# matrix3: [[1, 2, 0], [2, 1, 5], [1, 1, 2], [1, 0, 0], [4, 1, 2]]
# matrix4: [[2, 0], [1, 3], [0, 1]]
# matrix5: [[2, 0, 1], [1, 2, 2], [0, 3, 3]]
# zero_2_2: [[0, 0], [0, 0]]
# zero_2_3: [[0, 0, 0], [0, 0, 0]]
# identity_3: [[1, 0, 0], [0, 1, 0], [0, 0, 1]]
# vector: [2, 1, 0]
matrix = Matrix([[1, 2], [3, 4]])
matrix2 = Matrix([[10, 20], [30, 40]])
matrix3 = Matrix([[1, 2, 0], [2, 1, 5], [1, 1, 2], [1, 0, 0], [4, 1, 2]])
matrix4 = Matrix([[2, 0], [1, 3], [0, 1]])
matrix5 = Matrix([[2, 0, 1], [1, 2, 2], [0, 3, 3]])
zero_2_2 = Matrix.zero(2, 2)
zero_2_3 = Matrix.zero(2, 3)
identity_3 = Matrix.identity(3)
vector = Vector([2, 1, 0])
print("matrix:", matrix)
print("matrix2:", matrix2)
print("matrix3:", matrix3)
print("matrix4:", matrix4)
print("matrix5:", matrix5)
print("zero_2_2:", zero_2_2)
print("zero_2_3:", zero_2_3)
print("identity_3:", identity_3)
print("vector:", vector)
print("------")
# matrix[0]: [1, 2]
# matrix[0, 1]: 2
# matrix.shape(): (2, 2)
from la.vector import Vector
if __name__ == "__main__":
# vector = [5, 2]
# vector2 = [3, 1]
# zero_2 = [0, 0]
# zero_3 = [0, 0, 0]
vector = Vector([5, 2])
vector2 = Vector([3, 1])
zero_2 = Vector.zero(2)
zero_3 = Vector.zero(3)
print("vector = {}".format(vector))
print("vector2 = {}".format(vector2))
print("zero_2 = {}".format(zero_2))
print("zero_3 = {}".format(zero_3))
print("------")
# len(vector) = 2
# vector[0] = 5, vector[1] = 2
print("len(vector) = {}".format(len(vector)))
print("vector[0] = {}, vector[1] = {}".format(vector[0], vector[1]))
print("------")
# [5, 2] + [3, 1] = [8, 3]
# [5, 2] + [0, 0] = [5, 2]
# [5, 2] - [3, 1] = [2, 1]
# [5, 2] - [0, 0] = [5, 2]
# [5, 2] * 3 = [15, 6]
# 3 * [5, 2] = [15, 6]
from la.vector import Vector
if __name__ == "__main__":
# vector = [5, 2]
# vector2 = [3, 1]
# zero_2 = [0, 0]
# zero_3 = [0, 0, 0]
vector = Vector([5, 2])
vector2 = Vector([3, 1])
zero_2 = Vector.zero(2)
zero_3 = Vector.zero(3)
print("vector = {}".format(vector))
print("vector2 = {}".format(vector2))
print("zero_2 = {}".format(zero_2))
print("zero_3 = {}".format(zero_3))
print("------")
# len(vector) = 2
# vector[0] = 5, vector[1] = 2
print("len(vector) = {}".format(len(vector)))
print("vector[0] = {}, vector[1] = {}".format(vector[0], vector[1]))
print("------")
# [5, 2] + [3, 1] = [8, 3]
# [5, 2] + [0, 0] = [5, 2]
# [5, 2] - [3, 1] = [2, 1]
# [5, 2] - [0, 0] = [5, 2]
# [5, 2] * 3 = [15, 6]
# 3 * [5, 2] = [15, 6]
from la.linear_system import LinearSystem
from la.matrix import Matrix
from la.vector import Vector
if __name__ == "__main__":
# 1.0 0.0 0.0 | 2.0
# -0.0 1.0 0.0 | -1.5
# 0.0 0.0 1.0 | 1.0
matrix = Matrix([[0, 4, 8], [2, 2, 1], [4, 8, 8]])
vector = Vector([2, 2, 4])
linear_system = LinearSystem(matrix, vector)
linear_system.gauss_jordan_elimination()
linear_system.augmented_matrix_fancy_print()
print("------")
# 1.0 0.0 0.0 | -1.0
# 0.0 1.0 0.0 | -2.0
# -0.0 -0.0 1.0 | 3.0
matrix = Matrix([[1, 2, 4], [3, 7, 2], [2, 3, 3]])
vector = Vector([7, -11, 1])
linear_system = LinearSystem(matrix, vector)
linear_system.gauss_jordan_elimination()
linear_system.augmented_matrix_fancy_print()
print("------")
# 1.0 0.0 0.0 | 2.0
# 0.0 1.0 0.0 | -3.0
# 0.0 0.0 1.0 | -4.0
matrix = Matrix([[1, -3, 5], [2, -1, -3], [3, 1, 4]])
from la.vector import Vector
if __name__ == "__main__":
# vector = [5, 2]
# vector2 = [3, 1]
vector = Vector([5, 2])
vector2 = Vector([3, 1])
print("vector = {}".format(vector))
print("vector2 = {}".format(vector2))
print("------")
# len(vector) = 2
# vector[0] = 5, vector[1] = 2
print("len(vector) = {}".format(len(vector)))
print("vector[0] = {}, vector[1] = {}".format(vector[0], vector[1]))
from la.linear_system import LinearSystem
from la.matrix import Matrix
from la.vector import Vector
if __name__ == "__main__":
# 1.0 0.0 0.0 | 2.0
# -0.0 1.0 0.0 | -1.5
# 0.0 0.0 1.0 | 1.0
# ONE
# [0, 1, 2]
matrix = Matrix([[0, 4, 8], [2, 2, 1], [4, 8, 8]])
vector = Vector([2, 2, 4])
linear_system = LinearSystem(matrix, vector)
linear_system.gauss_jordan_elimination()
linear_system.augmented_matrix_fancy_print()
print(linear_system.determine_solution())
print(linear_system.pivots)
print("------")
# 1.0 0.0 0.0 | -1.0
# 0.0 1.0 0.0 | -2.0
# -0.0 -0.0 1.0 | 3.0
# ONE
# [0, 1, 2]
matrix = Matrix([[1, 2, 4], [3, 7, 2], [2, 3, 3]])
vector = Vector([7, -11, 1])
linear_system = LinearSystem(matrix, vector)
linear_system.gauss_jordan_elimination()
linear_system.augmented_matrix_fancy_print()
print(linear_system.determine_solution())
# coding: utf-8
'''
@author: jessezhu
@file: main_vector.py
@time: 2019/8/15 2:46 PM
@desc:
'''
from la.vector import Vector
if __name__ == '__main__':
vector = Vector([1, 2, 3])
print("vector={}".format(vector))
print('vector[0]={},vector[1]={}'.format(vector[0], vector[1]))
vector2 = Vector([1, 2, 3])
print("{}+{}={}".format(vector, vector2, vector + vector2))
print("{}-{}={}".format(vector, vector2, vector - vector2))
print("{}*{}={}".format(vector, 3, vector * 3))
print("{}*{}={}".format(3, vector, 3 * vector))
print("+{}={}".format(vector, +vector))
print("-{}={}".format(vector, -vector))
zero = Vector.zero(2)
print("zero 2 = {} ".format(zero))
norm_vec = Vector([3, 4])
print('norm({}) = {}'.format(norm_vec, norm_vec.norm()))
print('normalize({}) = {} and its norm = {}'.format(