Develop Reference

How to fill intervals under KDE curve with different colors

I am looking for a way to color the intervals below the curve with different colors; on the interval x < 0, I would like to fill the area under the curve with one color and on the interval x >= 0 with another color, like the following image:
This is the code for basic kde plot:
fig, (ax1) = plt.subplots(1, 1, figsize = ((plot_size + 1.5) * 1,(plot_size + 1.5)))
sns.kdeplot(data=pd.DataFrame(w_contrast, columns=['contrast']), x="contrast", ax=ax1);
ax1.set_xlabel(f"Dry Yield Posterior Contrast (kg)");
Is there a way to fill the area under the curve with different colors using seaborn?

seaborn is a high level api for matplotlib, so the curve will have to be calculated; similar to, but simpler than this answer.
Calculate the values for the kde curve with scipy.stats.gaussian_kde
Use matplotlib.pyplot.fill_between to fill the areas.
Use scipy.integrate.simpson to calculate the area under the curve, which will be passed to matplotlib.pyplot.annotate to annotate.
import seaborn as sns
from scipy.stats import gaussian_kde
from scipy.integrate import simps
import numpy as np
# load sample data
df = sns.load_dataset('planets')
# create the kde model
kde = gaussian_kde(df.mass.dropna())
# plot
fig, ax = plt.subplots(figsize=(9, 6))
g = sns.kdeplot(data=df.mass, ax=ax, c='k')
# remove margins; optional
g.margins(x=0, y=0)
# get the min and max of the x-axis
xmin, xmax = g.get_xlim()
# create points between the min and max
x = np.linspace(xmin, xmax, 1000)
# calculate the y values from the model
kde_y = kde(x)
# select x values below 0
x0 = x[x < 0]
# get the len, which will be used for slicing the other arrays
x0_len = len(x0)
# slice the arrays
y0 = kde_y[:x0_len]
x1 = x[x0_len:]
y1 = kde_y[x0_len:]
# calculate the area under the curves
area0 = np.round(simps(y0, x0, dx=1) * 100, 0)
area1 = np.round(simps(y1, x1, dx=1) * 100, 0)
# fill the areas
g.fill_between(x=x0, y1=y0, color='r', alpha=.5)
g.fill_between(x=x1, y1=y1, color='b', alpha=.5)
# annotate
g.annotate(f'{area0:.0f}%', xy=(-1, 0.075), xytext=(10, 0.150), arrowprops=dict(arrowstyle="->", color='r', alpha=.5))
g.annotate(f'{area1:.0f}%', xy=(1, 0.05), xytext=(10, 0.125), arrowprops=dict(arrowstyle="->", color='b', alpha=.5))

Multiple 2D histogram on same plot

I have this script to extract data from an image and roi. I have everything working perfectly except the end when I output the graphs. Basically I'm having trouble with the windowing of both histograms. It doesn't matter if I change the gridsize, mincount, figure size, or x and y limits one of the histograms will always be slightly stretched. When I plot them individually they aren't stretched. Is there a way to make the hexagons on the same plot a consistent "non-stretched" shape?
Down below is my graph and plotting methods. (I left out my data extraction methods because it was quite specialized).
plt.ion()
plt.figure(figsize=(16,8))
plt.title('2D Histogram of Entorhinal Cortex ROIs')
plt.xlabel(x_inputs)
plt.ylabel(y_inputs)
colors = ['Reds','Blues']
x = []
y= []
#image extraction code
hist1 = plt.hexbin(x[0],y[0], gridsize=100,cmap='Reds',mincnt=10, alpha=0.35)
hist2 = plt.hexbin(x[1],y[1], gridsize=100,cmap='Blues',mincnt=10, alpha=0.35)
plt.colorbar(hist1, orientation="vertical")
plt.colorbar(hist2, orientation="vertical")
plt.ioff()
plt.show()
enter image description here

