def distance_squared_grad(self, com1, p1, com2, p2):
"""
calculate spring force between 2 sites
Parameters
----------
com1:
center of mass of 1st site
p1:
angle axis vector of 1st site
com2:
center of mass of 2nd site
p2:
angle axis vector of 2nd site
sitetype: AASiteType, optional
amgle axis site type with mass and moment of inertia tensor
returns: tuple
spring cart, spring rot
"""
return sitedist_grad(self.get_smallest_rij(com1, com2), p1, p2, self.S, self.W, self.cog)
def distance_squared_grad(self, com1, p1, com2, p2):
'''
calculate spring force between 2 sites
Parameters
----------
com1:
center of mass of 1st site
p1:
angle axis vector of 1st site
com2:
center of mass of 2nd site
p2:
angle axis vector of 2nd site
sitetype: AASiteType, optional
amgle axis site type with mass and moment of inertia tensor
returns: tuple
spring cart, spring rot
'''
return _aadist.sitedist_grad(self.get_smallest_rij(com1, com2), p1, p2, self.S, self.W, self.cog)
R1, R11, R12, R13 = rotMatDeriv(p1, True)
R2 = rotations.aa2mx(p2)
dR = R2 - R1
dR = dR
g_M = -2.*self.W*(com2-com1)
# dR_kl S_lm dR_km
g_P = np.zeros(3)
g_P[0] = -2.*np.trace(np.dot(R11, np.dot(self.S, dR.transpose())))
g_P[1] = -2.*np.trace(np.dot(R12, np.dot(self.S, dR.transpose())))
g_P[2] = -2.*np.trace(np.dot(R13, np.dot(self.S, dR.transpose())))
g_M -= 2.*self.W * np.dot(dR, self.cog)
g_P[0] -= 2.*self.W * np.dot((com2-com1), np.dot(R11, self.cog))
g_P[1] -= 2.*self.W * np.dot((com2-com1), np.dot(R12, self.cog))
g_P[2] -= 2.*self.W * np.dot((com2-com1), np.dot(R13, self.cog))
return g_M, g_P
def distance_squared_grad(self, com1, p1, com2, p2):
"""
calculate spring force between 2 sites
Parameters
----------
com1:
center of mass of 1st site
p1:
angle axis vector of 1st site
com2:
center of mass of 2nd site
p2:
angle axis vector of 2nd site
sitetype: AASiteType, optional
amgle axis site type with mass and moment of inertia tensor
returns: tuple
spring cart, spring rot
"""
return sitedist_grad(self.get_smallest_rij(com1, com2), p1, p2, self.S,
self.W, self.cog)
def test(): # pragma: no cover
natoms = 3
x = np.random.random([natoms, 3]) * 5
masses = [1., 1., 16.] # np.random.random(natoms)
print masses
x -= np.average(x, axis=0, weights=masses)
cog = np.average(x, axis=0)
S = np.zeros([3, 3])
for i in xrange(3):
for j in xrange(3):
S[i][j] = np.sum(x[:, i] * x[:, j])
site = AASiteType(M=natoms, S=S, W=natoms, cog=cog)
X1 = 10.1 * np.random.random(3)
X2 = 10.1 * np.random.random(3)
p1 = rotations.random_aa()
p2 = rotations.random_aa()
R1 = rotations.aa2mx(p1)
R2 = rotations.aa2mx(p2)
x1 = np.dot(R1, x.transpose()).transpose() + X1
x2 = np.dot(R2, x.transpose()).transpose() + X2
import _aadist
print "site representation:", np.sum((x1 - x2) ** 2)
print "distance function: ", site.distance_squared(X1, p1, X2, p2)
print "fortran function: ", _aadist.sitedist(X2 - X1, p1, p2, site.S, site.W, cog)
import time
t0 = time.time()
for i in xrange(1000):
site.distance_squared(X1, p1, X2, p2)
t1 = time.time()
print "time python", t1 - t0
for i in xrange(1000):
sitedist(X2 - X1, p1, p2, site.S, site.W, cog)
# _aadist.aadist(coords1, coords2, site.S, site.W, cog)
t2 = time.time()
print "time fortran", t2 - t1
# for i in xrange(1000/20):
# #_aadist.sitedist(X1, p1, X2, p2, site.S, site.W, cog)
# _aadist.aadist(coords1, coords2, site.S, site.W, cog)
t2 = time.time()
