1444-User Defined Variables.sagews

User Defined Variables

f(xt): updating function associated with DTDS
x0: initial condition

f(xt) = sin(pi*xt/2)+xt
x0 = .5

#---------------------------- do not change ---------------------------------
s = []
s.append(x0)
stop = 0
i = 0
while stop == 0:
    s.append(f(s[i]))
    i = i+1
    if (abs(s[i] - s[i-1]).n(16) < .05):
        stop = 1
    if (i > 10):
        stop = 1

#Set up graph of function
P = plot(f,0, max(s)+.1)

# Set up graph of diagonal
P = P + plot(xt,0, max(s)+.1, color='black', linestyle = '--')

# Set up cobwebbing
P = P + line([(s[0],0),(s[0],s[1])], rgbcolor=(1,0,0), linestyle = '--')
P = P + point([(s[0],s[1])], rgbcolor=(1,0,0), pointsize=30)
P = P + line([(s[0],s[1]),(s[1],s[1])], rgbcolor=(1,0,0), linestyle = '--')
for i in range(1,len(s)-1):
    P = P + line([(s[i],s[i]),(s[i],s[i+1])], rgbcolor=(1,0,0), linestyle = '--')
    P = P + point([(s[i],s[i+1])], rgbcolor=(1,0,0), pointsize=30)
    P = P + line([(s[i],s[i+1]),(s[i+1],s[i+1])], rgbcolor=(1,0,0),  linestyle = '--', axes_labels=['$x_t$','$x_{t+1}$'])

# Graph it all
P.show(aspect_ratio=1 )