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276 строки
10 KiB
Python
276 строки
10 KiB
Python
import numpy as np
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import matplotlib.pyplot as plt
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from matplotlib.gridspec import GridSpec
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import seaborn as sns
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from scipy.signal import hilbert
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import pytest
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from pathlib import Path
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class TestComplexDynamics:
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"""Test suite for complex dynamical behaviors."""
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@pytest.fixture(autouse=True)
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def setup(self, tmp_path):
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"""Setup test fixtures."""
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plt.style.use('seaborn')
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sns.set_palette("husl")
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self.output_dir = tmp_path / "figures"
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self.output_dir.mkdir(exist_ok=True)
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# Test parameters
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self.dt = 0.01
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self.t_max = 10.0
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self.num_steps = int(self.t_max / self.dt)
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self.time = np.linspace(0, self.t_max, self.num_steps)
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# System parameters
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self.omega = 2.0 # Natural frequency
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self.damping = 0.1
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self.amplitude = 1.0
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self.frequency = 2.5
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yield
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# Cleanup
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plt.close('all')
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def simulate_harmonic_motion(self):
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"""Simulate harmonic oscillator dynamics."""
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states = np.zeros((self.num_steps, 2))
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states[0] = [1.0, 0.0] # Initial conditions
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for i in range(1, self.num_steps):
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# Simple harmonic motion with damping
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states[i, 0] = states[i-1, 0] + self.dt * states[i-1, 1]
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states[i, 1] = states[i-1, 1] - self.dt * (
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self.omega**2 * states[i-1, 0] +
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2 * self.damping * states[i-1, 1]
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)
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return states
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def test_harmonic_motion(self):
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"""Test visualization of harmonic motion dynamics."""
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states = self.simulate_harmonic_motion()
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free_energy = self.compute_free_energy(states)
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fig = plt.figure(figsize=(15, 10))
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gs = GridSpec(2, 3, figure=fig)
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# Phase space trajectory
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ax1 = fig.add_subplot(gs[0, 0])
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ax1.plot(states[:, 0], states[:, 1], 'b-', label='Phase trajectory')
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ax1.set_xlabel('Position')
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ax1.set_ylabel('Velocity')
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ax1.set_title('Phase Space')
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ax1.grid(True)
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ax1.legend()
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# Time series
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ax2 = fig.add_subplot(gs[0, 1:])
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ax2.plot(self.time, states[:, 0], 'b-', label='Position')
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ax2.plot(self.time, states[:, 1], 'r--', label='Velocity')
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ax2.set_xlabel('Time (s)')
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ax2.set_ylabel('State Variables')
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ax2.set_title('Time Evolution')
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ax2.grid(True)
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ax2.legend()
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# Energy plot
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ax3 = fig.add_subplot(gs[1, 0])
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kinetic = 0.5 * states[:, 1]**2
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potential = 0.5 * self.omega**2 * states[:, 0]**2
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total = kinetic + potential
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ax3.plot(self.time, kinetic, 'g-', label='Kinetic')
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ax3.plot(self.time, potential, 'r-', label='Potential')
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ax3.plot(self.time, total, 'k--', label='Total')
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ax3.set_xlabel('Time (s)')
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ax3.set_ylabel('Energy')
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ax3.set_title('Energy Components')
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ax3.grid(True)
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ax3.legend()
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# Free energy evolution
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ax4 = fig.add_subplot(gs[1, 1:])
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if len(free_energy) > 0: # Only plot if free energy is computed
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ax4.plot(self.time, free_energy, 'b-', label='Free Energy')
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ax4.legend()
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ax4.set_xlabel('Time (s)')
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ax4.set_ylabel('Free Energy')
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ax4.set_title('Free Energy Evolution')
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ax4.grid(True)
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plt.tight_layout()
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plt.savefig(self.output_dir / 'harmonic_motion_analysis.png', dpi=300, bbox_inches='tight')
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plt.close()
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# Assertions to verify the simulation
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assert np.all(np.isfinite(states)), "States contain invalid values"
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assert np.all(np.abs(total - total[0]) < 1e-2), "Energy is not conserved"
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def test_driven_oscillator(self):
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"""Test visualization of driven oscillator dynamics."""
