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numerical_methods.py
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from sympy import *
from sympy.parsing.sympy_parser import parse_expr
from numpy import *
def bisection(xl, xu, f, es, imax):
res_ar = []
xr = 0
ea = 1
i = 0
if f(xl) * f(xu) > 0:
# print("Incorrect bracket")
return
else:
# print(f"i\txl\txu\txr\tf(xl)\t\tf(xr)\tea")
for i in range(imax):
temp_ar = []
if i > 0:
xr_prev = xr
xr = (xl + xu) / 2
temp_ar.append(i + 1)
temp_ar.append(round(xl, 5))
temp_ar.append(round(f(xl), 5))
temp_ar.append(round(xu, 5))
temp_ar.append(round(f(xu), 5))
temp_ar.append(round(xr, 5))
temp_ar.append(round(f(xr), 5))
if f(xl) * f(xr) == 0:
break
elif f(xl) * f(xr) < 0:
xu = xr
else:
xl = xr
if i > 0:
ea = abs((xr - xr_prev) / xr)
temp_ar.append(round(ea, 5))
# print(f"{i}\t{xl}\t{xu}\t{xr}\t{f(xl)}\t{f(xr)}\t{ea}")
if ea < es:
break
else:
temp_ar.append("")
res_ar.append(temp_ar)
temp_ar = [i + 1, round(xl, 5), round(f(xl), 5), round(xu, 5), round(f(xu), 5), round(xr, 5), round(f(xr), 5),
round(ea, 5)]
res_ar.append(temp_ar)
return res_ar
def false_position(xl, xu, f, es, imax):
xr = 0
res_ar = []
if f(xl) * f(xu) > 0:
# print("Incorrect bracket")
return
else:
# print(f"i\txl\txu\txr\tf(xl)\t\tf(xr)\tea")
for i in range(imax):
temp_ar = []
if i > 0:
xr_prev = xr
xr = (xl * f(xu) - xu * f(xl)) / (f(xu) - f(xl))
temp_ar.append(i + 1)
temp_ar.append(round(xl, 5))
temp_ar.append(round(f(xl), 5))
temp_ar.append(round(xu, 5))
temp_ar.append(round(f(xu), 5))
temp_ar.append(round(xr, 5))
temp_ar.append(round(f(xr), 5))
if f(xr) == 0:
break
elif f(xr) < 0:
xl = xr
else:
xu = xr
if i > 0:
ea = abs((xr - xr_prev) / xr)
temp_ar.append(round(ea, 5))
# print(f"{i}\t{xl}\t{xu}\t{xr}\t{f(xl)}\t{f(xr)}\t{ea}")
if ea < es:
break
else:
temp_ar.append("")
res_ar.append(temp_ar)
temp_ar = [i + 1, round(xl, 5), round(f(xl), 5), round(xu, 5), round(f(xu), 5), round(xr, 5), round(f(xr), 5),
round(ea, 5)]
res_ar.append(temp_ar)
return res_ar
def fixed_point(x, g, es, imax):
res_ar = []
xr = x
for i in range(imax):
temp_ar = []
xr_old = xr
xr = g(xr_old)
temp_ar.append(i + 1)
temp_ar.append(round(xr_old, 5))
temp_ar.append(round(xr, 5))
if xr != 0:
ea = abs((xr - xr_old) / xr)
temp_ar.append(round(ea, 5))
if ea < es:
break
res_ar.append(temp_ar)
temp_ar = [i + 1, round(xr_old, 5), round(xr, 5), round(ea, 5)]
res_ar.append(temp_ar)
return res_ar
def newton_raphson(x_0, eq, es, imax):
res_ar = []
x = Symbol('x')
f = lambda x: eval(eq)
y = parse_expr(eq)
yprime = y.diff(x)
xr = x_0
for i in range(imax):
temp_ar = []
ea = 1
xr_old = xr
temp_ar.append(i + 1)
temp_ar.append(round(xr_old, 5))
# temp_ar.append(round(f(xr_old), 3))
if float(yprime.subs(x, xr)) != 0:
xr = xr - (f(xr) / float(yprime.subs(x, xr)))
# temp_ar.append(round(float(yprime.subs(x, xr_old)), 3))
temp_ar.append(round(xr, 5))
if xr != 0:
ea = abs((xr - xr_old) / xr)
temp_ar.append(round(ea, 5))
if ea < es:
break
res_ar.append(temp_ar)
temp_ar = [i + 1, round(xr_old, 5), round(xr, 5), round(ea, 5)]
res_ar.append(temp_ar)
return res_ar
def secant(x_iminus1, xi, f, es, imax):
res_ar = []
xr = xi
for i in range(imax):
temp_ar = [i + 1, round(x_iminus1, 5)]
if i > 0:
x_iminus1 = xi
xi = xr
temp_ar.append(round(xi, 5))
xr = xi - (f(xi) * (x_iminus1 - xi)) / (f(x_iminus1) - f(xi))
temp_ar.append(round(f(x_iminus1), 5))
temp_ar.append(round(f(xi), 5))
if xr != 0:
ea = abs((xr - xi) / xr)
temp_ar.append(round(ea, 5))
if ea < es:
break
res_ar.append(temp_ar)
temp_ar = [i + 1, round(x_iminus1, 5), round(xi, 5), round(f(x_iminus1), 5), round(f(xi), 5), round(ea, 5)]
res_ar.append(temp_ar)
return res_ar