ns.potapov/compute-math
1
0
Fork 0
Code Issues Pull Requests Actions Packages Projects Releases Wiki Activity

погрешность

Browse Source
This commit is contained in:
Никита Потапов
2025-04-27 19:34:08 +04:00
parent d08ffcb895
commit 6e7354af93
1 changed files with 137 additions and 42 deletions
Download Patch File Download Diff File Expand all files Collapse all files

179
lab2/HookJeeves.py
View File

@@ -1,4 +1,6 @@
import numpy as np
import AbsoluteMeasurementErrors as abserror
from itertools import product
result_log = ""
@@ -9,16 +11,42 @@ def log(*values, sep=" ", end="\n"):
print(*values, sep=sep, end=end)
def point_info(x, f):
return f"x = {x}, f(x) = {f(x)}"
def get_errors_vector(x):
return np.array(list(map(abserror.get_error, x)))
def sum_errors_vector(a, b):
return np.array([abserror.sum_error(a[i], b[i]) for i in range(len(a))])
def frac_errors_vector(a, b):
return np.array([abserror.frac_error(a[i], b) for i in range(len(a))])
def point_info(x, f, x_err):
return f"x = {x}, x_err = {x_err}, f(x) = {f(x)}"
def hooke_jeeves(
f, x0, delta0, epsilon, alpha, r=lambda x: True, fit=lambda a, b: a < b
f,
x0,
delta0,
epsilon,
alpha,
r=lambda x: True,
fit=lambda a, b: a < b,
x_err=None,
delta_err=None,
):
x = np.array(x0)
delta = np.array(delta0)
if x_err is None:
x_err = get_errors_vector(x)
if delta_err is None:
delta_err = get_errors_vector(delta)
iteration = 0
while np.linalg.norm(delta) > epsilon:
@@ -28,77 +56,141 @@ def hooke_jeeves(
log("=" * 40)
log("Итерация", iteration)
log("Текущая базовая точка", point_info(x, f))
log("Текущая базовая точка", point_info(x, f, x_err))
sample_x = exploratory_search(f, x, delta, r=r, fit=fit)
sample_x, sample_x_err = exploratory_search(
f, x, delta, r=r, fit=fit, x_err=x_err, delta_err=delta_err
)
if fit(f(sample_x), f(x)):
log("Исследующий поиск УДАЧНЫЙ")
x_p = sample_search(f, x, sample_x, r=r, fit=fit)
x_p, x_p_err = sample_search(
f, x, sample_x, r=r, fit=fit, x1_err=x_err, x2_err=sample_x_err
)
if fit(f(x_p), f(x)):
log("Поиск по образцу УДАЧНЫЙ")
x = x_p
x, x_err = x_p, x_p_err
else:
log("Поиск по образцу ПРОВАЛЕН")
x = sample_x
x, x_err = sample_x, sample_x_err
log()
log("Новая базовая точка", point_info(x, f))
log("Новая базовая точка", point_info(x, f, x_err))
else:
log("Исследующий поиск ПРОВАЛЕН")
log("Уменьшаем шаг", delta, "->", delta / alpha)
delta = delta / alpha
delta_err = frac_errors_vector(delta, alpha)
log("ε =", np.linalg.norm(delta))
return x, f(x)
return x, f(x), x_err
def exploratory_search(f, x, delta, r=lambda x: True, fit=lambda a, b: a < b):
# def exploratory_search(
# f, x, delta, r=lambda x: True, fit=lambda a, b: a < b, x_err=None
# ):
# log()
# log("Выполняем исследующий поиск")
# if x_err is None:
# x_err = get_errors_vector(x)
# x_new = np.array(x)
# f_x_new = f(x_new)
# for i in range(len(x)):
# x_up = x_new.copy()
# x_down = x_new.copy()
# x_up[i] += delta[i]
# x_down[i] -= delta[i]
# f_x_up = f(x_up)
# f_x_down = f(x_down)
# if not r(x_up) or not r(x_down):
# log("Ограничение ОДЗ")
# if fit(f_x_up, f_x_new) and fit(f_x_up, f_x_down) and r(x_up):
# x_new = x_up
# f_x_new = f_x_up
# elif fit(f_x_down, f_x_new) and r(x_down):
# x_new = x_down
# f_x_new = f_x_down
# if any([x_new[i] != x[i] for i in range(len(x))]):
# log("Найдена точка", x_new, f(x_new))
# return x_new, x_err
def exploratory_search(
f, x, delta, r=lambda x: True, fit=lambda a, b: a < b, x_err=None, delta_err=None
):
log()
log("Выполняем исследующий поиск")
x_new = np.array(x)
f_x_new = f(x_new)
if x_err is None:
x_err = get_errors_vector(x)
for i in range(len(x)):
x_up = x_new.copy()
x_down = x_new.copy()
if delta_err is None:
delta_err = get_errors_vector(delta)
x_up[i] += delta[i]
x_down[i] -= delta[i]
dxs = product(*[[d, -d] for d in delta])
f_x_up = f(x_up)
f_x_down = f(x_down)
x = np.array(x)
t_x_err = None
t_f = f(x)
t_x = None
if not r(x_up) or not r(x_down):
log("Ограничение ОДЗ")
for dx in dxs:
if fit(f(x + dx), t_f) and r(x + dx):
t_f = f(x + dx)
t_x = x + dx
t_x_err = x_err + delta_err
if fit(f_x_up, f_x_new) and fit(f_x_up, f_x_down) and r(x_up):
x_new = x_up
f_x_new = f_x_up
elif fit(f_x_down, f_x_new) and r(x_down):
x_new = x_down
f_x_new = f_x_down
if t_x is not None:
log("Найдена точка", t_x, t_f)
return t_x, t_x_err
if any([x_new[i] != x[i] for i in range(len(x))]):
log("Найдена точка", x_new, f(x_new))
return x_new
return x, x_err
def sample_search(f, x1, x2, r=lambda x: True, fit=lambda a, b: a < b):
def sample_search(
f, x1, x2, r=lambda x: True, fit=lambda a, b: a < b, x1_err=None, x2_err=None
):
log()
log("Выполняем поиск по образцу")
if x1_err is None:
x1_err = get_errors_vector(x1)
if x2_err is None:
x2_err = get_errors_vector(x2)
x2_last = x2.copy()
x2_last_err = x2_err.copy()
while fit(f(x2), f(x1)):
x2_last = x2.copy()
x2_last_err = x2_err.copy()
if not r(x2 + (x2 - x1)):
log("Ограничение ОДЗ")
break
x2, x1 = x2 + (x2 - x1), x2
log("Найдена точка", x2, f(x2))
return x2
t_err = x2_err.copy()
x2_err = x2_err + (x2_err + x1_err)
x1_err = t_err.copy()
log("Найдена точка", x2_last, f(x2_last))
return x2_last, x2_last_err
def example():
@@ -143,18 +235,21 @@ def example():
]
)
x, val = hooke_jeeves(f, x0, delta0, epsilon, alpha, r=r, fit=fit)
return x, val
if __name__ == "__main__":
x, val = example()
x, val, x_err = hooke_jeeves(f, x0, delta0, epsilon, alpha, r=r, fit=fit)
log()
log("=" * 40)
log("Точка экстремумв:", x)
log("Минимальное значение функции:", val)
log("Абсолютная погрешность:", x_err)
log("Максимальное значение функции:", val)
with open("result.log", "w", encoding="utf-8") as file:
file.write(result_log)
def main():
example()
if __name__ == "__main__":
main()