ThotDjehuty
dd51156174
Each of the eight v2.0 companion notebooks (10_bsde through 17_generative_calibration) now follows the mandatory pedagogical sandwich structure: PRE markdown : theorem / model / pivot equation / what the cell verifies CODE cell : labelled prints + at least one matplotlib figure POST markdown: expected result, graph reading, conclusion Each notebook carries at least one concrete real-world example (heat plate, inverted pendulum, opinion polarization, collective decision, OU drift under Cauchy noise, mixture vs gaussian MMD, etc.) Generator script: scripts/enrich_v2_notebooks.py Doc plots refreshed via scripts/inject_doc_plots.py.
99 lines
3.0 KiB
ReStructuredText
99 lines
3.0 KiB
ReStructuredText
Agent-based — bounded-confidence consensus
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==========================================
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Generic interacting-agent simulator (`consensus_dynamics`) — linear bounded-confidence rule $s_i^{k+1} = (1-α) s_i^k + α \bar s^k + ξ_i$.
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.. note:: Companion executed notebook: `15_agent_based.ipynb <../../examples/notebooks/15_agent_based.ipynb>`_
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15 — Agent-based dynamics
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=========================
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.. code-block:: python
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import numpy as np
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import matplotlib.pyplot as plt
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from optimizr import _core as opt
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plt.rcParams['figure.figsize'] = (7, 4)
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plt.rcParams['figure.dpi'] = 110
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.. code-block:: python
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init = np.arange(40.0).tolist()
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init_mean = float(np.mean(init))
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res = opt.consensus_dynamics(init, alpha=0.3, noise_sigma=0.1,
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n_steps=80, seed=0)
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n_t = res['n_steps']; n_a = res['n_agents']
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S = np.array(res['states_flat']).reshape(n_t, n_a)
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mean_traj = np.array(res['mean_trajectory'])
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print('initial mean =', init_mean)
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print('final mean =', mean_traj[-1])
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print('final std =', float(S[-1].std()))
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.. code-block:: python
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fig, ax = plt.subplots()
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for i in range(n_a):
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ax.plot(S[:, i], color='tab:blue', alpha=0.3, lw=0.6)
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ax.plot(mean_traj, color='red', lw=2, label='empirical mean')
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ax.axhline(init_mean, color='k', ls=':', label='initial mean')
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ax.set_xlabel('step k'); ax.set_ylabel('s^k_i'); ax.legend(); ax.grid(alpha=0.3)
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ax.set_title('Bounded-confidence consensus, α = 0.3')
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fig.tight_layout(); plt.show()
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.. AUTO-PLOT-BEGIN
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.. image:: ../_static/auto/algorithms__agent_based/block_03_fig_01.png
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:align: center
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:width: 80%
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.. AUTO-PLOT-END
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.. image:: ../_static/v2/agent_based/plot_01.png
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:align: center
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:width: 80%
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.. code-block:: python
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fig, ax = plt.subplots()
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for alpha in [0.05, 0.1, 0.3, 0.6, 1.0]:
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r = opt.consensus_dynamics(init, alpha=alpha, noise_sigma=0.0, n_steps=60, seed=0)
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S = np.array(r['states_flat']).reshape(r['n_steps'], r['n_agents'])
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spread = S.max(axis=1) - S.min(axis=1)
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ax.semilogy(spread, label=f'α = {alpha:g}')
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ax.set_xlabel('step k'); ax.set_ylabel('max_i s − min_i s')
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ax.set_title('Convergence rate vs averaging weight α'); ax.legend(); ax.grid(alpha=0.3)
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fig.tight_layout(); plt.show()
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.. AUTO-PLOT-BEGIN
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.. image:: ../_static/auto/algorithms__agent_based/block_04_fig_01.png
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:align: center
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:width: 80%
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.. AUTO-PLOT-END
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.. image:: ../_static/v2/agent_based/plot_02.png
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:align: center
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:width: 80%
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**Verified:** without noise, the empirical mean is exactly preserved and the spread decays geometrically.
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API
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---
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.. code-block:: rust
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pub fn simulate_agent_based<T>(initial: &[f64], transition: T, cfg: &AgentBasedConfig) -> Result<AgentBasedResult>
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where T: Fn(f64, &[f64], usize) -> f64;
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pub struct AgentBasedConfig { pub n_agents: usize, pub n_steps: usize, pub noise_sigma: f64, pub seed: u64 }
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pub struct AgentBasedResult { pub states: Array2<f64>, pub mean_trajectory: Array1<f64> }
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