.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/plot_performance_comparison_with_scipy.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. .. rst-class:: sphx-glr-example-title .. _sphx_glr_auto_examples_plot_performance_comparison_with_scipy.py: Performance comparison with scipy --------------------------------- In this example we will compare splinebox's performance to scipy's splines on the following three tasks: - Spline creation - Spline evalution - Data fitting .. GENERATED FROM PYTHON SOURCE LINES 11-21 .. code-block:: Python import time import matplotlib.pyplot as plt import numpy as np import pandas as pd import scipy import seaborn as sns import splinebox .. GENERATED FROM PYTHON SOURCE LINES 22-30 First we compare the time it takes to create spline with a given set of knots and to evalutate it. The measurement is repeated 11 and the first repretition is discarded, because of the necessary numba compilation. The compiled code is cached such that it can be reused for future runs. Times are computes for different numbers of knots (M), open and closed splines, and curves with different dimensionality. .. GENERATED FROM PYTHON SOURCE LINES 30-116 .. code-block:: Python n_repetitions = 10 Ms = np.arange(10, 101, 10) results_creation = [] results_evaluation = [] for closed in [True, False]: for ndim in (1, 2, 3, 10): for M in Ms: for repetition in range(n_repetitions + 1): knots = np.random.rand(M, ndim) start = time.perf_counter_ns() spline = splinebox.Spline(M, splinebox.B3(), closed=closed) spline.knots = knots stop = time.perf_counter_ns() if repetition != 0: results_creation.append( [ "splinebox", f"{ndim}D", M, "closed" if closed else "open", stop - start, ] ) for nt in [10, 100, 1000, 10000]: t = np.linspace(0, M if closed else M - 1, nt) start_eval = time.perf_counter_ns() spline.eval(t) stop_eval = time.perf_counter_ns() if repetition != 0: results_evaluation.append( [ "splinebox", f"{ndim}D", M, nt, "closed" if closed else "open", stop - start, ] ) if closed: start = time.perf_counter_ns() t_knots = np.arange(M + 1) knots_periodic = np.concatenate([knots, knots[0][np.newaxis, :]], axis=0) spline = scipy.interpolate.make_interp_spline(t_knots, knots_periodic, k=3, bc_type="periodic") stop = time.perf_counter_ns() else: start = time.perf_counter_ns() t_knots = np.arange(M) spline = scipy.interpolate.make_interp_spline(t_knots, knots, k=3, bc_type="natural") stop = time.perf_counter_ns() if repetition != 0: results_creation.append( [ "scipy", f"{ndim}D", M, "closed" if closed else "open", stop - start, ] ) for nt in [10, 100, 1000, 10000]: t = np.linspace(0, M if closed else M - 1, nt) start_eval = time.perf_counter_ns() spline(t) stop_eval = time.perf_counter_ns() if repetition != 0: results_evaluation.append( [ "scipy", f"{ndim}D", M, nt, "closed" if closed else "open", stop - start, ] ) .. GENERATED FROM PYTHON SOURCE LINES 117-118 Now, that we have collected all of the times, we can turn the results into a data frame and plot the results using seaborn. .. GENERATED FROM PYTHON SOURCE LINES 118-134 .. code-block:: Python df = pd.DataFrame(results_creation, columns=["Package", "Dimensionality", "Number of knots", "closed", "time [ns]"]) for periodicity in ["closed", "open"]: fig, ax = plt.subplots() ax.set(yscale="log") sns.set_palette(sns.color_palette(["#228b18", "#0053a6"])) sns.lineplot( x="Number of knots", y="time [ns]", hue="Package", style="Dimensionality", data=df.loc[df["closed"] == periodicity], ax=ax, ) plt.title(f"Creation of {periodicity} splines") plt.show() .. rst-class:: sphx-glr-horizontal * .. image-sg:: /auto_examples/images/sphx_glr_plot_performance_comparison_with_scipy_001.png :alt: Creation of closed splines :srcset: /auto_examples/images/sphx_glr_plot_performance_comparison_with_scipy_001.png :class: sphx-glr-multi-img * .. image-sg:: /auto_examples/images/sphx_glr_plot_performance_comparison_with_scipy_002.png :alt: Creation of open splines :srcset: /auto_examples/images/sphx_glr_plot_performance_comparison_with_scipy_002.png :class: sphx-glr-multi-img .. GENERATED FROM PYTHON SOURCE LINES 135-137 The results show that splinbox outperforms scipy in all condition for the