class sage.plot.histogram.Histogram(datalist, options)

Bases: sage.plot.primitive.GraphicPrimitive

Graphics primitive that represents a histogram. This takes quite a few options as well.


sage: from sage.plot.histogram import Histogram
sage: g = Histogram([1,3,2,0], {}); g
Histogram defined by a data list of size 4
sage: type(g)
<class 'sage.plot.histogram.Histogram'>
sage: opts = { 'bins':20, 'label':'mydata'}
sage: g = Histogram([random() for _ in range(500)], opts); g
Histogram defined by a data list of size 500

We can accept multiple sets of the same length:

sage: g = Histogram([[1,3,2,0], [4,4,3,3]], {}); g
Histogram defined by 2 data lists

Get minimum and maximum horizontal and vertical ranges for the Histogram object.


sage: H = histogram([10,3,5], density=True); h = H[0]
sage: h.get_minmax_data()  # rel tol 1e-15
{'xmax': 10.0, 'xmin': 3.0, 'ymax': 0.4761904761904765, 'ymin': 0}
sage: G = histogram([random() for _ in range(500)]); g = G[0]
sage: g.get_minmax_data() # random output
{'xmax': 0.99729312925213209, 'xmin': 0.00013024562219410285, 'ymax': 61, 'ymin': 0}
sage: Y = histogram([random()*10 for _ in range(500)], range=[2,8]); y = Y[0]
sage: ymm = y.get_minmax_data(); ymm['xmax'], ymm['xmin']
(8.0, 2.0)
sage: Z = histogram([[1,3,2,0], [4,4,3,3]]); z = Z[0]
sage: z.get_minmax_data()
{'xmax': 4.0, 'xmin': 0, 'ymax': 2, 'ymin': 0}
sage.plot.histogram.histogram(datalist, edgecolor='black', align='mid', range=None, weights=None, aspect_ratio='automatic', bins=10, **options)

Computes and draws the histogram for list(s) of numerical data. See examples for the many options; even more customization is available using matplotlib directly.


  • datalist – A list, or a list of lists, of numerical data
  • align – (default: “mid”) How the bars align inside of each bin. Acceptable values are “left”, “right” or “mid”
  • alpha – (float in [0,1], default: 1) The transparency of the plot
  • bins – The number of sections in which to divide the range. Also can be a sequence of points within the range that create the partition
  • color – The color of the face of the bars or list of colors if multiple data sets are given
  • cumulative – (boolean - default: False) If True, then a histogram is computed in which each bin gives the counts in that bin plus all bins for smaller values. Negative values give a reversed direction of accumulation
  • edgecolor – The color of the border of each bar
  • fill – (boolean - default: True) Whether to fill the bars
  • hatch – (default: None) symbol to fill the bars with - one of “/”, “”, “|”, “-“, “+”, “x”, “o”, “O”, “.”, “*”, “” (or None)
  • hue – The color of the bars given as a hue. See hue for more information on the hue
  • label – A string label for each data list given
  • linewidth – (float) width of the lines defining the bars
  • linestyle – (default: ‘solid’) Style of the line. One of ‘solid’ or ‘-‘, ‘dashed’ or ‘–’, ‘dotted’ or ‘:’, ‘dashdot’ or ‘-.’
  • density – (boolean - default: False) If True, the result is the value of the probability density function at the bin, normalized such that the integral over the range is 1.
  • range – A list [min, max] which define the range of the histogram. Values outside of this range are treated as outliers and omitted from counts
  • rwidth – (float in [0,1], default: 1) The relative width of the bars as a fraction of the bin width
  • stacked – (boolean - default: False) If True, multiple data are stacked on top of each other
  • weights – (list) A sequence of weights the same length as the data list. If supplied, then each value contributes its associated weight to the bin count
  • zorder – (integer) the layer level at which to draw the histogram


The weights option works only with a single list. List of lists representing multiple data are not supported.


A very basic histogram for four data points:

sage: histogram([1,2,3,4], bins=2)
Graphics object consisting of 1 graphics primitive

We can see how the histogram compares to various distributions. Note the use of the density keyword to guarantee the plot looks like the probability density function:

sage: nv = normalvariate
sage: H = histogram([nv(0,1) for _ in range(1000)], bins=20, density=True, range=[-5,5])
sage: P = plot( 1/sqrt(2*pi)*e^(-x^2/2), (x,-5,5), color='red', linestyle='--')
sage: H+P
Graphics object consisting of 2 graphics primitives

There are many options one can use with histograms. Some of these control the presentation of the data, even if it is boring:

sage: histogram(list(range(100)), color=(1,0,0), label='mydata',              rwidth=.5, align="right")
Graphics object consisting of 1 graphics primitive

This includes many usual matplotlib styling options:

sage: T = RealDistribution('lognormal', [0,1])
sage: histogram( [T.get_random_element() for _ in range(100)], alpha=0.3,              edgecolor='red', fill=False, linestyle='dashed', hatch='O', linewidth=5)
Graphics object consisting of 1 graphics primitive
sage: histogram( [T.get_random_element() for _ in range(100)],linestyle='-.')
Graphics object consisting of 1 graphics primitive

We can do several data sets at once if desired:

sage: histogram([srange(0,1,.1)*10, [nv(0, 1) for _ in range(100)]], color=['red','green'], bins=5)
Graphics object consisting of 1 graphics primitive

We have the option of stacking the data sets too:

sage: histogram([ [1,1,1,1,2,2,2,3,3,3], [4,4,4,4,3,3,3,2,2,2] ], stacked=True, color=['blue', 'red'])
Graphics object consisting of 1 graphics primitive

It is possible to use weights with the histogram as well:

sage: histogram(list(range(10)), bins=3, weights=[1,2,3,4,5,5,4,3,2,1])
Graphics object consisting of 1 graphics primitive