This issue can be solved by setting limits for the bins with the extent parameter. This can be done automatically by computing the minimum and maximum x and y values across all the data being plotted. In cases where gridsize is small (e.g. 10), this approach may result in some of the bins being partially outside of the plot limits. If so, setting a margin with plt.margins can help display all the bins within the plot.
import numpy as np # v 1.20.2
import matplotlib.pyplot as plt # v 3.3.4
# Create a random dataset
rng = np.random.default_rng(seed=123) # random number generator
size = 10000
x1 = rng.normal(loc=5, scale=10, size=size)
y1 = rng.normal(loc=5, scale=2, size=size)
x2 = rng.normal(loc=-30, scale=5, size=size)
y2 = rng.normal(loc=-20, scale=5, size=size)
# Define hexbin grid extent
xmin = min(*x1, *x2)
xmax = max(*x1, *x2)
ymin = min(*y1, *y2)
ymax = max(*y1, *y2)
ext = (xmin, xmax, ymin, ymax)
# Draw figure with colorbars
plt.figure(figsize=(10, 6))
hist1 = plt.hexbin(x1, y1, gridsize=30, cmap='Reds', mincnt=10, alpha=0.3, extent=ext)
hist2 = plt.hexbin(x2, y2, gridsize=30, cmap='Blues', mincnt=10, alpha=0.3, extent=ext)
plt.colorbar(hist1, orientation='vertical')
plt.colorbar(hist2, orientation='vertical')
# plt.margins(0.1) # Uncomment this if hex bins are partially outside of plot limits
plt.show()

Python: Filling colors between curves and axes & to regionalize the areas

I have a set of x,y values for two curves on excel sheets.
Using xlrd module, I have been able to plot them as below:
Question:
How do I shade the three areas with different fill colors? Had tried with fill_between but been unsuccessful due to not knowing how to associate with the x and y axes. The end in mind is as diagram below.
Here is my code:
import xlrd
import numpy as np
import matplotlib.pyplot as plt
workbook = xlrd.open_workbook('data.xls')
sheet = workbook.sheet_by_name('p1')
rowcount = sheet.nrows
colcount = sheet.ncols
result_data_p1 =[]
for row in range(1, rowcount):
row_data = []
for column in range(0, colcount):
data = sheet.cell_value(row, column)
row_data.append(data)
#print(row_data)
result_data_p1.append(row_data)
sheet = workbook.sheet_by_name('p2')
rowcount = sheet.nrows
colcount = sheet.ncols
result_data_p2 =[]
for row in range(1, rowcount):
row_data = []
for column in range(0, colcount):
data = sheet.cell_value(row, column)
row_data.append(data)
result_data_p2.append(row_data)
x1 = []
y1 = []
for i,k in result_data_p1:
cx1,cy1 = i,k
x1.append(cx1)
y1.append(cy1)
x2 = []
y2 = []
for m,n in result_data_p2:
cx2,cy2 = m,n
x2.append(cx2)
y2.append(cy2)
plt.subplot(1,1,1)
plt.yscale('log')
plt.plot(x1, y1, label = "Warm", color = 'red')
plt.plot(x2, y2, label = "Blue", color = 'blue')
plt.xlabel('Color Temperature (K)')
plt.ylabel('Illuminance (lm)')
plt.title('Kruithof Curve')
plt.legend()
plt.xlim(xmin=2000,xmax=7000)
plt.ylim(ymin=10,ymax=50000)
plt.show()
Please guide or lead to other references, if any.
Thank you.

