.. only:: html .. note:: :class: sphx-glr-download-link-note Click :ref:`here ` 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``. .. code-block:: default from copy import copy import time import numpy as np import numpy.matlib import matplotlib.pyplot as plt from matplotlib.colors import LogNorm fig, axes = plt.subplots(nrows=3, figsize=(6, 8), constrained_layout=True) # 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 = int(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))[None, :] # random walk RMS scaling factor * (np.sin(x[None, :] - 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.empty((num_series, num_fine), dtype=float) for i in range(num_series): y_fine[i, :] = np.interp(x_fine, x, Y[i, :]) y_fine = y_fine.flatten() x_fine = np.matlib.repmat(x_fine, num_series, 1).flatten() # 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 = copy(plt.cm.plasma) cmap.set_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=LogNorm(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:: /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 :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out Out: .. code-block:: none 0.278 sec. elapsed 0.188 sec. elapsed ------------ References """""""""" The use of the following functions and methods is shown in this example: .. code-block:: default import matplotlib matplotlib.axes.Axes.pcolormesh matplotlib.pyplot.pcolormesh matplotlib.figure.Figure.colorbar .. rst-class:: sphx-glr-script-out Out: .. code-block:: none .. rst-class:: sphx-glr-timing **Total running time of the script:** ( 0 minutes 1.916 seconds) .. _sphx_glr_download_gallery_statistics_time_series_histogram.py: .. only :: html .. container:: sphx-glr-footer :class: sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: time_series_histogram.py ` .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: time_series_histogram.ipynb ` .. only:: html .. rst-class:: sphx-glr-signature Keywords: matplotlib code example, codex, python plot, pyplot `Gallery generated by Sphinx-Gallery `_