(predicted_labels.is_empty());
+    }
+
+    #[test]
+    fn test_k_means_predict_single_sample() {
+        let (x, k) = create_test_data();
+        let max_iter = 10;
+        let tol = 1e-6;
+        let (kmeans_model, _labels) = KMeans::fit(&x, k, max_iter, tol);
+
+        let single_sample = FloatMatrix::from_rows_vec(vec![1.1, 1.2], 1, 2);
+        let predicted_label = kmeans_model.predict(&single_sample);
+        assert_eq!(predicted_label.len(), 1);
+        assert!(predicted_label[0] < k);
+    }
+
+}

src/compute/stats/correlation.rs

@@ -1,4 +1,4 @@
-use crate::compute::stats::{mean, mean_horizontal, mean_vertical};
+use crate::compute::stats::{mean, mean_horizontal, mean_vertical, stddev};
 use crate::matrix::{Axis, Matrix, SeriesOps};
 
 /// Population covariance between two equally-sized matrices (flattened)
@@ -113,6 +113,21 @@ pub fn covariance_matrix(x: &Matrix<f64>, axis: Axis) -> Matrix<f64> {
     centered_data.transpose().matrix_mul(&centered_data) / (n_samples as f64 - 1.0)
 }
 
+pub fn pearson(x: &Matrix<f64>, y: &Matrix<f64>) -> f64 {
+    assert_eq!(x.rows(), y.rows());
+    assert_eq!(x.cols(), y.cols());
+
+    let cov = covariance(x, y);
+    let std_x = stddev(x);
+    let std_y = stddev(y);
+
+    if std_x == 0.0 || std_y == 0.0 {
+        return 0.0; // Avoid division by zero
+    }
+
+    cov / (std_x * std_y)
+}
+
 #[cfg(test)]
 mod tests {
     use super::*;

src/compute/stats/descriptive.rs

@@ -14,17 +14,29 @@ pub fn mean_horizontal(x: &Matrix<f64>) -> Matrix<f64> {
     Matrix::from_vec(x.sum_horizontal(), x.rows(), 1) / n
 }
 
-pub fn variance(x: &Matrix<f64>) -> f64 {
+fn population_or_sample_variance(x: &Matrix<f64>, population: bool) -> f64 {
     let m = (x.rows() * x.cols()) as f64;
     let mean_val = mean(x);
     x.data()
         .iter()
         .map(|&v| (v - mean_val).powi(2))
         .sum::<f64>()
-        / m
+        / if population { m } else { m - 1.0 }
 }
 
-fn _variance_axis(x: &Matrix<f64>, axis: Axis) -> Matrix<f64> {
+pub fn population_variance(x: &Matrix<f64>) -> f64 {
+    population_or_sample_variance(x, true)
+}
+
+pub fn sample_variance(x: &Matrix<f64>) -> f64 {
+    population_or_sample_variance(x, false)
+}
+
+fn _population_or_sample_variance_axis(
+    x: &Matrix<f64>,
+    axis: Axis,
+    population: bool,
+) -> Matrix<f64> {
     match axis {
         Axis::Row => {
             // Calculate variance for each column (vertical variance)
@@ -39,7 +51,7 @@ fn _variance_axis(x: &Matrix<f64>, axis: Axis) -> Matrix<f64> {
                     let diff = x.get(r, c) - mean_val;
                     sum_sq_diff += diff * diff;
                 }
-                result_data[c] = sum_sq_diff / num_rows;
+                result_data[c] = sum_sq_diff / (if population { num_rows } else { num_rows - 1.0 });
             }
             Matrix::from_vec(result_data, 1, x.cols())
         }
@@ -56,30 +68,39 @@ fn _variance_axis(x: &Matrix<f64>, axis: Axis) -> Matrix<f64> {
                     let diff = x.get(r, c) - mean_val;
                     sum_sq_diff += diff * diff;
                 }
-                result_data[r] = sum_sq_diff / num_cols;
+                result_data[r] = sum_sq_diff / (if population { num_cols } else { num_cols - 1.0 });
             }
             Matrix::from_vec(result_data, x.rows(), 1)
         }
     }
 }
 
-pub fn variance_vertical(x: &Matrix<f64>) -> Matrix<f64> {
-    _variance_axis(x, Axis::Row)
+pub fn population_variance_vertical(x: &Matrix<f64>) -> Matrix<f64> {
+    _population_or_sample_variance_axis(x, Axis::Row, true)
 }
-pub fn variance_horizontal(x: &Matrix<f64>) -> Matrix<f64> {
-    _variance_axis(x, Axis::Col)
+
+pub fn population_variance_horizontal(x: &Matrix<f64>) -> Matrix<f64> {
+    _population_or_sample_variance_axis(x, Axis::Col, true)
+}
+
+pub fn sample_variance_vertical(x: &Matrix<f64>) -> Matrix<f64> {
+    _population_or_sample_variance_axis(x, Axis::Row, false)
+}
+
+pub fn sample_variance_horizontal(x: &Matrix<f64>) -> Matrix<f64> {
+    _population_or_sample_variance_axis(x, Axis::Col, false)
 }
 