Here is a way to recreate the curves and the gradients. It resulted very complicated to draw the background using the logscale. Therefore, the background is created in linear space and put on a separate y-axis. There were some problems getting the background behind the rest of the plot if it were drawn on the twin axis. Therefore, the background is drawn on the main axis, and the plot on the second axis. Afterwards, that second y-axis is placed again at the left.
To draw the curves, a spline is interpolated using six points. As the interpolation didn't give acceptable results using the plain coordinates, everything was interpolated in logspace.
The background is created column by column, checking where the two curves are for each x position. The red curve is extended artificially to have a consistent area.
import numpy as np
import matplotlib.pyplot as plt
import matplotlib.ticker as mticker
from scipy import interpolate
xmin, xmax = 2000, 7000
ymin, ymax = 10, 50000
# a grid of 6 x,y coordinates for both curves
x_grid = np.array([2000, 3000, 4000, 5000, 6000, 7000])
y_blue_grid = np.array([15, 100, 200, 300, 400, 500])
y_red_grid = np.array([20, 400, 10000, 500000, 500000, 500000])
# create interpolating curves in logspace
tck_red = interpolate.splrep(x_grid, np.log(y_red_grid), s=0)
tck_blue = interpolate.splrep(x_grid, np.log(y_blue_grid), s=0)
x = np.linspace(xmin, xmax)
yr = np.exp(interpolate.splev(x, tck_red, der=0))
yb = np.exp(interpolate.splev(x, tck_blue, der=0))
# create the background image; it is created fully in logspace
# the background (z) is zero between the curves, negative in the blue zone and positive in the red zone
# the values are close to zero near the curves, gradually increasing when they are further
xbg = np.linspace(xmin, xmax, 50)
ybg = np.linspace(np.log(ymin), np.log(ymax), 50)
z = np.zeros((len(ybg), len(xbg)), dtype=float)
for i, xi in enumerate(xbg):
yi_r = interpolate.splev(xi, tck_red, der=0)
yi_b = interpolate.splev(xi, tck_blue, der=0)
for j, yj in enumerate(ybg):
if yi_b >= yj:
z[j][i] = (yj - yi_b)
elif yi_r <= yj:
z[j][i] = (yj - yi_r)
fig, ax2 = plt.subplots(figsize=(8, 8))
# draw the background image, set vmax and vmin to get the desired range of colors;
# vmin should be -vmax to get the white at zero
ax2.imshow(z, origin='lower', extent=[xmin, xmax, np.log(ymin), np.log(ymax)], aspect='auto', cmap='bwr', vmin=-12, vmax=12, interpolation='bilinear', zorder=-2)
ax2.set_ylim(ymin=np.log(ymin), ymax=np.log(ymax)) # the image fills the complete background
ax2.set_yticks([]) # remove the y ticks of the background image, they are confusing
ax = ax2.twinx() # draw the main plot using the twin y-axis
ax.set_yscale('log')
ax.plot(x, yr, label="Warm", color='crimson')
ax.plot(x, yb, label="Blue", color='dodgerblue')
ax2.set_xlabel('Color Temperature')
ax.set_ylabel('Illuminance (lm)')
ax.set_title('Kruithof Curve')
ax.legend()
ax.set_xlim(xmin=xmin, xmax=xmax)
ax.set_ylim(ymin=ymin, ymax=ymax)
ax.grid(True, which='major', axis='y')
ax.grid(True, which='minor', axis='y', ls=':')
ax.yaxis.tick_left() # switch the twin axis to the left
ax.yaxis.set_label_position('left')
ax2.grid(True, which='major', axis='x')
ax2.xaxis.set_major_formatter(mticker.StrMethodFormatter('{x:.0f} K')) # show x-axis in Kelvin
ax.text(5000, 2000, 'Pleasing', fontsize=16)
ax.text(5000, 20, 'Appears bluish', fontsize=16)
ax.text(2300, 15000, 'Appears reddish', fontsize=16)
plt.show()

Color the shaded area under the curve distribution plot different colors

I'm using seaborn's kdeplot to draw the distribution of my data.
sns.kdeplot(data['numbers'], shade=True)
I want to divide the shaded area under the line into three parts, showing the "high" percentile and the "low" percentile. It would be ideal if I can color the shaded area with three different colors.
Any idea how I can go about doing that?
I want it to look something like the below where I can decide the cutoff value between the colors.

