faddeev_leverrier.py

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#  EL SIGUIENTE SCRIPT PERMITE CONSTRUIR EL POLINOMIO CARCTERISTICO DE UNA 
#  DADA MATRIZ A TRAVES DEL ALGORITMO DE FADDEEV - LEVERRIER Y DETERMINAR SUS 
#  RAICES (AUTOVALORES)
#  
#  (https://en.wikipedia.org/wiki/Faddeev%E2%80%93LeVerrier_algorithm)

import math as mth 
#[1,2]
import numpy as np 
#[1,3]

A = np.array([[3,1],[8,3]]) 
#[4]

n = 2
#[5,6]

C = np.zeros(n+1) 
#[7]
M = list([]) 
#[8]

for k in range(0,n+1): 
  #[9]
  if k == 0:
    M.append(np.zeros((n,n))) 
    #[8]
    C[n-k] = 1
  else:
    M.append(np.dot(A,M[k-1])+np.dot(C[n-k+1],np.identity(n))) 
    #[10,11]
    C[n-k] = -1/k*np.trace(np.dot(A,M[k])) 
    #[12]

C = np.fliplr([C])[0] 
#[13]

pol= str("p(x) = ")
for i in range(n+1):
  pol = pol + "("+ str(C[i]) + ")"+ " * x^"+str(n-i)+" + "

print("Polinomio caracteristico:","\n",pol[:-8])
print("\n")
print("Autovalores:","\n",np.roots(C)) 
#[14]

#  REFERENCIAS
#  [  1 ]  MODULOS: http://webs.ucm.es/info/aocg/python/lenguaje_programacion/index.html#modulos
#  [  2 ]  MATH: https://programacion.net/articulo/modulos_matematicos_en_python_math_y_cmath_1750
#  [  3 ]  NUMPY: http://webs.ucm.es/info/aocg/python/modulos_cientificos/numpy/index.html
#  [  4 ]  NUMPY.ARRAY: https://docs.scipy.org/doc/numpy-1.15.0/reference/generated/numpy.array.html?highlight=array#numpy.array
#  [  5 ]  NUMPY.NDARRAY.SIZE: https://docs.scipy.org/doc/numpy-1.15.0/reference/generated/numpy.ndarray.size.html?highlight=size#numpy-ndarray-size
#  [  6 ]  MATH.SQRT: https://docs.python.org/2/library/math.html#power-and-logarithmic-functions
#  [  7 ]  NUMPY.ZEROS: https://docs.scipy.org/doc/numpy-1.15.0/reference/generated/numpy.zeros.html#numpy.zeros
#  [  8 ]  LISTAS Y TUPLAS: http://webs.ucm.es/info/aocg/python/lenguaje_programacion/index.html#listas-y-tuplas
#  [  9 ]  RANGE: http://webs.ucm.es/info/aocg/python/lenguaje_programacion/index.html#listas-por-comprension
#  [ 10 ]  NUMPY.DOT: https://docs.scipy.org/doc/numpy-1.15.0/reference/generated/numpy.dot.html?highlight=dot#numpy.dot
#  [ 11 ]  NUMPY.IDENTITY: https://docs.scipy.org/doc/numpy-1.15.0/reference/generated/numpy.identity.html
#  [ 12 ]  NUMPY.TRACE: https://docs.scipy.org/doc/numpy-1.15.0/reference/generated/numpy.trace.html?highlight=trace#numpy.trace
#  [ 13 ]  NUMPY.FLIPLR: https://docs.scipy.org/doc/numpy-1.15.0/reference/generated/numpy.fliplr.html?highlight=flip#numpy.fliplr
#  [ 14 ]  NUMPY.ROOTS: https://docs.scipy.org/doc/numpy-1.15.0/reference/generated/numpy.roots.html