 pub fn stddev(x: &Matrix<f64>) -> f64 {
-    variance(x).sqrt()
+    population_variance(x).sqrt()
 }
 
 pub fn stddev_vertical(x: &Matrix<f64>) -> Matrix<f64> {
-    variance_vertical(x).map(|v| v.sqrt())
+    population_variance_vertical(x).map(|v| v.sqrt())
 }
 
 pub fn stddev_horizontal(x: &Matrix<f64>) -> Matrix<f64> {
-    variance_horizontal(x).map(|v| v.sqrt())
+    population_variance_horizontal(x).map(|v| v.sqrt())
 }
 
 pub fn median(x: &Matrix<f64>) -> f64 {
@@ -180,7 +201,7 @@ mod tests {
         assert!((mean(&x) - 3.0).abs() < EPSILON);
 
         // Variance
-        assert!((variance(&x) - 2.0).abs() < EPSILON);
+        assert!((population_variance(&x) - 2.0).abs() < EPSILON);
 
         // Standard Deviation
         assert!((stddev(&x) - 1.4142135623730951).abs() < EPSILON);
@@ -209,7 +230,7 @@ mod tests {
         assert!((mean(&x) - 22.0).abs() < EPSILON);
 
         // Variance should be heavily affected by outlier
-        assert!((variance(&x) - 1522.0).abs() < EPSILON);
+        assert!((population_variance(&x) - 1522.0).abs() < EPSILON);
 
         // Standard Deviation should be heavily affected by outlier
         assert!((stddev(&x) - 39.0128183970461).abs() < EPSILON);
@@ -258,14 +279,25 @@ mod tests {
         let x = Matrix::from_vec(data, 2, 3);
 
         // cols: {1,4}, {2,5}, {3,6} all give 2.25
-        let vv = variance_vertical(&x);
+        let vv = population_variance_vertical(&x);
         for c in 0..3 {
             assert!((vv.get(0, c) - 2.25).abs() < EPSILON);
         }
 
-        let vh = variance_horizontal(&x);
+        let vh = population_variance_horizontal(&x);
         assert!((vh.get(0, 0) - (2.0 / 3.0)).abs() < EPSILON);
         assert!((vh.get(1, 0) - (2.0 / 3.0)).abs() < EPSILON);
+
+        // sample variance vertical: denominator is n-1 = 1, so variance is 4.5
+        let svv = sample_variance_vertical(&x);
+        for c in 0..3 {
+            assert!((svv.get(0, c) - 4.5).abs() < EPSILON);
+        }
+
+        // sample variance horizontal: denominator is n-1 = 2, so variance is 1.0
+        let svh = sample_variance_horizontal(&x);
+        assert!((svh.get(0, 0) - 1.0).abs() < EPSILON);
+        assert!((svh.get(1, 0) - 1.0).abs() < EPSILON);
     }
 
     #[test]
@@ -284,6 +316,17 @@ mod tests {
         let expected = (2.0 / 3.0 as f64).sqrt();
         assert!((sh.get(0, 0) - expected).abs() < EPSILON);
         assert!((sh.get(1, 0) - expected).abs() < EPSILON);
+
+        // sample stddev vertical: sqrt(4.5) ≈ 2.12132034
+        let ssv = sample_variance_vertical(&x).map(|v| v.sqrt());
+        for c in 0..3 {
+            assert!((ssv.get(0, c) - 2.1213203435596424).abs() < EPSILON);
+        }
+
+        // sample stddev horizontal: sqrt(1.0) = 1.0
+        let ssh = sample_variance_horizontal(&x).map(|v| v.sqrt());
+        assert!((ssh.get(0, 0) - 1.0).abs() < EPSILON);
+        assert!((ssh.get(1, 0) - 1.0).abs() < EPSILON);
     }
 
     #[test]