So I figured out how to do it. I would retrieve and x and y arrays from the seaborn plot, then use fill_between to color under the curve.
points = sns.kdeplot(data['numbers'], shade=True).get_lines()[0].get_data()
x = points[0]
y = points[1]
plt.fill_between(x,y, where = x >=0.75, color='r')
plt.fill_between(x,y, where = x <=0.1, color='g')
plt.fill_between(x,y, where = (x<=0.75) & (x>=0.1), color='y')

The only difference since the original answer was posted is that shade=True needs to be changed to shaded=False.
I also just wanted to share a slightly more complete answer for those who want to copy-paste.
import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns
mean = 0
std = 1
np.random.seed(0)
x = np.random.normal(loc=mean, scale=std, size=10000)
points = sns.kdeplot(x, shade=False, bw_method=1.0, color='black').get_lines()[0].get_data()
x = points[0]
y = points[1]
plt.fill_between(x, y, color='y')
plt.fill_between(x, y, where = (x<=0.5*std) & (x >= -0.5 * std), color='g') #
plt.fill_between(x, y, where = (x>=2*std) | (x<=-2*std), color='r')

Generate a heatmap using a scatter data set

I have a set of X,Y data points (about 10k) that are easy to plot as a scatter plot but that I would like to represent as a heatmap.
I looked through the examples in Matplotlib and they all seem to already start with heatmap cell values to generate the image.
Is there a method that converts a bunch of x, y, all different, to a heatmap (where zones with higher frequency of x, y would be "warmer")?

If you don't want hexagons, you can use numpy's histogram2d function:
import numpy as np
import numpy.random
import matplotlib.pyplot as plt
# Generate some test data
x = np.random.randn(8873)
y = np.random.randn(8873)
heatmap, xedges, yedges = np.histogram2d(x, y, bins=50)
extent = [xedges[0], xedges[-1], yedges[0], yedges[-1]]
plt.clf()
plt.imshow(heatmap.T, extent=extent, origin='lower')
plt.show()
This makes a 50x50 heatmap. If you want, say, 512x384, you can put bins=(512, 384) in the call to histogram2d.
Example:

In Matplotlib lexicon, i think you want a hexbin plot.
If you're not familiar with this type of plot, it's just a bivariate histogram in which the xy-plane is tessellated by a regular grid of hexagons.
So from a histogram, you can just count the number of points falling in each hexagon, discretiize the plotting region as a set of windows, assign each point to one of these windows; finally, map the windows onto a color array, and you've got a hexbin diagram.
Though less commonly used than e.g., circles, or squares, that hexagons are a better choice for the geometry of the binning container is intuitive:
hexagons have nearest-neighbor symmetry (e.g., square bins don't,
e.g., the distance from a point on a square's border to a point
inside that square is not everywhere equal) and
hexagon is the highest n-polygon that gives regular plane
tessellation (i.e., you can safely re-model your kitchen floor with hexagonal-shaped tiles because you won't have any void space between the tiles when you are finished--not true for all other higher-n, n >= 7, polygons).
(Matplotlib uses the term hexbin plot; so do (AFAIK) all of the plotting libraries for R; still i don't know if this is the generally accepted term for plots of this type, though i suspect it's likely given that hexbin is short for hexagonal binning, which is describes the essential step in preparing the data for display.)
from matplotlib import pyplot as PLT
from matplotlib import cm as CM
from matplotlib import mlab as ML
import numpy as NP
n = 1e5
x = y = NP.linspace(-5, 5, 100)
X, Y = NP.meshgrid(x, y)
Z1 = ML.bivariate_normal(X, Y, 2, 2, 0, 0)
Z2 = ML.bivariate_normal(X, Y, 4, 1, 1, 1)
ZD = Z2 - Z1
x = X.ravel()
y = Y.ravel()
z = ZD.ravel()
gridsize=30
PLT.subplot(111)
# if 'bins=None', then color of each hexagon corresponds directly to its count
# 'C' is optional--it maps values to x-y coordinates; if 'C' is None (default) then
# the result is a pure 2D histogram
PLT.hexbin(x, y, C=z, gridsize=gridsize, cmap=CM.jet, bins=None)
PLT.axis([x.min(), x.max(), y.min(), y.max()])
cb = PLT.colorbar()
cb.set_label('mean value')
PLT.show()

