# -*- coding: utf-8 -*-
"""
Created on Thu Apr 26 10:32:50 2018

@author: Thomas
"""

from scipy import *
from pylab import *
import sys
import numpy as np
import math
import matplotlib.pyplot as plt

class Interval:
    def __init__(self,a,*args):
        if args:
            self.a = float(a)
            self.b = float(args[0]) #If statement to make an interval from one real number
            #print(float(args[0]))
        else:
            self.a = float(a)
            self.b = float(a)

    def __repr__(self):
        return '[%g,%g]' % (self.a,self.b) #First two functions in this class for Task 1

    def __add__(self,other):
        if isinstance(other, (int,float)): #If statement for task 8
            other = Interval(other,other)
            a1 = self.a + other.a
            a2 = self.b + other.b
        else:
            a1 = self.a + other.a #Basically task 2
            a2 = self.b + other.b
        return Interval(a1, a2)

    def __radd__(self,other):
        if isinstance(other, (int,float)): #Resverse add
            other = Interval(other,other)
        return other + self

    def __sub__(self,other):
        if isinstance(other, (int,float)):
            other = Interval(other,other)
            s1 = self.a - other.b
            s2 = self.b - other.a
        else:
            s1 = self.a - other.b
            s2 = self.b - other.a
        return Interval(s1, s2)

    def __rsub__(self,other):
        if isinstance(other, (int,float)):
            other = Interval(other,other)
        return other - self

    def __mul__(self,other):
        if isinstance(other, (int,float)):
            other = Interval(other,other)
            m1 = min(self.a*other.a,self.a*other.b,self.b*other.a,self.b*other.b)
            m2 = max(self.a*other.a,self.a*other.b,self.b*other.a,self.b*other.b)
        else:
            m1 = min(self.a*other.a,self.a*other.b,self.b*other.a,self.b*other.b)
            m2 = max(self.a*other.a,self.a*other.b,self.b*other.a,self.b*other.b)
        return Interval(m1, m2)

    def __rmul__(self,other):
        if isinstance(other, (int,float)):
            other = Interval(other,other)
        return other * self

    def __pow__(self,other):
        if other % 2 == 0:
            if self.a < 0:
                p1 = 0
                p2 = max(self.b ** other, self.a ** other)
            elif self.b < 0:
                p1 = self.b ** other
                p2 = self.a ** other
            elif self.a > 0:
                p1 = self.a ** other
                p2 = self.b ** other
            else:
                p1 = self.a ** other
                p2 = self.b ** other
        else:
            p1 = self.a ** other
            p2 = self.b ** other
        return Interval(p1,p2)

    def divide(self,other):
        if other.a == 0:
            print("cannot divide by zero")
            p1 = 0
            p2 = 0
        else:
            if other.b == 0:
                print("cannot divide by zero")
                p1 = 0
                p2 = 0
            else:
                if other.a > 1000:
                    print("too large value")
                    p1 = 0
                    p2 = 0
                else:
                    if other.b > 1000:
                        print("too large value")
                        p1 = 0
                        p2 = 0
                    else:
                        p1 = min(self.a/other.a,self.a/other.b,self.b/other.a,self.b/other.b)
                        p2 = max(self.a/other.a,self.a/other.b,self.b/other.a,self.b/other.b)
        return p1, p2

    def __contains__(self,realnumber):
        if max(realnumber,self.b) == self.b:
            if min(realnumber,self.a) == self.a:
                print("contains")
            else:
                print("outside")
        else:
            print("outside")

#q = Interval(1,4)
#p = Interval(-2,-1)
#print(q.__add__(p))
#x = Interval(-2,2)
#print(x**2)


#Task 10 Thomas version
"""
xl = np.linspace(0.,1,1000)
xu = np.linspace(0.,1,1000) + 0.5

Ilist = []
yl = []
yu = []

for n in range(0,1000):
    Ilist.append((3*(Interval(xl[n],xu[n]))**3 ) - (2*(Interval(xl[n],xu[n]))**2) - (5*(Interval(xl[n],xu[n]))) - 1)
    yl.append(Ilist[n].a)
    yu.append(Ilist[n].b)

plt.plot(xl,yl)
plt.plot(xl,yu)
"""

#Task 10 Better
def p(I):
    return 3*I**3 - 2*I**2 - 5*I -1

xl = np.linspace(0.,1,1000)
xu = xl+0.5
y=[p(Interval(xl[i], xu[i])) for i in range (len(xl))]
yl=[y[i].a for i in range(len(y))]
yu=[y[i].b for i in range(len(y))]
plt.plot(xl,yl)
plt.plot(xl,yu)