def matrix_element(self, bra, ket):
"""Calculates a matrix element.
Gives matrix for the Qobj sandwiched between a `bra` and `ket`
vector.
Parameters
-----------
bra : qobj
Quantum object of type 'bra'.
ket : qobj
Quantum object of type 'ket'.
Returns
-------
elem : complex
Complex valued matrix element.
Raises
------
TypeError
Can only calculate matrix elements between a bra and ket quantum object.
"""
if isoper(self):
if isbra(bra) and isket(ket):
return (bra.data * self.data * ket.data)[0,0]
if isket(bra) and isket(ket):
return (bra.data.T * self.data * ket.data)[0,0]
raise TypeError("Can only calculate matrix elements for operators and between ket and bra Qobj")
def matrix_element(self, bra, ket):
"""Calculates a matrix element.
Gives matrix for the Qobj sandwiched between a `bra` and `ket`
vector.
Parameters
-----------
bra : qobj
Quantum object of type 'bra'.
ket : qobj
Quantum object of type 'ket'.
Returns
-------
elem : complex
Complex valued matrix element.
Raises
------
TypeError
Can only calculate matrix elements between a bra and ket quantum object.
"""
if isoper(self):
if isbra(bra) and isket(ket):
return (bra.data * self.data * ket.data)[0, 0]
if isket(bra) and isket(ket):
return (bra.data.T * self.data * ket.data)[0, 0]
raise TypeError(
"Can only calculate matrix elements for operators and between ket and bra Qobj"
)
def transform(self, inpt, inverse=False):
"""Performs a basis transformation defined by an input array.
Input array can be a ``matrix`` defining the transformation,
or a ``list`` of kets that defines the new basis.
Parameters
----------
inpt : array_like
A ``matrix`` or ``list`` of kets defining the transformation.
inverse : bool
Whether to return inverse transformation.
Returns
-------
oper : qobj
Operator in new basis.
Notes
-----
This function is still in development.
"""
if isinstance(inpt, list) or isinstance(inpt, np.ndarray):
if len(inpt) != self.shape[0] or len(inpt) != self.shape[1]:
raise TypeError('Invalid size of ket list for basis transformation')
S = np.matrix([inpt[n].full()[:,0] for n in range(len(inpt))]).H
elif isinstance(inpt,np.ndarray):
S = np.matrix(inpt)
else:
raise TypeError('Invalid operand for basis transformation')
# normalize S just in case the supplied basis states aren't normalized
#S = S/la.norm(S)
out=Qobj(type=self.type)
out.dims=[self.dims[1],self.dims[0]]
out.shape=[self.shape[1],self.shape[0]]
out.isherm=self.isherm
out.type=self.type
# transform data
if inverse:
if isket(self):
out.data = S.H * self.data
elif isbra(self):
out.data = self.data * S
else:
out.data = S * self.data * S.H
else:
if isket(self):
out.data = S * self.data
elif isbra(self):
out.data = self.data * S.H
else:
out.data = S.H * self.data * S
# force sparse
out.data = sp.csr_matrix(out.data,dtype=complex)
return out
def transform(self, inpt, inverse=False):
"""Performs a basis transformation defined by an input array.
Input array can be a ``matrix`` defining the transformation,
or a ``list`` of kets that defines the new basis.
Parameters
----------
inpt : array_like
A ``matrix`` or ``list`` of kets defining the transformation.
inverse : bool
Whether to return inverse transformation.
Returns
-------
oper : qobj
Operator in new basis.
Notes
-----
This function is still in development.
"""
if isinstance(inpt, list) or isinstance(inpt, np.ndarray):
if len(inpt) != self.shape[0] or len(inpt) != self.shape[1]:
raise TypeError(
'Invalid size of ket list for basis transformation')
S = np.matrix([inpt[n].full()[:, 0] for n in range(len(inpt))]).H
elif isinstance(inpt, np.ndarray):
S = np.matrix(inpt)
else:
raise TypeError('Invalid operand for basis transformation')
# normalize S just in case the supplied basis states aren't normalized
#S = S/la.norm(S)
out = Qobj(type=self.type)
out.dims = [self.dims[1], self.dims[0]]
out.shape = [self.shape[1], self.shape[0]]
out.isherm = self.isherm
out.type = self.type
# transform data
if inverse:
if isket(self):
out.data = S.H * self.data
elif isbra(self):
out.data = self.data * S
else:
out.data = S * self.data * S.H
else:
if isket(self):
out.data = S * self.data
elif isbra(self):
out.data = self.data * S.H
else:
out.data = S.H * self.data * S
# force sparse
out.data = sp.csr_matrix(out.data, dtype=complex)
return out