def kineticEnergy(prefix, temp, ss=0, unit=""):
"""
Computes the virial centroid estimator for the kinetic energy and PPI correction.
"""
# Adding fortran functions (when exist)
sys.path.append(os.path.abspath(os.path.dirname(sys.argv[0]))[:-2] + "f90")
fast_code = True
try:
import fortran
except ImportError:
fast_code = False
print(
"WARNING: No compiled fortran module for fast calculations have been found.\n"
"Calculations will use a slower python script.")
temperature = unit_to_internal("temperature", "kelvin",
float(temp)) # simulation temperature
skipSteps = int(ss) # steps to skip for thermalization
f2_av, KPa_av, KVir_av, f2KPa_av = 0.0, 0.0, 0.0, 0.0 # some required sums
fns_pos = sorted(glob.glob(prefix + ".pos*"))
fns_for = sorted(glob.glob(prefix + ".for*"))
fns_iU = glob.glob(prefix + ".out")[0]
fn_out_en = prefix + ".kinetic_energy.dat"
# check that we found the same number of positions and forces files
nbeads = len(fns_pos)
if nbeads != len(fns_for):
print(fns_pos)
print(fns_for)
raise ValueError(
"Mismatch between number of input files for forces and positions.")
# print some information
print("temperature = {:f} K".format(float(temp)))
print()
print("number of beads = {:d}".format(nbeads))
print()
print("positions and forces file names:")
for fn_pos, fn_for in zip(fns_pos, fns_for):
print("{:s} {:s}".format(fn_pos, fn_for))
print()
print("potential energy file: {:s}".format(fns_iU))
print()
print("output file name:")
print(fn_out_en)
print()
# open input and output files
ipos = [open(fn, "r") for fn in fns_pos]
ifor = [open(fn, "r") for fn in fns_for]
iU = open(fns_iU, "r")
iE = open(fn_out_en, "w")
# Some constants
beta = 1.0 / (Constants.kb * temperature)
const_1 = 0.5 * nbeads / (beta * Constants.hbar)**2
const_2 = 1.5 * nbeads / beta
const_3 = 1.5 / beta
const_4 = Constants.kb**2 / Constants.hbar**2
const_5 = Constants.hbar**2 * beta**3 / (24.0 * nbeads**3)
timeUnit, potentialEnergyUnit, time_index = extractUnits(
iU) # extracting simulation time
# and potential energy units
# Defining the output energy unit
if unit == "":
unit = potentialEnergyUnit
iE.write(
"# Simulation time (in %s), virial kinetic energy and PPI kinetic energy corrections (in %s)\n"
% (timeUnit, unit))
natoms = 0
ifr = 0
time0 = 0
q, f, m = None, None, None
while True: # Reading input files and calculating PPI correction
if ifr % 100 == 0:
print("\rProcessing frame {:d}".format(ifr), end=" ")
sys.stdout.flush()
try:
for i in range(nbeads):
ret = read_file("xyz", ipos[i], output="arrays")
if natoms == 0:
m, natoms = ret["masses"], ret["natoms"]
q = np.zeros((nbeads, 3 * natoms))
f = np.zeros((nbeads, 3 * natoms))
q[i, :] = ret["data"]
f[i, :] = read_file("xyz", ifor[i], output="arrays")["data"]
time = read_time(iU, time_index)
except EOFError: # finished reading files
