numpy.histogram2d(x, y, bins=10, range=None, normed=False, weights=None)

Compute the bi-dimensional histogram of two data samples.

Parameters :

x : array_like, shape(N,)

A sequence of values to be histogrammed along the first dimension.

y : array_like, shape(M,)

A sequence of values to be histogrammed along the second dimension.

bins : int or [int, int] or array_like or [array, array], optional

The bin specification:

  • If int, the number of bins for the two dimensions (nx=ny=bins).
  • If [int, int], the number of bins in each dimension (nx, ny = bins).
  • If array_like, the bin edges for the two dimensions (x_edges=y_edges=bins).
  • If [array, array], the bin edges in each dimension (x_edges, y_edges = bins).

range : array_like, shape(2,2), optional

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

normed : bool, optional

If False, returns the number of samples in each bin. If True, returns the bin density, i.e. the bin count divided by the bin area.

weights : array_like, shape(N,), optional

An array of values w_i weighing each sample (x_i, y_i). Weights are normalized to 1 if normed is True. If normed is False, the values of the returned histogram are equal to the sum of the weights belonging to the samples falling into each bin.

Returns :

H : ndarray, shape(nx, ny)

The bi-dimensional histogram of samples x and y. Values in x are histogrammed along the first dimension and values in y are histogrammed along the second dimension.

xedges : ndarray, shape(nx,)

The bin edges along the first dimension.

yedges : ndarray, shape(ny,)

The bin edges along the second dimension.

See also

1D histogram
Multidimensional histogram


When normed is True, then the returned histogram is the sample density, defined such that:

\sum_{i=0}^{nx-1} \sum_{j=0}^{ny-1} H_{i,j} \Delta x_i \Delta y_j = 1

where H is the histogram array and \Delta x_i \Delta y_i the area of bin {i,j}.

Please note that the histogram does not follow the Cartesian convention where x values are on the abcissa and y values on the ordinate axis. Rather, x is histogrammed along the first dimension of the array (vertical), and y along the second dimension of the array (horizontal). This ensures compatibility with histogramdd.


>>> x, y = np.random.randn(2, 100)
>>> H, xedges, yedges = np.histogram2d(x, y, bins=(5, 8))
>>> H.shape, xedges.shape, yedges.shape
((5, 8), (6,), (9,))

We can now use the Matplotlib to visualize this 2-dimensional histogram:

>>> extent = [yedges[0], yedges[-1], xedges[-1], xedges[0]]
>>> import matplotlib.pyplot as plt
>>> plt.imshow(H, extent=extent, interpolation='nearest')
<matplotlib.image.AxesImage object at ...>
>>> plt.colorbar()
<matplotlib.colorbar.Colorbar instance at ...>

(Source code, png, pdf)


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