Edit: For a better approximation of Alejandro's answer, see below.
I know this is an old question, but wanted to add something to Alejandro's anwser: If you want a nice smoothed image without using py-sphviewer you can instead use np.histogram2d and apply a gaussian filter (from scipy.ndimage.filters) to the heatmap:
import numpy as np
import matplotlib.pyplot as plt
import matplotlib.cm as cm
from scipy.ndimage.filters import gaussian_filter
def myplot(x, y, s, bins=1000):
heatmap, xedges, yedges = np.histogram2d(x, y, bins=bins)
heatmap = gaussian_filter(heatmap, sigma=s)
extent = [xedges[0], xedges[-1], yedges[0], yedges[-1]]
return heatmap.T, extent
fig, axs = plt.subplots(2, 2)
# Generate some test data
x = np.random.randn(1000)
y = np.random.randn(1000)
sigmas = [0, 16, 32, 64]
for ax, s in zip(axs.flatten(), sigmas):
if s == 0:
ax.plot(x, y, 'k.', markersize=5)
ax.set_title("Scatter plot")
else:
img, extent = myplot(x, y, s)
ax.imshow(img, extent=extent, origin='lower', cmap=cm.jet)
ax.set_title("Smoothing with $\sigma$ = %d" % s)
plt.show()
Produces:
The scatter plot and s=16 plotted on top of eachother for Agape Gal'lo (click for better view):
One difference I noticed with my gaussian filter approach and Alejandro's approach was that his method shows local structures much better than mine. Therefore I implemented a simple nearest neighbour method at pixel level. This method calculates for each pixel the inverse sum of the distances of the n closest points in the data. This method is at a high resolution pretty computationally expensive and I think there's a quicker way, so let me know if you have any improvements.
Update: As I suspected, there's a much faster method using Scipy's scipy.cKDTree. See Gabriel's answer for the implementation.
Anyway, here's my code:
import numpy as np
import matplotlib.pyplot as plt
import matplotlib.cm as cm
def data_coord2view_coord(p, vlen, pmin, pmax):
dp = pmax - pmin
dv = (p - pmin) / dp * vlen
return dv
def nearest_neighbours(xs, ys, reso, n_neighbours):
im = np.zeros([reso, reso])
extent = [np.min(xs), np.max(xs), np.min(ys), np.max(ys)]
xv = data_coord2view_coord(xs, reso, extent[0], extent[1])
yv = data_coord2view_coord(ys, reso, extent[2], extent[3])
for x in range(reso):
for y in range(reso):
xp = (xv - x)
yp = (yv - y)
d = np.sqrt(xp**2 + yp**2)
im[y][x] = 1 / np.sum(d[np.argpartition(d.ravel(), n_neighbours)[:n_neighbours]])
return im, extent
n = 1000
xs = np.random.randn(n)
ys = np.random.randn(n)
resolution = 250
fig, axes = plt.subplots(2, 2)
for ax, neighbours in zip(axes.flatten(), [0, 16, 32, 64]):
if neighbours == 0:
ax.plot(xs, ys, 'k.', markersize=2)
ax.set_aspect('equal')
ax.set_title("Scatter Plot")
else:
im, extent = nearest_neighbours(xs, ys, resolution, neighbours)
ax.imshow(im, origin='lower', extent=extent, cmap=cm.jet)
ax.set_title("Smoothing over %d neighbours" % neighbours)
ax.set_xlim(extent[0], extent[1])
ax.set_ylim(extent[2], extent[3])
plt.show()
Result:

