class ATLJ(BasePotential):
"""
Lennard Jones + three body Axilrod-Teller term
V = sum_ij VLJ_ij + sum_ijk Z * (1 + 3*cos(t1)*cos(t2)*cos(t3)) / (rij * rjk * rik)**3 )
where t1, t2, t3 are the internal angles of the triangle ijk
Z > 0 stabilizes linear vs. triangular geometries
"""
def __init__(self, eps=1.0, sig=1.0, Z=1.):
""" simple lennard jones potential"""
self.sig = sig
self.eps = eps
self.Z = Z
self.lj = LJ(self.sig, self.eps)
def getEnergyWeave(self, coords):
"""
use weave inline
"""
Elj = self.lj.getEnergy(coords)
natoms = coords.size/3
coords = np.reshape(coords, [natoms,3])
energy=0.
Z = self.Z
#support_code
code = """
double drij[3];
double drik[3];
double drjk[3];
energy = 0.;
for (int i=0; i < natoms; ++i){
for (int j=0; j<i; ++j){
for (int k=0; k<j; ++k){
double rij = 0.;
double rik = 0.;
double rjk = 0.;
for (int d=0; d<3; ++d){
drij[d] = coords(i,d) - coords(j,d);
rij += drij[d]*drij[d];
}
for (int d=0; d<3; ++d){
drjk[d] = coords(j,d) - coords(k,d);
rjk += drjk[d]*drjk[d];
}
for (int d=0; d<3; ++d){
drik[d] = coords(i,d) - coords(k,d);
rik += drik[d]*drik[d];
}
rij = sqrt(rij);
rjk = sqrt(rjk);
rik = sqrt(rik);
double ctijk = ( -(drij[0]*drjk[0] + drij[1]*drjk[1] + drij[2]*drjk[2]) / (rij * rjk) );
double ctjki = ( (drjk[0]*drik[0] + drjk[1]*drik[1] + drjk[2]*drik[2]) / (rjk * rik) );
double ctkij = ( (drik[0]*drij[0] + drik[1]*drij[1] + drik[2]*drij[2]) / (rik * rij) );
double r3 = rij*rjk*rik;
energy += Z*(1. + 3. * ctijk * ctjki * ctkij) / (r3*r3*r3);
}
}
}
return_val= energy;
"""
energy = weave.inline(code, ["coords", "energy", "Z", "natoms"], type_converters=converters.blitz, verbose=2)
#print "fast energy", Elj, energy
energy += Elj
return energy
def getEnergySlow(self, coords):
Elj = self.lj.getEnergy(coords)
natoms = coords.size/3
X = np.reshape(coords, [natoms,3])
Z = self.Z
energy = 0.
for i in range(natoms):
for j in range(i):
for k in range(j):
#print i, j, k
drij = X[i,:] - X[j,:]
drik = X[i,:] - X[k,:]
drjk = X[j,:] - X[k,:]
rij = np.linalg.norm( drij )
rik = np.linalg.norm( drik )
rjk = np.linalg.norm( drjk )
energy += Z * (1. + 3.*\
np.dot( drij, -drjk ) * \
np.dot(-drij, -drik ) * \
np.dot( drik, drjk ) / (rij*rik*rjk)**2) \
/ (rij*rik*rjk)**3
#print "slow energy", Elj, energy
energy += Elj
return energy
def getEnergyFortran(self, coords):
#grad,potel = axt(x,gradt,zstar,[n])
natoms = len(coords)/3
garbage, e = ATfort.axt(coords, False, self.Z, [natoms])
Elj = self.lj.getEnergy(coords)
return e + Elj
def getEnergyGradientFortran(self, coords):
#grad,potel = axt(x,gradt,zstar,[n])
natoms = len(coords)/3
grad, e = ATfort.axt(coords, True, self.Z, [natoms])
elj, gradlj = self.lj.getEnergyGradient(coords)
return e + elj, grad + gradlj
def getEnergy(self, coords):
return self.getEnergyFortran(coords)
def getEnergyGradient(self, coords):
#return self.getEnergyGradientNumerical(coords)
return self.getEnergyGradientFortran(coords)
def getEnergyGradient(self, coords):
atom_coords = self.aatopology.to_atomistic(coords)
e, atom_grad = LJ.getEnergyGradient(self, atom_coords.flatten())
grad = self.aatopology.transform_gradient(coords, atom_grad)
return e, grad
def getEnergyGradient(self, coords):
atom_coords = self.aatopology.to_atomistic(coords)
e, atom_grad = LJ.getEnergyGradient(self, atom_coords.flatten())
grad = self.aatopology.transform_gradient(coords, atom_grad)
return e, grad
t0 = time.time()
for i in xrange(100):
x = 1. * (np.random.random(3 * natoms) - 0.5)
ret = clbfgs.run(x)
#print ret
#print ret[0]
#print pot.get_energy(ret[0])
e, g = pot.get_energy_gradient(ret[0])
print "C", np.linalg.norm(g)
t1 = time.time()
for i in xrange(100):
x = 1. * np.random.random(3 * natoms)
ret = mylbfgs(x, pot_old, tol=1e-5)
print "PY:", np.linalg.norm(pot_old.getEnergyGradient(ret[0])[1])
print time.time() - t1, t1 - t0
t0 = time.time()
for i in xrange(N):
e, g = pot_old.getEnergyGradient(x)
