Basic Linear Algebra

def vector_size_check(*vector_variables):

    return all(len(vector_variables[0]) == x

               for x in [len(vector) for vector in vector_variables[1:]])

 

# 실행결과

print(vector_size_check([1,2,3], [2,3,4], [5,6,7])) # Expected value: True

print(vector_size_check([1, 3], [2,4], [6,7])) # Expected value: True

print(vector_size_check([1, 3, 4], [4], [6,7])) # Expected value: False

 

 

def vector_addition(*vector_variables):

    if vector_size_check(*vector_variables) == False:

        raise ArithmeticError

    return [sum(elements) for elements in zip(*vector_variables)]

 

# 실행결과

print(vector_addition([1, 3], [2, 4], [6, 7])) # Expected value: [9, 14]

print(vector_addition([1, 5], [10, 4], [4, 7])) # Expected value: [15, 16]

print(vector_addition([1, 3, 4], [4], [6,7])) # Expected value: ArithmeticError

 

 

def vector_subtraction(*vector_variables):

    if vector_size_check(*vector_variables) == False:

        raise ArithmeticError

    return [elements[0]*2 - sum(elements)

            for elements in zip(*vector_variables)]

 

# 실행결과

print(vector_subtraction([1, 3], [2, 4])) # Expected value: [-1, -1]

print(vector_subtraction([1, 5], [10, 4], [4, 7])) # Expected value: [-13, -6]

 

 

def scalar_vector_product(alpha, vector_variable):

    return [alpha * element for element in vector_variable]

 

# 실행결과

print (scalar_vector_product(5,[1,2,3])) # Expected value: [5, 10, 15]

print (scalar_vector_product(3,[2,2])) # Expected value: [6, 6]

print (scalar_vector_product(4,[1])) # Expected value: [4]

 

 

def matrix_size_check(*matrix_variables):

    return all([len(set(len(matrix[0]) for matrix in matrix_variables)) == 1]) and all([len(matrix_variables[0]) == len(matrix) for matrix in matrix_variables])

 

# 실행결과

matrix_x = [[2, 2], [2, 2], [2, 2]]

matrix_y = [[2, 5], [2, 1]]

matrix_z = [[2, 4], [5, 3]]

matrix_w = [[2, 5], [1, 1], [2, 2]]

 

print (matrix_size_check(matrix_x, matrix_y, matrix_z)) # Expected value: False

print (matrix_size_check(matrix_y, matrix_z)) # Expected value: True

print (matrix_size_check(matrix_x, matrix_w)) # Expected value: True

 

 

def is_matrix_equal(*matrix_variables):

    # print([maxtix for matrix in zip(*matrix_variables)])

    return all([ all([len(set(row)) == 1 for row in zip(*matrix)])

                     for matrix in zip(*matrix_variables) ])

 

# 실행결과

matrix_x = [[2, 2], [2, 2]]

matrix_y = [[2, 5], [2, 1]]

 

print (is_matrix_equal(matrix_x, matrix_y, matrix_y, matrix_y)) # Expected value: False

print (is_matrix_equal(matrix_x, matrix_x)) # Expected value: True

 

 

def matrix_addition(*matrix_variables):

    if matrix_size_check(*matrix_variables) == False:

        raise ArithmeticError

    return [[sum(row) for row in zip(*matrix)]

            for matrix in zip(*matrix_variables)]

 

# 실행결과

matrix_x = [[2, 2], [2, 2]]

matrix_y = [[2, 5], [2, 1]]

matrix_z = [[2, 4], [5, 3]]

 

print (matrix_addition(matrix_x, matrix_y)) # Expected value: [[4, 7], [4, 3]]

print (matrix_addition(matrix_x, matrix_y, matrix_z)) # Expected value: [[6, 11], [9, 6]]

 

 

def matrix_subtraction(*matrix_variables):

    if matrix_size_check(*matrix_variables) == False:

        raise ArithmeticError

    return [[row[0]*2 - sum(row)

             for row in zip(*matrix)]

            for matrix in zip(*matrix_variables)]

 

# 실행결과

matrix_x = [[2, 2], [2, 2]]

matrix_y = [[2, 5], [2, 1]]

matrix_z = [[2, 4], [5, 3]]

 

print (matrix_subtraction(matrix_x, matrix_y)) # Expected value: [[0, -3], [0, 1]]

print (matrix_subtraction(matrix_x, matrix_y, matrix_z)) # Expected value: [[-2, -7], [-5, -2]]

 

 

def matrix_transpose(matrix_variable):

    return [ [element for element in row] for row in zip(*matrix_variable)]

 

# 실행결과

matrix_w = [[2, 5], [1, 1], [2, 2]]

print (matrix_transpose(matrix_w)) # [[2, 1, 2], [5, 1, 2]]

 

 

def scalar_matrix_product(alpha, matrix_variable):

    return [ scalar_vector_product(alpha, row) for row in matrix_variable]

 

# 실행결과

matrix_x = [[2, 2], [2, 2], [2, 2]]

matrix_y = [[2, 5], [2, 1]]

matrix_z = [[2, 4], [5, 3]]

matrix_w = [[2, 5], [1, 1], [2, 2]]

 

print(scalar_matrix_product(3, matrix_x)) #Expected value: [[6, 6], [6, 6], [6, 6]]

print(scalar_matrix_product(2, matrix_y)) #Expected value: [[4, 10], [4, 2]]

print(scalar_matrix_product(4, matrix_z)) #Expected value: [[8, 16], [20, 12]]

print(scalar_matrix_product(3, matrix_w)) #Expected value: [[6, 15], [3, 3], [6, 6]]

 

 

def is_product_availability_matrix(matrix_a, matrix_b):

    return len([column_vector for column_vector in zip(*matrix_a)]) == len(matrix_b)

 

# 실행결과

matrix_x= [[2, 5], [1, 1]]

matrix_y = [[1, 1, 2], [2, 1, 1]]

matrix_z = [[2, 4], [5, 3], [1, 3]]

 

print(is_product_availability_matrix(matrix_y, matrix_z)) # Expected value: True

print(is_product_availability_matrix(matrix_z, matrix_x)) # Expected value: True

print(is_product_availability_matrix(matrix_z, matrix_w)) # Expected value: False //matrix_w가없습니다

print(is_product_availability_matrix(matrix_x, matrix_x)) # Expected value: True

 

 

def matrix_product(matrix_a, matrix_b):

    if is_product_availability_matrix(matrix_a, matrix_b) == False:

        raise ArithmeticError

    return [ [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]

 

# 실행결과

matrix_x= [[2, 5], [1, 1]]

matrix_y = [[1, 1, 2], [2, 1, 1]]

matrix_z = [[2, 4], [5, 3], [1, 3]]

 

print(matrix_product(matrix_y, matrix_z)) # Expected value: [[9, 13], [10, 14]]

print(matrix_product(matrix_z, matrix_x)) # Expected value: [[8, 14], [13, 28], [5, 8]]

print(matrix_product(matrix_x, matrix_x)) # Expected value: [[9, 15], [3, 6]]

print(matrix_product(matrix_z, matrix_w)) # Expected value: False

 

 

 

 

 

참조 : http://www.boostcourse.org/ -> 머신러닝을 위한 파이썬