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‎doc_source/modules/SP/index.rst

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@@ -13,4 +13,5 @@ The signal processing module include various methods of analyzing a time series.
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Information Module <information.rst>
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Miscellaneous <misc.rst>
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Texture Analysis <texture_analysis.rst>
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Stochastic P-Bifurcation Detection <stoch_bif.md>
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Stochastic P-Bifurcation Detection <stoch_bif.md>
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Parameter Path Optimization <parameter_path_opt.rst>

‎doc_source/modules/SP/parameter_path_opt.rst

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Parameter Path Optimization
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=========================================================
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This page contains the necessary functions for performing dynamical system parameter space optimization and allows for obtaining a path in the parameter space to minimize a defined loss function in terms of functions of persistence.
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.. automodule:: teaspoon.SP.parameter_path_opt
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:members:
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**Example**::
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import torch
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from torchdiffeq import odeint
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from torch.optim.lr_scheduler import LambdaLR
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from teaspoon.SP.parameter_path_opt import PathOptimizer
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from IPython.display import clear_output
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device = torch.device("cuda" if torch.cuda.is_available() else "cpu")
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# Set bounds for the parameters
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x_min = 80
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x_max = 300
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y_min = 4
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y_max = 50
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# Define the system of ODEs using PyTorch
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class LorenzSystem(torch.nn.Module):
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def __init__(self, params):
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super().__init__()
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self.params = torch.nn.Parameter(params)
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def forward(self, t, state):
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x, y, z = state
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rho, sigma = self.params
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dxdt = sigma * (y - x)
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dydt = x * (rho - z) - y
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dzdt = x * y - (8.0/3.0) * z
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return torch.stack([dxdt, dydt, dzdt])
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# Time settings
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t_main = torch.linspace(0, 10, 1000, device=device, dtype=torch.float64) # Main simulation
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# Initial conditions
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x0 = torch.tensor([1.0, 1.0, 1.0], requires_grad=True, device=device, dtype=torch.float64)
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# Combine parameters into a single vector
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params = torch.nn.Parameter(torch.tensor([190.0, 20.0], device=device))
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# Instantiate the system with the combined parameter vector
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lorenz = LorenzSystem(params).to(device)
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# Initialize optimizer and learning rate scheduler
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optimizer = torch.optim.Adam([lorenz.params], lr=1.0)
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scheduler = LambdaLR(optimizer, lr_lambda=lambda epoch: 0.995**epoch)
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# Initialize lists for saving the path and losses
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path = [[lorenz.params[0].item(), lorenz.params[1].item()]]
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losses = []
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# Define the forbidden regions for the parameter path
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forbidden_regions = [
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lambda params, pd1: (params[0] - x_max),
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lambda params, pd1: -(params[0] - x_min),
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lambda params, pd1: (params[1] - y_max),
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lambda params, pd1: -(params[1] - y_min),
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lambda params, pd1: -((1/400)*(params[0]-190)**2+(1/25)*(params[1]-10)**2 - 1.0), # Example constraint: unit disk of radius 5 centered at (190, 27)
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]
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# Initialize the PathOptimizer with the Lorenz system and forbidden regions
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p_opt = PathOptimizer({
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'maxPers': -1}, forbidden_regions=forbidden_regions)
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for epoch in range(5):
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# Perform the optimization step
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y, pd1, loss, grads = p_opt.optimize(lorenz, x0, t_main, optimizer, scheduler)
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# Extract the gradients with resspect to the parameters
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d_rho, d_sigma = grads[0], grads[1]
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# Print result of optimization step
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clear_output(wait=True)
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print(f"d(Loss)/d(sigma): {d_sigma.item():.5}")
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print(f"d(Loss)/d(rho): {d_rho.item():.5}")
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print(f"Loss: {loss.item():.8}")
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print(f"Rho: {lorenz.params[0].item():.8} -- Sigma: {lorenz.params[1].item():.8}")
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# Save the path and the loss
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path.append([lorenz.params[0].item(), lorenz.params[1].item()])
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losses.append(loss.item())
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Output of example (first step of optimization)
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::
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d(Loss)/d(sigma): 0.97641
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d(Loss)/d(rho): 0.21593
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Loss: -1.0
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Rho: 189.0 -- Sigma: 19.0
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.. note::
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Results may vary depending on the operating system for chaotic dynamics. The result shown is for demonstration purposes only.

