def eigenvalues(self):
"""
@returns: the eigenvalues of the tensor
@rtype: C{Numeric.array}
@raises ValueError: if rank !=2
"""
if self.rank == 2:
from Scientific.LA import eigenvalues
return eigenvalues(self.array)
else:
raise ValueError('Undefined operation')
def eigenvalues(self):
"""
@returns: the eigenvalues of the tensor
@rtype: C{Numeric.array}
@raises ValueError: if rank !=2
"""
if self.rank == 2:
from Scientific.LA import eigenvalues
return eigenvalues(self.array)
else:
raise ValueError('Undefined operation')
def poles(self):
"""
@returns: the poles of the model in the complex M{z}-plane
@rtype: C{Numeric.array} of C{complex}
"""
if self._poles is None:
from Scientific.LA import eigenvalues
n = len(self.coeff)
if n == 1:
self._poles = self.coeff
else:
a = N.zeros_st((n, n), self.coeff)
a[1:, :-1] = N.identity(n-1)
a[:, -1] = self.coeff
self._poles = eigenvalues(a)
return self._poles
def poles(self):
"""
@returns: the poles of the model in the complex M{z}-plane
@rtype: C{Numeric.array} of C{complex}
"""
if self._poles is None:
from Scientific.LA import eigenvalues
n = len(self.coeff)
if n == 1:
self._poles = self.coeff
else:
a = N.zeros_st((n, n), self.coeff)
a[1:, :-1] = N.identity(n - 1)
a[:, -1] = self.coeff
self._poles = eigenvalues(a)
return self._poles
def zeros(self):
"""
Find the X{zeros} (X{roots}) of the polynomial by diagonalization
of the associated Frobenius matrix.
@returns: an array containing the zeros
@rtype: C{Numeric.array}
@note: this is defined only for polynomials in one variable
@raise ValueError: is the polynomial has more than one variable
"""
if self.dim != 1:
raise ValueError("not implemented")
n = len(self.coeff)-1
if n == 0:
return Numeric.array([])
a = Numeric.zeros_st((n, n), self.coeff)
if n > 1:
a[1:, :-1] = Numeric.identity(n-1)
a[:, -1] = -self.coeff[:-1]/self.coeff[-1]
from Scientific.LA import eigenvalues
return eigenvalues(a)
def zeros(self):
"""
Find the X{zeros} (X{roots}) of the polynomial by diagonalization
of the associated Frobenius matrix.
@returns: an array containing the zeros
@rtype: C{Numeric.array}
@note: this is defined only for polynomials in one variable
@raise ValueError: is the polynomial has more than one variable
"""
if self.dim != 1:
raise ValueError("not implemented")
n = len(self.coeff) - 1
if n == 0:
return Numeric.array([])
a = Numeric.zeros_st((n, n), self.coeff)
if n > 1:
a[1:, :-1] = Numeric.identity(n - 1)
a[:, -1] = -self.coeff[:-1] / self.coeff[-1]
from Scientific.LA import eigenvalues
return eigenvalues(a)