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simplex_gui.py
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simplex_gui.py
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# Authors: Aidan Lynch, Bryce Gernon, Jim Godin, Ryan Devoe, Sam Ford
from ctypes import Union
import sys
from typing import Tuple # Command line argument handling
import numpy # Python matrix ops
from fractions import Fraction
import os # Could be useful for saving output to file if desired
import tkinter as tk # GUI
from functools import partial # Helper for GUI methods
import numpy as np
def format_frac(frac):
if frac.numerator == 0:
return "0"
elif frac.denominator == 1:
return "{}".format(frac.numerator)
else:
return "{}/{}".format(frac.numerator, frac.denominator)
'''
* Struct for storing a tableau
*
* m: matrix
* s_size: length of S
* x_size: length of X
* rows: number of rows in m
* cols: number of columns in m
'''
class Tableau:
# this is equivalent to create_tableau in Aidan's simplex.c
def __init__(self, base_rows, base_cols):
self.rows = base_rows + 1
self.cols = base_cols + base_rows + 1
self.k = 0
# print( self.rows, self.cols, "in tableau constructor")
# numpy makes 2 for loops in C into a line of code - SF 10/13
self.m = numpy.zeros((self.rows, self.cols)).astype('object') # Generate m here
for row, _ in enumerate(self.m):
for col, _ in enumerate(self.m[row]):
self.m[row][col] = Fraction(0)
self.finished = False
# equivalent to print_tableau in Aidan's simplex.c
def __str__(self):
tableau_str = ""
for row in range(self.rows):
if row == self.rows - 1:
tableau_str += "-" * (8 * self.cols + 2) + "\n"
for col in range(self.cols):
if col == self.cols - 1 or col == self.rows + self.cols:
tableau_str += "|"
frac = Fraction(self.m[row][col])
tableau_str += "{:^8}".format(format_frac(frac))
if row < self.rows - 1:
tableau_str += "\n"
return tableau_str
def pivot_tableau(self):
pivot_col = np.argmin(self.m[self.rows - 1])
min_value = sys.maxsize
pivot_row = Fraction(-1)
for row, entry in enumerate(np.swapaxes(self.m, 0, 1)[pivot_col][0:-1]):
if (entry == 0):
value = 0
else:
value = Fraction(self.m[row][self.cols-1] / entry)
if 0 < value < min_value:
min_value = value
pivot_row = row
if pivot_row == -1:
self.finished = True
return
pivot_value = Fraction(self.m[pivot_row][pivot_col])
print(pivot_value)
prev_tableau = np.copy(self.m)
for col, _ in enumerate(self.m[pivot_row]):
self.m[pivot_row][col] = Fraction(self.m[pivot_row][col] / pivot_value)
for row, _ in enumerate(self.m):
for col, _ in enumerate(self.m[row]):
if row != pivot_row:
self.m[row][col] = Fraction(
self.m[row][col] - Fraction(prev_tableau[row][pivot_col] * self.m[pivot_row][col]))
return
'''
* Print the usage statement for this program.
'''
def print_usage():
print("usage: simplex m n")
print("\tm: number of rows, integer greater than 0")
print("\tn: number of columns, integer greater than 0")
'''
* Prompt user for payoff matrix and process its entry.
*
* m: number of rows
* n: number of columns
*
* return: payoff result structure
'''
'''
* Builds the initial tableau using the given payoff matrix
*
* payoff: payoff matrix
* m: number of rows
* n: number of columns
*
* return: initial tableau
'''
def get_init_tableau(payoff, m, n) -> Tableau:
tableau: Tableau = Tableau(m, n)
min = sys.maxsize
for row in range(0, m):
for col in range(0, n):
if payoff[row][col] < min:
min = payoff[row][col]
# Python ternary assignment of booster val k
k = Fraction(1 - min) if (min < 1) else Fraction(0)
# populate the initial tableau so that every entry >=
# in the elif the == will eval to 1 or 0 since
# True or False is equiv to those respectively
for row in range(0, tableau.rows):
for col in range(0, tableau.cols):
if col < n:
tableau.m[row][col] = Fraction(payoff[row][col] + k) \
if (row < m) else Fraction(-1)
elif col < n + m:
tableau.m[row][col] = Fraction((row == col - n)) \
if (row < m) else Fraction(0)