‎docs/.buildinfo

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# Sphinx build info version 1
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# This file hashes the configuration used when building these files. When it is not found, a full rebuild will be done.
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config: 57959a0acaf4fa6441a0088b37c57423
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‎docs/_modules/index.html

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<li class="toctree-l3"><a class="reference internal" href="../modules/SP/misc.html">2.3.4. Miscellaneous</a></li>
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<li class="toctree-l3"><a class="reference internal" href="../modules/SP/texture_analysis.html">2.3.5. Texture Analysis</a></li>
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<li class="toctree-l3"><a class="reference internal" href="../modules/SP/stoch_bif.html">2.3.6. Stochastic P-Bifurcation Detection</a></li>
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<li class="toctree-l3"><a class="reference internal" href="../modules/SP/parameter_path_opt.html">2.3.7. Parameter Path Optimization</a></li>
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</ul>
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<li class="toctree-l2"><a class="reference internal" href="../modules/TDA/index.html">2.4. Topological Data Analaysis (TDA) Module</a><ul>
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<div class="rst-content style-external-links">
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<div role="navigation" aria-label="Page navigation">
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<ul class="wy-breadcrumbs">
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<li class="breadcrumb-item active">Overview: module code</li>
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<li><a href="teaspoon/SP/information/entropy.html">teaspoon.SP.information.entropy</a></li>
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<li><a href="teaspoon/SP/network.html">teaspoon.SP.network</a></li>
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<li><a href="teaspoon/SP/network_tools.html">teaspoon.SP.network_tools</a></li>
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<li><a href="teaspoon/SP/parameter_path_opt.html">teaspoon.SP.parameter_path_opt</a></li>
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<li><a href="teaspoon/SP/texture_analysis.html">teaspoon.SP.texture_analysis</a></li>
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<li><a href="teaspoon/SP/tsa_tools.html">teaspoon.SP.tsa_tools</a></li>
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<li><a href="teaspoon/TDA/Distance.html">teaspoon.TDA.Distance</a></li>

‎docs/_modules/teaspoon/DAF/data_assimilation.html

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<li class="toctree-l3"><a class="reference internal" href="../../../modules/SP/misc.html">2.3.4. Miscellaneous</a></li>
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<li class="toctree-l3"><a class="reference internal" href="../../../modules/SP/texture_analysis.html">2.3.5. Texture Analysis</a></li>
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<li class="toctree-l3"><a class="reference internal" href="../../../modules/SP/stoch_bif.html">2.3.6. Stochastic P-Bifurcation Detection</a></li>
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<li class="toctree-l3"><a class="reference internal" href="../../../modules/SP/parameter_path_opt.html">2.3.7. Parameter Path Optimization</a></li>
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</ul>
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<li class="toctree-l2"><a class="reference internal" href="../../../modules/TDA/index.html">2.4. Topological Data Analaysis (TDA) Module</a><ul>

‎docs/_modules/teaspoon/DAF/forecasting.html

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<li class="toctree-l3"><a class="reference internal" href="../../../modules/SP/misc.html">2.3.4. Miscellaneous</a></li>
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<li class="toctree-l3"><a class="reference internal" href="../../../modules/SP/texture_analysis.html">2.3.5. Texture Analysis</a></li>
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<li class="toctree-l3"><a class="reference internal" href="../../../modules/SP/stoch_bif.html">2.3.6. Stochastic P-Bifurcation Detection</a></li>
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<li class="toctree-l3"><a class="reference internal" href="../../../modules/SP/parameter_path_opt.html">2.3.7. Parameter Path Optimization</a></li>
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‎docs/_modules/teaspoon/ML/PD_Classification.html

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<li class="toctree-l3"><a class="reference internal" href="../../../modules/SP/misc.html">2.3.4. Miscellaneous</a></li>
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<li class="toctree-l3"><a class="reference internal" href="../../../modules/SP/texture_analysis.html">2.3.5. Texture Analysis</a></li>
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<li class="toctree-l3"><a class="reference internal" href="../../../modules/SP/stoch_bif.html">2.3.6. Stochastic P-Bifurcation Detection</a></li>
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<li class="toctree-l3"><a class="reference internal" href="../../../modules/SP/parameter_path_opt.html">2.3.7. Parameter Path Optimization</a></li>
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<span class="k">return</span> <span class="n">training_dgms</span><span class="o">.</span><span class="n">reset_index</span><span class="p">(),</span> <span class="n">testing_dgms</span><span class="o">.</span><span class="n">reset_index</span><span class="p">()</span>
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