FMatx

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FMatx, as f(ull accuraty) mat(rix), is a library written in pure python determined to resolve Linear algebra and Linear programming problems in a fast and easy way with keeping high quality.

Features

• Implemented in Pure Python with no third parties requires
• Use simple global context manager to handle actions
• Support more than API for users including determinant, RREF, linear programming (also ilp), simplex method, and more

Installation

Stable version:

pip install -U fmatx

Development version:

pip install -U git+https://github.com/hibays/fmatx.git

Prerequisites: FMatx requires Python 3.8 or newer

Basic usage

Import basic core class.

>>> from fmatx import Mat

Import global context manager.

>>> from fmatx import mst

Matrix Create

>>> Mat([9, 7, 3]) # vectors

>>> Mat().tolist()
[]

>>> Mat(3).tolist()
[[], [], []]

>>> Mat([[1, 2], [3, 4]])
Mat(
┌ 1 2 ┐
└ 1 2 ┘)

>>> Mat([(1, 2), (3, 4)])
Mat(
┌ 1 2 ┐
└ 1 2 ┘)

>>> Mat(((1, 2), (3, 4))) # to use it all elements have to be tuple
Mat(
┌ 1 2 ┐
└ 1 2 ┘)

Convenient advanced functions are available for creating various standard matrices, see zeros, ones, diag, eye, randmat and hilbert.

>>> eye(5)
Mat(
┌ 1  0  0  0  0 ┐
│ 0  1  0  0  0 │
│ 0  0  1  0  0 │
│ 0  0  0  1  0 │
└ 0  0  0  0  1 ┘)

Matrix operators

>>> a = Mat([[1, 2, 2,  2], [2, 4, 6,  8], [3, 6, 8, 10]])
>>> a
Mat(
┌ 1  2  2   2 ┐
│ 2  4  6   8 │
└ 3  6  8  10 ┘)
>>> 6*a/5 + 1 - 4 # full accuraty calculation
Mat(
┌ -9/5  -3/5  -3/5  -3/5 ┐
│ -3/5   9/5  21/5  33/5 │
└  3/5  21/5  33/5     9 ┘)

also calculates between matrix and matrix

>>> a + a
Mat(
┌ 2   4   4   4 ┐
│ 4   8  12  16 │
└ 6  12  16  20 ┘)

You can raise powers of square matrices.

>>> A = Mat([[7, 9], [8, 5]])
>>> A**2
Mat(
┌ 121  108 ┐
└  96   97 ┘)

Negative powers will calculate the inverse.

>>> A**-1
Mat(
┌ -5/37   9/37 ┐
└  8/37  -7/37 ┘)
>>> A * A**-1
Mat(
┌ 1  0 ┐
└ 0  1 ┘)

Matrix transposition is straightforward. Also conjugate transposition via Mat.H.

>>> A = ones(2, 3)
>>> A
Mat(
┌ 1  1  1 ┐
└ 1  1  1 ┘)
>>> A.T
Mat(
┌ 1  1 ┐
│ 1  1 │
└ 1  1 ┘)
>>> A.H
Mat(
┌ 1  1 ┐
│ 1  1 │
└ 1  1 ┘)

Linear Algebra

RREF return tuple(rref of matrix, pivot_cols)

>>> a.rref()
(Mat(
┌ 1  2  0  -2 ┐
│ 0  0  1   2 │
└ 0  0  0   0 ┘), (0, 2))

To compute determinant.

>>> a.det()
0

Note: Bareiss algorithm is used to compute determinant internally. So following operation is ok.

>>> mst.accuracy_protect = None # don't use full accuracy to compute
	
>>> Mat(
... [[ 67,  68,  -3,  71],
...  [ 75,  27, -21,  30],
...  [104, -34,  46, 163],
...  [165, 110, 144,  25]])
Mat(
┌  67   68   -3   71 ┐
│  75   27  -21   30 │
│ 104  -34   46  163 │
└ 165  110  144   25 ┘)

>>> _.det()
139971819.0

To compute Nullspace and column space.

>>> a.nullspace()
[Mat(
┌ -2 ┐
│  1 │
│  0 │
└  0 ┘), Mat(
┌  2 ┐
│  0 │
│ -2 │
└  1 ┘)]

>>> a.columnspace()
[Mat(
┌ 1 ┐
│ 0 │
└ 0 ┘), Mat(
┌ 0 ┐
│ 1 │
└ 0 ┘)]

To compute Rank (using Gauss Method).

>>> a.rank()
2

Linear Programming (Also ILP)

It provided several methods that can solve LP, MLP, and ILP problems in full accuracy.

Example 1: solving following LP question using simplex method.

max z = 2x + y
	subject to
		 5y <= 15
	6x + 2y <= 24
	 x +  y <= 5
		x,y >= 0

>>> C = Mat([2, 1])
>>> A = Mat([[0, 5], [6, 2], [1, 1]])
>>> b = Mat([15, 24, 5])

>>> C.simplex(A, b, maximize=True)
(Rational(17, 2), {1: Rational(7, 2), 2: Rational(3, 2)})

Example 2: solving following ILP question using branch and bound method.

max z = 2x + y
	subject to
		 5y <= 15
	6x + 2y <= 24
	 x +  y <= 5
		x,y >= 0
		x,y ∈ Integers
		
>>> C = Mat([2, 1])
>>> A = Mat([[0, 5], [6, 2], [1, 1]])
>>> b = Mat([15, 24, 5])

>>> C.branch_bound(A, b, maximize=True)
(Rational(8, 1), {1: Rational(4, 1), 2: Rational(0, 1)})

Context manager

Testing

Note: To run testsuite, you must ensure your python had mpmath and SymPy installed.

python -m pytest ./testing -v