else:
tableau.m[row][col] = Fraction((row < m))
return tableau
'''
* Pivots the provided tableau
*
* tableau: struct to pivot
'''
def main_tableau():
# Parse inputs
return
# parse_result: ArgResult = parse_args(len(sys.argv), sys.argv)
if not parse_result.success:
print_usage()
return -1
# Get initial matrix
return
payoff_result = get_payoff(parse_result.m, parse_result.n)
if not payoff_result.success:
return -1
m: int = payoff_result.m
n: int = payoff_result.n
tableau: Tableau = get_init_tableau(payoff_result.payoff, m, n)
order = [-1] * n
pivot_count = 0
# while true hype...incomplete SF 10/13
while True:
if pivot_count == 0:
print("Initial Tableau:")
else:
print("Tableau {}:".format(pivot_count))
print(tableau)
(tableau, pivot_row, pivot_col) = pivot_tableau(tableau)
if pivot_count < n:
order[pivot_count] = pivot_row
print("Pivot: ( {}, {} )\n".format(pivot_row, pivot_col))
pivot_count += 1
if np.min(tableau.m[tableau.rows - 1]) >= 0:
break
print("Final Tableau:")
print(tableau)
v = tableau.m[tableau.rows - 1][tableau.cols - 1]
value = (1 / v) - tableau.k
p1_strategy = [tableau.m[tableau.rows - 1][n + col] / v for col in range(m)]
p2_strategy = [tableau.m[order[index]][tableau.cols - 1] / v if order[index] >= 0 else 0 for index in range(n)]
print("\nPlayer 1 Optimal Strategy: (", ", ".join(format_frac(p) for p in p1_strategy), ")")
print("Player 2 Optimal Strategy: (", ", ".join(format_frac(q) for q in p2_strategy), ")")
print("Value: {}".format(format_frac(value)))
return 0
class GUI(tk.Frame):
def __init__(self, *args, **kwargs):
tk.Frame.__init__(self, *args, **kwargs)
self.matrixAnalysisButton = tk.Button(self, text="Matrix Analysis", command=self.matrixAnalysis)
self.matrixAnalysisButton.pack(side="top")
def matrixAnalysis(self):
self.subwindow = tk.Toplevel(self)
# self.row_options = ('1', '2', '3', '4', '5', '6', '7', '8', '9', '10', '11', '12')
# self.column_options = ('1', '2', '3', '4', '5', '6', '7', '8', '9', '10', '11', '12')
row_options = (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12)
column_options = (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12)
self.subwindow.columnconfigure(2, weight=3)
self.subwindow.wm_title("Your one-stop shop for matrix analysis!")
# self.label = tk.Label(self.self.subwindow, text="Your one-stop shop for matrix analysis!")
# self.label.pack(side="top", fill="both", expand=True)
self.text_entry = tk.Text(self.subwindow)
self.text_entry.grid(column=2, row=2)
self.row_var = tk.IntVar(self)
self.column_var = tk.IntVar(self)
row_entry = tk.OptionMenu(self.subwindow, self.row_var, *row_options)
column_entry = tk.OptionMenu(self.subwindow, self.column_var, *column_options)
row_entry.grid(column=1, row=0)
column_entry.grid(column=1, row=1)
row_label = tk.Label(self.subwindow, text="Rows:")
row_label.grid(row=0, column=0)
column_label = tk.Label(self.subwindow, text="Columns:")
column_label.grid(row=1, column=0)
button_grid = tk.Frame(self.subwindow)
button_grid.grid(row=0, column=2)
graphic_button = tk.Button(button_grid, text="Solve\nGraphically", command=self.solveGraphically)
graphic_button.grid(row=0, column=0)
saddle_point_button = tk.Button(button_grid, text="Search for\nSaddle Points", command=self.findSaddle)
saddle_point_button.grid(row=0, column=1)
simplex_button = tk.Button(button_grid, text="Solve with\nSimplex method", command=self.solveWithSimplex)
simplex_button.grid(row=1, column=0)
strats_button = tk.Button(button_grid, text="Find strategies\nand game value", command=self.findStrats)
strats_button.grid(row=1, column=1)
self.buttons_label = tk.Label(button_grid, text="Enter the numbers of rows and columns using\nthe dropdowns "
"to the left, enter the matrix\nbelow, then press one of"
" these buttons!")
self.buttons_label.grid(column=2, row=0, columnspan=2, rowspan=2)
def solveGraphically(self):
self.buttons_label.config(text="Not implemented\nyet.")