Instead of using np.hist2d, which in general produces quite ugly histograms, I would like to recycle py-sphviewer, a python package for rendering particle simulations using an adaptive smoothing kernel and that can be easily installed from pip (see webpage documentation). Consider the following code, which is based on the example:
import numpy as np
import numpy.random
import matplotlib.pyplot as plt
import sphviewer as sph
def myplot(x, y, nb=32, xsize=500, ysize=500):
xmin = np.min(x)
xmax = np.max(x)
ymin = np.min(y)
ymax = np.max(y)
x0 = (xmin+xmax)/2.
y0 = (ymin+ymax)/2.
pos = np.zeros([len(x),3])
pos[:,0] = x
pos[:,1] = y
w = np.ones(len(x))
P = sph.Particles(pos, w, nb=nb)
S = sph.Scene(P)
S.update_camera(r='infinity', x=x0, y=y0, z=0,
xsize=xsize, ysize=ysize)
R = sph.Render(S)
R.set_logscale()
img = R.get_image()
extent = R.get_extent()
for i, j in zip(xrange(4), [x0,x0,y0,y0]):
extent[i] += j
print extent
return img, extent
fig = plt.figure(1, figsize=(10,10))
ax1 = fig.add_subplot(221)
ax2 = fig.add_subplot(222)
ax3 = fig.add_subplot(223)
ax4 = fig.add_subplot(224)
# Generate some test data
x = np.random.randn(1000)
y = np.random.randn(1000)
#Plotting a regular scatter plot
ax1.plot(x,y,'k.', markersize=5)
ax1.set_xlim(-3,3)
ax1.set_ylim(-3,3)
heatmap_16, extent_16 = myplot(x,y, nb=16)
heatmap_32, extent_32 = myplot(x,y, nb=32)
heatmap_64, extent_64 = myplot(x,y, nb=64)
ax2.imshow(heatmap_16, extent=extent_16, origin='lower', aspect='auto')
ax2.set_title("Smoothing over 16 neighbors")
ax3.imshow(heatmap_32, extent=extent_32, origin='lower', aspect='auto')
ax3.set_title("Smoothing over 32 neighbors")
#Make the heatmap using a smoothing over 64 neighbors
ax4.imshow(heatmap_64, extent=extent_64, origin='lower', aspect='auto')
ax4.set_title("Smoothing over 64 neighbors")
plt.show()
which produces the following image:
As you see, the images look pretty nice, and we are able to identify different substructures on it. These images are constructed spreading a given weight for every point within a certain domain, defined by the smoothing length, which in turns is given by the distance to the closer nb neighbor (I've chosen 16, 32 and 64 for the examples). So, higher density regions typically are spread over smaller regions compared to lower density regions.
The function myplot is just a very simple function that I've written in order to give the x,y data to py-sphviewer to do the magic.

If you are using 1.2.x
import numpy as np
import matplotlib.pyplot as plt
x = np.random.randn(100000)
y = np.random.randn(100000)
plt.hist2d(x,y,bins=100)
plt.show()

Seaborn now has the jointplot function which should work nicely here:
import numpy as np
import seaborn as sns
import matplotlib.pyplot as plt
# Generate some test data
x = np.random.randn(8873)
y = np.random.randn(8873)
sns.jointplot(x=x, y=y, kind='hex')
plt.show()

