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359 lines
11 KiB
Python
359 lines
11 KiB
Python
# An OOP approach to representing and manipulating matrices
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class Matrix:
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"""
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Matrix object generated from a 2D array where each element is an array representing
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a row.
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Rows can contain type int or float.
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Common operations and information available.
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>>> rows = [
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... [1, 2, 3],
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... [4, 5, 6],
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... [7, 8, 9]
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... ]
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>>> matrix = Matrix(rows)
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>>> print(matrix)
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[[1. 2. 3.]
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[4. 5. 6.]
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[7. 8. 9.]]
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Matrix rows and columns are available as 2D arrays
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>>> print(matrix.rows)
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[[1, 2, 3], [4, 5, 6], [7, 8, 9]]
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>>> print(matrix.columns())
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[[1, 4, 7], [2, 5, 8], [3, 6, 9]]
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Order is returned as a tuple
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>>> matrix.order
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(3, 3)
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Squareness and invertability are represented as bool
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>>> matrix.is_square
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True
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>>> matrix.is_invertable()
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False
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Identity, Minors, Cofactors and Adjugate are returned as Matrices. Inverse can be
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a Matrix or Nonetype
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>>> print(matrix.identity())
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[[1. 0. 0.]
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[0. 1. 0.]
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[0. 0. 1.]]
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>>> print(matrix.minors())
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[[-3. -6. -3.]
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[-6. -12. -6.]
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[-3. -6. -3.]]
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>>> print(matrix.cofactors())
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[[-3. 6. -3.]
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[6. -12. 6.]
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[-3. 6. -3.]]
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>>> # won't be apparent due to the nature of the cofactor matrix
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>>> print(matrix.adjugate())
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[[-3. 6. -3.]
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[6. -12. 6.]
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[-3. 6. -3.]]
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>>> print(matrix.inverse())
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None
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Determinant is an int, float, or Nonetype
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>>> matrix.determinant()
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0
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Negation, scalar multiplication, addition, subtraction, multiplication and
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exponentiation are available and all return a Matrix
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>>> print(-matrix)
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[[-1. -2. -3.]
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[-4. -5. -6.]
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[-7. -8. -9.]]
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>>> matrix2 = matrix * 3
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>>> print(matrix2)
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[[3. 6. 9.]
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[12. 15. 18.]
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[21. 24. 27.]]
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>>> print(matrix + matrix2)
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[[4. 8. 12.]
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[16. 20. 24.]
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[28. 32. 36.]]
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>>> print(matrix - matrix2)
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[[-2. -4. -6.]
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[-8. -10. -12.]
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[-14. -16. -18.]]
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>>> print(matrix ** 3)
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[[468. 576. 684.]
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[1062. 1305. 1548.]
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[1656. 2034. 2412.]]
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Matrices can also be modified
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>>> matrix.add_row([10, 11, 12])
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>>> print(matrix)
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[[1. 2. 3.]
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[4. 5. 6.]
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[7. 8. 9.]
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[10. 11. 12.]]
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>>> matrix2.add_column([8, 16, 32])
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>>> print(matrix2)
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[[3. 6. 9. 8.]
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[12. 15. 18. 16.]
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[21. 24. 27. 32.]]
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>>> print(matrix * matrix2)
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[[90. 108. 126. 136.]
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[198. 243. 288. 304.]
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[306. 378. 450. 472.]
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[414. 513. 612. 640.]]
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"""
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def __init__(self, rows):
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error = TypeError(
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"Matrices must be formed from a list of zero or more lists containing at "
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"least one and the same number of values, each of which must be of type "
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"int or float."
