def run_all_methods(file, f, Df, D2f, a, b, x):
csv_file = open('%s.csv' % file, mode='w')
writer = csv.writer(csv_file,
delimiter=';',
quotechar='"',
quoting=csv.QUOTE_MINIMAL)
writer.writerow(['Method', 'Iteration', 'Convergence'])
i = methods.newton(f, Df, a, 10**(-16))
p = methods.convergenceOrder(get_abs(i, x))
write_result(writer, 'Newton', i, p)
print("Newton found solution:", i[-1], "in", len(i), "iterations")
i = methods.halley(f, Df, D2f, a, 10**(-16))
p = methods.convergenceOrder(get_abs(i, x))
write_result(writer, 'Halley', i, p)
print("Halley found solution:", i[-1], "in", len(i), "iterations")
i = methods.bisection(f, b, a, 10**(-16))
p = methods.convergenceOrder(get_abs(i, x))
write_result(writer, 'Bisection', i, p)
print("Bisection found solution:", i[-1], "in", len(i), "iterations")
i = methods.secant(f, b, a, 10**(-16))
p = methods.convergenceOrder(get_abs(i, x))
write_result(writer, 'Secant', i, p)
print("Secant found solution:", i[-1], "in", len(i), "iterations")
def calculate(self):
"""Does all the work"""
item_number = self.fields.curselection()
polynomial = self.json_data["functions"][int(item_number[0])]
result_floating = None
result_interval = None
if self.json_data["method"] == "regula_falsi":
try:
result_floating = regula_falsi(polynomial["a"],
polynomial["b"],
function_from_list,
polynomial["coeff"]
)
except MyError as error:
result_floating = error.value
except ZeroDivisionError:
result_floating = "Unfortunately, division by 0 happened"
try:
result_interval = regula_falsi_interval(polynomial["a"],
polynomial["b"],
function_from_list,
polynomial["coeff"]
)
result_interval = result_interval.format('%.20E')[9:]
result_interval = result_interval[:-1]
except MyError as error:
result_interval = error.value
elif self.json_data["method"] == "newton":
try:
result_floating = newton(polynomial["x"],
polynomial["epsilon"],
polynomial["max_iterations"],
function_from_list,
polynomial["coeff"],
polynomial["derivative_coeff"]
)
except ZeroDivisionError:
result_floating = "Unfortunately, division by zero happened"
except MyError as error:
result_floating = error.value
try:
result_interval = newton_interval(polynomial["x"],
polynomial["epsilon"],
polynomial["max_iterations"],
function_from_list,
polynomial["coeff"],
polynomial["derivative_coeff"]
)
result_interval = result_interval.format('%.20E')[9:]
result_interval = result_interval[:-1]
except MyError as error:
result_interval = error.value
else:
result_interval = "You propably"
result_floating = "gave me wrong JSON"
self.show_result_floating.config(text=result_interval)
self.show_result_interval.config(text=result_floating)
def ddf1(x):
return -math.sin(x)
def f2(x):
return x**3 - 18 * x - 83
xn = 1.0
xnm1 = 1.0005
xnm2 = 1.005
eps = 0.1
x0 = -1.00
x1 = 1.00
print("Метод Ньютона", methods.newton(f, df, xn, eps))
print("Метод Чебышева", methods.chebishev(f, df, ddf, xn, eps))
print("Метод Хэлли", methods.helley(f, df, ddf, xn, eps))
print("Метод обратной параболической интерполяции",
methods.inverseInterpolation(f, xn, xnm1, xnm2, eps))
print("Для другой функции: ")
print("Метод секущих", methods.secant(f1, x0, x1, eps))
print("Метод Ньютона", methods.newton(f1, df1, xn, eps))
print("Метод Чебышева", methods.chebishev(f1, df1, ddf1, xn, eps))
def gerar_resultados(minGrau, maxGrau, quantidade, MU, SIGMA, ERROR):
random_polinomials = generate_random_polynomials(quantidade, MU, SIGMA, minGrau, maxGrau)
results = {
"minGrau": minGrau,
"maxGrau": maxGrau,
"quantidade": quantidade,
"mu": MU,
"sigma": SIGMA,
"error": ERROR,
"calculadoPorTodos": 0,
"graus": {},
"bissection": {
"iterations": 0,
"time": 0,
"avgF(x)": 0,
"ignored": 0,
"graus": {}
},
"newton": {