Here's Jurgy's great nearest neighbour approach but implemented using scipy.cKDTree. In my tests it's about 100x faster.
import numpy as np
import matplotlib.pyplot as plt
import matplotlib.cm as cm
from scipy.spatial import cKDTree
def data_coord2view_coord(p, resolution, pmin, pmax):
dp = pmax - pmin
dv = (p - pmin) / dp * resolution
return dv
n = 1000
xs = np.random.randn(n)
ys = np.random.randn(n)
resolution = 250
extent = [np.min(xs), np.max(xs), np.min(ys), np.max(ys)]
xv = data_coord2view_coord(xs, resolution, extent[0], extent[1])
yv = data_coord2view_coord(ys, resolution, extent[2], extent[3])
def kNN2DDens(xv, yv, resolution, neighbours, dim=2):
"""
"""
# Create the tree
tree = cKDTree(np.array([xv, yv]).T)
# Find the closest nnmax-1 neighbors (first entry is the point itself)
grid = np.mgrid[0:resolution, 0:resolution].T.reshape(resolution**2, dim)
dists = tree.query(grid, neighbours)
# Inverse of the sum of distances to each grid point.
inv_sum_dists = 1. / dists[0].sum(1)
# Reshape
im = inv_sum_dists.reshape(resolution, resolution)
return im
fig, axes = plt.subplots(2, 2, figsize=(15, 15))
for ax, neighbours in zip(axes.flatten(), [0, 16, 32, 63]):
if neighbours == 0:
ax.plot(xs, ys, 'k.', markersize=5)
ax.set_aspect('equal')
ax.set_title("Scatter Plot")
else:
im = kNN2DDens(xv, yv, resolution, neighbours)
ax.imshow(im, origin='lower', extent=extent, cmap=cm.Blues)
ax.set_title("Smoothing over %d neighbours" % neighbours)
ax.set_xlim(extent[0], extent[1])
ax.set_ylim(extent[2], extent[3])
plt.savefig('new.png', dpi=150, bbox_inches='tight')

and the initial question was... how to convert scatter values to grid values, right?
histogram2d does count the frequency per cell, however, if you have other data per cell than just the frequency, you'd need some additional work to do.
x = data_x # between -10 and 4, log-gamma of an svc
y = data_y # between -4 and 11, log-C of an svc
z = data_z #between 0 and 0.78, f1-values from a difficult dataset
So, I have a dataset with Z-results for X and Y coordinates. However, I was calculating few points outside the area of interest (large gaps), and heaps of points in a small area of interest.
Yes here it becomes more difficult but also more fun. Some libraries (sorry):
from matplotlib import pyplot as plt
from matplotlib import cm
import numpy as np
from scipy.interpolate import griddata
pyplot is my graphic engine today,
cm is a range of color maps with some initeresting choice.
numpy for the calculations,
and griddata for attaching values to a fixed grid.
The last one is important especially because the frequency of xy points is not equally distributed in my data. First, let's start with some boundaries fitting to my data and an arbitrary grid size. The original data has datapoints also outside those x and y boundaries.
#determine grid boundaries
gridsize = 500
x_min = -8
x_max = 2.5
y_min = -2
y_max = 7
So we have defined a grid with 500 pixels between the min and max values of x and y.
In my data, there are lots more than the 500 values available in the area of high interest; whereas in the low-interest-area, there are not even 200 values in the total grid; between the graphic boundaries of x_min and x_max there are even less.
So for getting a nice picture, the task is to get an average for the high interest values and to fill the gaps elsewhere.
I define my grid now. For each xx-yy pair, i want to have a color.
xx = np.linspace(x_min, x_max, gridsize) # array of x values
yy = np.linspace(y_min, y_max, gridsize) # array of y values
grid = np.array(np.meshgrid(xx, yy.T))
grid = grid.reshape(2, grid.shape[1]*grid.shape[2]).T
Why the strange shape? scipy.griddata wants a shape of (n, D).
Griddata calculates one value per point in the grid, by a predefined method.
I choose "nearest" - empty grid points will be filled with values from the nearest neighbor. This looks as if the areas with less information have bigger cells (even if it is not the case). One could choose to interpolate "linear", then areas with less information look less sharp. Matter of taste, really.
points = np.array([x, y]).T # because griddata wants it that way
z_grid2 = griddata(points, z, grid, method='nearest')
# you get a 1D vector as result. Reshape to picture format!
z_grid2 = z_grid2.reshape(xx.shape[0], yy.shape[0])
And hop, we hand over to matplotlib to display the plot
fig = plt.figure(1, figsize=(10, 10))
ax1 = fig.add_subplot(111)
ax1.imshow(z_grid2, extent=[x_min, x_max,y_min, y_max, ],
origin='lower', cmap=cm.magma)
ax1.set_title("SVC: empty spots filled by nearest neighbours")
ax1.set_xlabel('log gamma')
ax1.set_ylabel('log C')
plt.show()
Around the pointy part of the V-Shape, you see I did a lot of calculations during my search for the sweet spot, whereas the less interesting parts almost everywhere else have a lower resolution.

