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 gradVCW(self, X, T):
'''
Calculate the gradient of VCW for counterterm calculation.
'''
try:
f = self._gradVCW
except:
self._gradVCW = helper_functions.gradientFunction(
self.V1, self.x_eps, self.Ndim, self.deriv_order)
f = self._gradVCW
T = np.asanyarray(T)[...,np.newaxis,np.newaxis]
return f(X, T)
def gradV0(self, X):
"""
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._gradV0
except:
# Create the gradient function
self._gradV0 = helper_functions.gradientFunction(
self.V0, self.x_eps, self.Ndim, self.deriv_order)
f = self._gradV0
return f(X)
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)
def Dhss(X, T, m):
return helper_functions.gradientFunction(Dhs, m.x_eps, m.Ndim,
m.deriv_order)(X, T, m)[..., 1]
