86 lines
2.7 KiB
Python
86 lines
2.7 KiB
Python
import numpy as np
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import math
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class Simplex:
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def __init__(self, source):
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self.m, self.n = source.shape
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self.table = np.zeros((self.m, self.n + self.m - 1))
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self.basis = []
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for i in range(self.m):
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for j in range(self.n):
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self.table[i, j] = source[i, j]
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if (self.n + i) < self.table.shape[1]:
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self.table[i, self.n + i] = 1
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self.basis.append(self.n + i)
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self.n = self.table.shape[1]
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def calculate(self, result):
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while not self.is_it_end():
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main_col = self.find_main_col()
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main_row = self.find_main_row(main_col)
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self.basis[main_row] = main_col
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new_table = np.zeros((self.m, self.n))
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for j in range(self.n):
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new_table[main_row, j] = self.table[main_row, j] / self.table[main_row, main_col]
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for i in range(self.m):
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if i == main_row:
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continue
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for j in range(self.n):
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new_table[i, j] = self.table[i, j] - self.table[i, main_col] * new_table[main_row, j]
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self.table = new_table
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for i in range(len(result)):
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k = self.basis.index(i + 1) if i + 1 in self.basis else None
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if k != None:
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result[i] = self.table[k, 0]
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else:
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result[i] = 0
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return self.table
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def is_it_end(self):
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return all(self.table[self.m - 1, 1:] >= 0)
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def find_main_col(self):
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return np.argmin(self.table[self.m - 1, 1:]) + 1
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def find_main_row(self, main_col):
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main_row = 0
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for i in range(self.m - 1):
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if self.table[i, main_col] > 0:
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main_row = i
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break
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for i in range(main_row + 1, self.m - 1):
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if (self.table[i, main_col] > 0) and ((self.table[i, 0] / self.table[i, main_col]) < (self.table[main_row, 0] / self.table[main_row, main_col])):
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main_row = i
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return main_row
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if __name__ == "__main__":
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table = np.array([[18, 1, 3],
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[16, 2, 1],
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[5, 0, 0],
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[21, 3, 0],
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[0, -2, -3]])
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result = np.zeros(2)
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table_result = Simplex(table).calculate(result)
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print("Оптимальная таблица:")
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for i in range(table_result.shape[0]):
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for j in range(table_result.shape[1]):
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print("%5.2f " % table_result[i][j], end='')
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print()
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print("\nРешение:")
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print(f"x1 = {result[0]}")
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print(f"x2 = {math.ceil(result[1])}")
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print(f"max = {-table[-1][-2] * result[0] + -table[-1][-1] * math.ceil(result[1])}") |