print "time fortran acc", t2 - t1
print site.distance_squared_grad(X1, p1, X2, p2)
g_M = np.zeros(3)
g_P = np.zeros(3)
for i in xrange(3):
eps = 1e-6
delta = np.zeros(3)
delta[i] = eps
g_M[i] = (site.distance_squared(X1 + delta, p1, X2, p2)
- site.distance_squared(X1, p1, X2, p2)) / eps
g_P[i] = (site.distance_squared(X1, p1 + delta, X2, p2)
- site.distance_squared(X1, p1, X2, p2)) / eps
print g_M, g_P
xx = site.distance_squared_grad(X1, p1, X2, p2)
print g_M / xx[0], g_P / xx[1]
print _aadist.sitedist_grad(X2 - X1, p1, p2, site.S, site.W, cog)
for i in xrange(1000):
_aadist.sitedist(X2 - X1, p1, p2, site.S, site.W, cog)
#_aadist.aadist(coords1, coords2, site.S, site.W, cog)
t2 = time.time()
print "time fortran", t2-t1
# for i in xrange(1000/20):
# #_aadist.sitedist(X1, p1, X2, p2, site.S, site.W, cog)
# _aadist.aadist(coords1, coords2, site.S, site.W, cog)
t2 = time.time()
print "time fortran acc", t2-t1
print site.distance_squared_grad(X1, p1, X2, p2)
g_M = np.zeros(3)
g_P = np.zeros(3)
for i in xrange(3):
eps = 1e-6
delta = np.zeros(3)
delta[i] = eps
g_M[i] = (site.distance_squared(X1+delta, p1, X2, p2)
- site.distance_squared(X1, p1, X2, p2))/eps
g_P[i] = (site.distance_squared(X1, p1+delta, X2, p2)
- site.distance_squared(X1, p1, X2, p2))/eps
print g_M, g_P
xx = site.distance_squared_grad(X1, p1, X2, p2)
print g_M/xx[0], g_P/xx[1]
print _aadist.sitedist_grad(X2 - X1, p1, p2, site.S, site.W, cog)
# print _aadist.sitedist_grad(com1, p1, com2, p2, self.S, self.W, self.cog)
def test(): # pragma: no cover
natoms = 3
x = np.random.random([natoms, 3]) * 5
masses = [1., 1., 16.] # np.random.random(natoms)
print masses
x -= np.average(x, axis=0, weights=masses)
cog = np.average(x, axis=0)
S = np.zeros([3, 3])
for i in xrange(3):
for j in xrange(3):
S[i][j] = np.sum(x[:, i] * x[:, j])
site = AASiteType(M=natoms, S=S, W=natoms, cog=cog)
X1 = 10.1 * np.random.random(3)
X2 = 10.1 * np.random.random(3)
p1 = rotations.random_aa()
p2 = rotations.random_aa()
R1 = rotations.aa2mx(p1)
R2 = rotations.aa2mx(p2)
x1 = np.dot(R1, x.transpose()).transpose() + X1
x2 = np.dot(R2, x.transpose()).transpose() + X2
import _aadist
print "site representation:", np.sum((x1 - x2)**2)
print "distance function: ", site.distance_squared(X1, p1, X2, p2)
print "fortran function: ", _aadist.sitedist(X2 - X1, p1, p2, site.S,
site.W, cog)
import time
t0 = time.time()
for i in xrange(1000):
site.distance_squared(X1, p1, X2, p2)
t1 = time.time()
print "time python", t1 - t0
for i in xrange(1000):
sitedist(X2 - X1, p1, p2, site.S, site.W, cog)
# _aadist.aadist(coords1, coords2, site.S, site.W, cog)
t2 = time.time()
print "time fortran", t2 - t1
# for i in xrange(1000/20):
# #_aadist.sitedist(X1, p1, X2, p2, site.S, site.W, cog)
# _aadist.aadist(coords1, coords2, site.S, site.W, cog)
t2 = time.time()
print "time fortran acc", t2 - t1
print site.distance_squared_grad(X1, p1, X2, p2)
g_M = np.zeros(3)
g_P = np.zeros(3)
for i in xrange(3):
eps = 1e-6
delta = np.zeros(3)
delta[i] = eps
g_M[i] = (site.distance_squared(X1 + delta, p1, X2, p2) -
site.distance_squared(X1, p1, X2, p2)) / eps
g_P[i] = (site.distance_squared(X1, p1 + delta, X2, p2) -
site.distance_squared(X1, p1, X2, p2)) / eps
print g_M, g_P
xx = site.distance_squared_grad(X1, p1, X2, p2)
print g_M / xx[0], g_P / xx[1]
print _aadist.sitedist_grad(X2 - X1, p1, p2, site.S, site.W, cog)
