linreg-core 0.8.1

Lightweight regression library (OLS, Ridge, Lasso, Elastic Net, WLS, LOESS, Polynomial) with 14 diagnostic tests, cross validation, and prediction intervals. Pure Rust - no external math dependencies. WASM, Python, FFI, and Excel XLL bindings.
Documentation 
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124

"""LOESS (Locally Estimated Scatterplot Smoothing) example.

Run with:
    pip install linreg-core
    python loess_example.py

Demonstrates:
- Fitting LOESS to linear and non-linear data
- Effect of span parameter on smoothness
- Linear (degree=1) vs quadratic (degree=2) local fits
- Prediction at new points using loess_predict
"""

import math
import linreg_core


def main():
    print("╔══════════════════════════════════════════════════════════════════════╗")
    print("║         LOESS REGRESSION — PYTHON BINDINGS                         ║")
    print("╚══════════════════════════════════════════════════════════════════════╝")
    print()

    # ── 1. Simple Linear Relationship ─────────────────────────────────────────
    print("━━━ 1. Linear Relationship (y = 2x + 1) ━━━━━━━━━━━━━━━━━━━━━━━━━━━━")
    x1 = [float(i) for i in range(101)]          # 0 .. 100
    y1 = [2.0 * xi + 1.0 for xi in x1]

    fit1 = linreg_core.loess_fit(y1, [x1], span=0.75, degree=1)
    print(f"  {'x':>5}  {'y (true)':>10}  {'fitted':>10}  {'residual':>10}")
    print(f"  {'─'*40}")
    for i in range(5):
        print(f"  {x1[i]:>5.1f}  {y1[i]:>10.2f}  {fit1.fitted[i]:>10.2f}  "
              f"{fit1.residuals[i]:>10.4f}")
    print(f"  MSE:  {fit1.mse:.6f}  (should be ~0 for perfect linear data)")
    print()

    # ── 2. Non-Linear Sine Wave — Comparing Spans ─────────────────────────────
    print("━━━ 2. Non-Linear Sine Wave — Effect of Span ━━━━━━━━━━━━━━━━━━━━━━━")
    print("  Smaller span = wigglier fit, larger span = smoother fit")
    print()

    x2 = [i / 5.0 for i in range(501)]           # 0 .. 100 in steps of 0.2
    y2 = [math.sin(xi * 0.5) * 10.0 + 5.0 for xi in x2]

    print(f"  {'Span':>6}  {'MSE':>10}  {'RMSE':>10}")
    print(f"  {'─'*30}")
    for span in [0.1, 0.3, 0.5, 0.75]:
        fit = linreg_core.loess_fit(y2, [x2], span=span, degree=1)
        print(f"  {span:>6.2f}  {fit.mse:>10.4f}  {fit.rmse:>10.4f}")
    print()

    # ── 3. Degree 1 vs Degree 2 on a Quadratic Curve ──────────────────────────
    print("━━━ 3. Linear vs Quadratic Degree on y = 0.1x² − x + 5 ━━━━━━━━━━━━")
    x3 = [i / 2.0 for i in range(201)]           # 0 .. 100 in steps of 0.5
    y3 = [0.1 * xi**2 - xi + 5.0 for xi in x3]

    fit_lin  = linreg_core.loess_fit(y3, [x3], span=0.5, degree=1)
    fit_quad = linreg_core.loess_fit(y3, [x3], span=0.5, degree=2)

    # Find index closest to x=5.0
    idx5 = min(range(len(x3)), key=lambda i: abs(x3[i] - 5.0))
    true_y5 = y3[idx5]
    print(f"  At x=5.0 (true y = {true_y5:.2f}):")
    print(f"    Degree 1 fitted:  {fit_lin.fitted[idx5]:.4f}  "
          f"(error {abs(fit_lin.fitted[idx5] - true_y5):.4f})")
    print(f"    Degree 2 fitted:  {fit_quad.fitted[idx5]:.4f}  "
          f"(error {abs(fit_quad.fitted[idx5] - true_y5):.4f})")
    print()
    print(f"  Overall MSE — degree 1: {fit_lin.mse:.4f}   "
          f"degree 2: {fit_quad.mse:.4f}")
    print()

    # ── 4. Prediction at New Points ───────────────────────────────────────────
    print("━━━ 4. Prediction at New Points ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━")
    train_x = [0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0]
    train_y = [1.5, 2.1, 3.8, 5.2, 6.7, 8.1, 9.8, 11.2, 12.5, 14.1]
    new_x   = [1.5, 3.5, 5.5, 7.5]

    preds = linreg_core.loess_predict(
        new_x, train_x, train_y, span=0.6, degree=1
    )
    print(f"  {'x':>6}  {'predicted':>12}")
    print(f"  {'─'*22}")
    for xi, yi in zip(new_x, preds):
        print(f"  {xi:>6.1f}  {yi:>12.4f}")
    print()

    # ── 5. Span Sweep — MSE Table ─────────────────────────────────────────────
    print("━━━ 5. Span Sweep on Noisy Trend (span 0.2 -> 0.8) ━━━━━━━━━━━━━━━━━")
    x5 = [float(i) for i in range(301)]          # 0 .. 300
    y5 = [0.5 * xi + 5.0 + math.cos(xi * 0.3) * 3.0 for xi in x5]

    print(f"  {'Span':>6}  {'MSE':>10}  {'RMSE':>10}  Notes")
    print(f"  {'─'*50}")
    for span in [0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8]:
        fit = linreg_core.loess_fit(y5, [x5], span=span, degree=1)
        note = ""
        if span <= 0.3:
            note = "← wiggly"
        elif span >= 0.7:
            note = "← very smooth"
        print(f"  {span:>6.1f}  {fit.mse:>10.4f}  {fit.rmse:>10.4f}  {note}")
    print()

    # ── Key Parameters Reference ──────────────────────────────────────────────
    print("━━━ Key LOESS Parameters ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━")
    print("  span    Fraction of data used per local fit  (0 < span ≤ 1)")
    print("            0.2-0.3  Wiggly, follows data closely")
    print("            0.5-0.6  Balanced smoothness")
    print("            0.7-0.9  Very smooth, may underfit")
    print()
    print("  degree  Polynomial degree for local fits")
    print("            1  Linear (faster, adequate for mild curvature)")
    print("            2  Quadratic (handles stronger curvature)")
    print()
    print("  When to use LOESS:")
    print("    - Exploring unknown or non-linear relationships")
    print("    - Smoothing noisy data to reveal underlying trend")
    print("    - Small to medium datasets (n < 10 000)")


if __name__ == "__main__":
    main()