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Coordinate System.py
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Coordinate System.py
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import numpy as np
def creating_matrix(rows, columns):
print("Enter row 1: ", end="")
row = input()
mat = np.zeros(int(columns))
numbers = row.split(' ')
for i in range(0, int(columns)):
mat[i] = int(numbers[i])
for i in range(1, int(rows)):
print("Enter row {}: ".format(i + 1), end="")
row = input()
numbers = row.split(' ')
new_row = np.zeros(int(columns))
for j in range(0, int(columns)):
new_row[j] = int(numbers[j])
mat = np.vstack((mat, new_row))
print("Enter constant values: ", end="")
values = input()
numbers = values.split(' ')
values_array = np.zeros((int(rows), 1))
for i in range(0, int(rows)):
values_array[i][0] = int(numbers[i])
mat = np.hstack((mat, values_array))
# print(matrix)
return mat
def finding_pivot_column(mat, column_number, row, pivot_number):
not_zero = 0
for i in range(int(pivot_number), int(row)):
if mat[i][int(column_number)] != 0:
not_zero += 1
if not_zero > 0:
return True
else:
return False
def find_row(mat, pivot_number, current_column, row):
r = pivot_number
while r < row:
if mat[r][current_column] != 0:
return r
else:
r += 1
def interchange(mat, columns, x, y, proper_number):
for k in range(0, columns + 1):
temp = matrix[x][k]
matrix[x][k] = matrix[proper_number][k]
matrix[proper_number][k] = temp
return mat
def row_replacement(mat, column_number, row_number, row, column):
for k in range(row_number + 1, row):
# print(k)
if mat[k][column_number] != 0:
# print(mat[k][column_number])
num = mat[k][column_number] / mat[row_number][column_number]
# print("num")
# print(num)
for r in range(column_number, column + 1):
# print("u")
# print(mat[row_number][r])
# print("d")
# print(mat[k][r])
mat[k][r] -= num * mat[row_number][r]
return mat
def making_echelon_form(mat, pivot_matrix, row, column_number):
for k in range(0, row):
for q in range(0, int(pivot_matrix[k][0])):
if mat[q][int(pivot_matrix[k][1])] != 0:
# print(mat)
# print(q, pivot_matrix[k][1], mat[q][int(pivot_matrix[k][1])])
num = mat[q][int(pivot_matrix[k][1])] / mat[k][int(pivot_matrix[k][1])]
# print(mat[k][int(pivot_matrix[k][1])])
# print(num)
for z in range(0, column_number + 1):
# print(mat[q][z])
# print(mat[k][z])
mat[q][z] -= num * mat[k][z]
def finding_free_variables(mat, pivot_matrix, row, coloumns):
free_variables = []
free_variable_num = 0
for x in range(0, row):
requested_row = int(pivot_matrix[x][0])
requested_column = int(pivot_matrix[x][1])
for y in range(0, coloumns):
cnt = 0
if mat[requested_row][y] != 0 and y != requested_column and mat[requested_row][coloumns] != 0:
for z in range(0, free_variable_num):
if free_variables[z] == (y):
cnt += 1
break
if cnt == 0:
free_variables.append(y)
free_variable_num += 1
return free_variables
def print_result(mat, free_variables, columns, rows, pivot_matrix, pivot_row):
p = 0
# print(pivot_row)
free_num = len(free_variables_list)
for z in range(0, columns):
if p < pivot_row and pivot_matrix[p][1] == z:
r = int(pivot_matrix[p][0])
c = int(pivot_matrix[p][1])
print("x{} is ".format(z + 1), end="")
if mat[r][c] != 1:
print("{}*".format((1 / mat[r][c])), end="")
print("({}".format(mat[r][columns]), end="")
for q in range(0, columns):
if mat[r][q] != 0 and q != c:
print("+{}".format(mat[r][q]), end="")
print(")")
p +=1
else:
for f in range(0, free_num):
if free_variables[f] == z:
print("x{} is free".format(z+1))
# print("\n")
print("Coefficient matrix")
print("Enter number of rows: ", end="")
rows = input()
print("Enter number of columns: ", end="")
columns = input()
matrix = creating_matrix(rows, columns)
columns = int(columns)
rows = int(rows)
print("Given Matrix:")
print(matrix)
# for i in range(0, columns):
i = 0
pivot_array = np.zeros((1, 2))
row_numbers = 0
while i < columns:
j = i
while j < columns:
proper_row = j
if finding_pivot_column(matrix, j, rows, i) is True:
if matrix[i][j] == 0:
proper_row = find_row(matrix, i, j, rows)
if i == 0:
pivot_array[0][0] = i
pivot_array[0][1] = j
row_numbers += 1
else:
new_pivot_array = np.zeros((1, 2))
new_pivot_array[0][0] = i
new_pivot_array[0][1] = j
pivot_array = np.vstack((pivot_array, new_pivot_array))
row_numbers += 1
break
else:
j += 1
if proper_row != j and i < rows and proper_row < rows:
matrix = interchange(matrix, columns, i, j, proper_row)
# print(matrix)
matrix = row_replacement(matrix, j, i, rows, columns)
# print("**************")
# print(matrix)
i += 1
# print(matrix)
making_echelon_form(matrix, pivot_array, row_numbers, columns)
# print(matrix)
# print(columns)
free_variables_list = finding_free_variables(matrix, pivot_array, row_numbers, columns)
# print(free_variables_list)
print_result(matrix, free_variables_list, columns, rows, pivot_array, row_numbers)