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#-*- coding: utf-8 -*-
import matplotlib.pyplot as plt
import math;
from LibreriaNumerosComplejos import *
"""Librería computación Cuántica: Números complejos
librería para hacer operaciones entre vectores y matrices de complejos.
@author (Juan Camilo Posso G.)
@version (1.0 or 16/01/2020)rr
"""
class matriz:
def __init__(self,c):
self.c=c
for j in range(len(self.c)):
for k in range(len(self.c[0])):
if(not(isinstance(self.c[j][k],complejo))):
self.c[j][k]=complejo(self.c[j][k][0],self.c[j][k][1])
def __eq__(self, other):
"""Override"""
if(len(self.c[0])==len(other.c[0])and len(self.c)==len(other.c)):
for j in range(len(self.c)):
for k in range(len(self.c[0])):
if isinstance(other.c[j][k], complejo):
if(round(self.c[j][k].real,4) != round(other.c[j][k].real,4) or round(self.c[j][k].img,4) != round(other.c[j][k].img,4)):
return False
return True
return False
def iniciar(f,c):
m=[]
for i in range(f):
m.append([ [0,0] ]*c)
return matriz(m)
def unitaria(c):
m=[]
temp=matriz.iniciar(c,c)
for i in range(c):
temp.c[i][i]=complejo(1,0)
return temp
def trace(C):
suma=complejo(0,0)
for j in range(len(C.c[0])):
suma=suma.suma(C.c[j][j])
return suma
def instanciar(self):
v2=matriz.iniciar(len(self.c),len(self.c[0]))
for j in range(len(self.c)):
for k in range(len(self.c[0])):
v2.c[j][k]=self.c[j][k]
return v2
def suma(self,W):
m=len(self.c);n=len(self.c[0]);n2=len(W.c);p=len(W.c[0])
if(m!=n2 or n!=p):return( "Las matrices no tienen el tamaño apropiado")
res=matriz.iniciar(len(self.c),len(self.c[0]))
for j in range(len(self.c)):
for k in range(len(self.c[0])):
res.c[j][k]=(self.c[j][k]).suma(W.c[j][k])
return res
def inversa(self):
for j in range(len(self.c)):
for k in range(len(self.c[0])):
self.c[j][k]=(self.c[j][k]).multiplica(complejo(-1,0))
return self
def multiplica(self,W):
m=len(self.c);n=len(self.c[0]);n2=len(W.c);p=len(W.c[0])
if(n!=n2): return "Las matrices no tienen el tamaño apropiado"
res=matriz.iniciar(len(self.c),len(W.c[0]))
for j in range(m):
for k in range(p):
cont=complejo(0,0)
for h in range(n):
cont=cont.suma( (self.c[j][h]).multiplica(W.c[h][k]) )
res.c[j][k]=cont
return res
def multiplicaEscalar(self,e):
if(isinstance(self,complejo)):temp=e;e=self;self=temp
res=matriz.iniciar(len(self.c),len(self.c[0]))
for j in range(len(self.c)):
for k in range(len(self.c[0])):
res.c[j][k]=(self.c[j][k]).multiplica(e)
return res
def transpuesta(self):
m=matriz.iniciar(len(self.c[0]),len(self.c))
for j in range(len(self.c[0])):
for k in range(len(self.c)):
m.c[j][k]=self.c[k][j]
self.c=m.c
return self
def conjugada(self):
for j in range(len(self.c)):
for k in range(len(self.c[0])):
self.c[j][k]=self.c[j][k].conjugado()
return self
def adjunta(self):
self=(self.transpuesta()).conjugada()
return self
def alcanceSobre(self,vector):
if(len(vector.c[0])==1 ):
res=matriz.iniciar(len(vector.c),1)
for j in range(len(self.c)):
for k in range(len(self.c[0])):
res.c[j][0] =res.c[j][0].suma( self.c[j][k].multiplica(vector.c[k][0]) )
return res
return "no ingresó un vector, intente nuevamente!"
def productoInterno(self,W):
producto= (self.adjunta() ).multiplica(W)
if( len(self.c[0])==len(W.c[0])==1):
return producto
return producto.trace()
def isHermitian(self):
n=matriz.instanciar(self)
for j in range(len(self.c)):
for k in range(len(self.c[0])):
if( self.c[j][k]!=n.c[k][j].conjugado()):
return False
return True
def isUnitary(self):
n=matriz.instanciar(self)
if(len(self.c[0])==len(self.c)):
if( self.multiplica(n.adjunta())==(self.adjunta().multiplica(n) )):
return True
return False
def norma(self):
m= matriz(self.c)
return round(math.sqrt(int(str(self.productoInterno(m)))),2)
def distancia(self,v2):
return (self.suma( v2.inversa()).norma( ))
def productoTensor(self,B):
f=len(B.c)*len(self.c)
c=len(self.c[0])*len(B.c[0])
matrix=matriz.iniciar(f,c)
o=0;p=0
for j in range(len(matrix.c)):
for k in range(len(matrix.c[0])):
matrix.c[j][k]=self.c[j//len(B.c)][k//len(B.c[0])].multiplica(B.c[j%len(B.c)][k%len(B.c[0])])
return matrix
def potencia(self,n):
if(n==1):
return self
else:
if( (n%2)==0):
return (self.potencia(n//2)).multiplica(self.potencia(n//2))
else:
return (self.potencia(n//2).multiplica(self.potencia(n//2))).multiplica(self)
def state(self,v,times):
if(times==0):return self
return (self.potencia(times)).alcanceSobre(v)
def combinar(m1,m2,v1,v2,n):
if (n==0):
e1=v1
e2=v2
else:
e1=m1.potencia(n).multiplica(v1)
e2=m2.potencia(n).multiplica(v2)
return e1.productoTensor(e2)
def cuadrada(self):
return len(self.c)==len(self.c[0])
def n_BlancosOptimo(n,n2):
return n+( ((n//2)+1)*(n2-1))
def isDoublyStochastic(self):
vPrueba=matriz.iniciar(len(self.c),1)
for i in range(len(self.c)):
vPrueba.c[i][0]=complejo(1,0)
return self.alcanceSobre(vPrueba)==vPrueba
def __str__(self):
s=""
for j in range(len(self.c)):
s+="[ "
for k in range(len(self.c[0])):
s+=str(self.c[j][k])+" "
s+=']\n'
return s