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class Matrix:

"""

Matrix structure.

"""

def __init__(self, row: int, column: int, default_value: float = 0):

"""

Initialize matrix with given size and default value.

Example:

>>> a = Matrix(2, 3, 1)

>>> a

Matrix consist of 2 rows and 3 columns

[1, 1, 1]

"""

self.row, self.column = row, column

self.array = [[default_value for c in range(column)] for r in range(row)]

def __str__(self):

"""

Return string representation of this matrix.

"""

# Prefix

s = "Matrix consist of %d rows and %d columns\n" % (self.row, self.column)

# Make string identifier

max_element_length = 0

for row_vector in self.array:

for obj in row_vector:

max_element_length = max(max_element_length, len(str(obj)))

string_format_identifier = "%%%ds" % (max_element_length,)

# Make string and return

def single_line(row_vector):

nonlocal string_format_identifier

line = "["

line += ", ".join(string_format_identifier % (obj,) for obj in row_vector)

line += "]"

return line

s += "\n".join(single_line(row_vector) for row_vector in self.array)

return s

def __repr__(self):

return str(self)

def validateIndices(self, loc: tuple):

"""

Check if given indices are valid to pick element from matrix.

Example:

>>> a = Matrix(2, 6, 0)

>>> a.validateIndices((2, 7))

False

>>> a.validateIndices((0, 0))

True

"""

if not (isinstance(loc, (list, tuple)) and len(loc) == 2):

return False

elif not (0 <= loc[0] < self.row and 0 <= loc[1] < self.column):

return False

else:

return True

def __getitem__(self, loc: tuple):

"""

Return array[row][column] where loc = (row, column).

Example:

>>> a = Matrix(3, 2, 7)

>>> a[1, 0]

"""

assert self.validateIndices(loc)

return self.array[loc[0]][loc[1]]

def __setitem__(self, loc: tuple, value: float):

"""

Set array[row][column] = value where loc = (row, column).

Example:

>>> a = Matrix(2, 3, 1)

>>> a[1, 2] = 51

>>> a

Matrix consist of 2 rows and 3 columns

[ 1, 1, 1]

[ 1, 1, 51]

"""

assert self.validateIndices(loc)

self.array[loc[0]][loc[1]] = value

def __add__(self, another):

"""

Return self + another.

Example:

>>> a = Matrix(2, 1, -4)

>>> b = Matrix(2, 1, 3)

>>> a+b

Matrix consist of 2 rows and 1 columns

[-1]

"""

# Validation

assert isinstance(another, Matrix)

assert self.row == another.row and self.column == another.column

# Add

result = Matrix(self.row, self.column)

for r in range(self.row):

for c in range(self.column):

result[r, c] = self[r, c] + another[r, c]

return result

def __neg__(self):

"""

Return -self.

Example:

>>> a = Matrix(2, 2, 3)

>>> a[0, 1] = a[1, 0] = -2

>>> -a

Matrix consist of 2 rows and 2 columns

[-3, 2]

[ 2, -3]

"""

result = Matrix(self.row, self.column)

for r in range(self.row):

for c in range(self.column):

result[r, c] = -self[r, c]

return result

def __sub__(self, another):

return self + (-another)

def __mul__(self, another):

"""

Return self * another.

Example:

>>> a = Matrix(2, 3, 1)

>>> a[0,2] = a[1,2] = 3

>>> a * -2

Matrix consist of 2 rows and 3 columns

[-2, -2, -6]

"""

if isinstance(another, (int, float)): # Scalar multiplication

result = Matrix(self.row, self.column)

for r in range(self.row):

for c in range(self.column):

result[r, c] = self[r, c] * another

return result

elif isinstance(another, Matrix): # Matrix multiplication

assert self.column == another.row

result = Matrix(self.row, another.column)

for r in range(self.row):

for c in range(another.column):

for i in range(self.column):

result[r, c] += self[r, i] * another[i, c]

return result

else:

raise TypeError(

"Unsupported type given for another ({})".format(type(another))

)

def transpose(self):

"""

Return self^T.

Example:

>>> a = Matrix(2, 3)

>>> for r in range(2):

... for c in range(3):

... a[r,c] = r*c

...

>>> a.transpose()

Matrix consist of 3 rows and 2 columns

[0, 0]

[0, 1]

[0, 2]

"""

result = Matrix(self.column, self.row)

for r in range(self.row):

for c in range(self.column):

result[c, r] = self[r, c]

return result

def ShermanMorrison(self, u, v):

"""

Apply Sherman-Morrison formula in O(n^2).

To learn this formula, please look this:

https://en.wikipedia.org/wiki/Sherman%E2%80%93Morrison_formula

This method returns (A + uv^T)^(-1) where A^(-1) is self. Returns None if it's

impossible to calculate.

Warning: This method doesn't check if self is invertible.

Make sure self is invertible before execute this method.

Example:

>>> ainv = Matrix(3, 3, 0)

>>> for i in range(3): ainv[i,i] = 1

...

>>> u = Matrix(3, 1, 0)

>>> u[0,0], u[1,0], u[2,0] = 1, 2, -3

>>> v = Matrix(3, 1, 0)

>>> v[0,0], v[1,0], v[2,0] = 4, -2, 5

>>> ainv.ShermanMorrison(u, v)

Matrix consist of 3 rows and 3 columns

[ 1.2857142857142856, -0.14285714285714285, 0.3571428571428571]

[ 0.5714285714285714, 0.7142857142857143, 0.7142857142857142]

[ -0.8571428571428571, 0.42857142857142855, -0.0714285714285714]

"""

# Size validation

assert isinstance(u, Matrix) and isinstance(v, Matrix)

assert self.row == self.column == u.row == v.row # u, v should be column vector

assert u.column == v.column == 1 # u, v should be column vector

# Calculate

vT = v.transpose()

numerator_factor = (vT * self * u)[0, 0] + 1

if numerator_factor == 0:

return None # It's not invertable

return self - ((self * u) * (vT * self) * (1.0 / numerator_factor))

# Testing

if __name__ == "__main__":

def test1():

# a^(-1)

ainv = Matrix(3, 3, 0)

for i in range(3):

ainv[i, i] = 1

print(f"a^(-1) is {ainv}")

# u, v

u = Matrix(3, 1, 0)

u[0, 0], u[1, 0], u[2, 0] = 1, 2, -3

v = Matrix(3, 1, 0)

v[0, 0], v[1, 0], v[2, 0] = 4, -2, 5

print(f"u is {u}")

print(f"v is {v}")

print("uv^T is %s" % (u * v.transpose()))

# Sherman Morrison

print("(a + uv^T)^(-1) is {}".format(ainv.ShermanMorrison(u, v)))

def test2():

import doctest

doctest.testmod()

test2()

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