def __init__(self, A, b=None):
assert b is None or A.row_num() == len(
b), "row number of A must be equal to the length of b"
self._m = A.row_num()
self._n = A.col_num()
if b is None:
self.Ab = [A.row_vector(i) for i in range(self._m)]
if isinstance(b, Vector):
self.Ab = [
Vector(A.row_vector(i).underlying_list() + [b[i]])
for i in range(self._m)
]
if isinstance(b, Matrix):
self.Ab = [
Vector(
A.row_vector(i).underlying_list() +
b.row_vector(i).underlying_list()) for i in range(self._m)
]
self.pivots = []
def dot(self, another):
if isinstance(another, Vector):
assert self.col_num() == len(
another), "Error in Matrix-Vector Multiplication."
return Vector([
self.row_vector(i).dot(another) for i in range(self.row_num())
])
if isinstance(another, Matrix):
assert self.col_num() == another.row_num(
), "Error in Matrix-Matrix Multiplication."
return Matrix([[
self.row_vector(i).dot(another.col_vector(j))
for j in range(another.col_num())
] for i in range(self.row_num())])
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()))
I = Matrix.identity(2)
print(I)
print("A.dot(I) = {}".format(matrix.dot(I)))
print("I.dot(A) = {}".format(I.dot(matrix)))
from src.linear_system.LinearSystem import LinearSystem, inv, rank
from src.matrix.matrix import Matrix
from src.vectors.vector import Vector
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)
ls4.gauss_jordan_elimination()
ls4.fancy_print()
def col_vector(self, index):
return Vector([row[index] for row in self._values])
def row_vector(self, index):
return Vector(self._values[index])
from itertools import product
from src.matrix.matrix import Matrix
from src.orthonormal.gram_schmidt import gram_schmidt_process, qr
from src.vectors.vector import Vector
if __name__ == "__main__":
basis1 = [Vector([2, 1]), Vector([1, 1])]
res1 = gram_schmidt_process(basis1)
for row in res1:
print(row)
res1 = [row / row.norm() for row in res1]
for row in res1:
print(row)
print(res1[0].dot(res1[1]))
print()
basis2 = [Vector([2, 3]), Vector([4, 5])]
res2 = gram_schmidt_process(basis2)
res2 = [row / row.norm() for row in res2]
for row in res2:
print(row)
print(res2[0].dot(res2[1]))
print()
basis3 = [Vector([1, 0, 1]), Vector([3, 1, 1]), Vector([-1, -1, -1])]
res3 = gram_schmidt_process(basis3)
res3 = [row / row.norm() for row in res3]
for row in res3:
def rank(A):
ls = LinearSystem(A)
ls.gauss_jordan_elimination()
zero = Vector.zero(A.col_num())
return sum([row != zero for row in ls.Ab])