Problema 1 - Proyecto 1 - Métodos numéricos - Ciclo 2 2012 - UVG: Definición de los 2 métodos cerrados y los 2 abiertos, y código driver para resolución del problema planteado

P1.py

# -*- coding: utf-8 -*-
"""
Created on Wed Jul 18 15:56:11 2012

@author: hectorh30
"""

def punto_fijo(f,g,x_init,max_error=0.01,max_iterations=100):
    """
    INPUT
    - Functions f and g: functions required by the method
    - Float x: initial estimation
    - Float max_error, max_iterations: self-explanatory 

    OUTPUT
    A tuple of (final_result,iteration_number,final_relative_porcentual_error)    
    """
    
    error = max_error + 1.0
    i = 0
    x0 = x_init
    x1 = x0
    while (error > max_error and i < max_iterations):
        x1 = g(x0)
        error = abs(((x1 - x0)/x1)*100)
        x0 = x1
        i += 1

    return x1,i,error
    
    
def newton_raphson(f,f1,max_error=0.01,max_iterations=100):
    """
    INPUT
    - Functions f and g: functions required by the method
    - Float x: initial estimation
    - Float max_error, max_iterations: self-explanatory 

    OUTPUT
    A tuple of (final_result,iteration_number,final_relative_porcentual_error)    
    """
    error = max_error + 1.0
    i = 0
    x0 = x_init
    x1 = x0
    
    while (error > max_error and i < max_iterations):
        x1 = x0 - (f(x0)/f1(x0))
        error = abs(((x1 - x0)/x1)*100)
        x0 = x1
        i += 1
    
    return x1,i,error
    
def biseccion(f,lower_x,upper_x,max_error=0.01,max_iterations=100):
    """
    INPUT
    - Function f: function required by the method
    - Float lower_x,upper_x: boundaries of the initial interval
    - Float max_error, max_iterations: self-explanatory 

    OUTPUT
    A tuple of (final_result,iteration_number,final_relative_porcentual_error)    
    """
    error = max_error + 1.0
    i = 0
    left_x = lower_x
    right_x = upper_x
    continue_flag = True
        
    if (f(left_x)*f(right_x) < 0):
        x0 = left_x
        while (error > max_error and i < max_iterations and continue_flag):
            xr = (left_x + right_x)/2
            
            if (f(left_x)*f(xr) < 0):
                right_x = xr
            elif (f(left_x)*f(xr) > 0):
                left_x = xr
            else:
                continue_flag = False
                
            error = abs(((xr - x0)/xr)*100)
            i += 1
            x0 = xr
            
        return xr,i,error
    else:
        return lower_x,-1.0,-1.0
    
    
    
    
def falsa_posicion(f,lower_x,upper_x,max_error=0.01,max_iterations=100):
    """
    INPUT
    - Function f: function required by the method
    - Float lower_x,upper_x: boundaries of the initial interval
    - Float max_error, max_iterations: self-explanatory 

    OUTPUT
    A tuple of (final_result,iteration_number,final_relative_porcentual_error)    
    """
    error = max_error + 1.0
    i = 0
    left_x = lower_x
    right_x = upper_x
    continue_flag = True
        
    if (f(left_x)*f(right_x) < 0):
        x0 = left_x
        while (error > max_error and i < max_iterations and continue_flag):
            xr = right_x - (f(right_x)*(left_x - right_x))/(f(left_x)-f(right_x))    
            
            if (f(left_x)*f(xr) < 0):
                right_x = xr
            elif (f(left_x)*f(xr) > 0):
                left_x = xr
            else:
                continue_flag = False
                
            error = abs(((xr - x0)/xr)*100)
            i += 1
            x0 = xr
            
        return xr,i,error
    else:
        return lower_x,-1.0,-1.0
    
    
    
    
    
"""
Driver para métodos abiertos
"""
print ''
print '-------------------------'
print ' -- Métodos abiertos'
print '-------------------------'
print ''
x_init = float(raw_input("Ingrese una estimación inicial: "))
max_error = float(raw_input("Ingrese el porcentaje de error deseado: "))
max_iteraciones = int(raw_input("Ingrese el numero máximo de iteraciones: "))

"""
Método del punto fijo
"""
print '-------------------------'
print ' -- Metodo de punto fijo'
print '-------------------------'

def f(x):
    return -20.0 + 10.0/(1.0+x) + 10/((1.0+x)**2) + 10/((1.0+x)**3)

def g(x):
    return (-1.0/2.0) + 1.0/(2.0+2.0*x) + 1.0/(2*(1+x)**2)

x1_pf,i_pf,error_pf = punto_fijo(f,g,x_init,max_error,max_iteraciones)

print 'Cantidad de iteraciones: ',i_pf
print 'Resultado final: ',x1_pf
print 'Error final: ',error_pf

"""
Método de Newton-Raphson
"""
print '-------------------------'
print ' -- Metodo de Newton-Raphson'
print '-------------------------'

def f(x):
    return -20.0 + 10.0/(1.0+x) + 10/((1.0+x)**2) + 10/((1.0+x)**3)
    
def f1(x):
    return -10.0/((1.0+x)**2)-20.0/((1.0+x)**3)-30.0/((1.0+x)**4)

x1_nr,i_nr,error_nr = punto_fijo(f,g,x_init,max_error,max_iteraciones)

print 'Cantidad de iteraciones: ',i_nr
print 'Resultado final: ',x1_nr
print 'Error final: ',error_nr





"""
Driver para métodos cerrados
"""

print ''
print '-------------------------'
print ' -- Métodos cerrados'
print '-------------------------'
print ''

left_x_init = float(raw_input("Ingrese un x menor que la raíz: "))
right_x_init = float(raw_input("Ingrese un x mayor que la raíz: "))
max_error = float(raw_input("Ingrese el porcentaje de error deseado: "))
max_iteraciones = int(raw_input("Ingrese el numero máximo de iteraciones: "))

"""
Método de bisección
"""

print '-------------------------'
print ' -- Método de bisección'
print '-------------------------'

def f(x):
    return -20.0 + 10.0/(1.0+x) + 10/((1.0+x)**2) + 10/((1.0+x)**3)

x1_b,i_b,error_b = biseccion(f,left_x_init,right_x_init,max_error,max_iteraciones)

if i_b < 0:
    print "El intervalo no define un cambio de signo explícito"
else:
    print 'Cantidad de iteraciones: ',i_b
    print 'Resultado final: ',x1_b
    print 'Error final: ',error_b
    
    
"""
Método de falsa posición
"""

print '-------------------------'
print ' -- Método de falsa posición'
print '-------------------------'

def f(x):
    return -20.0 + 10.0/(1.0+x) + 10/((1.0+x)**2) + 10/((1.0+x)**3)
    
x1_fp,i_fp,error_fp = falsa_posicion(f,left_x_init,right_x_init,max_error,max_iteraciones)

if i_b < 0:
    print "El intervalo no define un cambio de signo explícito"
else:
    print 'Cantidad de iteraciones: ',i_fp
    print 'Resultado final: ',x1_fp
    print 'Error final: ',error_fp