task of creating a spline from a given set of knots. .. GENERATED FROM PYTHON SOURCE LINES 137-157 .. code-block:: Python df = pd.DataFrame( results_evaluation, columns=["Package", "Dimensionality", "Number of knots", "Number of parameter values", "closed", "time [ns]"], ) for periodicity in ["closed", "open"]: fig, ax = plt.subplots(figsize=(7, 7)) ax.set(yscale="log") sns.set_palette(sns.color_palette(["#228b18", "#0053a6"])) sns.lineplot( x="Number of knots", y="time [ns]", hue="Package", style="Number of parameter values", data=df.loc[df["closed"] == periodicity], ax=ax, ) plt.title(f"Evaluation of {periodicity} splines") plt.show() .. rst-class:: sphx-glr-horizontal * .. image-sg:: /auto_examples/images/sphx_glr_plot_performance_comparison_with_scipy_003.png :alt: Evaluation of closed splines :srcset: /auto_examples/images/sphx_glr_plot_performance_comparison_with_scipy_003.png :class: sphx-glr-multi-img * .. image-sg:: /auto_examples/images/sphx_glr_plot_performance_comparison_with_scipy_004.png :alt: Evaluation of open splines :srcset: /auto_examples/images/sphx_glr_plot_performance_comparison_with_scipy_004.png :class: sphx-glr-multi-img .. GENERATED FROM PYTHON SOURCE LINES 158-160 Once again, splinebox outperforms scipy, in all conditions for the spline evaluation task. Lastly, we will compare the fitting (i.e. determining the control points of spline with M knots using least-squares given N > M datapoints) performance. .. GENERATED FROM PYTHON SOURCE LINES 160-230 .. code-block:: Python results_fitting = [] for closed in [True, False]: for ndim in (1, 2, 3, 10): for M in Ms: for repetition in range(n_repetitions + 1): data = np.random.rand(M * 10, ndim) start = time.perf_counter_ns() spline = splinebox.Spline(M, splinebox.B3(), closed=closed) spline.fit(data) stop = time.perf_counter_ns() if repetition != 0: results_fitting.append( [ "splinebox", f"{ndim}D", M, "closed" if closed else "open", stop - start, ] ) k = 3 if closed: start = time.perf_counter_ns() N = len(data) t = np.arange(-k, M + k + 1) u = np.linspace(0, M, N + 1)[:-1] tck, u = scipy.interpolate.splprep(data.T, k=k, u=u, t=t, task=-1, s=0, per=N) stop = time.perf_counter_ns() else: start = time.perf_counter_ns() N = len(data) t = np.arange(-k, M + k) u = np.linspace(0, M - 1, N) tck, u = scipy.interpolate.splprep(data.T, k=k, u=u, t=t, task=-1, s=0) stop = time.perf_counter_ns() if repetition != 0: results_fitting.append( [ "scipy", f"{ndim}D", M, "closed" if closed else "open", stop - start, ] ) df = pd.DataFrame( results_fitting, columns=["Package", "Dimensionality", "Number of knots", "closed", "time [ns]"], ) for periodicity in ["closed", "open"]: fig, ax = plt.subplots(figsize=(7, 7)) ax.set(yscale="log") sns.set_palette(sns.color_palette(["#228b18", "#0053a6"])) sns.lineplot( x="Number of knots", y="time [ns]", hue="Package", style="Dimensionality", data=df.loc[df["closed"] == periodicity], ax=ax, ) plt.title(f"Fitting of {periodicity} splines") plt.show() .. rst-class:: sphx-glr-horizontal * .. image-sg:: /auto_examples/images/sphx_glr_plot_performance_comparison_with_scipy_005.png :alt: Fitting of closed splines :srcset: /auto_examples/images/sphx_glr_plot_performance_comparison_with_scipy_005.png :class: sphx-glr-multi-img * .. image-sg:: /auto_examples/images/sphx_glr_plot_performance_comparison_with_scipy_006.png :alt: Fitting of open splines :srcset: /auto_examples/images/sphx_glr_plot_performance_comparison_with_scipy_006.png :class: sphx-glr-multi-img .. GENERATED FROM PYTHON SOURCE LINES 231-233 In the fitting task splinebox is outperformed by scipy's `splprep`, but is competetive for splines with relatively few knots (i.e. < 20). .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 28.345 seconds) .. _sphx_glr_download_auto_examples_plot_performance_comparison_with_scipy.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_performance_comparison_with_scipy.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_performance_comparison_with_scipy.py ` .. container:: sphx-glr-download sphx-glr-download-zip :download:`Download zipped: plot_performance_comparison_with_scipy.zip ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_