Density plots

class sage.plot.density_plot.DensityPlot(xy_data_array, xrange, yrange, options)[source]

Bases: GraphicPrimitive

Primitive class for the density plot graphics type. See density_plot? for help actually doing density plots.

INPUT:

  • xy_data_array – list of lists giving evaluated values of the function on the grid

  • xrange – tuple of 2 floats indicating range for horizontal direction

  • yrange – tuple of 2 floats indicating range for vertical direction

  • options – dictionary of valid plot options to pass to constructor

EXAMPLES:

Note this should normally be used indirectly via density_plot:

sage: from sage.plot.density_plot import DensityPlot
sage: D = DensityPlot([[1,3],[2,4]], (1,2), (2,3),options={})
sage: D
DensityPlot defined by a 2 x 2 data grid
sage: D.yrange
(2, 3)
sage: D.options()
{}

>>> from sage.all import *
>>> from sage.plot.density_plot import DensityPlot
>>> D = DensityPlot([[Integer(1),Integer(3)],[Integer(2),Integer(4)]], (Integer(1),Integer(2)), (Integer(2),Integer(3)),options={})
>>> D
DensityPlot defined by a 2 x 2 data grid
>>> D.yrange
(2, 3)
>>> D.options()
{}

from sage.plot.density_plot import DensityPlot
D = DensityPlot([[1,3],[2,4]], (1,2), (2,3),options={})
D
D.yrange
D.options()
get_minmax_data()[source]

Return a dictionary with the bounding box data.

EXAMPLES:

sage: x,y = var('x,y')
sage: f(x, y) = x^2 + y^2
sage: d = density_plot(f, (3,6), (3,6))[0].get_minmax_data()
sage: d['xmin']
3.0
sage: d['ymin']
3.0

>>> from sage.all import *
>>> x,y = var('x,y')
>>> __tmp__=var("x,y"); f = symbolic_expression(x**Integer(2) + y**Integer(2)).function(x,y)
>>> d = density_plot(f, (Integer(3),Integer(6)), (Integer(3),Integer(6)))[Integer(0)].get_minmax_data()
>>> d['xmin']
3.0
>>> d['ymin']
3.0

x,y = var('x,y')
f(x, y) = x^2 + y^2
d = density_plot(f, (3,6), (3,6))[0].get_minmax_data()
d['xmin']
d['ymin']
sage.plot.density_plot.density_plot(f, xrange, yrange, plot_points=25, cmap='gray', interpolation='catrom', **options)[source]

density_plot takes a function of two variables, \(f(x,y)\) and plots the height of the function over the specified xrange and yrange as demonstrated below.

density_plot(f, (xmin,xmax), (ymin,ymax), ...)

INPUT:

  • f – a function of two variables

  • (xmin, xmax) – 2-tuple, the range of x values OR 3-tuple (x,xmin,xmax)

  • (ymin, ymax) – 2-tuple, the range of y values OR 3-tuple (y,ymin,ymax)

The following inputs must all be passed in as named parameters:

  • plot_points – integer (default: 25); number of points to plot in each direction of the grid

  • cmap – a colormap (default: 'gray'), the name of a predefined colormap, a list of colors or an instance of a matplotlib Colormap. Type: import matplotlib.cm; matplotlib.cm.datad.keys() for available colormap names.

  • interpolation – string (default: 'catrom'); the interpolation method to use: 'bilinear', 'bicubic', 'spline16', 'spline36', 'quadric', 'gaussian', 'sinc', 'bessel', 'mitchell', 'lanczos', 'catrom', 'hermite', 'hanning', 'hamming', 'kaiser'

EXAMPLES:

Here we plot a simple function of two variables. Note that since the input function is an expression, we need to explicitly declare the variables in 3-tuples for the range:

sage: x,y = var('x,y')
sage: density_plot(sin(x) * sin(y), (x,-2,2), (y,-2,2))
Graphics object consisting of 1 graphics primitive

>>> from sage.all import *
>>> x,y = var('x,y')
>>> density_plot(sin(x) * sin(y), (x,-Integer(2),Integer(2)), (y,-Integer(2),Integer(2)))
Graphics object consisting of 1 graphics primitive

x,y = var('x,y')
density_plot(sin(x) * sin(y), (x,-2,2), (y,-2,2))
../../_images/density_plot-1.svg

Here we change the ranges and add some options; note that here f is callable (has variables declared), so we can use 2-tuple ranges:

sage: x,y = var('x,y')
sage: f(x,y) = x^2 * cos(x*y)
sage: density_plot(f, (x,-10,5), (y,-5,5), interpolation='sinc', plot_points=100)
Graphics object consisting of 1 graphics primitive

