def lu(matrix: Matrix):
assert matrix.row_num() == matrix.col_num(
), "matrix must be a square matrix"
n = matrix.row_num()
A = [matrix.row_vector(i) for i in range(n)]
L = [[1.0 if i == j else 0.0 for i in range(n)] for j in range(n)]
for i in range(n):
# 看A[i][i]位置是否可以是主元
if is_zero(A[i][i]):
return None, None
else:
for j in range(i + 1, n):
p = A[j][i] / A[i][i]
A[j] = A[j] - p * A[i]
L[j][i] = p
return Matrix(L), Matrix([A[i].underlying_list() for i in range(n)])
from playLA.Matrix import Matrix
from playLA.Vector import Vector
if __name__ == '__main__':
matrix = Matrix([[1, 2], [3, 4]])
print(matrix)
print("矩阵的形状：{}".format(matrix.shape()))
print("矩阵的行数：{}，矩阵的列数：{}".format(matrix.row_num(), matrix.col_num()))
print("矩阵的元素个数：{}".format(matrix.size()))
print("矩阵元素：{}".format(matrix[1, 1]))
print("矩阵行向量：{}".format(matrix.row_vector(1)))
print("矩阵列向量：{}".format(matrix.col_vector(1)))
m2 = Matrix([[2, 4], [4, 6]])
print("add:{}".format(matrix + m2))
print("sub:{}".format(matrix - m2))
print("multi:{}".format(matrix * 2))
print("rMulti:{}".format(2 * matrix))
print("div:{}".format(m2 / 2))
print("neg:{}".format(-m2))
print("零矩阵:{}".format(Matrix.zero(3, 2)))
T = Matrix([[1.5, 0], [0, 2]])
p = Vector([5, 3])
print("T.dot(p) = {}".format(T.dot(p)))
T2 = Matrix([[0, 4, 5], [0, 0, 3]])
print("T.dot(T2) = {}".format(T.dot(T2)))
print("转置：{}".format(T2.T()))
I = Matrix.identity(2)
from playLA.Matrix import Matrix
if __name__ == '__main__':
matrix = Matrix([[1, 3, 5], [2, 4, 6]])
print(matrix)
print(matrix.shape())
print("row num = {}, col num = {}".format(matrix.row_num(),
matrix.col_num()))
print("matrix[0][0] = {}".format(matrix[0, 0]))
matrix2 = Matrix([[3, 6, 9], [1, 4, 7]])
print("add: {}".format(matrix + matrix2))
print("sub: {}".format(matrix - matrix2))
print("{} * {} = {}".format(matrix2, 3, matrix2 * 3))
print("{} * {} = {}".format(2, matrix2, 2 * matrix2))
print("{}".format(-matrix2))
print("{}".format(Matrix.zero(2, 2)))
A = Matrix([[1, 2], [3, 4]])
B = Matrix([[5, 6], [7, 8]])
print("A.dot(B) = {}".format(A.dot(B)))
print("B.dot(A) = {}".format(B.dot(A)))
I = Matrix.identity(3)
print("单位矩阵I = {}".format(I))
print("matrix2.dot(I) = {}".format(matrix2.dot(I)))
