numpy.histogram2d#

numpy.histogram2d(x,y,bins=10,range=None,density=None,weights=None)[source]#

Compute the bi-dimensional histogram of two data samples.

Parameters:

xarray_like, shape (N,)

An array containing the x coordinates of the points to behistogrammed.

yarray_like, shape (N,)

An array containing the y coordinates of the points to behistogrammed.

binsint or array_like or [int, int] or [array, array], optional

The bin specification:

• If int, the number of bins for the two dimensions (nx=ny=bins).

• If array_like, the bin edges for the two dimensions(x_edges=y_edges=bins).

• If [int, int], the number of bins in each dimension(nx, ny = bins).

• If [array, array], the bin edges in each dimension(x_edges, y_edges = bins).

• A combination [int, array] or [array, int], where intis the number of bins and array is the bin edges.

rangearray_like, shape(2,2), optional

The leftmost and rightmost edges of the bins along each dimension(if not specified explicitly in thebins parameters):[[xmin,xmax],[ymin,ymax]]. All values outside of this rangewill be considered outliers and not tallied in the histogram.

densitybool, optional

If False, the default, returns the number of samples in each bin.If True, returns the probabilitydensity function at the bin,bin_count/sample_count/bin_area.

weightsarray_like, shape(N,), optional

An array of valuesw_i weighing each sample(x_i,y_i).Weights are normalized to 1 ifdensity is True. Ifdensity isFalse, the values of the returned histogram are equal to the sum ofthe weights belonging to the samples falling into each bin.

Returns:

Hndarray, shape(nx, ny)

The bi-dimensional histogram of samplesx andy. Values inxare histogrammed along the first dimension and values iny arehistogrammed along the second dimension.

xedgesndarray, shape(nx+1,)

The bin edges along the first dimension.

yedgesndarray, shape(ny+1,)

The bin edges along the second dimension.

See also

histogram

1D histogram

histogramdd

Multidimensional histogram

Notes

Whendensity is True, then the returned histogram is the sampledensity, defined such that the sum over bins of the productbin_value*bin_area is 1.

Please note that the histogram does not follow the Cartesian conventionwherex values are on the abscissa andy values on the ordinateaxis. Rather,x is histogrammed along the first dimension of thearray (vertical), andy along the second dimension of the array(horizontal). This ensures compatibility withhistogramdd.

Examples

Try it in your browser!

>>>importnumpyasnp>>>frommatplotlib.imageimportNonUniformImage>>>importmatplotlib.pyplotasplt

Construct a 2-D histogram with variable bin width. First define the binedges:

>>>xedges=[0,1,3,5]>>>yedges=[0,2,3,4,6]

Next we create a histogram H with random bin content:

>>>x=np.random.normal(2,1,100)>>>y=np.random.normal(1,1,100)>>>H,xedges,yedges=np.histogram2d(x,y,bins=(xedges,yedges))>>># Histogram does not follow Cartesian convention (see Notes),>>># therefore transpose H for visualization purposes.>>>H=H.T

imshow can only display square bins:

>>>fig=plt.figure(figsize=(7,3))>>>ax=fig.add_subplot(131,title='imshow: square bins')>>>plt.imshow(H,interpolation='nearest',origin='lower',...extent=[xedges[0],xedges[-1],yedges[0],yedges[-1]])<matplotlib.image.AxesImage object at 0x...>

pcolormesh can display actual edges:

>>>ax=fig.add_subplot(132,title='pcolormesh: actual edges',...aspect='equal')>>>X,Y=np.meshgrid(xedges,yedges)>>>ax.pcolormesh(X,Y,H)<matplotlib.collections.QuadMesh object at 0x...>

NonUniformImage can be used todisplay actual bin edges with interpolation:

>>>ax=fig.add_subplot(133,title='NonUniformImage: interpolated',...aspect='equal',xlim=xedges[[0,-1]],ylim=yedges[[0,-1]])>>>im=NonUniformImage(ax,interpolation='bilinear')>>>xcenters=(xedges[:-1]+xedges[1:])/2>>>ycenters=(yedges[:-1]+yedges[1:])/2>>>im.set_data(xcenters,ycenters,H)>>>ax.add_image(im)>>>plt.show()

It is also possible to construct a 2-D histogram without specifying binedges:

>>># Generate non-symmetric test data>>>n=10000>>>x=np.linspace(1,100,n)>>>y=2*np.log(x)+np.random.rand(n)-0.5>>># Compute 2d histogram. Note the order of x/y and xedges/yedges>>>H,yedges,xedges=np.histogram2d(y,x,bins=20)

Now we can plot the histogram usingpcolormesh, and ahexbin for comparison.

>>># Plot histogram using pcolormesh>>>fig,(ax1,ax2)=plt.subplots(ncols=2,sharey=True)>>>ax1.pcolormesh(xedges,yedges,H,cmap='rainbow')>>>ax1.plot(x,2*np.log(x),'k-')>>>ax1.set_xlim(x.min(),x.max())>>>ax1.set_ylim(y.min(),y.max())>>>ax1.set_xlabel('x')>>>ax1.set_ylabel('y')>>>ax1.set_title('histogram2d')>>>ax1.grid()

>>># Create hexbin plot for comparison>>>ax2.hexbin(x,y,gridsize=20,cmap='rainbow')>>>ax2.plot(x,2*np.log(x),'k-')>>>ax2.set_title('hexbin')>>>ax2.set_xlim(x.min(),x.max())>>>ax2.set_xlabel('x')>>>ax2.grid()

>>>plt.show()

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