sys.exit(0)
if ifr < skipSteps:
time0 = time
if ifr >= skipSteps: # PPI correction
time -= time0
KPa, f2, KVir = 0.0, 0.0, 0.0
if not fast_code:
for j in range(nbeads):
for i in range(natoms):
f2 += (np.dot(f[j, i * 3:i * 3 + 3],
f[j, i * 3:i * 3 + 3]) / m[i])
for i in range(natoms):
KPa -= (np.dot(
q[0, i * 3:i * 3 + 3] - q[nbeads - 1, i * 3:i * 3 + 3],
q[0, i * 3:i * 3 + 3] - q[nbeads - 1, i * 3:i * 3 + 3],
) * m[i])
for j in range(nbeads - 1):
for i in range(natoms):
KPa -= (np.dot(
q[j + 1, i * 3:i * 3 + 3] - q[j, i * 3:i * 3 + 3],
q[j + 1, i * 3:i * 3 + 3] - q[j, i * 3:i * 3 + 3],
) * m[i])
rc = np.zeros(3)
for i in range(natoms):
rc[:] = 0.0
for j in range(nbeads):
rc[:] += q[j, i * 3:i * 3 + 3]
rc[:] /= nbeads
for j in range(nbeads):
KVir += np.dot(rc[:] - q[j, i * 3:i * 3 + 3],
f[j, i * 3:i * 3 + 3])
KPa *= const_1
KPa += const_2 * natoms
KVir /= 2.0 * nbeads
KVir += const_3 * natoms
else:
f2 = fortran.f2divm(np.array(f, order="F"),
np.array(m, order="F"), natoms, nbeads)
KPa = fortran.findcoupling(
np.array(q, order="F"),
np.array(m, order="F"),
temperature,
natoms,
nbeads,
)
KVir = fortran.findcentroidvirialkineticenergy(
np.array(f, order="F"), np.array(q, order="F"), natoms,
nbeads)
KPa *= const_4
KPa += const_2 * natoms
KVir += const_3 * natoms
f2_av += f2
KPa_av += KPa
f2KPa_av += f2 * KPa
KVir_av += KVir
ifr += 1
norm = float(ifr - skipSteps)
dK = (Constants.kb * temperature +
KPa_av / norm) * f2_av / norm - f2KPa_av / norm
dK *= const_5
dK = unit_to_user("energy", unit, dK)
eVir = unit_to_user("energy", unit, KVir_av / norm)
iE.write("%f %f %f\n" % (time, eVir, dK))
else:
ifr += 1
def heatCapacity(prefix, temp, ss=0):
"""
Computes a primitive estimator for the heat capacity and PPI correction.
"""
# Adding fortran functions (when exist)
sys.path.append(os.path.abspath(os.path.dirname(sys.argv[0]))[:-2] + "f90")
fast_code = True
try:
import fortran
except ImportError:
fast_code = False
print(
"WARNING: No compiled fortran module for fast calculations have been found.\n"
"Calculations will use a slower python script."
)
temperature = unit_to_internal(
"temperature", "kelvin", float(temp)
) # simulation temperature
skipSteps = int(ss) # steps to skip for thermalization
# some required sums
KPa_av, U_av, f2_av, f2KPa_av, f2U_av, E2_av, f2E_av, f2E2_av = (
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
)
fns_pos = sorted(glob.glob(prefix + ".pos*"))
fns_for = sorted(glob.glob(prefix + ".for*"))
fns_iU = glob.glob(prefix + ".out")[0]
fn_out_en = prefix + ".heat_capacity.dat"
# check that we found the same number of positions and forces files
nbeads = len(fns_pos)
if nbeads != len(fns_for):
print(fns_pos)
print(fns_for)
raise ValueError(
"Mismatch between number of input files for forces and positions."