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)
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if len(rows) != 0:
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cols = len(rows[0])
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if cols == 0:
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raise error
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for row in rows:
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if len(row) != cols:
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raise error
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for value in row:
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if not isinstance(value, (int, float)):
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raise error
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self.rows = rows
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else:
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self.rows = []
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# MATRIX INFORMATION
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def columns(self):
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return [[row[i] for row in self.rows] for i in range(len(self.rows[0]))]
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@property
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def num_rows(self):
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return len(self.rows)
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@property
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def num_columns(self):
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return len(self.rows[0])
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@property
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def order(self):
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return (self.num_rows, self.num_columns)
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@property
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def is_square(self):
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return self.order[0] == self.order[1]
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def identity(self):
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values = [
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[0 if column_num != row_num else 1 for column_num in range(self.num_rows)]
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for row_num in range(self.num_rows)
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]
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return Matrix(values)
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def determinant(self):
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if not self.is_square:
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return None
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if self.order == (0, 0):
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return 1
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if self.order == (1, 1):
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return self.rows[0][0]
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if self.order == (2, 2):
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return (self.rows[0][0] * self.rows[1][1]) - (
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self.rows[0][1] * self.rows[1][0]
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)
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else:
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return sum(
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self.rows[0][column] * self.cofactors().rows[0][column]
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for column in range(self.num_columns)
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)
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def is_invertable(self):
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return bool(self.determinant())
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def get_minor(self, row, column):
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values = [
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[
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self.rows[other_row][other_column]
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for other_column in range(self.num_columns)
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if other_column != column
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]
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for other_row in range(self.num_rows)
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if other_row != row
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]
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return Matrix(values).determinant()
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def get_cofactor(self, row, column):
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if (row + column) % 2 == 0:
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return self.get_minor(row, column)
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return -1 * self.get_minor(row, column)
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def minors(self):
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return Matrix(
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[
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[self.get_minor(row, column) for column in range(self.num_columns)]
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for row in range(self.num_rows)
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]
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)
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def cofactors(self):
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return Matrix(
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[
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[
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self.minors().rows[row][column]
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if (row + column) % 2 == 0
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else self.minors().rows[row][column] * -1
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for column in range(self.minors().num_columns)
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]
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for row in range(self.minors().num_rows)
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]
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)
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def adjugate(self):
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values = [
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[self.cofactors().rows[column][row] for column in range(self.num_columns)]
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for row in range(self.num_rows)
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]
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return Matrix(values)
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def inverse(self):
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determinant = self.determinant()
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return None if not determinant else self.adjugate() * (1 / determinant)
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def __repr__(self):
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return str(self.rows)
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def __str__(self):
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if self.num_rows == 0:
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return "[]"
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if self.num_rows == 1:
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return "[[" + ". ".join(self.rows[0]) + "]]"
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return (
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"["
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+ "\n ".join(
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[
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"[" + ". ".join([str(value) for value in row]) + ".]"
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for row in self.rows
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]
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)
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+ "]"
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)
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# MATRIX MANIPULATION
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def add_row(self, row, position=None):
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type_error = TypeError("Row must be a list containing all ints and/or floats")
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if not isinstance(row, list):
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raise type_error
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for value in row:
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if not isinstance(value, (int, float)):
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raise type_error
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if len(row) != self.num_columns:
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raise ValueError(
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"Row must be equal in length to the other rows in the matrix"
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)
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if position is None:
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self.rows.append(row)
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else:
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self.rows = self.rows[0:position] + [row] + self.rows[position:]
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def add_column(self, column, position=None):
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type_error = TypeError(
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"Column must be a list containing all ints and/or floats"
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)
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if not isinstance(column, list):
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raise type_error
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for value in column:
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if not isinstance(value, (int, float)):
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raise type_error
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if len(column) != self.num_rows:
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raise ValueError(
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"Column must be equal in length to the other columns in the matrix"
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)
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if position is None:
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self.rows = [self.rows[i] + [column[i]] for i in range(self.num_rows)]
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else:
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self.rows = [
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self.rows[i][0:position] + [column[i]] + self.rows[i][position:]
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for i in range(self.num_rows)
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]
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# MATRIX OPERATIONS
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def __eq__(self, other):
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if not isinstance(other, Matrix):
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raise TypeError("A Matrix can only be compared with another Matrix")
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return self.rows == other.rows
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def __ne__(self, other):
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return not self == other
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def __neg__(self):
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return self * -1
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def __add__(self, other):
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if self.order != other.order:
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raise ValueError("Addition requires matrices of the same order")
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return Matrix(
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[
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[self.rows[i][j] + other.rows[i][j] for j in range(self.num_columns)]
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for i in range(self.num_rows)
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]
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)
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def __sub__(self, other):
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if self.order != other.order:
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raise ValueError("Subtraction requires matrices of the same order")
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return Matrix(
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[
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[self.rows[i][j] - other.rows[i][j] for j in range(self.num_columns)]
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for i in range(self.num_rows)
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]
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)
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def __mul__(self, other):
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if isinstance(other, (int, float)):
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return Matrix([[element * other for element in row] for row in self.rows])
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elif isinstance(other, Matrix):
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if self.num_columns != other.num_rows:
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raise ValueError(
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"The number of columns in the first matrix must "
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"be equal to the number of rows in the second"
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)
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return Matrix(
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[
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[Matrix.dot_product(row, column) for column in other.columns()]
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for row in self.rows
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]
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)
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else:
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raise TypeError(
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"A Matrix can only be multiplied by an int, float, or another matrix"
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)
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def __pow__(self, other):
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if not isinstance(other, int):
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raise TypeError("A Matrix can only be raised to the power of an int")
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if not self.is_square:
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raise ValueError("Only square matrices can be raised to a power")
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if other == 0:
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return self.identity()
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if other < 0:
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if self.is_invertable:
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return self.inverse() ** (-other)
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raise ValueError(
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"Only invertable matrices can be raised to a negative power"
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)
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result = self
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for i in range(other - 1):
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result *= self
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return result
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@classmethod
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def dot_product(cls, row, column):
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return sum(row[i] * column[i] for i in range(len(row)))
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if __name__ == "__main__":
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import doctest
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doctest.testmod()
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