Streamline Plots¶

class
sage.plot.streamline_plot.
StreamlinePlot
(xpos_array, ypos_array, xvec_array, yvec_array, options)¶ Bases:
sage.plot.primitive.GraphicPrimitive
Primitive class that initializes the StreamlinePlot graphics type

get_minmax_data
()¶ Returns a dictionary with the bounding box data.
EXAMPLES:
sage: x, y = var('x y') sage: d = streamline_plot((.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.streamline_plot.
streamline_plot
(f_g, xrange, yrange, frame=True, plot_points=20, density=1.0, **options)¶ Return a streamline plot in a vector field.
streamline_plot
can take either one or two functions. Consider two variables \(x\) and \(y\).If given two functions \((f(x,y), g(x,y))\), then this function plots streamlines in the vector field over the specified ranges with
xrange
being of \(x\), denoted byxvar
below, betweenxmin
andxmax
, andyrange
similarly (see below).streamline_plot((f, g), (xvar, xmin, xmax), (yvar, ymin, ymax))
Similarly, if given one function \(f(x, y)\), then this function plots streamlines in the slope field \(dy/dx = f(x,y)\) over the specified ranges as given above.
PLOT OPTIONS:
plot_points
– (default: 200) the minimal number of plot pointsdensity
– float (default: 1.); controls the closeness of streamlinesstart_points
– (optional) list of coordinates of starting points for the streamlines; coordinate pairs can be tuples or lists
EXAMPLES:
Plot some vector fields involving \(\sin\) and \(\cos\):
sage: x, y = var('x y') sage: streamline_plot((sin(x), cos(y)), (x,3,3), (y,3,3)) Graphics object consisting of 1 graphics primitive
sage: streamline_plot((y, (cos(x)2) * sin(x)), (x,pi,pi), (y,pi,pi)) Graphics object consisting of 1 graphics primitive
We increase the density of the plot:
sage: streamline_plot((y, (cos(x)2) * sin(x)), (x,pi,pi), (y,pi,pi), density=2) Graphics object consisting of 1 graphics primitive
We ignore function values that are infinite or NaN:
sage: x, y = var('x y') sage: streamline_plot((x/sqrt(x^2+y^2), y/sqrt(x^2+y^2)), (x,10,10), (y,10,10)) Graphics object consisting of 1 graphics primitive
Extra options will get passed on to
show()
, as long as they are valid:sage: streamline_plot((x, y), (x,2,2), (y,2,2), xmax=10) Graphics object consisting of 1 graphics primitive sage: streamline_plot((x, y), (x,2,2), (y,2,2)).show(xmax=10) # These are equivalent
We can also construct streamlines in a slope field:
sage: x, y = var('x y') sage: streamline_plot((x + y) / sqrt(x^2 + y^2), (x,3,3), (y,3,3)) Graphics object consisting of 1 graphics primitive
We choose some particular points the streamlines pass through:
sage: pts = [[1, 1], [2, 2], [1, 3/2]] sage: g = streamline_plot((x + y) / sqrt(x^2 + y^2), (x,3,3), (y,3,3), start_points=pts) sage: g += point(pts, color='red') sage: g Graphics object consisting of 2 graphics primitives
Note
Streamlines currently pass close to
start_points
but do not necessarily pass directly through them. That is part of the behavior of matplotlib, not an error on your part.