.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/04_adaptive_regression_splines/02_lambda_sweep_animation.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note :ref:`Go to the end ` to download the full example code or to run this example in your browser via Binder. .. rst-class:: sphx-glr-example-title .. _sphx_glr_auto_examples_04_adaptive_regression_splines_02_lambda_sweep_animation.py: Lambda Sweep Animation ====================== This example animates the fidelity–sparsity trade-off of the adaptive regression splines module by sweeping the regularization parameter :math:`\lambda`. Each frame shows: - Original samples (fixed). - TV-denoised samples (changes with :math:`\lambda`). - Sparsest piecewise-linear spline (changes with :math:`\lambda`). - Detected knots (changes with :math:`\lambda`). .. GENERATED FROM PYTHON SOURCE LINES 20-22 Imports ------- .. GENERATED FROM PYTHON SOURCE LINES 22-36 .. code-block:: Python import os from pathlib import Path import numpy as np import matplotlib.pyplot as plt from matplotlib import animation from splineops.adaptive_regression_splines.denoising import denoise_y from splineops.adaptive_regression_splines.sparsification import ( sparsest_interpolant, linear_spline, ) .. GENERATED FROM PYTHON SOURCE LINES 38-42 Data ---- Embedded (x, y) dataset. .. GENERATED FROM PYTHON SOURCE LINES 42-107 .. code-block:: Python data = np.array([ [0.0107766212868331, 0.260227935166001], [0.0310564395737153, 0.124128829346261], [0.0568406178471921, -0.0319625924377939], [0.0624834663023982, -0.305487158118621], [0.0855836735802228, 0.0198584921896104], [0.111715185429166, 0.132374842819488], [0.139391914966393, 0.0346881909310438], [0.151220604385114, 0.225044726396834], [0.160372945787459, -0.0839333693634482], [0.196012653453612, 0.100524891786437], [0.20465948547682, 0.286553206119747], [0.236142103912376, -0.0969023194982265], [0.247757212881283, 0.344416030734225], [0.277270837091189, 0.322338105021903], [0.294942432854744, 0.628493233708394], [0.311124804679808, 0.238685146788896], [0.322729104513214, 0.0314182350548619], [0.341198353790244, 0.554001442697049], [0.362426869114815, 0.658491185386012], [0.380891037570895, 0.622866466731061], [0.402149882582122, 0.832680133314763], [0.424514186772157, 0.282871329344068], [0.454259779607654, 0.418961645149398], [0.471194339641083, 0.765569673816136], [0.480251119603182, 0.936269519087734], [0.50143948559379, 1.21690697362292], [0.539345526600005, 0.856785149480669], [0.551362009238399, 0.918563536364133], [0.56406586469322, 1.04369945227154], [0.585046514891406, 0.891659244596406], [0.614876517081502, 1.01020862285029], [0.623908589622186, 1.05646068606692], [0.651627178545465, 1.13455056187785], [0.679400399781766, 1.56682321923577], [0.696936576029801, 1.47238622944877], [0.704796955182952, 1.20492985044235], [0.729875394285375, 1.45329058102288], [0.752399114367628, 1.26394538858847], [0.776579617991004, 1.4052754431186], [0.783135827892922, 1.2534612824523], [0.800371524043548, 1.58782975330571], [0.821400442874384, 1.3740621261335], [0.849726902218741, 2.27247168443063], [0.872126589233067, 1.98304748773148], [0.89137702874173, 1.59274379691406], [0.906347248186443, 1.82991582958117], [0.939772323088249, 1.9344157693364], [0.951594904384916, 1.71570985938051], [0.967602823452471, 2.32573940626424], [0.991018964382358, 2.11540602201059], ]) x, y = data[:, 0], data[:, 1] fig, ax = plt.subplots() ax.plot(x, y, "x", label="Original data", markersize=8) ax.set_title("Original data") ax.set_xlabel("x") ax.set_ylabel("y") ax.grid(True, alpha=0.3) ax.legend() plt.show() .. image-sg:: /auto_examples/04_adaptive_regression_splines/images/sphx_glr_02_lambda_sweep_animation_001.png :alt: Original data :srcset: /auto_examples/04_adaptive_regression_splines/images/sphx_glr_02_lambda_sweep_animation_001.