def __pow__(self, other):
shape = self.shape
if len(shape) != 2 or shape[0] != shape[1]:
raise TypeError, "matrix is not square"
if type(other) in (type(1), type(1L)):
if other==0:
return matrix(N.identity(shape[0]))
if other<0:
x = self.I
other=-other
else:
x=self
result = x
if other <= 3:
while(other>1):
result=result*x
other=other-1
return result
# binary decomposition to reduce the number of Matrix
# Multiplies for other > 3.
beta = binary_repr(other)
t = len(beta)
Z,q = x.copy(),0
while beta[t-q-1] == '0':
Z *= Z
q += 1
result = Z.copy()
for k in range(q+1,t):
Z *= Z
if beta[t-k-1] == '1':
result *= Z
return result
def __pow__(self, other):
shape = self.shape
if len(shape) != 2 or shape[0] != shape[1]:
raise TypeError, "matrix is not square"
if type(other) in (type(1), type(1L)):
if other==0:
return matrix(N.identity(shape[0]))
if other<0:
x = self.I
other=-other
else:
x=self
result = x
if other <= 3:
while(other>1):
result=result*x
other=other-1
return result
# binary decomposition to reduce the number of Matrix
# Multiplies for other > 3.
beta = binary_repr(other)
t = len(beta)
Z,q = x.copy(),0
while beta[t-q-1] == '0':
Z *= Z
q += 1
result = Z.copy()
for k in range(q+1,t):
Z *= Z
if beta[t-k-1] == '1':
result *= Z
return result
else:
raise TypeError, "exponent must be an integer"
def matrix_power(M,n):
"""Raise a square matrix to the (integer) power n.
For positive integers n, the power is computed by repeated matrix
squarings and matrix multiplications. If n=0, the identity matrix
of the same type as M is returned. If n<0, the inverse is computed
and raised to the exponent.
Parameters
----------
M : array-like
Must be a square array (that is, of dimension two and with
equal sizes).
n : integer
The exponent can be any integer or long integer, positive
negative or zero.
Returns
-------
M to the power n
The return value is a an array the same shape and size as M;
if the exponent was positive or zero then the type of the
elements is the same as those of M. If the exponent was negative
the elements are floating-point.
Raises
------
LinAlgException
If the matrix is not numerically invertible, an exception is raised.
See Also
--------
The matrix() class provides an equivalent function as the exponentiation
operator.
Examples
--------
>>> matrix_power(array([[0,1],[-1,0]]),10)
array([[-1, 0],
[ 0, -1]])
"""
if len(M.shape) != 2 or M.shape[0] != M.shape[1]:
raise ValueError("input must be a square array")
if not issubdtype(type(n),int):
raise TypeError("exponent must be an integer")
from numpy.linalg import inv
if n==0:
M = M.copy()
M[:] = identity(M.shape[0])
return M
elif n<0:
M = inv(M)
n *= -1
result = M
if n <= 3:
for _ in range(n-1):
result=N.dot(result,M)
return result
# binary decomposition to reduce the number of Matrix
# multiplications for n > 3.
beta = binary_repr(n)
Z,q,t = M,0,len(beta)
while beta[t-q-1] == '0':
Z = N.dot(Z,Z)
q += 1
result = Z
for k in range(q+1,t):
Z = N.dot(Z,Z)
if beta[t-k-1] == '1':
result = N.dot(result,Z)
return result
def matrix_power(M,n):
"""
Raise a square matrix to the (integer) power n.
For positive integers n, the power is computed by repeated matrix
squarings and matrix multiplications. If n=0, the identity matrix
of the same type as M is returned. If n<0, the inverse is computed
and raised to the exponent.
Parameters
----------
M : array_like
Must be a square array (that is, of dimension two and with
equal sizes).
n : integer
The exponent can be any integer or long integer, positive
negative or zero.
Returns
-------
M to the power n
The return value is a an array the same shape and size as M;
if the exponent was positive or zero then the type of the
elements is the same as those of M. If the exponent was negative
the elements are floating-point.
Raises
------
LinAlgException
If the matrix is not numerically invertible, an exception is raised.
See Also
--------
The matrix() class provides an equivalent function as the exponentiation
operator.
Examples
--------
>>> np.linalg.matrix_power(np.array([[0,1],[-1,0]]),10)
array([[-1, 0],
[ 0, -1]])
"""
if len(M.shape) != 2 or M.shape[0] != M.shape[1]:
raise ValueError("input must be a square array")
if not issubdtype(type(n),int):
raise TypeError("exponent must be an integer")
from numpy.linalg import inv
if n==0:
M = M.copy()
M[:] = identity(M.shape[0])
return M
elif n<0:
M = inv(M)
n *= -1
result = M
if n <= 3:
for _ in range(n-1):
result=N.dot(result,M)
return result
# binary decomposition to reduce the number of Matrix
# multiplications for n > 3.
beta = binary_repr(n)
Z,q,t = M,0,len(beta)
while beta[t-q-1] == '0':
Z = N.dot(Z,Z)
q += 1
result = Z
for k in range(q+1,t):
Z = N.dot(Z,Z)
if beta[t-k-1] == '1':
result = N.dot(result,Z)
return result