def Align(self, coords1, coords2):
from pygmin.mindist import rmsfit,aamindist
potential = GMINPotential(GMIN)
ca1 = CoordsAdapter(nrigid=coords1.size/6, coords = coords1)
ca2 = CoordsAdapter(nrigid=coords2.size/6, coords = coords2)
rot = rmsfit.findrotation_kabsch(ca2.posRigid, ca1.posRigid)
ca2.posRigid[:] = np.dot(rot,ca2.posRigid.transpose()).transpose()
for p in ca2.rotRigid:
p[:] = rotations.mx2aa((np.dot(rot, rotations.aa2mx(p))))
print "before"
print potential.getEnergy(coords1), potential.getEnergy(coords2)
print ca2.rotRigid - ca1.rotRigid
for p1,p2 in zip(ca1.rotRigid, ca2.rotRigid):
p1[:],p2[:] = aamindist.aadistance(p1, p2)
print "after"
print potential.getEnergy(coords1), potential.getEnergy(coords2)
print ca2.rotRigid - ca1.rotRigid
path = InterpolatedPath(coords1, coords2, 40)
print potential.getEnergy(path[0])
print "Interpolated energies"
for x in InterpolatedPath(coords1, coords2, 40):
print potential.getEnergy(x)
print "done"
return coords1, coords2
def takeStep(self, coords, **kwargs):
# easy access to coordinates
ca = CoordsAdapter(nrigid=coords.size/6, coords = coords)
# random rotation for angle-axis vectors
for j in xrange(ca.nrigid):
# choose bond to rotate around, index is first bead that changes
index = np.random.randint(1, ca.nrigid)
# determine backbone beads
a1 = np.dot(rotations.aa2mx(ca.rotRigid[index-1]), np.array([1., 0., 0.]))
a2 = np.dot(rotations.aa2mx(ca.rotRigid[index]), np.array([1., 0., 0.]))
x1 = ca.posRigid[index-1] - 0.4*a1 # backbone bead
x2 = ca.posRigid[index] - 0.4*a2 # backbone bead
# get bond vector as axis of rotation + random magnitude
p = x2 - x1
p /= np.linalg.norm(p)
p *= np.random.random()*self.stepsize
# convert random rotation to a matrix
mx = rotations.aa2mx(p)
# center of rotation is in middle of backbone bond
center = 0.5*(x1 + x2)
# apply rotation to positions and orientations
for i in xrange(index, ca.nrigid):
a = np.dot(rotations.aa2mx(ca.rotRigid[i]), np.array([1., 0., 0.]))
ca.rotRigid[i] = rotations.rotate_aa(p, ca.rotRigid[i])
x = ca.posRigid[i] - 0.4*a
ca.posRigid[i] = np.dot(mx, x - center) + center
a = np.dot(rotations.aa2mx(ca.rotRigid[i]), np.array([1., 0., 0.]))
ca.posRigid[i]+=0.4*a
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.]))
for x, r in zip(ca.posRigid, RMX)
]
xbase = [
x - 0.4 * np.dot(r[0], np.array([1., 0., 0.]))
for x, r in zip(ca.posRigid, RMX)
]
gback = np.zeros_like(xback)
Eangle = 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. / np.sqrt(1. - 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.])
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
def takeStep(self, coords, **kwargs):
# easy access to coordinates
ca = CoordsAdapter(nrigid=coords.size/6, coords = coords)
# random displacement for positions
ca.posRigid[:] = 2.*self.radius*(np.random.random(ca.posRigid.shape)-0.5)
# random rotation for angle-axis vectors
for rot in ca.rotRigid:
rot[:] = rotations.random_aa()
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.]))
for x, r in zip(ca.posRigid, RMX)
])
xbase = np.array([
x + 0.4 * np.dot(r[0], np.array([1., 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 takeStep(self, coords, **kwargs):
# easy access to coordinates
ca = CoordsAdapter(nrigid=coords.size / 6, coords=coords)
# random displacement for positions
ca.posRigid[:] += 2. * self.displace * (
np.random.random(ca.posRigid.shape) - 0.5)
# random rotation for angle-axis vectors
takestep.rotate(self.rotate, ca.rotRigid)
def export_xyz(fl, coords):
ca = CoordsAdapter(nrigid=coords.size / 6, coords=coords)
fl.write("%d\n\n" % (2 * ca.nrigid))
for i in xrange(ca.nrigid):
a = np.dot(rotations.aa2mx(ca.rotRigid[i]), np.array([1., 0., 0.]))
