Plotting fields

class sage.plot.plot_field.PlotField(xpos_array, ypos_array, xvec_array, yvec_array, options)

Bases: sage.plot.primitive.GraphicPrimitive

Primitive class that initializes the PlotField graphics type

get_minmax_data()

Returns a dictionary with the bounding box data.

EXAMPLES:

sage: x,y = var('x,y')
sage: d = plot_vector_field((.01*x,x+y), (x,10,20), (y,10,20))[0].get_minmax_data()
sage: d['xmin']
10.0
sage: d['ymin']
10.0

sage.plot.plot_field.plot_slope_field(f, xrange, yrange, **kwds)

plot_slope_field takes a function of two variables xvar and yvar (for instance, if the variables are and , take ), and at representative points between xmin, xmax, and ymin, ymax respectively, plots a line with slope (see below).

plot_slope_field(f, (xvar, xmin, xmax), (yvar, ymin, ymax))

EXAMPLES:

A logistic function modeling population growth:

sage: x,y = var('x y')
sage: capacity = 3 # thousand
sage: growth_rate = 0.7 # population increases by 70% per unit of time
sage: plot_slope_field(growth_rate*(1-y/capacity)*y, (x,0,5), (y,0,capacity*2)).show(aspect_ratio=1)

Plot a slope field involving sin and cos:

sage: x,y = var('x y')
sage: plot_slope_field(sin(x+y)+cos(x+y), (x,-3,3), (y,-3,3)).show(aspect_ratio=1)

sage.plot.plot_field.plot_vector_field(*args, **kwds)

plot_vector_field takes two functions of two variables xvar and yvar (for instance, if the variables are and , take ) and plots vector arrows of the function over the specified ranges, with xrange being of xvar between xmin and xmax, and yrange similarly (see below).

plot_vector_field((f, g), (xvar, xmin, xmax), (yvar, ymin, ymax))

EXAMPLES:

Plot some vector fields involving sin and cos:

sage: x,y = var('x y')
sage: plot_vector_field((sin(x), cos(y)), (x,-3,3), (y,-3,3))
sage: plot_vector_field(( y, (cos(x)-2)*sin(x)), (x,-pi,pi), (y,-pi,pi))

Plot a gradient field:

sage: u,v = var('u v')
sage: f = exp(-(u^2+v^2))
sage: plot_vector_field(f.gradient(), (u,-2,2), (v,-2,2), color='blue')

Plot two orthogonal vector fields:

sage: x,y = var('x,y')
sage: a=plot_vector_field((x,y), (x,-3,3),(y,-3,3),color='blue')
sage: b=plot_vector_field((y,-x),(x,-3,3),(y,-3,3),color='red')
sage: show(a+b,aspect_ratio=1)

We ignore function values that are infinite or NaN:

sage: x,y = var('x,y')
sage: plot_vector_field( (-x/sqrt(x^2+y^2), -y/sqrt(x^2+y^2)), (x, -10, 10), (y, -10, 10))
sage: plot_vector_field( (-x/sqrt(x+y), -y/sqrt(x+y)), (x, -10, 10), (y, -10, 10))

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

sage: plot_vector_field((x, y), (x, -2, 2), (y, -2, 2), xmax=10)
sage: plot_vector_field((x, y), (x, -2, 2), (y, -2, 2)).show(xmax=10) # These are equivalent