SimplexMethod

.gitignore

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+.idea

README.md

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+#Участники команды
++ Малин Данил - выполнивший задание
++ Сорокин Павел - помощник
++ Пятаков Кирилл - помощник
++ Распаев Николай -помощник
+#Задание
+![Задание](/assets/image.png)

main.py

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+import math
+
+import numpy as np
+
+c = [0, 0, 0, 1, -2]
+c_num = 3
+A = [
+    [1, 0, 0, -1, 1],
+    [0, 1, 0, 2, 3],
+    [0, 0, 1, 1, -2]
+]
+b = [2, 7, 1]
+
+
+# c = [1, 1, 0, 0, 0]
+# c_num = 2
+# A = [
+#    [-1, 1, 1, 0, 0],
+#    [ 1, 0, 0, 1, 0],
+#    [ 0, 1, 0, 0, 1]
+# ]
+# b = [2, 4, 4]
+
+def simplex(c, A, b):
+    tableau = to_tableau(c, A, b)
+
+    while can_be_improved(tableau):
+        pivot_position = get_pivot_position(tableau)
+        tableau = pivot_step(tableau, pivot_position)
+
+    return get_solution(tableau)
+
+
+def to_tableau(c, A, b):
+    xb = [eq + [x] for eq, x in zip(A, b)]
+    z = c + [0]
+    return xb + [z]
+
+
+def can_be_improved(tableau):
+    z = tableau[-1]
+    return any(x < 0 for x in z[:-1])
+
+
+def get_pivot_position(tableau):
+    z = tableau[-1]
+    column = next(i for i, x in enumerate(z[:-1]) if x < 0)
+
+    restrictions = []
+    for eq in tableau[:-1]:
+        el = eq[column]
+        restrictions.append(math.inf if el <= 0 else eq[-1] / el)
+
+    row = restrictions.index(min(restrictions))
+    return row, column
+
+
+def pivot_step(tableau, pivot_position):
+    new_tableau = [[] for eq in tableau]
+
+    i, j = pivot_position
+    pivot_value = tableau[i][j]
+    new_tableau[i] = np.array(tableau[i]) / pivot_value
+
+    for eq_i, eq in enumerate(tableau):
+        if eq_i != i:
+            multiplier = np.array(new_tableau[i]) * tableau[eq_i][j]
+            new_tableau[eq_i] = np.array(tableau[eq_i]) - multiplier
+
+    return new_tableau
+
+
+def is_basic(column):
+    return sum(column) == 1 and len([c for c in column if c == 0]) == len(column) - 1
+
+
+def get_solution(tableau):
+    columns = np.array(tableau).T
+    solutions = []
+    for column in columns[:-1]:
+        solution = 0
+        if is_basic(column):
+            one_index = column.tolist().index(1)
+            solution = columns[-1][one_index]
+        solutions.append(solution)
+
+    return solutions
+
+
+solution = simplex(c, A, b)
+print('solution: ', solution)
+result = 0
+for i in range(len(solution)):
+    result += c[i] * solution[i]
+result += c_num
+print(result)