>>> from sage.all import *
>>> x,y = var('x,y')
>>> __tmp__=var("x,y"); f = symbolic_expression(x**Integer(2) * cos(x*y)).function(x,y)
>>> density_plot(f, (x,-Integer(10),Integer(5)), (y,-Integer(5),Integer(5)), interpolation='sinc', plot_points=Integer(100))
Graphics object consisting of 1 graphics primitive

x,y = var('x,y')
f(x,y) = x^2 * cos(x*y)
density_plot(f, (x,-10,5), (y,-5,5), interpolation='sinc', plot_points=100)
../../_images/density_plot-2.svg

An even more complicated plot:

sage: x,y = var('x,y')
sage: density_plot(sin(x^2+y^2) * cos(x) * sin(y), (x,-4,4), (y,-4,4), cmap='jet', plot_points=100)
Graphics object consisting of 1 graphics primitive

>>> from sage.all import *
>>> x,y = var('x,y')
>>> density_plot(sin(x**Integer(2)+y**Integer(2)) * cos(x) * sin(y), (x,-Integer(4),Integer(4)), (y,-Integer(4),Integer(4)), cmap='jet', plot_points=Integer(100))
Graphics object consisting of 1 graphics primitive

x,y = var('x,y')
density_plot(sin(x^2+y^2) * cos(x) * sin(y), (x,-4,4), (y,-4,4), cmap='jet', plot_points=100)
../../_images/density_plot-3.svg

This should show a “spotlight” right on the origin:

sage: x,y = var('x,y')
sage: density_plot(1/(x^10 + y^10), (x,-10,10), (y,-10,10))
Graphics object consisting of 1 graphics primitive

>>> from sage.all import *
>>> x,y = var('x,y')
>>> density_plot(Integer(1)/(x**Integer(10) + y**Integer(10)), (x,-Integer(10),Integer(10)), (y,-Integer(10),Integer(10)))
Graphics object consisting of 1 graphics primitive

x,y = var('x,y')
density_plot(1/(x^10 + y^10), (x,-10,10), (y,-10,10))
../../_images/density_plot-4.svg

Some elliptic curves, but with symbolic endpoints. In the first example, the plot is rotated 90 degrees because we switch the variables \(x\), \(y\):

sage: density_plot(y^2 + 1 - x^3 - x, (y,-pi,pi), (x,-pi,pi))
Graphics object consisting of 1 graphics primitive

>>> from sage.all import *
>>> density_plot(y**Integer(2) + Integer(1) - x**Integer(3) - x, (y,-pi,pi), (x,-pi,pi))
Graphics object consisting of 1 graphics primitive

density_plot(y^2 + 1 - x^3 - x, (y,-pi,pi), (x,-pi,pi))
../../_images/density_plot-5.svg 
sage: density_plot(y^2 + 1 - x^3 - x, (x,-pi,pi), (y,-pi,pi))
Graphics object consisting of 1 graphics primitive

>>> from sage.all import *
>>> density_plot(y**Integer(2) + Integer(1) - x**Integer(3) - x, (x,-pi,pi), (y,-pi,pi))
Graphics object consisting of 1 graphics primitive

density_plot(y^2 + 1 - x^3 - x, (x,-pi,pi), (y,-pi,pi))
../../_images/density_plot-6.svg

Extra options will get passed on to show(), as long as they are valid:

sage: density_plot(log(x) + log(y), (x,1,10), (y,1,10), aspect_ratio=1)
Graphics object consisting of 1 graphics primitive

>>> from sage.all import *
>>> density_plot(log(x) + log(y), (x,Integer(1),Integer(10)), (y,Integer(1),Integer(10)), aspect_ratio=Integer(1))
Graphics object consisting of 1 graphics primitive

density_plot(log(x) + log(y), (x,1,10), (y,1,10), aspect_ratio=1)
../../_images/density_plot-7.svg 
sage: density_plot(log(x) + log(y), (x,1,10), (y,1,10)).show(aspect_ratio=1) # These are equivalent

>>> from sage.all import *
>>> density_plot(log(x) + log(y), (x,Integer(1),Integer(10)), (y,Integer(1),Integer(10))).show(aspect_ratio=Integer(1)) # These are equivalent

density_plot(log(x) + log(y), (x,1,10), (y,1,10)).show(aspect_ratio=1) # These are equivalent