LORENZ

=LORENZ(x_initial, y_initial, z_initial, sigma, rho, beta, t_start, t_end, [timesteps], [solve_ivp_method])

=LORENZ(1.0, 1.0, 1.0, 10.0, 28.0, 2.667, 0.0, 2.0, 10)

=LORENZ(1.0, 1.0, 1.0, 10.0, 28.0, 2.667, 0.0, 2.0, 10, "RK23")

=LORENZ(0.0, 1.0, 2.0, 10.0, 28.0, 2.667, 0.0, 0.1, 10)

=LORENZ(2.0, 3.0, 4.0, 14.0, 35.0, 3.0, 0.0, 1.0, 10)

import micropip
await micropip.install(['scipy', 'numpy'])
from scipy.integrate import solve_ivp
import numpy as np
 
def lorenz(x_initial, y_initial, z_initial, sigma, rho, beta, t_start, t_end, timesteps=10, solve_ivp_method='RK45'):
    """
    Numerically solves the Lorenz system of ordinary differential equations for chaotic dynamics.
 
    Args:
        x_initial: Initial x value.
        y_initial: Initial y value.
        z_initial: Initial z value.
        sigma: Prandtl number.
        rho: Rayleigh number.
        beta: Geometric factor.
        t_start: Start time of integration.
        t_end: End time of integration.
        timesteps: Number of timesteps to solve for. Default is 10.
        solve_ivp_method: Integration method ('RK45', 'RK23', 'DOP853', 'Radau', 'BDF', 'LSODA'). Default is 'RK45'.
 
    Returns:
        2D list with header row: t, X, Y, Z. Each row contains time and variable values, or an error message (str) if input is invalid.
 
    This example function is provided as-is without any representation of accuracy.
    """
    # Validate input types and ranges
    try:
        x0 = float(x_initial)
        y0 = float(y_initial)
        z0 = float(z_initial)
        sig = float(sigma)
        rh = float(rho)
        bet = float(beta)
        t0 = float(t_start)
        t1 = float(t_end)
        ntp = int(timesteps)
    except Exception:
        return "Invalid input: All initial values, parameters, and timesteps must be numbers."
    if t1 <= t0:
        return "Invalid input: t_end must be greater than t_start."
    if ntp <= 0:
        return "Invalid input: timesteps must be a positive integer."
    if solve_ivp_method not in ['RK45', 'RK23', 'DOP853', 'Radau', 'BDF', 'LSODA']:
        return "Invalid input: solve_ivp_method must be one of 'RK45', 'RK23', 'DOP853', 'Radau', 'BDF', 'LSODA'."
    # Create time array for evaluation
    t_eval = np.linspace(t0, t1, ntp)
    
    # Lorenz system definition
    def lorenz_ode(t, xyz):
        x, y, z = xyz
        dxdt = sig * (y - x)
        dydt = x * (rh - z) - y
        dzdt = x * y - bet * z
        return [dxdt, dydt, dzdt]
    # Integrate ODE
    try:
        sol = solve_ivp(
            lorenz_ode,
            [t0, t1],
            [x0, y0, z0],
            method=solve_ivp_method,
            dense_output=False,
            t_eval=t_eval
        )
    except Exception as e:
        return f"Integration error: {e}"
    if not sol.success:
        return f"Integration failed: {sol.message}"
    # Format output: header row then data rows
    result = [['t', 'X', 'Y', 'Z']]
    for i in range(len(sol.t)):
        t_val = float(sol.t[i])
        x_val = float(sol.y[0][i])
        y_val = float(sol.y[1][i])
        z_val = float(sol.y[2][i])
        # Disallow nan/inf
        if any([
            not isinstance(t_val, float) or not isinstance(x_val, float) or not isinstance(y_val, float) or not isinstance(z_val, float),
            t_val != t_val or x_val != x_val or y_val != y_val or z_val != z_val,  # NaN check
            abs(t_val) == float('inf') or abs(x_val) == float('inf') or abs(y_val) == float('inf') or abs(z_val) == float('inf')
        ]):
            return "Invalid output: nan or inf detected."
        result.append([t_val, x_val, y_val, z_val])
    return result