Below is a module (matrix.py) with a class to implement some basic

matrix operations on a 2D list. Some things puzzle me about the best

way to do this (please don't refer to scipy, numpy and numeric because

this is a personal programming exercise for me in creating an

operational class in pure python for some *basic* matrix operations).

1. Please take a look at the __init__ function and comment on the

initialization of the list data with respect to unique memory

allocation.

2. In the operator overloading of __add__, __sub__, etc., the

statement isinstance(q, Matrix) raises exceptions every time. This

statement works fine outside of the class definition, but not during

the operator evaluation. What is going here?

## BEGIN MODULE FILE

class Matrix:

"""

Create and manipulate a matrix object

Matrix(data, dim)

data = list of lists (currently only 2D)

dim=(row,col) tuple of int

For example,

#data = [[0.0] * c for i in xrange(r)]

data = [[0.0,0.1],[1.0,1.1],[2.0,2.1]]

rowN =len(data)

colN =len(data[0])

m = Matrix(data)

m = Matrix(data,dim=(rowN, colN))

d1 = [[0.0, 0.1], [1.0, 1.1], [2.0, 2.1]] # 3x2 matrix

d2 = [[0.0, 0.1, 0.2], [1.0, 1.1, 1.2]] # 2x3 matrix

m1 = Matrix(d1)

m2 = Matrix(d2)

#m3 = m1 + m2 # dimension error

m3 = m1 + m2.transpose()

m3 = m1 - m2.transpose()

m3 = m1 * m2 # 3x3

m3 = m2 * m1 # 2x2

m1[2,:]

m1[:,2]

"""

def __init__(self, data=None, dim=None):

"""

create a matrix instance.

m = Matrix([data [, dim]])

<datais a 2D matrix comprised of a nested list of floats

<dimis a tuple of int values for the row and column size

(r,c)

eg:

data = [[0.0,0.1],[1.0,1.1],[2.0,2.1]]

dim = (3,2) # or (len(data),len(data[0]))

"""

if data != None:

self.data = data

r = len(data)

c = len(data[0])

# Are all the rows the same length?

rowLenCheck = sum([len(data[i]) != c for i in range(r)])

if rowLenCheck 0:

raise ValueError

else:

self.dim = (r,c)

if dim != None:

if (dim[0] == r) and (dim[1] == c):

self.dim = (r,c)

else:

# over-ride the dim input, do not reshape data!

# print a warning?

self.dim = (r,c)

else:

if dim != None:

if len(dim) == 2:

self.dim = tuple(dim)

r = dim[0]

c = dim[1]

else:

# maybe a new exception type?

arg = ("len(dim) != 2: ", dim)

raise ValueError, arg

# BEGIN ALT ----------------------------------------

# Does this give unique memory for each element?

# self.data = [[0.0] * c for i in xrange(r)]

# It seems that the initialization does not generate

# unique memory elements because all list elements

# refer to the same number object (0.0), but

# modification of any element creates a unique value,

# without changing any other values, eg:

##>>x = [[0.0] * 3 for i in xrange(2)]

##>>id(x)

# 3079625068L

# >>id(x[0][0])

# 136477300

# >>id(x[0][1])

# 136477300

# >>id(x[1][1])

# 136477300

# >>x[0][0] = 1.0

# >>x

# [[1.0, 0.0, 0.0], [0.0, 0.0, 0.0]]

# >>>

# END ALT ----------------------------------------

# create a zero row vector, with unique memory for

each element

self.data = [[x * 0.0 for x in range(c)]]

for i in range(1,r):

self.data.append([x * 0.0 for x in range(c)])

else:

self.data = []

self.dim = (0,0)

#print self.__doc__

def __getitem__(self, i):

"""

matrix[r,c] returns values from matrix.data, eg:

>>data = [[0.0,0.1],[1.0,1.1],[2.0,2.1]]

m = Matrix(data)

m[2,:]

[2.0, 2.1000000000000001]

"""

r = i[0]

c = i[1]

#print "index: (%s, %s)" % (r,c)

#print "value: ", self.data[r][c]

return self.data[r][c]

def reshape(self, newdim=None):

'reshape a matrix object: matrix.reshape(newdim)'

print "something to implement later"

pass

def transpose(self):

