Created
May 14, 2012 17:02
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interval arithmetic plotting
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import sympy.mpmath as mp | |
from sympy import * | |
from sympy.utilities import lambdify | |
import matplotlib.pyplot as plt | |
import math | |
import fractions | |
import time | |
#supports the following functions. | |
MPI = {'sin': mp.iv.sin, | |
'cos': mp.iv.cos, | |
'exp': mp.iv.exp, | |
'log': mp.iv.log, | |
'sqrt': mp.iv.sqrt, | |
'log10': mp.iv.log10} | |
x,y = symbols('x y') | |
func = lambdify((x, y),(y > 1 / x),MPI) | |
def plotImplicit(func, left, right, top, bottom): | |
W = 1024 # No. of horizontal pixels | |
H = 1024 # No. of vertical pixels | |
k = fractions.gcd(W, H) | |
k = int(math.log(fractions.gcd(k, 2**int(math.log(k, 2))))) | |
IntervalList = [] | |
PlotList = [] | |
a = 0 | |
while a*2**k < W: | |
b = 0 | |
while b*2**k < H: | |
xInter = mp.mpi(left + a * 2**k * (right - left)/W, left + (a + 1) * 2**k * (right - left) / W) | |
yInter = mp.mpi(bottom + b * 2**k * (top - bottom) / H, bottom + (b + 1) * 2**k * (top - bottom) / H) | |
IntervalList.append([xInter,yInter]) | |
b += 1 | |
a += 1 | |
while k > 0 and len(IntervalList): | |
IntervalList, plot = refinePixels(func, IntervalList) | |
PlotList.extend(plot) | |
k = k - 1 | |
print k | |
ylist2 = [] | |
plt.figure() | |
plt.axis([left, right, bottom, top]) | |
PlotList.extend(IntervalList) | |
plots = PlotList[0] | |
xlist = [] | |
ylist = [] | |
for plots in PlotList: | |
s, t = plots[0]._mpi_ | |
s = mp.libmp.to_float(s) | |
t = mp.libmp.to_float(t) | |
u, v = plots[1]._mpi_ | |
u = mp.libmp.to_float(u) | |
v = mp.libmp.to_float(v) | |
xlist.extend([s, s, t, t, None]) | |
ylist.extend([u, v, v, u, None]) | |
plt.fill(xlist,ylist, facecolor = 'b', alpha = 0.3, edgecolor = 'None') | |
def refinePixels(func, IntervalList): | |
tempIntervalList = [] | |
plotList = [] | |
for intervalList in IntervalList: | |
if func(intervalList[0], intervalList[1]) == True: | |
plotList.append([intervalList[0], intervalList[1]]) | |
elif func(intervalList[0], intervalList[1]) == None: | |
#divide into 4 sub regions | |
s, t = intervalList[0]._mpi_ | |
s = mp.libmp.to_float(s) | |
t = mp.libmp.to_float(t) | |
u, v = intervalList[1]._mpi_ | |
u = mp.libmp.to_float(u) | |
v = mp.libmp.to_float(v) | |
avgx = (s + t) / 2.0 | |
avgy = (u + v) / 2.0 | |
#create intervals | |
a = mp.mpi(s, avgx) | |
b = mp.mpi(avgx, t) | |
c = mp.mpi(u, avgy) | |
d = mp.mpi(avgy, v) | |
tempIntervalList.append([a,c]) | |
tempIntervalList.append([a,d]) | |
tempIntervalList.append([b,c]) | |
tempIntervalList.append([b,d]) | |
return tempIntervalList, plotList | |
plotImplicit(func, -1.0, 1.0, 5.0, -5.0 ) | |
plt.show() |
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Thanks. Will change it.