def Instanton(x0, f0, f1, h, update, asr, im, gm, big_step, opt, m, omaker):
"""Do one step. Update hessian for the new position. Update the position and force inside the mapper.
Input: x0 = last positions
f0 = last physical forces
f1 = last spring forces
h = physical hessian
update = how to update the hessian
asr = how to clean the hessian
im = spring mapper
gm = gradient mapper
big_step = limit on step length
opt = optimization algorithm to use
m = type of calculation: rate or splitting"""
info(" @Instanton_step", verbosity.high)
if opt == 'nichols':
# Construct hessian and get eigenvalues and eigenvector
h0 = red2comp(h, im.dbeads.nbeads, im.dbeads.natoms) # construct complete hessian from reduced
h1 = np.add(im.h, h0) # add spring terms to the physical hessian
d, w = clean_hessian(h1, im.dbeads.q, im.dbeads.natoms, im.dbeads.nbeads, im.dbeads.m, im.dbeads.m3, asr)
# Find new movement direction
if m == 'rate':
d_x = nichols(f0, f1, d, w, im.dbeads.m3, big_step)
elif m == 'splitting':
d_x = nichols(f0, f1, d, w, im.dbeads.m3, big_step, mode=0)
elif opt == 'NR':
h_up_band = banded_hessian(h, im) # create upper band matrix
f = (f0 + f1).reshape(im.dbeads.natoms * 3 * im.dbeads.nbeads, 1)
d_x = invmul_banded(h_up_band, f)
d_x.shape = im.dbeads.q.shape
# Rescale step
d_x_max = np.amax(np.absolute(d_x))
info(" @Instanton: Current step norm = %g" % d_x_max, verbosity.medium)
if np.amax(np.absolute(d_x)) > big_step:
info(" @Instanton: Attempted step norm = %g, scaled down to %g" % (d_x_max, big_step), verbosity.low)
d_x *= big_step / np.amax(np.absolute(d_x_max))
# Make movement and get new energy (u) and forces(f) using mapper
x = x0 + d_x
im(x, ret=False) # Only to update the mapper
u, g2 = gm(x)
f = -g2
# Update hessian
if update == 'powell':
d_g = np.subtract(f0, f)
i = im.dbeads.natoms * 3
for j in range(im.dbeads.nbeads):
aux = h[:, j * i:(j + 1) * i]
dg = d_g[j, :]
dx = d_x[j, :]
Powell(dx, dg, aux)
elif update == 'recompute':
get_hessian(h, gm, x, omaker)
asr = 'none'
else:
print 'We can not recognize the mode. STOP HERE'
sys.exit()
#----------------------------------------------------------START----------------------------------------------
beta = 1.0 / (kb * temp)
betaP = 1.0 / (kb * (nbeads) * temp)
print 'We have %i atoms.' % natoms
print 'We are using asr = %s' % asr
print ''
if not quiet:
print 'Diagonalization....'
d, w, detI = clean_hessian(h, pos, natoms, nbeads, m, m3, asr, mofi=True)
print "Final lowest 15 frequencies (cm^-1)"
print np.sign(d[0:15]) * np.absolute(
d[0:15])**0.5 / cm2au # convert to cm^-1
if case == 'reactant':
Qtras = ((np.sum(m)) / (2 * np.pi * beta * hbar**2))**1.5
if asr == 'poly':
Qrot = (8 * np.pi * detI / ((hbar)**6 * (beta)**3))**0.5
else:
Qrot = 1.0
outfile = open('freq.dat', 'w')
if asr == 'poly':
nzeros = 6
asr = 'none'
else:
print 'We can not recognize the mode. STOP HERE'
sys.exit()
# ----------------------------------------------------------START----------------------------------------------
beta = 1.0 / (kb * temp)
betaP = 1.0 / (kb * (nbeads) * temp)
print 'We have %i atoms.' % natoms
print 'We are using asr = %s' % asr
print ''
if not quiet:
print 'Diagonalization....'
d, w, detI = clean_hessian(h, pos, natoms, nbeads, m, m3, asr, mofi=True)
print "Final lowest 15 frequencies (cm^-1)"
print np.sign(d[0:15]) * np.absolute(d[0:15]) ** 0.5 / cm2au # convert to cm^-1
if case == 'reactant':
Qtras = ((np.sum(m)) / (2 * np.pi * beta * hbar**2))**1.5
if asr == 'poly':
Qrot = (8 * np.pi * detI / ((hbar)**6 * (beta)**3))**0.5
else:
Qrot = 1.0
outfile = open('freq.dat', 'w')
if asr == 'poly':
nzeros = 6
elif asr == 'crystal':