Linear algebra with python

python으로 vector 표현 방법

vector_a = [1,2,3] # List 
vector_b = (1,2,3) # Tuple
vector_c = {'x':1, 'y':2, 'z':3} #dict

vector 계산

• bad case

  u = [2,2]
  v = [2,3]
  z = [3,5]
    
  result = []
    
  for i in range( len(u)) :
      result.append(u[i] + v[i] + z[i])
        
  print(result)
  

• python 다운 코드

  u = [2,2]
  v = [2,3]
  z = [3,5]
    
  result = [sum(t) for t in zip(u,v,z)]
  print(result)
  

scala-vector 연산

• 코드

  u = [1,2,3]
  v = [4,4,4]
  alpha = 2
    
  result = [alpha*sum(t) for t in zip(u,v)]
  print(result)
  

• 결과

  2([1,2,3]+[4,4,4]) = 2[5,6,7] = [10,12,14]
  

python으로 Matrix 표현 방법

matrix_a = [[3,6], [4,5]]
matrix_b = [(3,6), (4,5)]
matrix_c = {(0,0):3, (0,1):6, (1,0):4, (1,1): 5}

Matrix 덧셈

matrix_a = [[3,6], [4,5]]
matrix_b = [[5,8], [6,7]]

result = [[sum(row) for row in zip(*t)] for t in zip(matrix_a, matrix_b)]

print(result)

[t for t in zip(matrix_a, matrix_b)] [([3, 6], [5, 8]), ([4, 5], [6, 7])]

[[row for row in zip(*t)] for t in zip(matrix_a, matrix_b)] [[(3, 5), (6, 8)], [(4, 6), (5, 7)]]

scalar-Matrix

matrix_a = [[3,6], [4,5]]
alpha = 4
result = [[alpha * element for element in t] for t in matrix_a]

print(result)

Matrix Transpose

matrix_a = [[1,2,3],[4,5,6]]
result = [[element for element in t] for t in zip(*matrix_a)]

[t for t in zip(*matrix_a)]

Matrix Product

matrix_a = [[1,1,2], [2,1,1]]
matrix_b = [[1,1],[2,1],[1,3]]
result = [[sum(a*b for a,b in zip(row_a, column_b)) for column_b in zip(*matrix_b)] for row_a in matrix_a]
print(result)

[row_a for row_a in matrix_a]

[column_b for column_b in zip(*matrix_b)]

Matrix Addition Function 만들기

def vector_addition(*args):
    print([sum(t) for t in zip(*args)])

vector_addition([1,2],[2,3],[3,4])

참고

w3schools.com-python example