'transpose a matrix: m2 = m1.transpose()'

m = Matrix(dim=(self.dim[1],self.dim[0]))

for r in range(self.dim[0]):

for c in range(self.dim[1]):

m.data[c][r] = self.data[r][c]

return m

def __add__(self, q):

'matrix addition: m3 = m1 + m2'

# if isinstance(q, Matrix):

# arg = ("q is not a matrix instance", q)

# raise TypeError, arg

if self.dim != q.dim:

arg = ("p.dim != q.dim", self.dim, q.dim)

raise IndexError, arg

else:

# do the addition

m = Matrix(dim=self.dim)

for r in range(self.dim[0]): # rows of p and q

m.data[r] = map(lambda x, y: x + y, self.data[r],

q.data[r])

return m

def __sub__(self, q):

'matrix subtraction: matrix - matrix'

# if isinstance(q, Matrix):

# arg = ("q is not a matrix instance", q)

# raise TypeError, arg

if self.dim != q.dim:

arg = ("p.dim != q.dim", self.dim, q.dim)

raise IndexError, arg

else:

# do the subtraction

m = Matrix(dim=self.dim)

for r in range(self.dim[0]): # rows of p and q

m.data[r] = map(lambda x, y: x - y, self.data[r],

q.data[r])

return m

def __mul__(self, q):

"""

multiply two matrices:

m = p * q # p and q are matrix objects and p.dim[1] ==

q.dim[0]

"""

# if isinstance(q, Matrix):

# arg = ("q is not a matrix instance", q)

# raise TypeError, arg

if self.dim[1] != q.dim[0]:

arg = ("p.dim[1] != q.dim[0]", self.dim[1], q.dim[0])

raise IndexError, arg

else:

# do the multiplication

m = Matrix(dim=(self.dim[0], q.dim[1]))

for r in range(self.dim[0]): # rows of p

for c in range(q.dim[1]): # cols of q

# get the dot product of p(r,:) with q(:,c)

pVec = self.data[r]

qVec = [q.data[a][c] for a in xrange(q.dim[0])]

m.data[r][c] = sum(map(lambda x, y: x * y, pVec,

qVec))

return m

# let's not try to divide for now (leave the inverse stuff to c/c+

+)

def __len__(self):

return self.dim[0] * self.dim[1]

def __str__(self):

# print the matrix data

s = ""

for r in range(self.dim[0]):

for c in range(self.dim[1]):

s += "%f " % (self.data[r][c])

s += "\n"

return s

def printFormat(self, format):

"""

print the matrix data nicely formatted, eg:

matrix.printFormat("%8.4f")

"""

for r in range(self.dim[0]):

for c in range(self.dim[1]):

print format % (self.data[r][c]),

print

def __repr__(self):

# return something that will recreate the object

return "Matrix(%s, %s)" % (self.data, self.dim)

#

--------------------------------------------------------------------------------

# Explore the functionality - should be unit testing

# >>m = Matrix(dim=(2,2))

# >>type(m)

# <class '__main__.matrix'>

# >>m.dim

#(2, 2)

# >>m.len()

# 4

# >>m.data

# [[0.0, 0.0], [0.0, 0.0]]

# >>m.dim

# (2, 2)

# >>id(m.data[0][0])

# 136477668

# >>id(m.data[0][1])

# 136477380

# >>id(m.data[1][0])

# 136477668

# >>id(m.data[1][1])

# 136477380

# >>m.data[0][0] = 1.0

# >>m.data[1][0] = 2.0

# >>m.data

# [[1.0, 0.0], [2.0, 0.0]]

testing = 1

if testing:

d1 = [[0.0, 0.1], [1.0, 1.1], [2.0, 2.1]] # 3x2 matrix

d2 = [[0.0, 0.1, 0.2], [1.0, 1.1, 1.2]] # 2x3 matrix

m1 = Matrix(d1)

m2 = Matrix(d2)

#m3 = m1 + m2 # "dimension" error

m3 = m1 + m2.transpose()

m3 = m1 - m2.transpose()

m3 = m1 * m2 # 3x3

m3 = m2 * m1 # 2x2

## END MODULE FILE