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271 lines
7.8 KiB
Python
271 lines
7.8 KiB
Python
class Matrix:
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"""
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<class Matrix>
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Matrix structure.
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"""
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def __init__(self, row: int, column: int, default_value: float = 0):
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"""
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<method Matrix.__init__>
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Initialize matrix with given size and default value.
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Example:
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>>> a = Matrix(2, 3, 1)
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>>> a
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Matrix consist of 2 rows and 3 columns
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[1, 1, 1]
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[1, 1, 1]
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"""
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self.row, self.column = row, column
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self.array = [[default_value for c in range(column)] for r in range(row)]
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def __str__(self):
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"""
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<method Matrix.__str__>
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Return string representation of this matrix.
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"""
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# Prefix
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s = "Matrix consist of %d rows and %d columns\n" % (self.row, self.column)
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# Make string identifier
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max_element_length = 0
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for row_vector in self.array:
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for obj in row_vector:
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max_element_length = max(max_element_length, len(str(obj)))
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string_format_identifier = "%%%ds" % (max_element_length,)
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# Make string and return
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def single_line(row_vector):
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nonlocal string_format_identifier
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line = "["
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line += ", ".join(string_format_identifier % (obj,) for obj in row_vector)
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line += "]"
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return line
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s += "\n".join(single_line(row_vector) for row_vector in self.array)
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return s
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def __repr__(self):
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return str(self)
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def validateIndices(self, loc: tuple):
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"""
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<method Matrix.validateIndices>
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Check if given indices are valid to pick element from matrix.
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Example:
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>>> a = Matrix(2, 6, 0)
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>>> a.validateIndices((2, 7))
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False
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>>> a.validateIndices((0, 0))
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True
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"""
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if not (isinstance(loc, (list, tuple)) and len(loc) == 2):
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return False
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elif not (0 <= loc[0] < self.row and 0 <= loc[1] < self.column):
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return False
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else:
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return True
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def __getitem__(self, loc: tuple):
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"""
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<method Matrix.__getitem__>
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Return array[row][column] where loc = (row, column).
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Example:
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>>> a = Matrix(3, 2, 7)
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>>> a[1, 0]
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7
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"""
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assert self.validateIndices(loc)
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return self.array[loc[0]][loc[1]]
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def __setitem__(self, loc: tuple, value: float):
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"""
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<method Matrix.__setitem__>
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Set array[row][column] = value where loc = (row, column).
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Example:
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>>> a = Matrix(2, 3, 1)
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>>> a[1, 2] = 51
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>>> a
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Matrix consist of 2 rows and 3 columns
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[ 1, 1, 1]
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[ 1, 1, 51]
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"""
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assert self.validateIndices(loc)
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self.array[loc[0]][loc[1]] = value
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def __add__(self, another):
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"""
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<method Matrix.__add__>
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Return self + another.
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Example:
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>>> a = Matrix(2, 1, -4)
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>>> b = Matrix(2, 1, 3)
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>>> a+b
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Matrix consist of 2 rows and 1 columns
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[-1]
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[-1]
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"""
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# Validation
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assert isinstance(another, Matrix)
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assert self.row == another.row and self.column == another.column
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# Add
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result = Matrix(self.row, self.column)
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for r in range(self.row):
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for c in range(self.column):
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result[r, c] = self[r, c] + another[r, c]
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return result
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def __neg__(self):
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"""
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<method Matrix.__neg__>
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Return -self.
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Example:
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>>> a = Matrix(2, 2, 3)
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>>> a[0, 1] = a[1, 0] = -2
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>>> -a
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Matrix consist of 2 rows and 2 columns
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[-3, 2]
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[ 2, -3]
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"""
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result = Matrix(self.row, self.column)
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for r in range(self.row):
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for c in range(self.column):
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result[r, c] = -self[r, c]
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return result
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def __sub__(self, another):
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return self + (-another)
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def __mul__(self, another):
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"""
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<method Matrix.__mul__>
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Return self * another.
