matrix.py

from math import *
import random

# This class was borrowed from Udacity's Artificial Intelligence for Robotics course 
#     2 functions were added from original work

class matrix:
    
    def __init__(self, value):
        self.value = value
        self.dimx  = len(value)
        self.dimy  = len(value[0])
        if value == [[]]:
            self.dimx = 0

    def zero(self, dimx, dimy):
        # check if valid dimensions
        if dimx < 1 or dimy < 1:
            raise ValueError, "Invalid size of matrix"
        else:
            self.dimx  = dimx
            self.dimy  = dimy
            self.value = [[0 for row in range(dimy)] for col in range(dimx)]

    def copy(self):
        res = matrix([[]])
        res.zero(self.dimx, self.dimy)
        for i in range(self.dimx):
            for j in range(self.dimy):
                res.value[i][j] = self.value[i][j]
        return res
                
    def identity(self, dim):
        # check if valid dimension
        if dim < 1:
            raise ValueError, "Invalid size of matrix"
        else:
            self.dimx  = dim
            self.dimy  = dim
            self.value = [[0 for row in range(dim)] for col in range(dim)]
            for i in range(dim):
                self.value[i][i] = 1

    def show(self):
        for i in range(self.dimx):
            print self.value[i]
        print ' '

	# function added for ease of use (not in original file)
    def matrix2array(self):
        arrayed = []
        for i in range(self.dimx):
            row = []
            for j in range(self.dimy):
                row.append(self.value[i][j])
            arrayed.append(row)
        return arrayed
    
    # function added for ease of use (not in original file)
    def array2matrix(arrayed):
        matrixed = matrix([[]])
        matrixed.zero(len(arrayed),len(arrayed[0]))
        for i in range(len(arrayed)):
            for j in range(len(arrayed[0])):
                matrixed.value[i][j] = arrayed[i][j]
        return matrixed
    
    def __add__(self, other):
        # check if correct dimensions
        if self.dimx != other.dimx or self.dimx != other.dimx:
            raise ValueError, "Matrices must be of equal dimension to add"
        else:
            # add if correct dimensions
            res = matrix([[]])
            res.zero(self.dimx, self.dimy)
            for i in range(self.dimx):
                for j in range(self.dimy):
                    res.value[i][j] = self.value[i][j] + other.value[i][j]
            return res

    def __sub__(self, other):
        # check if correct dimensions
        if self.dimx != other.dimx or self.dimx != other.dimx:
            raise ValueError, "Matrices must be of equal dimension to subtract"
        else:
            # subtract if correct dimensions
            res = matrix([[]])
            res.zero(self.dimx, self.dimy)
            for i in range(self.dimx):
                for j in range(self.dimy):
                    res.value[i][j] = self.value[i][j] - other.value[i][j]
            return res

    def __mul__(self, other):
        # check if correct dimensions
        if self.dimy != other.dimx:
            raise ValueError, "Matrices must be m*n and n*p to multiply"
        else:
            # multiply if correct dimensions
            res = matrix([[]])
            res.zero(self.dimx, other.dimy)
            for i in range(self.dimx):
                for j in range(other.dimy):
                    for k in range(self.dimy):
                        res.value[i][j] += self.value[i][k] * other.value[k][j]
        return res

    def transpose(self):
        # compute transpose
        res = matrix([[]])
        res.zero(self.dimy, self.dimx)
        for i in range(self.dimx):
            for j in range(self.dimy):
                res.value[j][i] = self.value[i][j]
        return res


    def Cholesky(self, ztol= 1.0e-5):
        # Computes the upper triangular Cholesky factorization of  
        # a positive definite matrix.
        # This code is based on http://adorio-research.org/wordpress/?p=4560
        res = matrix([[]])
        res.zero(self.dimx, self.dimx)

        for i in range(self.dimx):
            S = sum([(res.value[k][i])**2 for k in range(i)])
            d = self.value[i][i] - S
            if abs(d) < ztol:
                res.value[i][i] = 0.0
            else: 
                if d < 0.0:
                    raise ValueError, "Matrix not positive-definite"
                res.value[i][i] = sqrt(d)
            for j in range(i+1, self.dimx):
                S = sum([res.value[k][i] * res.value[k][j] for k in range(i)])
                if abs(S) < ztol:
                    S = 0.0
                res.value[i][j] = (self.value[i][j] - S)/res.value[i][i]
        return res 
 
    def CholeskyInverse(self):
	# Computes inverse of matrix given its Cholesky upper Triangular
	# decomposition of matrix.
        # This code is based on http://adorio-research.org/wordpress/?p=4560

        res = matrix([[]])
        res.zero(self.dimx, self.dimx)

	# Backward step for inverse.
        for j in reversed(range(self.dimx)):
            tjj = self.value[j][j]
            S = sum([self.value[j][k]*res.value[j][k] for k in range(j+1, self.dimx)])
            res.value[j][j] = 1.0/ tjj**2 - S/ tjj
	    for i in reversed(range(j)):
                res.value[j][i] = res.value[i][j] = -sum([self.value[i][k]*res.value[k][j] for k in range(i+1,self.dimx)])/self.value[i][i]
        return res
	

    def inverse(self):
        aux = self.Cholesky()
        res = aux.CholeskyInverse()
        return res

    def __repr__(self):
        return repr(self.value)