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determinantes_gauss_jordan.py
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determinantes_gauss_jordan.py
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import pandas as pd
import numpy as np
import time
number_columns = 3
# while number_columns < 2:
# number_columns = int(input('Escriba el número de incógnitas de las ecuaciones: '))
# if number_columns < 2:
# print("No válido, intente de nuevo")
array = np.array([
[2,1,-1,1,0],
[4,1,2,1,0],
[2,2,3,1,0],
])
print(array)
number_columns = array.shape[1]-2
number_equation = number_columns
number_columns +=1
array_comparation = np.zeros((number_equation, number_columns-1))
_RES_COLUMN = "res"
_TR_COLUMN = "transformed" #columna que indica si el pivote ya fue usado
matriz_df = pd.DataFrame(array,columns=[f"x{i+1}" for i in range(number_columns+1)],index=[f"ec{i+1}" for i in range(number_equation)])
matriz_comparation = pd.DataFrame(array_comparation,columns=[f"x{i+1}" for i in range(number_columns-1)],index=[f"ec{i+1}" for i in range(number_equation)])
matriz_df.columns = matriz_df.columns[:-2].tolist() + [_RES_COLUMN] + [_TR_COLUMN]
if number_columns > 2:
matriz_no_valid = [
matriz_comparation.iloc[1:,:number_columns-2].copy(),#esquina inferior izquierda
matriz_comparation.iloc[1:,1:number_columns-2].copy(),#esquina inferior derecha
matriz_comparation.iloc[1:,1:number_columns-2].copy(),#esquina inferior derecha
matriz_comparation.iloc[1:,1:number_columns-2].copy()#esquina inferior derecha
]
print("matriz_df")
print(matriz_df.iloc[:,:-1])
zeros_pivot = 0
for row_index in range(number_equation):
# for column_index in range(number_columns):
# value = float(input(f'Ingrese el valor de [{row_index},{column_index}]: '))
# matriz_df.iloc[row_index, column_index] = value
matriz_comparation.iloc[row_index,row_index] = 1
if (matriz_df.iloc[row_index,row_index] == 0): zeros_pivot += 1
def transform_pivot_to_1(matriz, pivot, operations, rows_changes):
print(f'F{pivot} => F{pivot} / {matriz.iloc[pivot,pivot]} ---------------')
if (matriz.iloc[pivot,pivot] == 0):
matriz, isValid, rows_changes = prepare_matrix(matriz, pivot, rows_changes)
return (matriz,isValid,operations, rows_changes)
operations.append(1/matriz.iloc[pivot,pivot])
matriz.iloc[pivot] = matriz.iloc[pivot].astype(float) / matriz.iloc[pivot,pivot].astype(float)
matriz.iloc[pivot,-1] = 1
return (matriz,True, operations,rows_changes)
def transform_to_0(matriz, pivot, row_index):
if pivot == row_index: return (matriz,True)
print(f'F{row_index} => F{row_index} + (F{pivot} * {-1} * {matriz.iloc[row_index,pivot]}) ---------------')
matriz.iloc[row_index] = matriz.iloc[row_index].astype(float) + (((matriz.iloc[pivot].astype(float)) * -1) * (matriz.iloc[row_index,pivot].astype(float)))
matriz.iloc[row_index,-1] = 0
return (matriz,True)
def gauss_jordan(matriz, pivot, operations_det, rows_changes):
# print(f'pivot => {pivot}--{range(matriz.shape[0]-1)}')
pivote_transform = False
isValid = True
for row_count in range(matriz.shape[0]):
# print(f'row_count => {row_count}')
if not pivote_transform:
if (matriz.iloc[row_count,pivot] != 1):
(matriz,isValid, operations_det, rows_changes) = transform_pivot_to_1(matriz,pivot, operations_det, rows_changes)
if not isValid:
return (matriz,False, operations_det)
pivote_transform = True
if (matriz.iloc[row_count,pivot] != 0):
(matriz,isValid) = transform_to_0(matriz,pivot,row_count)
print(matriz.iloc[:,:-1])
return (matriz,True, operations_det, rows_changes)
def prepare_matrix(matriz, pivot, rows_changes):
print('PREPARE')
row = matriz.iloc[pivot]
for i in range(matriz.shape[0]):
# print("(",matriz.iloc[i,pivot]," != 0) and ",matriz.iloc[i,-1]," == 0")
if (matriz.iloc[i,pivot] != 0) and matriz.iloc[i,-1] == 0:
row = matriz.iloc[i].copy()
matriz.iloc[i] = matriz.iloc[0]
matriz.iloc[0] = row
print(matriz.iloc[:,:-1])
rows_changes+=1
return matriz, True, rows_changes
print(matriz_df.iloc[:,:-1])
return matriz, False, rows_changes
def validate_matrix(matriz):
if (zeros_pivot > number_equation-1):
print('LA MATRIZ NO TIENE SOLUCIÓN 1')
return matriz, False
for i in matriz.columns:
if i != _RES_COLUMN and i != _TR_COLUMN:
ceros = matriz[matriz[i] == 0]
if ceros.shape[0] == matriz.shape[0]:
print('LA MATRIZ NO TIENE SOLUCIÓN 2')
return matriz, False
return matriz, True
def determinantes(matriz, operations, rows_changes):
res_op = 1
res_diag = 1
for i in range(len(operations)):
res_op = operations[i]*res_op
for i in range(matriz.shape[0]):
if i == 0:
res_diag = matriz.iloc[i,i]
res_diag = res_diag * matriz.iloc[i,i]
res = res_diag * (1/res_op) * ((-1)**rows_changes)
print(f"DETERMINANTE => {res}")
print('VALIDATE')
isValid = False
print(zeros_pivot," <= ",number_equation-1)
matriz_df,isValid = validate_matrix(matriz_df)
print(matriz_df.iloc[:,:-1])
if isValid:
count_column = 0
iterations_count = 0
operations_det = []
changes = 0
while not matriz_comparation.equals(matriz_df.iloc[:, :-2].astype(float)):
(matriz_df,isValid, operations_det, changes) = gauss_jordan(matriz_df, count_column, operations_det, changes)
if not isValid:
print('La matriz no tiene solución')
break
count_column += 1
iterations_count += 1
if count_column == matriz_df.columns.size-2: count_column = 0
# print("iterations_count => ",iterations_count)
if iterations_count > (number_columns**2)+10:
print("Límite de iteraciones, no se pudo solucionar la matriz")
isValid = False
break
time.sleep(0.5)
if isValid:
print("SOLUCIONADO:")
print(matriz_df.iloc[:,:-1])
determinantes(matriz_df,operations_det, changes)
else:
print("Sucedió un error")