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Matrix Stitcher

An elementary-transform tape system for matrix analysis education purpose which combines the advantage of eager and lazy execution. It runs dynamically and automatically tracks your transformations applied to the original matrix. It is a naive final project for Matrix Analysis and Applications course in UCAS including PLU Factorization (Gaussian elimination), QR Factorization (GramSchmidt, HouseHolder, and Givens).

Features

  • Intuitive implementation for education purpose
  • Index from 1 which is consistent with the mathematical declaration
  • Dynamicaly track the transformations applied to the orgin matrix
  • Easily extend your transforms and methods

Installation

# clone the project
git clone [email protected]:jhliu17/MatrixStitcher.git
cd MatrixStitcher

# install via pip
pip install .

Quick Guide

import numpy as np
import matrixstitcher as mats
from matrixstitcher.method import LUFactorization

# you can define matrix using int, float, list,
# tuple and numpy array
A = [[1, 2, -3],
     [4, 8, 12],
     [2, 3, 2]]

A = mats.Matrix(A, dtype=np.float) # get the matrix object from MatrixStitcher

with mats.TransformTape(): # tape all the transforms
    P, L, U = LUFactorization()(A) # apply LU Factorization on matrix A and get the factorization results

# show the execution state of the matrix A
print('Execution Path:')
result = A.forward(display=True)

Here is the execution result:

Execution Path:
-> Origin matrix:
array([[ 1.,  2., -3.],
       [ 4.,  8., 12.],
       [ 2.,  3.,  2.]])

-> Stage 1, RowTransform(1, -4.0, 2):
array([[ 1.,  2., -3.],
       [ 0.,  0., 24.],
       [ 2.,  3.,  2.]])

-> Stage 2, RowTransform(1, -2.0, 3):
array([[ 1.,  2., -3.],
       [ 0.,  0., 24.],
       [ 0., -1.,  8.]])

-> Stage 3, RowSwap('i=2', 'j=3'):
array([[ 1.,  2., -3.],
       [ 0., -1.,  8.],
       [ 0.,  0., 24.]])

If you don't want to track the transformations, applying your method outside the context of TransformTape().

import matrixstitcher as mats

# construct data ...

P, L, U = LUFactorization()(A)

A.forward(display=True)

# Output
# Execution Path:
# -> Origin matrix:
# array([[ 1.,  2., -3.],
#        [ 4.,  8., 12.],
#        [ 2.,  3.,  2.]])

You can get the same factorization results P, L, U. But the transformations would not be recorded into A's tape history.

Extend Transform and Method

You can esaily extend your transform and method. Here are two simple examples.

import numpy as np
import matrixstitcher.transform as T
from matrixstitcher.method import Method
from matrixstitcher.transform import Tranform


class Rank(Transform):
    def __init__(self, *args, **kwargs):
        '''
        In order to represent your transform correctly, you must
        tell the base object the parameters you have used.
        '''
        super().__init__(*args, **kwargs)

    def perform(self, matrix): # you must finish `perform` function
        return np.linalg.matrix_rank(matrix.matrix)


class LeastSquareTech(Method):
    def __init__(self):
        '''
        A `Method` can be seen as a container of several
        `Transform`s
        '''
        super().__init__()
        self.tape = False # setting whether the transformations
                          # used under this method would be tracked
        self.parameter = None
        self.error = None

    def perform(self, X, y): # you must finish `perform` function
        self.parameter = T.Inverse()(X.T * X) * X.T * y
        self.error = (self.predict(X) - y).T * (self.predict(X) - y)
        return self.parameter, self.error

    def predict(self, X):
        return X * self.parameter