__file__ = "bisection.py"
__description__ = "This is a function that calculates the roots of a polinomial function using the bisection numerical method"
__version__ = "1.01"
__usage__ = "bisection(rf,a,b,n,t)"
__dependencies__ = "none"
__python_version__ = "3.3.4"
__author__ = "JJ.Cadavid - SFTC - EAFIT University"
__date__ = "24/08/2014"

#required modules
%matplotlib inline
import parser
import matplotlib
from sys import exit as error


def bisection(rf,a,b,n,t):
    """Numerical method that finds roots of first grade polynomials"""
    f=parser.expr(rf).compile() #Parse string function into operable code by replacing x string with a number
    x=a;
    fa=eval(f); #f(a) interval eval
    x=b;
    fb=eval(f); #f(b) interval eval
    if ((fa*fb)>0): #Both images must cross the x-axis, a way to check is with sign
        sys.exit('[a,b] Interval does not cross the x-axis');
    fp=10;
    i=0;
    while (abs(fp)>t):
        x=a+(b-a)/2;    #Aproximation Calculation - changes every iteration
        fp=eval(f);
        print("f(p)={}".format(fp));
        if(fa*fp)>0:
            a=x;
        else:
            b=x;
        if(i>n):
            print("p={}".format(x));
            error('Tolerance not met by set iterations');
        i=i+1
    print("p={}".format(x));
    return(x);

function = "6.1*x + 23.64";
a = -5.0;
b = 0.0;
n = 10.0;
t = 0.05;
root = bisection(function, a, b, n, t);
print(root);

import matplotlib.pyplot as plt
from numpy import linspace

function=lambda x:6.1*x+23.64; # Function of obtained root
x = linspace(a, b, 100); # x domain values defined by [a,b] interval
y=function(x); 
font = {'family' : 'serif','color'  : 'darkred', 'weight' : 'normal', 'size'   : 16} # font used in axes legend
plt.plot(x,y);
plt.axis('auto') # according to list data, axes are adjust in the plot
plt.title('First order polynomial root', fontdict=font); 
plt.text(-3, 12, r'$6.1x+23.64$', fontdict=font);
plt.text(root, 0, r'$\circ$ Root', fontdict=font);
plt.xlabel('x position [a.u]', fontdict=font);
plt.ylabel('y position [a.u]', fontdict=font);
plt.grid();
plt.show();

x = 0.64; # Asumiendo que la variable de la expresión es x.

function_1 = ('1.2*x**3-0.6-x*2+0.85*x-78.9'); # Entrada de función polinómica tipo string
function_1P = parser.expr(function_1).compile();
print("Parser evaluated -> {}".format(eval(function_1P)));

function_2 = lambda x: 1.2*x**3-0.6-x*2+0.85*x-78.9; # Entrada de función polinómica como objeto matemático
function_2P= function_2(x);
print("Lambda evaluated -> {}".format(function_2P));

from numpy import arange
AR=arange(0.0,11.0,1);
print(AR);
LN=linspace(0.0,10.0,11);
print(LN);
plt.plot(AR,LN,'ro')
plt.show()

# Cambiar el formato del documento
from IPython.core.display import HTML
def css_styling():
    styles = open('../styles/custom_ketch.css', 'r').read()
    return HTML(styles)
css_styling()