погрешность

lab2/HookJeeves.py

@@ -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):
+def get_errors_vector(x):
-    return f"x = {x}, f(x) = {f(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)
+    if x_err is None:
-    f_x_new = f(x_new)
+        x_err = get_errors_vector(x)
 
-    for i in range(len(x)):
+    if delta_err is None:
-        x_up = x_new.copy()
+        delta_err = get_errors_vector(delta)
-        x_down = x_new.copy()
 
-        x_up[i] += delta[i]
+    dxs = product(*[[d, -d] for d in delta])
-        x_down[i] -= delta[i]
 
-        f_x_up = f(x_up)
+    x = np.array(x)
-        f_x_down = f(x_down)
+    t_x_err = None
+    t_f = f(x)
+    t_x = None
 
-        if not r(x_up) or not r(x_down):
+    for dx in dxs:
-            log("Ограничение ОДЗ")
+        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):
+    if t_x is not None:
-            x_new = x_up
+        log("Найдена точка", t_x, t_f)
-            f_x_new = f_x_up
+        return t_x, t_x_err
-        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))]):
+    return x, x_err
-        log("Найдена точка", x_new, f(x_new))
-    return x_new
 
 
-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)
+    x, val, x_err = hooke_jeeves(f, x0, delta0, epsilon, alpha, r=r, fit=fit)
-    return x, val
-
-
-if __name__ == "__main__":
-
-    x, val = example()
 
     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()