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matrix.py
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matrix.py
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class matrix:
# implements basic operations of a matrix class
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 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 ' '
def __add__(self, other):
# check if correct dimensions
if self.dimx != other.dimx or self.dimy != other.dimy:
raise ValueError, "Matrices must be of equal dimensions 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.dimy != other.dimy:
raise ValueError, "Matrices must be of equal dimensions 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:
# subtract 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
# Thanks to Ernesto P. Adorio for use of Cholesky and CholeskyInverse functions
def Cholesky(self, ztol=1.0e-5):
# Computes the upper triangular Cholesky factorization of
# a positive definite matrix.
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(self.dimx)])
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.
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)