x_back = ca.posRigid[i] - 0.4 * a # backbone bead
x_stack = ca.posRigid[i] + 0.4 * a
fl.write("C %f %f %f\n" % (x_back[0], x_back[1], x_back[2]))
fl.write("H %f %f %f\n" % (x_stack[0], x_stack[1], x_stack[2]))
def takeStep(self, coords, **kwargs):
# easy access to coordinates
ca = CoordsAdapter(nrigid=coords.size / 6, coords=coords)
# random displacement for positions
#ca.posRigid[:] = 2.*self.radius*(np.random.random(ca.posRigid.shape)-0.5)
# random rotation for angle-axis vectors
for rot in ca.rotRigid:
rot[:] = rotations.random_aa()
def map_to_aa(xyz):
coords = np.zeros(6*13)
ca = CoordsAdapter(nrigid=13, coords=coords)
for i in xrange(13):
ca.posRigid[i] = 0.5*(xyz[2*i] + xyz[2*i+1])
a1 = -(xyz[2*i] - xyz[2*i+1])
if(i<12):
a3 = -(xyz[2*i+1] - xyz[2*i+3])
else:
a3 = -(xyz[2*i-1] - xyz[2*i+1])
a2 = -np.cross(a1, a3)
a3 = np.cross(a1, a2)
a1/=np.linalg.norm(a1)
a2/=np.linalg.norm(a2)
a3/=np.linalg.norm(a3)
# print np.dot(a1, a2), np.dot(a1, a3), np.dot(a2, a3)
mx = np.array([a1, a2, a3]).transpose()
p = rotations.mx2aa(mx)
#print mx - rotations.aa2mx(p)
# print a1-np.dot(rotations.aa2mx(p), np.array([1., 0., 0.]))
ca.rotRigid[i] = p
return coords
def map_to_aa(xyz):
coords = np.zeros(6 * 13)
ca = CoordsAdapter(nrigid=13, coords=coords)
for i in xrange(13):
ca.posRigid[i] = 0.5 * (xyz[2 * i] + xyz[2 * i + 1])
a1 = -(xyz[2 * i] - xyz[2 * i + 1])
if (i < 12):
a3 = -(xyz[2 * i + 1] - xyz[2 * i + 3])
else:
a3 = -(xyz[2 * i - 1] - xyz[2 * i + 1])
a2 = -np.cross(a1, a3)
a3 = np.cross(a1, a2)
a1 /= np.linalg.norm(a1)
a2 /= np.linalg.norm(a2)
a3 /= np.linalg.norm(a3)
# print np.dot(a1, a2), np.dot(a1, a3), np.dot(a2, a3)
mx = np.array([a1, a2, a3]).transpose()
p = rotations.mx2aa(mx)
#print mx - rotations.aa2mx(p)
# print a1-np.dot(rotations.aa2mx(p), np.array([1., 0., 0.]))
ca.rotRigid[i] = p
return coords
def __init__(self, nrigid=0, natoms = 0):
CoordsAdapter.__init__(nrigd=nrigid, natoms=natoms)
db=Database(db="oxdna.sqlite")
path[0]=db.minima()[19].coords
path[-1]=db.minima()[0].coords
e1 = []
e2 = []
e1.append(pot.getEnergy(path[0]))
e2.append(pot.getEnergy(path[0]))
for i in xrange(1):
for i in xrange(len(path)-1):
e1.append(pot.getEnergy(path[i+1]))
c1 = CoordsAdapter(nrigid=13, coords = path[i])
c2 = CoordsAdapter(nrigid=13, coords = path[i+1])
com1 = np.sum(c1.posRigid,axis=0) / float(13)
com2 = np.sum(c1.posRigid,axis=0) / float(13)
c1.posRigid-=com1
c2.posRigid-=com2
mx = findrotation_kabsch(c2.posRigid, c1.posRigid)
#print mx
c2.posRigid[:] = np.dot(mx, c2.posRigid.transpose()).transpose()
for p in c2.rotRigid:
p[:] = rotations.rotate_aa(p, rotations.mx2aa(mx))
e2.append(pot.getEnergy(path[i+1]))
for p1,p2 in zip(c1.rotRigid, c2.rotRigid):
n2 = p2/np.linalg.norm(p2)*2.*pi
while True:
pickle.dump(path, open("interpolate.pickle", "w"))
exit()
db = Database(db="oxdna.sqlite")
path[0] = db.minima()[19].coords
path[-1] = db.minima()[0].coords
e1 = []
e2 = []
e1.append(pot.getEnergy(path[0]))
e2.append(pot.getEnergy(path[0]))
for i in xrange(1):
for i in xrange(len(path) - 1):
e1.append(pot.getEnergy(path[i + 1]))
c1 = CoordsAdapter(nrigid=13, coords=path[i])
c2 = CoordsAdapter(nrigid=13, coords=path[i + 1])
com1 = np.sum(c1.posRigid, axis=0) / float(13)
com2 = np.sum(c1.posRigid, axis=0) / float(13)
c1.posRigid -= com1
c2.posRigid -= com2
mx = findrotation_kabsch(c2.posRigid, c1.posRigid)
#print mx
c2.posRigid[:] = np.dot(mx, c2.posRigid.transpose()).transpose()
for p in c2.rotRigid:
p[:] = rotations.rotate_aa(p, rotations.mx2aa(mx))
e2.append(pot.getEnergy(path[i + 1]))
for p1, p2 in zip(c1.rotRigid, c2.rotRigid):
n2 = p2 / np.linalg.norm(p2) * 2. * pi