def getEnergy(self, coords):
E = GMINPotential.getEnergy(self, coords)
ca = CoordsAdapter(nrigid=coords.size / 6, coords=coords)
RMX = [rmdrvt(p, True) for p in ca.rotRigid]
xback = np.array([x - 0.4 * np.dot(r[0], np.array([1.0, 0.0, 0.0])) for x, r in zip(ca.posRigid, RMX)])
xbase = np.array([x + 0.4 * np.dot(r[0], np.array([1.0, 0.0, 0.0])) for x, r in zip(ca.posRigid, RMX)])
Eangle = 0
v2 = xback[1] - xback[0]
v2 /= np.linalg.norm(v2)
for i in xrange(1, ca.nrigid - 1):
v1 = -v2.copy()
v2 = xback[i + 1] - xback[i]
v2 /= np.linalg.norm(v2)
theta = np.arccos(np.dot(v1, v2))
Eangle += 0.5 * self.k * (theta - self.theta0) ** 2
# add the torsion angle
Etorsion = 0
if self.use_torsion:
for i in xrange(ca.nrigid - 3):
theta = dihedral_angle(xback[i : i + 4])
Etorsion += U_torsion_back(theta)
return E + Eangle + Etorsion
def getEnergyGradient(self, coords):
# return self.getEnergy(coords), self.NumericalDerivative(coords)
E, grad = GMINPotential.getEnergyGradient(self, coords)
ca = CoordsAdapter(nrigid=coords.size / 6, coords=coords)
RMX = [rmdrvt(p, True) for p in ca.rotRigid]
xback = [x - 0.4 * np.dot(r[0], np.array([1.0, 0.0, 0.0])) for x, r in zip(ca.posRigid, RMX)]
xbase = [x - 0.4 * np.dot(r[0], np.array([1.0, 0.0, 0.0])) for x, r in zip(ca.posRigid, RMX)]
gback = np.zeros_like(xback)
Eangle = 0.0
v2 = xback[1] - xback[0]
absv2 = np.linalg.norm(v2)
v2 /= absv2
for i in xrange(1, ca.nrigid - 1):
v1 = -v2
absv1 = absv2
v2 = xback[i + 1] - xback[i]
absv2 = np.linalg.norm(v2)
v2 /= absv2
v1v2 = np.dot(v1, v2)
theta = np.arccos(v1v2)
Eangle += 0.5 * self.k * (theta - self.theta0) ** 2
acos_prime = 1.0 / np.sqrt(1.0 - v1v2 ** 2)
s = self.k * (theta - self.theta0) * acos_prime
gback[i - 1] += s * (-v2 / absv1 + v1v2 * v1 / absv1)
gback[i] += s * (v1 / absv2 + v2 / absv1 - v1v2 * v1 / absv1 - v1v2 * v2 / absv2)
gback[i + 1] += s * (-v1 / absv2 + v1v2 * v2 / absv2)
Etorsion = 0
if self.use_torsion:
for i in xrange(ca.nrigid - 3):
r = xback[i : i + 4]
theta = dihedral_angle(r)
e_theta, g_theta = U_torsion_back_grad(theta)
Etorsion += e_theta
gback[i : i + 4] += g_theta * dihedral_gradient(r)
cg = CoordsAdapter(nrigid=ca.nrigid, coords=grad)
cg.posRigid += gback
for i in xrange(ca.nrigid):
x = -0.4 * np.array([1.0, 0.0, 0.0])
R = RMX[i]
cg.rotRigid[i][0] += np.dot(gback[i], np.dot(R[1], x))
cg.rotRigid[i][1] += np.dot(gback[i], np.dot(R[2], x))
cg.rotRigid[i][2] += np.dot(gback[i], np.dot(R[3], x))
return E + Eangle + Etorsion, grad