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 108-110 Animation Helper ---------------- .. GENERATED FROM PYTHON SOURCE LINES 110-200 .. code-block:: Python def _solve_for_lambda(lamb: float): """ Precompute all quantities needed to render one frame. Keeping the animation step light makes the HTML export fast and stable. """ y_d = denoise_y(x, y, lamb, rho=lamb) knots, amplitudes, polynomial = sparsest_interpolant(x, y_d) margin = (x[-1] - x[0]) / 10.0 t = np.linspace(x[0] - margin, x[-1] + margin, 400) y_s = linear_spline(t, knots, amplitudes, polynomial) if len(knots) > 0: y_k = linear_spline(knots, knots, amplitudes, polynomial) knot_xy = np.c_[knots, y_k] else: knot_xy = np.empty((0, 2)) return { "lamb": float(lamb), "y_d": y_d, "t": t, "y_s": y_s, "knot_xy": knot_xy, "K": int(len(knots)), } def create_lambda_sweep_animation(lambdas: np.ndarray, interval: int = 700): sols = [_solve_for_lambda(lmb) for lmb in lambdas] fig, ax = plt.subplots() ax.plot(x, y, "x", label="Original", markersize=8) # Initialize with first frame den_line, = ax.plot( x, sols[0]["y_d"], "x", label="Denoised", markersize=8, zorder=2, ) spline_line, = ax.plot( sols[0]["t"], sols[0]["y_s"], label="Sparsest", zorder=1, ) knot_scatter = ax.scatter( sols[0]["knot_xy"][:, 0], sols[0]["knot_xy"][:, 1], s=36, color="C3", marker="o", label="Knots", zorder=5, # <- on top of everything ) title = ax.set_title(f"λ = {sols[0]['lamb']:.2e} | K = {sols[0]['K']}") ax.set_xlabel("x") ax.set_ylabel("y") ax.grid(True, alpha=0.3) ax.legend() # Fix axis limits to avoid flicker while animating margin = (x[-1] - x[0]) / 10.0 ax.set_xlim(x[0] - margin, x[-1] + margin) y_all = np.concatenate([y] + [s["y_d"] for s in sols] + [s["y_s"] for s in sols]) pad = 0.05 * (y_all.max() - y_all.min() + 1e-12) ax.set_ylim(y_all.min() - pad, y_all.max() + pad) def animate(i: int): s = sols[i] den_line.set_ydata(s["y_d"]) spline_line.set_data(s["t"], s["y_s"]) knot_scatter.set_offsets(s["knot_xy"]) title.set_text(f"λ = {s['lamb']:.2e} | K = {s['K']}") return spline_line, den_line, knot_scatter, title return animation.FuncAnimation( fig, animate, frames=len(sols), interval=interval, blit=True, ) .. GENERATED FROM PYTHON SOURCE LINES 201-205 Build the Animation ------------------- Geometric spacing gives a nice “slow-to-fast” transition. .. GENERATED FROM PYTHON SOURCE LINES 205-211 .. code-block:: Python lambda_values = np.geomspace(1e-4, 2e-1, 12) INTERVAL_MS = 750 ani = create_lambda_sweep_animation(lambda_values, interval=INTERVAL_MS) .. container:: sphx-glr-animation .. raw:: html .. GENERATED FROM PYTHON SOURCE LINES 212-214 Export the Animation -------------------- .. GENERATED FROM PYTHON SOURCE LINES 214-223 .. code-block:: Python from splineops.utils.sphinx import export_animation_mp4_and_html export_animation_mp4_and_html( ani, stem="lambda_sweep_animation", interval_ms=INTERVAL_MS, # e.g. 750 dpi=80, force=True, ) .. rst-class:: sphx-glr-script-out .. code-block:: none (PosixPath('/home/runner/work/splineops/splineops/docs/_build/_generated_static/animations/lambda_sweep_animation.mp4'), PosixPath('/home/runner/work/splineops/splineops/docs/_build/_generated_static/animations/lambda_sweep_animation.html')) .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 3.590 seconds) .. _sphx_glr_download_auto_examples_04_adaptive_regression_splines_02_lambda_sweep_animation.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: binder-badge .. image:: images/binder_badge_logo.svg :target: https://mybinder.org/v2/gh/splineops/splineops.github.io/main?urlpath=lab/tree/notebooks_binder/auto_examples/04_adaptive_regression_splines/02_lambda_sweep_animation.ipynb :alt: Launch binder :width: 150 px .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: 02_lambda_sweep_animation.ipynb <02_lambda_sweep_animation.ipynb>` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: 02_lambda_sweep_animation.py <02_lambda_sweep_animation.py>` .. container:: sphx-glr-download sphx-glr-download-zip :download:`Download zipped: 02_lambda_sweep_animation.zip <02_lambda_sweep_animation.zip>` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_