from communs import util
def sec(x0, x1):
n = 0
f0 = util.f(x0)
f1 = util.f(x1)
x = 0.0
approximation = []
roots = []
while n < util.MAX:
print n
x = x1 - (x1 - x0) * f1 / (f1 - f0)
fx = util.f(x)
approximation.append(fx)
roots.append(x)
n += 1
if (fx == 0 or abs(x - x1) < util.EPSON):
return approximation, roots, range(1, n+3)
x0 = x1
x1 = x
f0 = util.f(x0)
f1 = util.f(x1)
return approximation, roots, range(1, n+3)
if __name__ == "__main__":
x0 = -10.0
x1 = 5.0
approx, roots, iteration = sec(x0, x1)
util.plotChart('Secante', approx, roots, iteration)
approximation = []
roots = []
while n < util.MAX:
fa = util.f(a)
fb = util.f(b)
if (fb - fa) == 0:
return approximation, roots, range(1, n + 3)
c = b - ((fb * (b - a)) / (fb - fa))
fc = util.f(c)
approximation.append(abs(fc))
roots.append(c)
n += 1
print c, fc
if abs(fc) <= util.EPSON or abs(b - a) <= util.EPSON:
return approximation, roots, range(1, n + 3)
if fa * fc > 0:
a = c
else:
b = c
return approximation, roots, range(1, n + 3)
if __name__ == "__main__":
a = -10.0
b = 5.0
approx, roots, iteration = fakePosition(a, b)
util.plotChart('fake_position', approx, roots, iteration)
#!/usr/bin/env python
# -*- coding: utf-8 -*-
from communs import util
def newtonRaphson(x0):
n = 0
x = x0
approximation = []
roots = []
while n < util.MAX:
xAux = x - util.f(x)/ util.f_(x)
fxAux = util.f(xAux)
approximation.append(abs(fxAux))
roots.append(xAux)
n += 1
if (fxAux == 0 or abs(x - xAux) < util.EPSON):
return approximation, roots, range(1, n+3)
x = xAux
return approximation, roots, range(1, n+3)
if __name__ == "__main__":
x0 = -10.0
approx, roots, iteration = newtonRaphson(x0)
print roots
util.plotChart('newton_raphson', approx, roots, iteration)
def bisection(a, b):
n = 0
approximation = []
roots = []
while n < util.MAX:
c = (a + b) / 2
fc = util.f(c)
fa = util.f(a)
approximation.append(abs(fc))
roots.append(c)
n += 1
if fc == 0 or abs(b - a) / 2 < util.EPSON:
return approximation, roots, range(1, n + 3)
if fa * fc > 0:
a = c
else:
b = c
return approximation, roots, range(1, n + 3)
if __name__ == "__main__":
a = -10.0
b = 5.0
approx, roots, iteration = bisection(a, b)
util.plotChart('Bisection', approx, roots, iteration)
b = interval[1]
for i in range(0, len(interval) - 2):
result += abs(a - b) / 2 * (util.f(a) + util.f(b))
a = b
b = interval[i + 2]
return result
if __name__ == "__main__":
a = -2.0
b = 1.0
i = 0
t = 20
d = abs(a - b)
values = []
for i in range(1, t):
interval = []
j = 0
while j <= i:
interval.append(j * d / i + a)
j += 1
values.append((i, trapezio(interval)))
iteration = [i[0] for i in values]
aprox = [i[1] for i in values]
util.plotChart('trapezio', aprox, [], iteration)
util.plotFuncChart('x^4 + 2x^3 - 13x^2 - 14x + 24', util.f, -6, 5)
med = (a + b) / 2.0
result += abs(a - b) / 3.0 * (util.f(a) + 4.0 * util.f(med) +
util.f(b))
a = b
b = interval[i + 2]
return result / 2
if __name__ == "__main__":
a = -2.0
b = 1.0
i = 0
t = 20.0
d = abs(a - b)
values = []
for i in range(1, 20):
j = 0
interval = []
while j <= i:
interval.append(j * d / i + a)
j += 1
values.append((i, integration(interval)))
iteration = [i[0] for i in values]
aprox = [i[1] for i in values]
util.plotChart('1_3_Simpson', aprox, [], iteration)