Matrix operations. This module contains basic matrix operations as well as a function to build square hyper-invertible matrices. The matrix implementation provides operator overloading and works with any type that acts like a number, including viff.field.GF256 and viff.field.GF() elements.
A matrix.
Adds another matrix or an element to this matrix.
Adds this matrix with another matrix, or adds the matrix with an element. The addition is done element-wise.
>>> A = Matrix([[x + 2*y for x in range(2)] for y in range(2)])
>>> print A
[[0 1]
[2 3]]
>>> print A + 10
[[10 11]
[12 13]]
>>> print A + A
[[0 2]
[4 6]]
Allows matrix entry access using z = M[x, y].
The access works as follows:
>>> M = Matrix([[1, 2], [3, 4]])
>>> print M[1,1]
4
Initializates a matrix.
The arguments can be either a number m and n counting rows and columns of an all-zero matrix, or a list of lists representing the rows of the matrix.
Matrix multiplication.
Multiplies this matrix with another matrix, or multiplies the matrix with an element.
>>> A = Matrix([[x + 2*y for x in range(2)] for y in range(2)])
>>> print A
[[0 1]
[2 3]]
>>> print A * 10
[[ 0 10]
[20 30]]
>>> print A * A
[[ 2 3]
[ 6 11]]
The matrices must have compatible dimensions:
>>> Matrix(1, 5) * Matrix(2, 3)
Traceback (most recent call last):
...
ValueError: Matrix dimensions do not match for multiplication
Allows matrix entry assignment using M[x, y] = z.
The assignment works as follows:
>>> M = Matrix(2, 2)
>>> M[0, 1] = 42
>>> print M
[[ 0 42]
[ 0 0]]
Calculates the determinant of a square matrix.
Returns the transpose of the matrix.
>>> M = Matrix([[x + 3*y for x in range(3)] for y in range(3)])
>>> print M
[[0 1 2]
[3 4 5]
[6 7 8]]
>>> print M.transpose()
[[0 3 6]
[1 4 7]
[2 5 8]]
Makes an n times n hyper-invertible square matrix. The matrix entries will belong to field.
A hyper-invertible matrix is a matrix where every sub-matrix is invertible. A sub-matrix consists of an arbitrary subset of the rows and columns of the original matrix (and is not necessarily a contiguous region).
>>> from field import GF
>>> Zp = GF(47)
>>> print hyper(2, Zp)
[[{46} {2}]
[{45} {3}]]
>>> print hyper(3, Zp)
[[ {1} {44} {3}]
[ {3} {39} {6}]
[ {6} {32} {10}]]