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states = self.simulate_driven_oscillator()
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fig = plt.figure(figsize=(15, 12))
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gs = GridSpec(3, 2, figure=fig)
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# Phase space with driving force
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ax1 = fig.add_subplot(gs[0, 0])
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ax1.plot(states[:, 0], states[:, 1], 'b-', label='Phase trajectory')
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ax1.set_xlabel('Position')
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ax1.set_ylabel('Velocity')
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ax1.set_title('Phase Space')
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ax1.grid(True)
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ax1.legend()
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# Time series with driving force
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ax2 = fig.add_subplot(gs[0, 1])
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driving_force = self.amplitude * np.sin(self.frequency * self.time)
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ax2.plot(self.time, states[:, 0], 'b-', label='Position')
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ax2.plot(self.time, states[:, 1], 'r--', label='Velocity')
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ax2.plot(self.time, driving_force, 'g:', label='Driving Force')
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ax2.set_xlabel('Time (s)')
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ax2.set_ylabel('State Variables')
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ax2.set_title('Time Evolution')
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ax2.grid(True)
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ax2.legend()
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# Power spectrum
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ax3 = fig.add_subplot(gs[1, :])
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frequencies = np.fft.fftfreq(len(states), self.dt)
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spectrum = np.abs(np.fft.fft(states[:, 0]))
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mask = frequencies > 0 # Only show positive frequencies
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ax3.plot(frequencies[mask], spectrum[mask], 'b-', label='Position Spectrum')
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ax3.set_xlabel('Frequency (Hz)')
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ax3.set_ylabel('Amplitude')
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ax3.set_title('Power Spectrum')
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ax3.grid(True)
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ax3.legend()
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# Phase difference analysis
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ax4 = fig.add_subplot(gs[2, 0])
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phase_diff = np.angle(hilbert(states[:, 0])) - np.angle(hilbert(driving_force))
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ax4.plot(self.time, np.unwrap(phase_diff), 'r-', label='Phase Difference')
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ax4.set_xlabel('Time (s)')
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ax4.set_ylabel('Phase Difference (rad)')
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ax4.set_title('Phase Relationship')
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ax4.grid(True)
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ax4.legend()
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# Response amplitude vs time
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ax5 = fig.add_subplot(gs[2, 1])
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envelope = np.abs(hilbert(states[:, 0]))
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ax5.plot(self.time, envelope, 'r-', label='Response Amplitude')
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ax5.plot(self.time, np.abs(driving_force), 'b--', label='Driving Amplitude')
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ax5.set_xlabel('Time (s)')
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ax5.set_ylabel('Amplitude')
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ax5.set_title('Response Amplitude')
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ax5.grid(True)
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ax5.legend()
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plt.tight_layout()
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plt.savefig(self.output_dir / 'driven_oscillator_analysis.png', dpi=300, bbox_inches='tight')
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plt.close()
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# Assertions to verify the simulation
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assert np.all(np.isfinite(states)), "States contain invalid values"
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assert np.max(np.abs(states[:, 0])) > 0, "No oscillation detected"
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def simulate_driven_oscillator(self):
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"""Simulate driven oscillator dynamics."""
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states = np.zeros((self.num_steps, 2))
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states[0] = [0.0, 0.0] # Initial conditions
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for i in range(1, self.num_steps):
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driving_force = self.amplitude * np.sin(self.frequency * self.time[i])
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states[i, 0] = states[i-1, 0] + self.dt * states[i-1, 1]
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states[i, 1] = states[i-1, 1] - self.dt * (
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self.omega**2 * states[i-1, 0] +
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2 * self.damping * states[i-1, 1] -
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driving_force
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)
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return states
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def compute_free_energy(self, states):
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"""Compute free energy for the system."""
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# Placeholder - implement actual free energy computation
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return np.zeros_like(self.time)
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class TestGeneralizedCoordinates:
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"""Test suite for generalized coordinates."""
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@pytest.fixture(autouse=True)
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def setup(self, tmp_path):
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"""Setup test fixtures."""
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plt.style.use('seaborn')
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sns.set_palette("husl")
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self.output_dir = tmp_path / "figures"
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self.output_dir.mkdir(exist_ok=True)
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yield
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plt.close('all')
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def test_generalized_coordinates_consistency(self):
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"""Test consistency of generalized coordinates predictions."""
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# ... existing test code ...
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# Plotting
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fig, (ax1, ax2, ax3, ax4) = plt.subplots(2, 2, figsize=(12, 10))
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# Plot position predictions
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lines1 = ax1.plot(time_points, positions, 'b-', label='Actual')
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ax1.plot(time_points, predicted_positions, 'r--', label='Predicted')
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ax1.set_xlabel('Time (s)')
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ax1.set_ylabel('Position')
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ax1.set_title('Position Prediction')
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if lines1: # Only add legend if there are plotted lines
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ax1.legend()
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ax1.grid(True)
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# Plot velocity predictions
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lines2 = ax2.plot(time_points, velocities, 'b-', label='Actual')
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ax2.plot(time_points, predicted_velocities, 'r--', label='Predicted')
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ax2.set_xlabel('Time (s)')
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ax2.set_ylabel('Velocity')
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ax2.set_title('Velocity Prediction')
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if lines2: # Only add legend if there are plotted lines
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ax2.legend()
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ax2.grid(True)
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# Plot acceleration predictions
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lines3 = ax3.plot(time_points, accelerations, 'b-', label='Actual')
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ax3.plot(time_points, predicted_accelerations, 'r--', label='Predicted')
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ax3.set_xlabel('Time (s)')
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ax3.set_ylabel('Acceleration')
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ax3.set_title('Acceleration Prediction')
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if lines3: # Only add legend if there are plotted lines
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ax3.legend()
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ax3.grid(True)
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# Plot prediction errors
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lines4 = []
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if len(position_errors) > 0:
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lines4.extend(ax4.plot(time_points[1:], position_errors, 'r-', label='Position Error'))
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if len(velocity_errors) > 0:
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lines4.extend(ax4.plot(time_points[1:], velocity_errors, 'b--', label='Velocity Error'))
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if len(acceleration_errors) > 0:
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lines4.extend(ax4.plot(time_points[1:], acceleration_errors, 'g:', label='Acceleration Error'))
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ax4.set_xlabel('Time (s)')
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ax4.set_ylabel('Prediction Error')
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ax4.set_title('Prediction Errors')
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if lines4: # Only add legend if there are plotted lines
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ax4.legend()
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ax4.grid(True)
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plt.tight_layout()
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plt.savefig(self.output_dir / 'generalized_coordinates_predictions.png', dpi=300, bbox_inches='tight')
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plt.close()
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# Assertions
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assert np.all(np.isfinite(positions)), "Invalid position values"
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assert np.all(np.isfinite(velocities)), "Invalid velocity values"
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assert np.all(np.isfinite(accelerations)), "Invalid acceleration values" |