from playLA.Matrix import Matrix
from playLA.LU import lu
if __name__ == "__main__":
A = Matrix([[1, 2, 3], [4, 5, 6], [3, -3, 5]])
L, U = lu(A)
print(L)
print(U)
print(L.dot(U))
from playLA.Matrix import Matrix
from playLA.Vector import Vector
from playLA.LinearSystem import LinearSystem
from playLA.LinearSystem import inv, rank
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]
import matplotlib.pyplot as plt
from playLA.Matrix import Matrix
from playLA.Vector import Vector
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 = [e[0] for e in points]
y = [e[1] for e in points]
plt.figure(figsize=(5, 5))
plt.xlim(-10, 10)
plt.ylim(-10, 10)
plt.plot(x, y)
# plt.show()
P = Matrix(points)
# print(P.shape())
# T = Matrix([[2, 0], [0, 1.5]])
T = Matrix([[1, 0], [0, -1]])
P2 = T.dot(P.T())
# plt.plot(P2.row_vector(0), P2.row_vector(1))
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())])
plt.show()
from playLA.Matrix import Matrix
from playLA.Vector import Vector
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]))
print("matrix's row[0] vector = {}".format(matrix.row_vector(0)))
print("matrix's col[0] vector = {}".format(matrix.col_vector(0)))
matrix2 = Matrix([[5, 6], [7, 8]])
print(matrix2)
print("add: {}".format(matrix + matrix2))
print("subtract: {}".format(matrix - matrix2))
print("scalar-mul: {}".format(matrix * 2))
print("re-scalar-mul: {}".format(2 * matrix))
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)))
from playLA.Matrix import Matrix
from playLA.Vector import Vector
if __name__ == "__main__":
matrix = Matrix([[1, 2], [3, 4]])
print(matrix)
print(matrix.row_vector(0))
matrix2 = Matrix([[5, 6], [7, 8]])
print("add: {}".format(matrix + matrix2))
print("sub: {}".format(matrix - matrix2))
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()))
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)
# print(P)
# T = Matrix([[2, 0], [0, 1.5]]) # T: 2 * 2 P: 10 * 2
# T = Matrix([[1, 0], [0, -1]])
# T = Matrix([[-1, 0], [0, 1]])
# T = Matrix([[-1, 0], [0, -1]])
# T = Matrix([[1, 1], [0, 1]])
# T = Matrix([[1, 0], [1, 1]])
# T = Matrix([[1, 0.5], [1, 1]])
# T = Matrix([[1, 0.5], [1, 1]])
theta = math.pi / 3
T = Matrix([[math.cos(theta), math.sin(theta)],
[-math.sin(theta), math.cos(theta)]])
P2 = T.dot(P.T()) # P2: 2 * 10
from playLA.Matrix import Matrix
from playLA.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()
from playLA.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]))
import matplotlib.pyplot as plt
from playLA.Matrix import Matrix
from playLA.Vector import Vector
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)
P = Matrix(points)
T = Matrix([[2, 0], [0, 1.5]])
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())])
plt.show()
from playLA.Matrix import Matrix
from playLA.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))