Make a 2-dimensional array that corresponds to the cells in your final image, called say heatmap_cells and instantiate it as all zeroes.
Choose two scaling factors that define the difference between each array element in real units, for each dimension, say x_scale and y_scale. Choose these such that all your datapoints will fall within the bounds of the heatmap array.
For each raw datapoint with x_value and y_value:
heatmap_cells[floor(x_value/x_scale),floor(y_value/y_scale)]+=1

Very similar to #Piti's answer, but using 1 call instead of 2 to generate the points:
import numpy as np
import matplotlib.pyplot as plt
pts = 1000000
mean = [0.0, 0.0]
cov = [[1.0,0.0],[0.0,1.0]]
x,y = np.random.multivariate_normal(mean, cov, pts).T
plt.hist2d(x, y, bins=50, cmap=plt.cm.jet)
plt.show()
Output:

Here's one I made on a 1 Million point set with 3 categories (colored Red, Green, and Blue). Here's a link to the repository if you'd like to try the function. Github Repo
histplot(
X,
Y,
labels,
bins=2000,
range=((-3,3),(-3,3)),
normalize_each_label=True,
colors = [
[1,0,0],
[0,1,0],
[0,0,1]],
gain=50)

I'm afraid I'm a little late to the party but I had a similar question a while ago. The accepted answer (by #ptomato) helped me out but I'd also want to post this in case it's of use to someone.
''' I wanted to create a heatmap resembling a football pitch which would show the different actions performed '''
import numpy as np
import matplotlib.pyplot as plt
import random
#fixing random state for reproducibility
np.random.seed(1234324)
fig = plt.figure(12)
ax1 = fig.add_subplot(121)
ax2 = fig.add_subplot(122)
#Ratio of the pitch with respect to UEFA standards
hmap= np.full((6, 10), 0)
#print(hmap)
xlist = np.random.uniform(low=0.0, high=100.0, size=(20))
ylist = np.random.uniform(low=0.0, high =100.0, size =(20))
#UEFA Pitch Standards are 105m x 68m
xlist = (xlist/100)*10.5
ylist = (ylist/100)*6.5
ax1.scatter(xlist,ylist)
#int of the co-ordinates to populate the array
xlist_int = xlist.astype (int)
ylist_int = ylist.astype (int)
#print(xlist_int, ylist_int)
for i, j in zip(xlist_int, ylist_int):
#this populates the array according to the x,y co-ordinate values it encounters
hmap[j][i]= hmap[j][i] + 1
#Reversing the rows is necessary
hmap = hmap[::-1]
#print(hmap)
im = ax2.imshow(hmap)
Here's the result

None of these solutions worked for my application, so this is what I came up with. Essentially I am placing a 2D Gaussian at every single point:
import cv2
import numpy as np
import matplotlib.pyplot as plt
def getGaussian2D(ksize, sigma, norm=True):
oneD = cv2.getGaussianKernel(ksize=ksize, sigma=sigma)
twoD = np.outer(oneD.T, oneD)
return twoD / np.sum(twoD) if norm else twoD
def pt2heat(pts, shape, kernel=16, sigma=5):
heat = np.zeros(shape)
k = getGaussian2D(kernel, sigma)
for y,x in pts:
x, y = int(x), int(y)
for i in range(-kernel//2, kernel//2):
for j in range(-kernel//2, kernel//2):
if 0 <= x+i < shape[0] and 0 <= y+j < shape[1]:
heat[x+i, y+j] = heat[x+i, y+j] + k[i+kernel//2, j+kernel//2]
return heat
heat = pts2heat(pts, img.shape[:2])
plt.imshow(heat, cmap='heat')
Here are the points overlayed ontop of it's associated image, along with the resulting heat map: