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]])
<data> is a 2D matrix comprised of a nested list of floats
<dim> is 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
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