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# numpy.histogram2d

`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

  `histogram`
    1D histogram
  `histogramdd`
    Multidimensional histogram

  Notes

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

  where H is the histogram array and 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

      >>> 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 ...>
      >>> plt.show()

  (Source code, png, pdf)

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