time_f2py = time.time() - t0
print "f2py potential", e, "time", time.time() - t0
t0 = time.time()
for i in xrange(N):
e, g = pot.get_energy_gradient(x)
time_cython = time.time() - t0
print "cython potential", e, "time", time.time() - t0
t0 = time.time()
for i in xrange(100):
x = 1.*(np.random.random(3*natoms) - 0.5)
ret = clbfgs.run(x)
#print ret
#print ret[0]
#print pot.get_energy(ret[0])
e, g = pot.get_energy_gradient(ret[0])
print "C", np.linalg.norm(g)
t1 = time.time()
for i in xrange(100):
x = 1.*np.random.random(3*natoms)
ret = mylbfgs(x, pot_old, tol=1e-5)
print "PY:", np.linalg.norm(pot_old.getEnergyGradient(ret[0])[1])
print time.time()-t1, t1-t0
t0 = time.time()
for i in xrange(N):
e, g = pot_old.getEnergyGradient(x)
time_f2py = time.time() - t0
print "f2py potential",e,"time",time.time() - t0
t0 = time.time()
for i in xrange(N):
e, g = pot.get_energy_gradient(x)
time_cython = time.time() - t0
print "cython potential",e,"time",time.time() - t0
class ATLJ(BasePotential):
"""
Lennard Jones + three body Axilrod-Teller term
V = sum_ij VLJ_ij + sum_ijk Z * (1 + 3*cos(t1)*cos(t2)*cos(t3)) / (rij * rjk * rik)**3 )
where t1, t2, t3 are the internal angles of the triangle ijk
Z > 0 stabilizes linear vs. triangular geometries
"""
def __init__(self, eps=1.0, sig=1.0, Z=1.):
""" simple lennard jones potential"""
self.sig = sig
self.eps = eps
self.Z = Z
self.lj = LJ(self.sig, self.eps)
def getEnergyWeave(self, coords):
"""
use weave inline
"""
Elj = self.lj.getEnergy(coords)
natoms = coords.size / 3
coords = np.reshape(coords, [natoms, 3])
energy = 0.
Z = self.Z
#support_code
code = """
double drij[3];
double drik[3];
double drjk[3];
energy = 0.;
for (int i=0; i < natoms; ++i){
for (int j=0; j<i; ++j){
for (int k=0; k<j; ++k){
double rij = 0.;
double rik = 0.;
double rjk = 0.;
for (int d=0; d<3; ++d){
drij[d] = coords(i,d) - coords(j,d);
rij += drij[d]*drij[d];
}
for (int d=0; d<3; ++d){
drjk[d] = coords(j,d) - coords(k,d);
rjk += drjk[d]*drjk[d];
}
for (int d=0; d<3; ++d){
drik[d] = coords(i,d) - coords(k,d);
rik += drik[d]*drik[d];
}
rij = sqrt(rij);
rjk = sqrt(rjk);
rik = sqrt(rik);
double ctijk = ( -(drij[0]*drjk[0] + drij[1]*drjk[1] + drij[2]*drjk[2]) / (rij * rjk) );
double ctjki = ( (drjk[0]*drik[0] + drjk[1]*drik[1] + drjk[2]*drik[2]) / (rjk * rik) );
double ctkij = ( (drik[0]*drij[0] + drik[1]*drij[1] + drik[2]*drij[2]) / (rik * rij) );
double r3 = rij*rjk*rik;
energy += Z*(1. + 3. * ctijk * ctjki * ctkij) / (r3*r3*r3);
}
}
}
return_val= energy;
"""
energy = weave.inline(code, ["coords", "energy", "Z", "natoms"],
type_converters=converters.blitz,
verbose=2)
#print "fast energy", Elj, energy
energy += Elj
return energy
def getEnergySlow(self, coords):
Elj = self.lj.getEnergy(coords)
natoms = coords.size / 3
X = np.reshape(coords, [natoms, 3])
Z = self.Z
energy = 0.
for i in range(natoms):
for j in range(i):
for k in range(j):
#print i, j, k
drij = X[i, :] - X[j, :]
drik = X[i, :] - X[k, :]
drjk = X[j, :] - X[k, :]
rij = np.linalg.norm(drij)
rik = np.linalg.norm(drik)
rjk = np.linalg.norm(drjk)
energy += Z * (1. + 3.*\
np.dot( drij, -drjk ) * \
np.dot(-drij, -drik ) * \
np.dot( drik, drjk ) / (rij*rik*rjk)**2) \
/ (rij*rik*rjk)**3
#print "slow energy", Elj, energy
energy += Elj
return energy
def getEnergyFortran(self, coords):
#grad,potel = axt(x,gradt,zstar,[n])
natoms = len(coords) / 3
garbage, e = ATfort.axt(coords, False, self.Z, [natoms])
Elj = self.lj.getEnergy(coords)
return e + Elj
def getEnergyGradientFortran(self, coords):
#grad,potel = axt(x,gradt,zstar,[n])
natoms = len(coords) / 3
grad, e = ATfort.axt(coords, True, self.Z, [natoms])
elj, gradlj = self.lj.getEnergyGradient(coords)
return e + elj, grad + gradlj
def getEnergy(self, coords):
return self.getEnergyFortran(coords)
def getEnergyGradient(self, coords):
#return self.getEnergyGradientNumerical(coords)
return self.getEnergyGradientFortran(coords)
