interval arithmetic plotting

plot.py

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()

Just a quick warning about something that will create problems during the review. You are using camelCase naming conventions when most of sympy is following the pythonic conventions (checkout PEP8). For instance: CamelCase for names of classes, underlines for names of functions and variables.

Thanks. Will change it.