SciPy

numpy.histogram2d

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

Compute the bi-dimensional histogram of two data samples.

Parameters :

x : array_like, shape (N,)

An array containing the x coordinates of the points to be histogrammed.

y : array_like, shape (N,)

An array containing the y coordinates of the points to be histogrammed.

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

histogram
1D histogram
histogramdd
Multidimensional histogram

Notes

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.

Examples

>>> import matplotlib as mpl
>>> import matplotlib.pyplot as plt

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

>>> xedges = [0, 1, 1.5, 3, 5]
>>> yedges = [0, 2, 3, 4, 6]

Next we create a histogram H with random bin content:

>>> x = np.random.normal(3, 1, 100)
>>> y = np.random.normal(1, 1, 100)
>>> H, xedges, yedges = np.histogram2d(y, x, bins=(xedges, yedges))

Or we fill the histogram H with a determined bin content:

>>> H = np.ones((4, 4)).cumsum().reshape(4, 4)
>>> print H[::-1]  # This shows the bin content in the order as plotted
[[ 13.  14.  15.  16.]
 [  9.  10.  11.  12.]
 [  5.   6.   7.   8.]
 [  1.   2.   3.   4.]]

Imshow can only do an equidistant representation of bins:

>>> fig = plt.figure(figsize=(7, 3))
>>> ax = fig.add_subplot(131)
>>> ax.set_title('imshow:
equidistant’)
>>> im = plt.imshow(H, interpolation='nearest', origin='low',
                    extent=[xedges[0], xedges[-1], yedges[0], yedges[-1]])

pcolormesh can display exact bin edges:

>>> ax = fig.add_subplot(132)
>>> ax.set_title('pcolormesh:
exact bin edges’)
>>> X, Y = np.meshgrid(xedges, yedges)
>>> ax.pcolormesh(X, Y, H)
>>> ax.set_aspect('equal')

NonUniformImage displays exact bin edges with interpolation:

>>> ax = fig.add_subplot(133)
>>> ax.set_title('NonUniformImage:
interpolated’)
>>> im = mpl.image.NonUniformImage(ax, interpolation='bilinear')
>>> xcenters = xedges[:-1] + 0.5 * (xedges[1:] - xedges[:-1])
>>> ycenters = yedges[:-1] + 0.5 * (yedges[1:] - yedges[:-1])
>>> im.set_data(xcenters, ycenters, H)
>>> ax.images.append(im)
>>> ax.set_xlim(xedges[0], xedges[-1])
>>> ax.set_ylim(yedges[0], yedges[-1])
>>> ax.set_aspect('equal')
>>> plt.show()

(Source code)

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