jupytersketcher/examples/mesh_function.py

from pysketcher import *

"""
u = SketchyFunc2('$u(t)$', name_pos='end')
n = 7
t_mesh = [i*2.25/(n-1) for i in range(n)]

u = SketchyFunc2('$u(t)$', name_pos='end')
t_mesh = [0, 2, 4, 6, 8]
"""

u = SketchyFunc3()
Nt = 5
t_mesh = linspace(0, 6, Nt+1)

# Add 20% space to the left and 30% to the right of the coordinate system
t_axis_extent = t_mesh[-1] - t_mesh[0]
t_min = t_mesh[0] - 0.2*t_axis_extent
t_max = t_mesh[-1] + 0.3*t_axis_extent
u_max = 1.3*max([u(t) for t in t_mesh])
u_min = -0.2*u_max

drawing_tool.set_coordinate_system(t_min, t_max, u_min, u_max, axis=False)
drawing_tool.set_linecolor('black')

r = 0.005*(t_max-t_min)     # radius of circles placed at mesh points
#import random; random.seed(12)
perturbations = [0, 0.1, 0.1, 0.2, -0.4, -0.1]
u_points = {}
u_values = []
for i, t in enumerate(t_mesh):
    u_value = u(t) + perturbations[i]
    u_values.append(u_value)
    u_points[i] = Composition(dict(
        circle=Circle(point(t, u_value), r).set_filled_curves('black'),
        u_point=Text('$u^%d$' % i,
                     point(t, u_value) + (point(0,3*r)
                                          if i > 0 else point(-3*r,0)))))
u_discrete = Composition(u_points)

interpolant = Composition({
    i: Line(point(t_mesh[i-1], u_values[i-1]),
            point(t_mesh[i], u_values[i])).set_linewidth(1)
    for i in range(1, len(t_mesh))})

axes = Composition(dict(
    x=Axis(point(0,0), t_mesh[-1] + 0.2*t_axis_extent, '$t$',
           label_spacing=(1/45.,-1/30.)),
    y=Axis(point(0,0), 0.8*u_max, '$u$',
           rotation_angle=90)))

h = 0.03*u_max  # tickmarks height
nodes = Composition({i: Composition(dict(
    node=Line(point(t,h), point(t,-h)),
    name=Text('$t_%d$' % i, point(t,-3.5*h))))
                     for i, t in enumerate(t_mesh)})
illustration = Composition(dict(u=u_discrete,
                                mesh=nodes,
                                axes=axes)).set_name('fdm_u')
drawing_tool.erase()
# Draw t_mesh with discrete u points
illustration.draw()
drawing_tool.display()
drawing_tool.savefig(illustration.get_name())

# Add exact u line (u is a Spline Shape that applies 500 intervals by default
# for drawing the curve)
exact = u.set_linestyle('dashed').set_linewidth(1)
exact.draw()
drawing_tool.display()
drawing_tool.savefig('%s_ue' % illustration.get_name())

# Add linear interpolant
interpolant.draw()
drawing_tool.display()
drawing_tool.savefig('%s_uei' % illustration.get_name())

# Linear interpolant without exact, smooth line
drawing_tool.erase()
illustration.draw()
interpolant.draw()
drawing_tool.display()
drawing_tool.savefig('%s_ui' % illustration.get_name())

input()