Algoritma Analizinde Matris Çarpımı

In [1]:

from random import randint
def create_A_vector(size):
    my_vector=[]
    for i in range(size):
        my_vector.append(randint(0,9))
    return my_vector

In [2]:

def create_a_matrix(m,n):
    my_matrix=[]
    for i in range(m):
        my_matrix.append(create_A_vector(n))
    return my_matrix

In [3]:

def vector_inner_product(v1,v2):
    if(len(v1)!=len(v2)):
        print("vectörler aynı boyutta olmalı")
        return 
    result=0
    for i in range (len (v1)):
        result =result+v1[i]*v2[i]
    return result

In [4]:

def matrix_multiplication(a,b):
    m=len(a)
    n=len(a[0])
    #n is also rows of the b
    p=len(b[0])
    
    my_matrix=create_a_matrix(m,p)
    
    for i in range(m):
        for j in range(p):
            vector_1=a[i]
            vector_2=[i[j] for i in b]# sütunu alma işlemi
            my_matrix[i][j]=vector_inner_product(vector_1,vector_2)
    return (my_matrix,m*n*p)
    

In [5]:

#VECTOR ornegi
size=10
my_vector_1=create_A_vector(size)
my_vector_2=create_A_vector(size)
print(my_vector_1,my_vector_2)

[0, 3, 8, 0, 9, 3, 7, 5, 7, 2] [0, 0, 1, 2, 0, 8, 6, 2, 5, 4]

In [6]:

#ORNEK
vector_product=vector_inner_product(my_vector_1,my_vector_2)
vector_product

Out[6]:

127

In [7]:

#Ornek
ornek_matris=create_a_matrix(2,3)
ornek_matris

Out[7]:

[[2, 5, 6], [0, 7, 0]]

In [9]:

#boyut
len(ornek_matris),len(ornek_matris[0])

Out[9]:

(2, 3)

In [10]:

#Ornek
a=create_a_matrix(2,3)
b=create_a_matrix(3,5)
c=matrix_multiplication(a,b)

In [11]:

print(a,"\n\n",b,"\n\n",c,"\n\n")

[[4, 8, 4], [0, 5, 0]] 

 [[1, 4, 2, 6, 8], [4, 8, 3, 6, 5], [4, 9, 7, 4, 9]] 

 ([[52, 116, 60, 88, 108], [20, 40, 15, 30, 25]], 30) 

In [12]:

[i for i in a] #diziyi farklı şekilde yazdırma örneği

Out[12]:

[[4, 8, 4], [0, 5, 0]]

In [13]:

[i[1] for i in a] #1. sutun

Out[13]:

[8, 5]

In [14]:

a_1=create_a_matrix(1,10)

a_2=create_a_matrix(10,1000)
a_3=create_a_matrix(1000,1)

a_4=create_a_matrix(1,10)
a_5=create_a_matrix(10,3)

islem_sayisi=0

r_1=matrix_multiplication(a_1,a_2)
islem_sayisi=islem_sayisi+r_1[1]

r_1=matrix_multiplication(r_1[0],a_3)
islem_sayisi=islem_sayisi+r_1[1]

r_1=matrix_multiplication(r_1[0],a_4)
islem_sayisi=islem_sayisi+r_1[1]

r_1=matrix_multiplication(r_1[0],a_5)
islem_sayisi=islem_sayisi+r_1[1]

In [15]:

print(r_1," toplam islem sayisi: ",islem_sayisi)

([[173587876, 285180082, 227693188]], 30)  toplam islem sayisi:  11040

In [16]:

a_1=create_a_matrix(1,10)
#öne 2 ile 3 ü sonra 1 ileçıkan sonucu çarp
a_2=create_a_matrix(10,1000)
a_3=create_a_matrix(1000,1)

a_4=create_a_matrix(1,10)
a_5=create_a_matrix(10,3)

islem_sayisi2=0

r_1=matrix_multiplication(a_2,a_3)
islem_sayisi2=islem_sayisi2+r_1[1]

r_1=matrix_multiplication(a_1,r_1[0])
islem_sayisi2=islem_sayisi2+r_1[1]

r_2=matrix_multiplication(a_4,a_5)
islem_sayisi2=islem_sayisi2+r_1[1]

r_1=matrix_multiplication(r_1[0],r_2[0])
islem_sayisi2=islem_sayisi2+r_1[1]

In [18]:

print(r_1," toplam islem sayisi: ",islem_sayisi2)

([[146661930, 111967710, 190818210]], 3)  toplam islem sayisi:  10023

In [19]:

print("İşlem sayisi: ",islem_sayisi-islem_sayisi2," kadar azaldı")

İşlem sayisi:  1017  kadar azaldı

In [ ]: