import math
if __name__ == "__main__":
points = [[0, 0], [0, 5], [3, 5], [3, 4], [1, 4], [1, 3], [2, 3], [2, 2],
[1, 2], [1, 0]]
x = [point[0] for point in points]
y = [point[1] for point in points]
plt.figure(figsize=(5, 5))
plt.xlim(-10, 10)
plt.ylim(-10, 10)
plt.plot(x, y)
# plt.show()
P = Matrix(points)
# T = Matrix([[2, 0], [0, 1.5]])
# T = Matrix([[1, 0], [0, -1]])
# T = Matrix([[-1, 0], [0, 1]])
# T = Matrix([[-1, 0], [0, -1]])
# T = Matrix([[1, 0.5], [0, 1]])
# T = Matrix([[1, 0], [0.5, 1]])
# theta = math.pi / 3
# T = Matrix([[math.cos(theta), math.sin(theta)], [-math.sin(theta), math.cos(theta)]])
# 逆时针旋转90度
# theta = math.pi / -2
# T = Matrix([[math.cos(theta), math.sin(theta)], [-math.sin(theta), math.cos(theta)]])
import math
if __name__ == "__main__":
points = [[0, 0], [0, 5], [3, 5], [3, 4], [1, 4], [1, 3], [2, 3], [2, 2],
[1, 2], [1, 0]]
x = [point[0] for point in points]
y = [point[1] for point in points]
plt.figure(figsize=(5, 5))
plt.xlim(-10, 10)
plt.ylim(-10, 10)
plt.plot(x, y)
# plt.show()
P = Matrix(points)
# T = Matrix([[2, 0], [0, 1.5]])
# T = Matrix([[1, 0], [0, -1]])
# T = Matrix([[-1, 0], [0, 1]])
# T = Matrix([[-1, 0], [0, -1]])
# T = Matrix([[1, 0.5], [0, 1]])
# T = Matrix([[1, 0], [0.5, 1]])
theta = math.pi / 3
T = Matrix([[math.cos(theta), math.sin(theta)],
[-math.sin(theta), math.cos(theta)]])
P2 = T.dot(P.T())
plt.plot([P2.col_vector(i)[0] for i in range(P2.col_num())],
[P2.col_vector(i)[1] for i in range(P2.col_num())])
from LA.Matrix import Matrix
if __name__ == "__main__":
matrix = Matrix([[1, 2], [3, 4]])
print(matrix)
print("matrix.shape = {}".format(matrix.shape()))
print("matrix.size = {}".format(matrix.size()))
print("len(matrix) = {}".format(len(matrix)))
print("matrix[0][0] = {}".format(matrix[0, 0]))
from LA.Matrix import Matrix
if __name__ == "__main__":
matrix = Matrix([[1, 2], [3, 4]])
print(matrix)
print("matrix.shape = {}".format(matrix.shape()))
print("matrix.size = {}".format(matrix.size()))
print("len(matrix) = {}".format(len(matrix)))
print("matrix[0][0] = {}".format(matrix[0, 0]))
matrix2 = Matrix([[5, 6], [7, 8]])
print(matrix2)
print("add: {}".format(matrix + matrix2))
print("subtract: {}".format(matrix - matrix2))
print("scalar-mul: {}".format(2 * matrix))
print("scalar-mul: {}".format(matrix * 2))
print("zero_2_3: {}".format(Matrix.zero(2, 3)))
from LA.Matrix import Matrix
from LA.Vector import Vector
from LA.LinearSystem import LinearSystem
from LA.LinearSystem import inv
if __name__ == "__main__":
A = Matrix([[1, 2, 4], [3, 7, 2], [2, 3, 3]])
b = Vector([7, -11, 1])
ls = LinearSystem(A, b)
ls.gauss_jordan_elimination()
ls.fancy_print()
print()
# [-1, -2, 3]
A2 = Matrix([[1, -3, 5], [2, -1, -3], [3, 1, 4]])
b2 = Vector([-9, 19, -13])
ls2 = LinearSystem(A2, b2)
ls2.gauss_jordan_elimination()
ls2.fancy_print()
print()
# [2, -3, -4]
A3 = Matrix([[1, 2, -2], [2, -3, 1], [3, -1, 3]])
b3 = Vector([6, -10, -16])
ls3 = LinearSystem(A3, b3)
ls3.gauss_jordan_elimination()
ls3.fancy_print()
print()
# [-2, 1, -3]
from LA.Vector import Vector
from LA.Matrix import Matrix
if __name__ == "__main__":
matrix = Matrix([[1, 2], [3, 4]])
print(matrix)
print("matrix.shape = {}".format(matrix.shape()))
print("matrix.size = {}".format(matrix.size()))
print("len(matrix) = {}".format(len(matrix)))
print("matrix[0][0] = {}".format(matrix[0, 0]))
matrix2 = Matrix([[5, 6], [7, 8]])
print(matrix2)
print("add: {}".format(matrix + matrix2))
print("subtract: {}".format(matrix - matrix2))
print("scalar-mul: {}".format(2 * matrix))
print("scalar-mul: {}".format(matrix * 2))
print("zero_2_3: {}".format(Matrix.zero(2, 3)))
T = Matrix([[1.5, 0], [0, 2]])
p = Vector([5, 3])
print("T.dot(p) = {}".format(T.dot(p)))
P = Matrix([[0, 4, 5], [0, 0, 3]])
print("T.dot(P) = {}".format(T.dot(P)))
print("A.dot(B) = {}".format(matrix.dot(matrix2)))
print("B.dot(A) = {}".format(matrix2.dot(matrix)))
print("P.T = {}".format(P.T()))
from LA.Matrix import Matrix
from LA.Vector import Vector
from LA.LinearSystem import LinearSystem
if __name__ == "__main__":
A = Matrix([[1, 2, 4], [3, 7, 2], [2, 3, 3]])
b = Vector([7, -11, 1])
ls = LinearSystem(A, b)
ls.gauss_jordan_elimination()
ls.fancy_print()
print()
A2 = Matrix([[1, -3, 5], [2, -1, -3], [3, 1, 4]])
b2 = Vector([-9, 19, -13])
ls2 = LinearSystem(A2, b2)
ls2.gauss_jordan_elimination()
ls2.fancy_print()
print()
A3 = Matrix([[1, 2, -2], [2, -3, 1], [3, -1, 3]])
b3 = Vector([6, -10, -16])
ls3 = LinearSystem(A3, b3)
ls3.gauss_jordan_elimination()
ls3.fancy_print()
print()
A4 = Matrix([[3, 1, -2], [5, -3, 10], [7, 4, 16]])
b4 = Vector([4, 32, 13])
ls4 = LinearSystem(A4, b4)
from LA.Matrix import Matrix
from LA.GramSchmidtProcess import qr
if __name__ == "__main__":
A1 = Matrix([[1, 1, 2],
[1, 1, 0],
[1, 0, 0]])
Q1, R1 = qr(A1)
print(Q1)
print(R1)
print(Q1.dot(R1))
print()
A2 = Matrix([[2, -1, -1],
[2, 0, 2],
[2, -1, 3]])
Q2, R2 = qr(A2)
print(Q2)
print(R2)
print(Q2.dot(R2))
from LA.Matrix import Matrix
from LA.Vector import Vector
if __name__ == "__main__":
matrix = Matrix([[1, 2], [3, 4]])
matrix2 = Matrix([[5, 6], [7, 8]])
print(matrix)
print("matrix.shape = {}".format(matrix.shape()))
print("matrix.row_num = {}".format(matrix.row_num()))
print("matrix.col_num = {}".format(matrix.col_num()))
print("matrix.size = {}".format(matrix.size()))
print("matrix.length = {}".format(len(matrix)))
print("matrix[0][0] = {}".format(matrix[0, 0]))
print("matrix.row_vector = {}".format(matrix.row_vector(0)))
print("matrix.col_vector = {}".format(matrix.col_vector(0)))
print("add: {}".format(matrix + matrix2))
print("sub: {}".format(matrix - matrix2))
print("matrix * 3 = {}".format(matrix * 3))
print("3 * matrix = {}".format(matrix * 3))
print("3 * matrix = {}".format(matrix * 3))
print("zero_2_3 = {}".format(Matrix.zero(2, 3)))
print("matrix.dot((1, 2)) = {}".format(matrix.dot(Vector([1, 2]))))
print("matrix1.dot(matrix2) = {}".format(matrix.dot(matrix2)))
P = Matrix([[1, 2, 3], [4, 5, 6]])
print("P.T() = {}".format(P.T()))
from LA.Matrix import Matrix
from LA.LU import lu
if __name__ == "__main__":
A1 = Matrix([[1, 2, 3], [4, 5, 6], [3, -3, 5]])
L1, U1 = lu(A1)
print(L1)
print(U1)
print(L1.dot(U1))
print()
A2 = Matrix([[1, 4, 5, 3], [5, 22, 27, 11], [6, 19, 27, 31],
[5, 28, 35, -8]])
L2, U2 = lu(A2)
print(L2)
print(U2)
print(L2.dot(U2))
print()
A3 = Matrix([[1, 2, 3], [3, 7, 14], [4, 13, 38]])
L3, U3 = lu(A3)
print(L3)
print(U3)
print(L3.dot(U3))
print()