reduced number of series for faster CI, modified alpha and vmax for better illustration, eliminated loop over each time series line plot, changed color map to plasma

Author: ecotner

examples/statistics/time_series_histogram.py

@@ -9,7 +9,8 @@
 
 The first plot shows the typical way of visualizing multiple time series by
 overlaying them on top of each other with ``plt.plot``. The second and third
-plots show how to reinterpret the data as a 2d histogram.
+plots show how to reinterpret the data as a 2d histogram, with optional
+interpolation.
 """
 from copy import copy
 import time
@@ -22,7 +23,7 @@
 _, axes = plt.subplots(nrows=3, figsize=(10, 6 * 3))
 
 # Make some data; a 1D random walk + small fraction of sine waves
-num_series = 10000
+num_series = 1000
 num_points = 100
 SNR = 0.10  # Signal to Noise Ratio
 x = np.linspace(0, 4 * np.pi, num_points)
@@ -31,32 +32,31 @@
 # sinusoidal signal
 num_signal = int(round(SNR * num_series))
 phi = (np.pi / 8) * np.random.randn(num_signal, 1)  # small random offest
-Y[-num_signal:] = ((
+Y[-num_signal:] = (
     np.sqrt(np.arange(num_points))[None, :]
-    * np.sin(x[None, :] - phi))
-    + 0.05 * np.random.randn(num_signal, num_points)
+    * (np.sin(x[None, :] - phi)
+       + 0.05 * np.random.randn(num_signal, num_points))
 )
 
-# Plot it using `plot` and the lowest nonzero value of alpha (1/256).
-# With this view it is extremely difficult to observe the sinusoidal behavior
-# because of how many overlapping series there are. It also takes some time
-# to run because so many individual plots that need to be generated.
+# Plot it 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 that need to be generated.
 tic = time.time()
-for i in range(Y.shape[0]):
-    axes[0].plot(x, Y[i], color="C0", alpha=1 / 256)
+axes[0].plot(x, Y.T, color="C0", alpha=0.1)
 toc = time.time()
 axes[0].set_title(
     r"Standard time series visualization using line plot")
-print(f"{toc-tic:.2f} sec. elapsed")  # ~4 seconds
+print(f"{toc-tic:.2f} sec. elapsed")  # ~0.26 seconds
 
 
-# Now we will convert the multiple time series into a heat map. Not only will
+# 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 = 400 * 3
+num_fine = 800
 x_fine = np.linspace(x.min(), x.max(), num_fine)
-y_fine = np.zeros((num_series, 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()
@@ -65,22 +65,21 @@
 
 # Plot (x, y) points in 2d histogram with log colorscale
 # It is pretty evident that there is some kind of structure under the noise
-cmap = copy(plt.cm.jet)
+# 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])
-axes[1].pcolormesh(xedges, yedges, h.T, cmap=cmap, norm=LogNorm())
+axes[1].pcolormesh(xedges, yedges, h.T, cmap=cmap, norm=LogNorm(vmax=1.5e2))
 axes[1].set_title(
     r"Alternative time series vis. using 2d histogram and log color scale")
 
 # Same thing on linear color scale but with different (more visible) cmap
-cmap = copy(plt.cm.Blues)
-cmap.set_bad(cmap(0))
 h, xedges, yedges = np.histogram2d(x_fine, y_fine, bins=[400, 100])
-# tune vmax to make signal more visible
-axes[2].pcolormesh(xedges, yedges, h.T, cmap=cmap, vmax=3e3)
+axes[2].pcolormesh(xedges, yedges, h.T, cmap=cmap, vmax=1.5e2)
 axes[2].set_title(
     r"Alternative time series vis. using 2d histogram and linear color scale")
 toc = time.time()
-print(f"{toc-tic:.2f} sec. elapsed")  # ~1 sec for both plots + interpolation
+# ~0.08 sec for both plots + interpolation
+print(f"{toc-tic:.2f} sec. elapsed")
 
 plt.show()