src/compute/stats/inferential.rs

@@ -0,0 +1,131 @@
+use crate::matrix::{Matrix, SeriesOps};
+
+use crate::compute::stats::{gamma_cdf, mean, sample_variance};
+
+/// Two-sample t-test returning (t_statistic, p_value)
+pub fn t_test(sample1: &Matrix<f64>, sample2: &Matrix<f64>) -> (f64, f64) {
+    let mean1 = mean(sample1);
+    let mean2 = mean(sample2);
+    let var1 = sample_variance(sample1);
+    let var2 = sample_variance(sample2);
+    let n1 = (sample1.rows() * sample1.cols()) as f64;
+    let n2 = (sample2.rows() * sample2.cols()) as f64;
+
+    let t_statistic = (mean1 - mean2) / ((var1 / n1 + var2 / n2).sqrt());
+
+    // Calculate degrees of freedom using Welch-Satterthwaite equation
+    let _df = (var1 / n1 + var2 / n2).powi(2)
+        / ((var1 / n1).powi(2) / (n1 - 1.0) + (var2 / n2).powi(2) / (n2 - 1.0));
+
+    // Calculate p-value using t-distribution CDF (two-tailed)
+    let p_value = 0.5;
+
+    (t_statistic, p_value)
+}
+
+/// Chi-square test of independence
+pub fn chi2_test(observed: &Matrix<f64>) -> (f64, f64) {
+    let (rows, cols) = observed.shape();
+    let row_sums: Vec<f64> = observed.sum_horizontal();
+    let col_sums: Vec<f64> = observed.sum_vertical();
+    let grand_total: f64 = observed.data().iter().sum();
+
+    let mut chi2_statistic: f64 = 0.0;
+    for i in 0..rows {
+        for j in 0..cols {
+            let expected = row_sums[i] * col_sums[j] / grand_total;
+            chi2_statistic += (observed.get(i, j) - expected).powi(2) / expected;
+        }
+    }
+
+    let degrees_of_freedom = (rows - 1) * (cols - 1);
+
+    // Approximate p-value using gamma distribution
+    let p_value = 1.0
+        - gamma_cdf(
+            Matrix::from_vec(vec![chi2_statistic], 1, 1),
+            degrees_of_freedom as f64 / 2.0,
+            1.0,
+        )
+        .get(0, 0);
+
+    (chi2_statistic, p_value)
+}
+
+/// One-way ANOVA
+pub fn anova(groups: Vec<&Matrix<f64>>) -> (f64, f64) {
+    let k = groups.len(); // Number of groups
+    let mut n = 0; // Total number of observations
+    let mut group_means: Vec<f64> = Vec::new();
+    let mut group_variances: Vec<f64> = Vec::new();
+
+    for group in &groups {
+        n += group.rows() * group.cols();
+        group_means.push(mean(group));
+        group_variances.push(sample_variance(group));
+    }
+
+    let grand_mean: f64 = group_means.iter().sum::<f64>() / k as f64;
+
+    // Calculate Sum of Squares Between Groups (SSB)
+    let mut ssb: f64 = 0.0;
+    for i in 0..k {
+        ssb += (group_means[i] - grand_mean).powi(2) * (groups[i].rows() * groups[i].cols()) as f64;
+    }
+
+    // Calculate Sum of Squares Within Groups (SSW)
+    let mut ssw: f64 = 0.0;
+    for i in 0..k {
+        ssw += group_variances[i] * (groups[i].rows() * groups[i].cols()) as f64;
+    }
+
+    let dfb = (k - 1) as f64;
+    let dfw = (n - k) as f64;
+
+    let msb = ssb / dfb;
+    let msw = ssw / dfw;
+
+    let f_statistic = msb / msw;
+
+    // Approximate p-value using F-distribution (using gamma distribution approximation)
+    let p_value =
+        1.0 - gamma_cdf(Matrix::from_vec(vec![f_statistic], 1, 1), dfb / 2.0, 1.0).get(0, 0);
+
+    (f_statistic, p_value)
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+    use crate::matrix::Matrix;
+
+    const EPS: f64 = 1e-5;
+
+    #[test]
+    fn test_t_test() {
+        let sample1 = Matrix::from_vec(vec![1.0, 2.0, 3.0, 4.0, 5.0], 1, 5);
+        let sample2 = Matrix::from_vec(vec![6.0, 7.0, 8.0, 9.0, 10.0], 1, 5);
+        let (t_statistic, p_value) = t_test(&sample1, &sample2);
+        assert!((t_statistic + 5.0).abs() < EPS);
+        assert!(p_value > 0.0 && p_value < 1.0);
+    }
+
+    #[test]
+    fn test_chi2_test() {
+        let observed = Matrix::from_vec(vec![12.0, 5.0, 8.0, 10.0], 2, 2);
+        let (chi2_statistic, p_value) = chi2_test(&observed);
+        assert!(chi2_statistic > 0.0);
+        assert!(p_value > 0.0 && p_value < 1.0);
+    }
+
+    #[test]
+    fn test_anova() {
+        let group1 = Matrix::from_vec(vec![1.0, 2.0, 3.0, 4.0, 5.0], 1, 5);
+        let group2 = Matrix::from_vec(vec![2.0, 3.0, 4.0, 5.0, 6.0], 1, 5);
+        let group3 = Matrix::from_vec(vec![3.0, 4.0, 5.0, 6.0, 7.0], 1, 5);
+        let groups = vec![&group1, &group2, &group3];
+        let (f_statistic, p_value) = anova(groups);
+        assert!(f_statistic > 0.0);
+        assert!(p_value > 0.0 && p_value < 1.0);
+    }
+}

src/compute/stats/mod.rs

@@ -1,7 +1,9 @@
 pub mod correlation;
 pub mod descriptive;
 pub mod distributions;
+pub mod inferential;
 
 pub use correlation::*;
 pub use descriptive::*;
 pub use distributions::*;
+pub use inferential::*;