"iterations": 0,
"time": 0,
"avgF(x)": 0,
"ignored": 0,
"graus": {}
},
"secant": {
"iterations": 0,
"time": 0,
"avgF(x)": 0,
"ignored": 0,
"graus": {}
}
}
for i in range(minGrau, maxGrau + 1):
results["graus"]["grau%i" % i] = 0
for name in ["bissection", "newton", "secant"]:
for i in range(minGrau, maxGrau + 1):
results[name]["graus"]["grau%i" % i] = {
"iterations": 0,
"time": 0,
"avgF(x)": 0,
"ignored": 0
}
for p in random_polinomials:
print(p)
grauName = "grau%i" % p.o
timeBstart = time.time()
xB, itrB = methods.bisection(p, ERROR)
timeBend = time.time()
timeB = (timeBend - timeBstart)
timeSstart = time.time()
xS, itrS = methods.secant(p, ERROR)
timeSend = time.time()
timeS = (timeSend - timeSstart)
timeNstart = time.time()
xN, itrN = methods.newton(p, ERROR)
timeNend = time.time()
timeN = (timeNend - timeNstart)
if xB == None:
results["bissection"]["ignored"] += 1
results["bissection"]["graus"][grauName]["ignored"] += 1
if xN == None:
results["newton"]["ignored"] += 1
results["newton"]["graus"][grauName]["ignored"] += 1
if xS == None:
results["secant"]["ignored"] += 1
results["secant"]["graus"][grauName]["ignored"] += 1
if xB != None and xN != None and xS != None:
results["calculadoPorTodos"] += 1
results["graus"][grauName] += 1
results["bissection"]["avgF(x)"] += (p.__call__(xB))/quantidade
results["bissection"]["graus"][grauName]["avgF(x)"] += (p.__call__(xB))/quantidade
results["bissection"]["iterations"] += itrB
results["bissection"]["graus"][grauName]["iterations"] += itrB
results["bissection"]["time"] += timeB
results["bissection"]["graus"][grauName]["time"] += timeB
results["newton"]["avgF(x)"] += (p.__call__(xN))/quantidade
results["newton"]["graus"][grauName]["avgF(x)"] += (p.__call__(xN))/quantidade
results["newton"]["iterations"] += itrN
results["newton"]["graus"][grauName]["iterations"] += itrN
results["newton"]["time"] += timeN
results["newton"]["graus"][grauName]["time"] += timeN
results["secant"]["avgF(x)"] += (p.__call__(xS))/quantidade
results["secant"]["graus"][grauName]["avgF(x)"] += (p.__call__(xS))/quantidade
results["secant"]["iterations"] += itrS
results["secant"]["graus"][grauName]["iterations"] += itrS
results["secant"]["time"] += timeS
results["secant"]["graus"][grauName]["time"] += timeS
for name in ["bissection", "newton", "secant"]:
results[name]["iterations"] = results[name]["iterations"]/results["calculadoPorTodos"]
results[name]["time"] = results[name]["time"]/results["calculadoPorTodos"]
for i in range(minGrau, maxGrau + 1):
results[name]["graus"]["grau%i" % i]["iterations"] = results[name]["graus"]["grau%i" % i]["iterations"]/results["graus"]["grau%i" % i]
results[name]["graus"]["grau%i" % i]["time"] = results[name]["graus"]["grau%i" % i]["time"]/results["graus"]["grau%i" % i]
return results
if 0 < stop_condition < 3:
correct = True
else:
print("Brak takiego kryterium")
except ValueError:
print("Brak takiego kryterium")
accuracy = 0
iteration = 0
if stop_condition == 1:
accuracy = abs(float(input("Podaj dokładność epsilon: ")))
iteration = -1
else:
iteration = int(input("Podaj liczbe iteracji: "))
accuracy = -1
result_bisection = bisection(left, right, accuracy, iteration, function_number) # miejsce zerowe (bisekcja)
result_newton = newton(left, right, accuracy, iteration, function_number) # miejsce zerowe (netwon)
if result_bisection is False:
print("Bisekcja: Funkcja nie spełnia założeń na danym przedziale")
else:
print("Bisekcja - " + str(result_bisection))
if result_newton is False:
print("Newton: Funkcja nie spełnia założeń na danym przedziale")
else:
print("Newton - " + str(result_newton))
show_plot(left, right, function_number, result_bisection, result_newton) # rysowanie wykresu