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Example:
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>>> a = Matrix(2, 3, 1)
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>>> a[0,2] = a[1,2] = 3
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>>> a * -2
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Matrix consist of 2 rows and 3 columns
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[-2, -2, -6]
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[-2, -2, -6]
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"""
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if isinstance(another, (int, float)): # Scalar multiplication
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result = Matrix(self.row, self.column)
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for r in range(self.row):
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for c in range(self.column):
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result[r, c] = self[r, c] * another
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return result
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elif isinstance(another, Matrix): # Matrix multiplication
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assert self.column == another.row
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result = Matrix(self.row, another.column)
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for r in range(self.row):
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for c in range(another.column):
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for i in range(self.column):
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result[r, c] += self[r, i] * another[i, c]
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return result
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else:
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raise TypeError(
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"Unsupported type given for another ({})".format(type(another))
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)
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def transpose(self):
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"""
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<method Matrix.transpose>
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Return self^T.
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Example:
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>>> a = Matrix(2, 3)
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>>> for r in range(2):
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... for c in range(3):
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... a[r,c] = r*c
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...
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>>> a.transpose()
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Matrix consist of 3 rows and 2 columns
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[0, 0]
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[0, 1]
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[0, 2]
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"""
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result = Matrix(self.column, self.row)
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for r in range(self.row):
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for c in range(self.column):
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result[c, r] = self[r, c]
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return result
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def ShermanMorrison(self, u, v):
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"""
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<method Matrix.ShermanMorrison>
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Apply Sherman-Morrison formula in O(n^2).
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To learn this formula, please look this:
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https://en.wikipedia.org/wiki/Sherman%E2%80%93Morrison_formula
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This method returns (A + uv^T)^(-1) where A^(-1) is self. Returns None if it's
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impossible to calculate.
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Warning: This method doesn't check if self is invertible.
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Make sure self is invertible before execute this method.
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Example:
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>>> ainv = Matrix(3, 3, 0)
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>>> for i in range(3): ainv[i,i] = 1
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...
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>>> u = Matrix(3, 1, 0)
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>>> u[0,0], u[1,0], u[2,0] = 1, 2, -3
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>>> v = Matrix(3, 1, 0)
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>>> v[0,0], v[1,0], v[2,0] = 4, -2, 5
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>>> ainv.ShermanMorrison(u, v)
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Matrix consist of 3 rows and 3 columns
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[ 1.2857142857142856, -0.14285714285714285, 0.3571428571428571]
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[ 0.5714285714285714, 0.7142857142857143, 0.7142857142857142]
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[ -0.8571428571428571, 0.42857142857142855, -0.0714285714285714]
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"""
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# Size validation
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assert isinstance(u, Matrix) and isinstance(v, Matrix)
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assert self.row == self.column == u.row == v.row # u, v should be column vector
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assert u.column == v.column == 1 # u, v should be column vector
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# Calculate
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vT = v.transpose()
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numerator_factor = (vT * self * u)[0, 0] + 1
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if numerator_factor == 0:
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return None # It's not invertable
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return self - ((self * u) * (vT * self) * (1.0 / numerator_factor))
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# Testing
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if __name__ == "__main__":
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def test1():
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# a^(-1)
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ainv = Matrix(3, 3, 0)
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for i in range(3):
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ainv[i, i] = 1
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print(f"a^(-1) is {ainv}")
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# u, v
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u = Matrix(3, 1, 0)
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u[0, 0], u[1, 0], u[2, 0] = 1, 2, -3
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v = Matrix(3, 1, 0)
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v[0, 0], v[1, 0], v[2, 0] = 4, -2, 5
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print(f"u is {u}")
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print(f"v is {v}")
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print("uv^T is %s" % (u * v.transpose()))
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# Sherman Morrison
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print("(a + uv^T)^(-1) is {}".format(ainv.ShermanMorrison(u, v)))
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def test2():
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import doctest
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doctest.testmod()
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test2()
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