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rref.py
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rref.py
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# -*- coding: utf-8 -*-
# File: rref.py
from copy import deepcopy
from fractions import Fraction
from numbers import Real
class RowVector(object):
def __init__(self, value: Real, *values: Real) -> None:
self._vector = [Fraction(str(v)) for v in (value, *values)]
def __str__(self) -> str:
return f"[{', '.join(self._get_str_fraction())}]"
def __repr__(self) -> str:
return f"RowVector({', '.join(self._get_str_fraction())})"
def __len__(self) -> int:
return len(self.vector)
def __add__(self, other: "RowVector") -> "RowVector":
assert len(self) == len(other)
return RowVector(*(self[i] + other[i] for i in range(len(self))))
def __sub__(self, other: "RowVector") -> "RowVector":
assert len(self) == len(other)
return RowVector(*(self[i] - other[i] for i in range(len(self))))
def __mul__(self, multiplier: Real) -> "RowVector":
return RowVector(*(v * multiplier for v in self))
def __truediv__(self, divisor: Real) -> "RowVector":
assert divisor != 0
return RowVector(*(v / divisor for v in self))
def __getitem__(self, index: int) -> Fraction:
return self.vector[index]
def __setitem__(self, index: int, value: Real) -> None:
self._vector[index] = Fraction(str(value))
def _get_str_fraction(self) -> tuple[str, ...]:
return tuple(str(v) for v in self)
def get_first_nonzero_index(self) -> int:
for i in range(len(self)):
if self[i] != 0:
return i
return len(self)
def get_max_len(self) -> int:
return max((len(str(v)) for v in self))
def is_nonzero(self) -> bool:
return self.get_first_nonzero_index() != len(self)
@property
def vector(self) -> list[Fraction]:
return self._vector
class Matrix(object):
def __init__(self, row: tuple[Real, ...], *rows: tuple[Real, ...]) -> None:
assert len({len(row), *(len(r) for r in rows)}) == 1
self._matrix = [RowVector(*r) for r in (row, *rows)]
def __str__(self) -> str:
max_len = max((v.get_max_len() for v in self))
return "\n".join(
(
" ".join((f"{str(v[i]):>{max_len}s}" for i in range(len(v))))
for v in self
)
)
def __repr__(self) -> str:
return f"Matrix({', '.join((str(v) for v in self))})"
def __len__(self) -> int:
return len(self.matrix)
def __getitem__(self, index: int) -> RowVector:
return self.matrix[index]
def __setitem__(self, index: int, vector: RowVector) -> None:
self._matrix[index] = vector
def get_rref(self):
matrix = deepcopy(self)
for i in range(len(matrix)):
matrix = Matrix(
*sorted(matrix.matrix, key=lambda x: x.get_first_nonzero_index())
)
if not matrix[i].is_nonzero():
break
matrix[i] /= matrix[i][matrix[i].get_first_nonzero_index()]
for j in range(len(matrix)):
if j != i:
matrix[j] -= (
matrix[i] * matrix[j][matrix[i].get_first_nonzero_index()]
)
return matrix
@property
def matrix(self) -> list[RowVector]:
return self._matrix
if __name__ == "__main__":
# Source: CUHK ENGG1120 Spring 2022 Assignments
test_cases = (
(
[[6, -2, 1, -3], [5, -1, 2, -4], [1, -2, 1, 2]],
"Matrix([1, 0, 0, -1], [0, 1, 0, -5/3], [0, 0, 1, -1/3])",
),
(
[[1, -1, 2, 2], [2, -6, 9, 14], [3, 1, 1, -4]],
"Matrix([1, 0, 3/4, -1/2], [0, 1, -5/4, -5/2], [0, 0, 0, 0])",
),
(
[[3, -2, 1, -3], [5, -3, 1, -6], [0, -1, 1, 5]],
"Matrix([1, 0, 0, -5], [0, 1, 0, -7], [0, 0, 1, -2])",
),
(
[[1, 1, 1, 1, 5], [2, 3, -4, 5, -2], [4, 2, 0, -3, 3]],
"Matrix([1, 0, 0, -39/16, -15/16], [0, 1, 0, 27/8, 27/8], [0, 0, 1, 1/16, 41/16])",
),
(
[[2, 3, -1, 3, 6], [1, 1, -4, -2, -1], [5, 7, -6, 4, 11]],
"Matrix([1, 0, -11, -9, -9], [0, 1, 7, 7, 8], [0, 0, 0, 0, 0])",
),
(
[[1, -1, 3, 5], [3, 2, 6, -3], [4, 1, -8, 0], [-1, 3, 0, 4]],
"Matrix([1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1])",
),
(
[[2, -4, 3, 2], [-1, 1, 10, -3], [3, 4, -8, 4], [2, 5, 4, 1]],
"Matrix([1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1])",
),
(
[[-1, -1, 3, 0], [3, 0, -2, 0]],
"Matrix([1, 0, -2/3, 0], [0, 1, -7/3, 0])",
),
(
[[1, -1, 3, 1, 1], [2, 4, 0, 2, -1], [0, 3, -5, 0, 0]],
"Matrix([1, 0, 0, 1, 2], [0, 1, 0, 0, -5/4], [0, 0, 1, 0, -3/4])",
),
(
[
[1, -2, 0, 3, -2, 4],
[0, 8, -4, 5, 6, 1],
[-1, 10, -4, 2, 8, -3],
[2, 4, -4, 11, 2, 9],
],
"Matrix([1, 0, -1, 17/4, -1/2, 17/4], [0, 1, -1/2, 5/8, 3/4, 1/8], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0])",
),
(
[
[1, -3, 4, 0, 1, 0, 0, 0],
[0, 8, 0, -5, 0, 1, 0, 0],
[0, 0, 2, 0, 0, 0, 1, 0],
[0, 0, 0, 4, 0, 0, 0, 1],
],
"Matrix([1, 0, 0, 0, 1, 3/8, -2, 15/32], [0, 1, 0, 0, 0, 1/8, 0, 5/32], [0, 0, 1, 0, 0, 0, 1/2, 0], [0, 0, 0, 1, 0, 0, 0, 1/4])",
),
)
for test_matrix, test_rref in test_cases:
assert repr(Matrix(*test_matrix).get_rref()) == test_rref