.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "gallery/statistics/time_series_histogram.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. meta:: :keywords: codex .. 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_gallery_statistics_time_series_histogram.py: ===================== Time Series Histogram ===================== This example demonstrates how to efficiently visualize large numbers of time series in a way that could potentially reveal hidden substructure and patterns that are not immediately obvious, and display them in a visually appealing way. In this example, we generate multiple sinusoidal "signal" series that are buried under a larger number of random walk "noise/background" series. For an unbiased Gaussian random walk with standard deviation of σ, the RMS deviation from the origin after n steps is σ*sqrt(n). So in order to keep the sinusoids visible on the same scale as the random walks, we scale the amplitude by the random walk RMS. In addition, we also introduce a small random offset ``phi`` to shift the sines left/right, and some additive random noise to shift individual data points up/down to make the signal a bit more "realistic" (you wouldn't expect a perfect sine wave to appear in your data). The first plot shows the typical way of visualizing multiple time series by overlaying them on top of each other with ``plt.plot`` and a small value of ``alpha``. The second and third plots show how to reinterpret the data as a 2d histogram, with optional interpolation between data points, by using ``np.histogram2d`` and ``plt.pcolormesh``. .. GENERATED FROM PYTHON SOURCE LINES 26-95 .. code-block:: Python import time import matplotlib.pyplot as plt import numpy as np fig, axes = plt.subplots(nrows=3, figsize=(6, 8), layout='constrained') # Fix random state for reproducibility np.random.seed(19680801) # Make some data; a 1D random walk + small fraction of sine waves num_series = 1000 num_points = 100 SNR = 0.10 # Signal to Noise Ratio x = np.linspace(0, 4 * np.pi, num_points) # Generate unbiased Gaussian random walks Y = np.cumsum(np.random.randn(num_series, num_points), axis=-1) # Generate sinusoidal signals num_signal = round(SNR * num_series) phi = (np.pi / 8) * np.random.randn(num_signal, 1) # small random offset Y[-num_signal:] = ( np.sqrt(np.arange(num_points)) # random walk RMS scaling factor * (np.sin(x - phi) + 0.05 * np.random.randn(num_signal, num_points)) # small random noise ) # Plot series using `plot` and a small value of `alpha`. With this view it is # very difficult to observe the sinusoidal behavior because of how many # overlapping series there are. It also takes a bit of time to run because so # many individual artists need to be generated. tic = time.time() axes[0].plot(x, Y.T, color="C0", alpha=0.1) toc = time.time() axes[0].set_title("Line plot with alpha") print(f"{toc-tic:.3f} sec. elapsed") # Now we will convert the multiple time series into a histogram. Not only will # the hidden signal be more visible, but it is also a much quicker procedure. tic = time.time() # Linearly interpolate between the points in each time series num_fine = 800 x_fine = np.linspace(x.min(), x.max(), num_fine) y_fine = np.concatenate([np.interp(x_fine, x, y_row) for y_row in Y]) x_fine = np.broadcast_to(x_fine, (num_series, num_fine)).ravel() # Plot (x, y) points in 2d histogram with log colorscale # It is pretty evident that there is some kind of structure under the noise # You can tune vmax to make signal more visible cmap = plt.colormaps["plasma"] cmap = cmap.with_extremes(bad=cmap(0)) h, xedges, yedges = np.histogram2d(x_fine, y_fine, bins=[400, 100]) pcm = axes[1].pcolormesh(xedges, yedges, h.T, cmap=cmap, norm="log", vmax=1.5e2, rasterized=True) fig.colorbar(pcm, ax=axes[1], label="# points", pad=0) axes[1].set_title("2d histogram and log color scale") # Same data but on linear color scale pcm = axes[2].pcolormesh(xedges, yedges, h.T, cmap=cmap, vmax=1.5e2, rasterized=True) fig.colorbar(pcm, ax=axes[2], label="# points", pad=0) axes[2].set_title("2d histogram and linear color scale") toc = time.time() print(f"{toc-tic:.3f} sec. elapsed") plt.show() .. image-sg:: /gallery/statistics/images/sphx_glr_time_series_histogram_001.png :alt: Line plot with alpha, 2d histogram and log color scale, 2d histogram and linear color scale :srcset: /gallery/statistics/images/sphx_glr_time_series_histogram_001.png, /gallery/statistics/images/sphx_glr_time_series_histogram_001_2_00x.png 2.00x :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out .. code-block:: none 0.226 sec. elapsed 0.064 sec. elapsed .. GENERATED FROM PYTHON SOURCE LINES 96-103 .. admonition:: References The use of the following functions, methods, classes and modules is shown in this example: - `matplotlib.axes.Axes.pcolormesh` / `matplotlib.pyplot.pcolormesh` - `matplotlib.figure.Figure.colorbar` .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 2.659 seconds) .. _sphx_glr_download_gallery_statistics_time_series_histogram.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: time_series_histogram.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: time_series_histogram.py ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_