def dgradV_dT(self, X, T):
"""
Find the derivative of the gradient with respect to temperature.
This is useful when trying to follow the minima of the potential as they
move with temperature.
"""
T_eps = self.T_eps
try:
gradVT = self._gradVT
except:
# Create the gradient function
self._gradVT = helper_functions.gradientFunction(
self.V1T_from_X, self.x_eps, self.Ndim, self.deriv_order)
gradVT = self._gradVT
# Need to add extra axes to T since extra axes get added to X in
# the helper function.
T = np.asanyarray(T)[...,np.newaxis,np.newaxis]
assert (self.deriv_order == 2 or self.deriv_order == 4)
if self.deriv_order == 2:
y = gradVT(X,T+T_eps,False) - gradVT(X,T-T_eps,False)
y *= 1./(2*T_eps)
else:
y = gradVT(X,T-2*T_eps,False)
y -= 8*gradVT(X,T-T_eps,False)
y += 8*gradVT(X,T+T_eps,False)
y -= gradVT(X,T+2*T_eps,False)
y *= 1./(12*T_eps)
return y
def gradV(self, X, T):
"""
Find the gradient of the full effective potential.
This uses :func:`helper_functions.gradientFunction` to calculate the
gradient using finite differences, with differences
given by `self.x_eps`. Note that `self.x_eps` is only used directly
the first time this function is called, so subsequently changing it
will not have an effect.
"""
try:
f = self._gradV
except:
# Create the gradient function
self._gradV = helper_functions.gradientFunction(
self.Vtot, self.x_eps, self.Ndim, self.deriv_order)
f = self._gradV
# Need to add extra axes to T since extra axes get added to X in
# the helper function.
T = np.asanyarray(T)[...,np.newaxis,np.newaxis]
return f(X,T,False)