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.
|
|---|
Notes
When normed is True, then the returned histogram is the sample density,
defined such that:
System Message: WARNING/2 (\sum_{i=0}^{nx-1} \sum_{j=0}^{ny-1} H_{i,j} \Delta x_i \Delta y_j = 1
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kurmanji, lao, latin, latvian, lithuanian, mongolian, mongolianlmc, bokmal, nyn
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where H is the histogram array and
System Message: WARNING/2 (\Delta x_i \Delta y_i)
latex exited with error:
[stderr]
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This is pdfTeX, Version 3.1415926-2.4-1.40.13 (TeX Live 2012/TeX Live for SUSE Linux)
restricted \write18 enabled.
entering extended mode
(./math.tex
LaTeX2e <2011/06/27>
Babel <v3.8m> and hyphenation patterns for english, dumylang, nohyphenation, ge
rman-x-2011-07-01, ngerman-x-2011-07-01, afrikaans, ancientgreek, ibycus, arabi
c, armenian, basque, bulgarian, catalan, pinyin, coptic, croatian, czech, danis
h, dutch, ukenglish, usenglishmax, esperanto, estonian, ethiopic, farsi, finnis
h, french, friulan, galician, german, ngerman, swissgerman, monogreek, greek, h
ungarian, icelandic, assamese, bengali, gujarati, hindi, kannada, malayalam, ma
rathi, oriya, panjabi, tamil, telugu, indonesian, interlingua, irish, italian,
kurmanji, lao, latin, latvian, lithuanian, mongolian, mongolianlmc, bokmal, nyn
orsk, polish, portuguese, romanian, romansh, russian, sanskrit, serbian, serbia
nc, slovak, slovenian, spanish, swedish, turkish, turkmen, ukrainian, uppersorb
ian, welsh, loaded.
(/usr/share/texmf/tex/latex/base/article.cls
Document Class: article 2007/10/19 v1.4h Standard LaTeX document class
(/usr/share/texmf/tex/latex/base/size12.clo))
(/usr/share/texmf/tex/latex/base/inputenc.sty
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Transcript written on math.log.
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)
