numforge 🧬

NumPy + engineering numerical methods cheatcode pack.

numforge (built as numpyy internally) is a lightweight Python library designed for engineering students. It wraps NumPy and adds essential numerical methods, formulas, and code snippets taught in introductory numerical analysis courses.

Installation

pip install numforge

Import Style

import numpyy as np

Why numforge?

🧪 Lab Assistant Mode

Need a quick workflow for your lab or project? Use solve_tp:

import numpyy as np
np.solve_tp("interpolation")

Want to generate a professional Markdown report for your results?

findings = [
    {'method': 'Simpson', 'result': 0.3333, 'error': 1e-7},
    {'method': 'Trapezoidal', 'result': 0.3437, 'error': 0.01}
]
np.tp_report("Integration Lab", "Student Name", findings)

🎓 Educational Features

Educational Mode

See intermediate steps, formulas, and error warnings:

np.set_mode("educational") # Global
np.simpson(f, 0, 1, educational=True) # Per call

Help & Summary

np.explain("simpson") # Instant revision guide
np.exam_formula_sheet() # Compact printable revision page 😭

🛠 Modules & Functions

1. Floating Point & Errors (np.floating)

• np.float_repr(x) - Exam Clutch: Sign, Exponent, Mantissa representation
• np.ieee754_encode(x) / np.ieee754_decode(bits) - IEEE754 components
• np.cancellation_demo() / np.absorption_demo() - Precision loss demos
• Constants: np.EPSILON, np.FLOAT32_EPSILON, np.FLOAT64_EPSILON

2. Interpolation (np.interpolation)

• np.lagrange(x_pts, y_pts) / np.newton_interpolation(x_pts, y_pts)
• np.newton_polynomial(x_pts, coeffs) - Newton form evaluation
• np.divided_differences(x, y) - Newton coefficients
• np.chebyshev_nodes(a, b, n) - Optimal nodes
• np.vandermonde_matrix(x) - Construct Vandermonde matrix
• np.legendre(n) - Legendre coefficients via recurrence

3. Approximation & Stability (np.approximation)

• np.least_squares(x, y, degree) / np.least_squares_origin(x, y)
• np.normal_equations(x, y, degree) - Returns $(A^T A, A^T y)$
• np.condition_number(A) / np.is_ill_conditioned(A) - Stability checks

4. Polynomials (np.polynomials)

• np.horner(coeffs, x) / np.horner_steps(coeffs, x) - Horner's evaluation
• np.pretty_polynomial(coeffs) - P(x) = 3x^2 - 2x + 1
• np.taylor(f, a, n) - Taylor series coefficients

5. Numerical Integration (np.integration)

• Methods: np.rectangle, np.midpoint, np.trapezoidal, np.simpson
• Composite: np.composite_trapezoidal, np.composite_simpson, np.composite_midpoint
• Error Formulas: np.trapezoidal_error, np.simpson_error, etc.
• Gauss: np.gauss_legendre(f, a, b, n)

6. Numerical Differentiation (np.differentiation)

• np.forward_diff, np.backward_diff, np.centered_diff
• np.second_derivative, np.third_derivative, np.nth_derivative
• np.optimal_h(f, x) / np.taylor_error(...)

7. ODE Solvers (np.ode)

• np.euler, np.rk4, np.adams_bashforth, np.adams_moulton

📊 Plotting Helpers

np.plot_interpolation(f, poly, x_pts, y_pts, a, b)
np.plot_runge_phenomenon(n_points)
np.plot_convergence(ns, errors)
np.plot_integration(f, a, b, method="simpson")

🚀 Examples

Check demo.py for a complete tour of the library.