def force(self, c, x):
b, db = dbond(
array([x[..., j, :] - x[..., i, :] for i, j in self.edges]))
u, du = self.f.y(c, b, 1)
en = sum(u, -1)
F = zeros(x.shape)
for k, (i, j) in enumerate(self.edges):
F[..., i, :] += du[k] * db[..., k, :]
F[..., j, :] -= du[k] * db[..., k, :]
return en, F
def force(self, c, x):
self.f.c = c
delta = calc_delta(x, self.edges, self.excl, self.L)
b, db = dbond(delta)
u, du = self.f.y(b, 1)
en = sum(u, -1)
F = zeros(x.shape)
for k, (i, j) in enumerate(ex_gen(self.edges, self.excl)):
delta[k] = x[..., j, :] - x[..., i, :]
F[..., i, :] += du[k] * db[..., k, :]
F[..., j, :] -= du[k] * db[..., k, :]
return en, F
def force(self, c, x):
delta = calc_delta(x, self.edges, self.excl, self.L)
r, db = dbond(delta) # r, dr/dx
u, du = self.f.y(c, r**-6, 1) # f(r^-6), df/du (u = r^-6)
# du/dr = -6 r^-7
du *= -6*r**-7
en = sum(u, -1)
de = zeros(x.shape)
for k,(i,j) in enumerate(ex_gen(self.edges, self.excl)):
de[...,i,:] += du[k]*db[...,k,:] # df/du du/dr dr/dx
de[...,j,:] -= du[k]*db[...,k,:]
return en, de
def design_pair(self, x, order=0):
A = []
delta = calc_delta(x, self.edges, self.excl, self.L)
if order == 0:
return sum(self.spline(bond(delta), order), -2)
elif order == 1:
Ad = zeros(x.shape + (self.f.n, ))
b, db = dbond(delta)
spl, dspl = self.spline(b, order)
for k, (i, j) in enumerate(ex_gen(self.edges, self.excl)):
Ad[...,i,:,:] -= db[...,k,:,newaxis] \
* dspl[...,k,newaxis,:]
Ad[...,j,:,:] += db[...,k,:,newaxis] \
* dspl[...,k,newaxis,:]
A = sum(spl, -2)
return A, Ad
else:
raise RuntimeError, "Error! >1 energy derivative not "\
"supported."
def design(self, x, order=0):
if order == 0:
b = bond(
array([x[..., j, :] - x[..., i, :] for i, j in self.edges]))
spl = self.spline(b, order)
return sum(spl, -2)
elif order == 1:
Ad = zeros(x.shape + (self.params, ))
b, db = dbond(
array([x[..., j, :] - x[..., i, :] for i, j in self.edges]))
spl, dspl = self.spline(b, order)
for k, (i, j) in enumerate(self.edges):
Ad[...,i,:,:] -= db[...,k,:,newaxis] \
* dspl[...,k,newaxis,:]
Ad[...,j,:,:] += db[...,k,:,newaxis] \
* dspl[...,k,newaxis,:]
A = sum(spl, -2)
return A, Ad
raise RuntimeError, "Error! >1 energy derivative not "\
"supported."
def design(self, x, order=0):
delta = calc_delta(x, self.edges, self.excl, self.L)
if order == 0:
return sum(self.spline(bond(delta)**-6, order), -2)
elif order == 1:
Ad = zeros(x.shape + (self.params,))
r, db = dbond(delta) # r, dr/dx
spl, dspl = self.spline(r**-6, order) # D(r^-6), dD(r^-6)/du
dspl *= -6*r[...,newaxis]**-7 # du/dr
for k,(i,j) in enumerate(ex_gen(self.edges, self.excl)): # dD/dx
Ad[...,i,:,:] -= db[...,k,:,newaxis] \
* dspl[...,k,newaxis,:]
Ad[...,j,:,:] += db[...,k,:,newaxis] \
* dspl[...,k,newaxis,:]
assert k+1 == len(delta)
A = sum(spl, -2)
return A, Ad
else:
raise RuntimeError, "Error! >1 energy derivative not "\
"supported."