return
print("GRAPHICS")
print(self.text_entry.get(0.0, tk.END))
start = self.getTableau()
if type(start) != Tableau:
return
def findStrats(self):
tableau = self.getTableau()
for x in range(1000):
tableau.pivot_tableau()
v = tableau.m[tableau.rows - 1][tableau.cols - 1]
#value = (1 / v) - tableau.k
order = [-1] * (tableau.cols - tableau.rows)
v = tableau.m[tableau.rows - 1][tableau.cols - 1]
if (v!= 0):
value = (1 / v) - tableau.k
else:
value = -tableau.k
m = tableau.rows - 1
n = tableau.cols - tableau.rows
p1_strategy = [tableau.m[tableau.rows - 1][n + col] / v for col in range(m)]
p2_strategy = [tableau.m[-1][index + n] / v for index in range(n)]
new_text = "Player 1 Optimal Strategy: (" + ", ".join(format_frac(p) for p in p1_strategy) + ")"
new_text += "\nPlayer 2 Optimal Strategy: (" + ", ".join(format_frac(q) for q in p2_strategy) + ")"
new_text += "\nValue: {}".format(format_frac(value))
self.buttons_label.config(text=new_text)
#print("\n)
#print("Player 2 Optimal Strategy: (", ", ".join(format_frac(q) for q in p2_strategy), ")")
#print("Value: {}".format(format_frac(value)))
def solveWithSimplex(self):
tableau = self.getTableau()
if type(tableau) != Tableau:
return
simplex_window = tk.Toplevel(self)
simplex_window.wm_title("Simplex Solution")
simplex_display = tk.Label(simplex_window, text=tableau.__str__())
simplex_display.grid(row=1, column=0, columnspan=2)
simplex_display.config(text=tableau.__str__())
# lbutton = tk.Button(simplex_window, text="Previous\nPivot", command=lambda )
# lbutton.grid(row=0, column=0)
rbutton = tk.Button(simplex_window, text="Next\nPivot", command=lambda: [self.nextPivot(tableau, simplex_display)])
rbutton.grid(row=0, column=1)
def findSaddle(self):
tableau = self.getTableau()
if type(tableau) != Tableau:
return
saddle_point_text = "Saddle points:\n"
for rownum in range(tableau.rows-1):
for columnnum in range(tableau.cols-tableau.rows):
entry = tableau.m[rownum][columnnum]
if (entry == np.min(tableau.m[rownum][0:tableau.cols-tableau.rows])) and (entry == np.max(np.swapaxes(tableau.m, 0, 1)[columnnum][0:tableau.rows-1])):
saddle_point_text += str(entry) + "(" + str(rownum) + "," + str(columnnum) + ")\n"
self.buttons_label.config(text=saddle_point_text)
def getTableau(self):
# initialize a mxn numpy array
m = self.row_var.get()
n = self.column_var.get()
text = self.text_entry.get(0.0, tk.END)
tableau = Tableau(m, n)
lineNum = 0
lines = text.split('\n')
while lineNum < m:
mat_str = lines[lineNum]
row_els = mat_str.split()
r_count = len(row_els)
if r_count != n:
self.buttons_label.config(text=f"Expected {n} entries in a row.\nGot {r_count}. Please fix and retry!")
return -1
# validate the input we got was numbers
for col in range(0, n):
try:
num = Fraction(row_els[col])
tableau.m[lineNum][col] = num
except ValueError:
self.buttons_label.config(text="Couldn't convert input string to fraction.\nMake sure you're only"
"using integers!")
return -1
# endfor
lineNum += 1
# endwhile
min = sys.maxsize
for row in range(0, m):
for col in range(0, n):
if tableau.m[row][col] < min:
min = tableau.m[row][col]
# Determine constant to add to tableau so all vals are positive
k = Fraction(1 - min) if (min < 1) else Fraction(0)
tableau.k = k
for row in range(0, tableau.rows):
for col in range(0, tableau.cols):
if col < n:
tableau.m[row][col] = Fraction(tableau.m[row][col] + k) \
if (row < m) else Fraction(-1)
elif col < n + m:
tableau.m[row][col] = Fraction((row == col - n)) \
if (row < m) else Fraction(0)
else:
tableau.m[row][col] = Fraction((row < m))
return tableau
def nextPivot(self, tableau, text):
tableau.pivot_tableau()
text.config(text=tableau.__str__())
# v = tableau.m[tableau.rows - 1][tableau.cols - 1]
# value = (1 / v) - tableau.k
# n = tableau.cols - tableau.rows
# m = tableau.rows - 1
# order = [-1] * (tableau.cols - tableau.rows)
#
# p1_strategy = [tableau.m[tableau.rows - 1][n + col] / v for col in range(m)]
# p2_strategy = [tableau.m[-1][index+n] / v for index in range(n)]
#
# print("\nPlayer 1 Optimal Strategy: (", ", ".join(format_frac(p) for p in p1_strategy), ")")
# print("Player 2 Optimal Strategy: (", ", ".join(format_frac(q) for q in p2_strategy), ")")
# print("Value: {}".format(format_frac(value)))
def main():
windowroot = tk.Tk("gametheoryapp", "Game Theory Compendium")
window = GUI(windowroot)
window.pack(side="top", fill="both", expand=True)
window.mainloop()
sys.exit()
if __name__ == '__main__':
main()