)
# print some information
print("temperature = {:f} K".format(float(temp)))
print()
print("number of beads = {:d}".format(nbeads))
print()
print("positions and forces file names:")
for fn_pos, fn_for in zip(fns_pos, fns_for):
print("{:s} {:s}".format(fn_pos, fn_for))
print()
print("potential energy file: {:s}".format(fns_iU))
print()
print("output file name:")
print(fn_out_en)
print()
# open input and output files
ipos = [open(fn, "r") for fn in fns_pos]
ifor = [open(fn, "r") for fn in fns_for]
iU = open(fns_iU, "r")
iC = open(fn_out_en, "w")
# Some constants
beta = 1.0 / (Constants.kb * temperature)
const_1 = 0.5 * nbeads / (beta * Constants.hbar) ** 2
const_2 = 1.5 * nbeads / beta
const_3 = Constants.kb ** 2 / Constants.hbar ** 2
const_4 = Constants.hbar ** 2 * beta ** 2 / (24.0 * nbeads ** 3)
const_5 = Constants.kb * beta ** 2
timeUnit, potentialEnergyUnit, potentialEnergy_index, time_index = extractUnits(
iU
) # extracting simulation time
# and potential energy units
iC.write(
"# Simulation time (in %s), improved heat capacity estimator, primitive heat capacity estimator, "
"and PPI correction for the heat capacity\n" % timeUnit
)
iC.close()
natoms = 0
ifr = 0
time0 = 0
q, f, m = None, None, None
while True: # Reading input files and calculating PPI correction
if ifr % 100 == 0:
print("\rProcessing frame {:d}".format(ifr), end=" ")
sys.stdout.flush()
try:
for i in range(nbeads):
ret = read_file("xyz", ipos[i], dimension="length")["atoms"]
if natoms == 0:
m, natoms = ret.m, ret.natoms
q = np.zeros((nbeads, 3 * natoms))
f = np.zeros((nbeads, 3 * natoms))
q[i, :] = ret.q
f[i, :] = read_file("xyz", ifor[i], dimension="force")["atoms"].q
U, time = read_U(iU, potentialEnergyUnit, potentialEnergy_index, time_index)
except EOFError: # finished reading files
sys.exit(0)
if ifr < skipSteps:
time0 = time
if ifr >= skipSteps: # PPI correction
time -= time0
KPa, f2 = 0.0, 0.0
if not fast_code:
for j in range(nbeads):
for i in range(natoms):
f2 += (
np.dot(f[j, i * 3 : i * 3 + 3], f[j, i * 3 : i * 3 + 3])
/ m[i]
)
for i in range(natoms):
KPa -= (
np.dot(
q[0, i * 3 : i * 3 + 3] - q[nbeads - 1, i * 3 : i * 3 + 3],
q[0, i * 3 : i * 3 + 3] - q[nbeads - 1, i * 3 : i * 3 + 3],
)
* m[i]
)
for j in range(nbeads - 1):
for i in range(natoms):
KPa -= (
np.dot(
q[j + 1, i * 3 : i * 3 + 3] - q[j, i * 3 : i * 3 + 3],
q[j + 1, i * 3 : i * 3 + 3] - q[j, i * 3 : i * 3 + 3],
)
* m[i]
)
KPa *= const_1
KPa += const_2 * natoms
else:
f2 = fortran.f2divm(
np.array(f, order="F"), np.array(m, order="F"), natoms, nbeads
)
KPa = fortran.findcoupling(
np.array(q, order="F"),
np.array(m, order="F"),
temperature,
natoms,
nbeads,
)
KPa *= const_3
KPa += const_2 * natoms
f2_av += f2
KPa_av += KPa
f2KPa_av += f2 * KPa
U_av += U
f2U_av += f2 * U
E2_av += (KPa + U) ** 2
f2E2_av += f2 * (KPa + U) ** 2
ifr += 1
norm = float(ifr - skipSteps)
dU = 2 * f2_av / norm - beta * (f2U_av / norm - f2_av * U_av / norm ** 2)
dU *= const_4
dK = f2_av / norm - beta * (f2KPa_av / norm - f2_av * KPa_av / norm ** 2)
dK *= const_4
C = (
E2_av / norm
- ((KPa_av + U_av) / norm) ** 2
+ (2.0 / beta) * KPa_av / norm
- 1.5 * nbeads * natoms / beta ** 2
)
C *= const_5
dC = (
2
* (5 + 3 * beta * (KPa_av + U_av) / norm)
* beta
* f2_av
* const_4
/ norm
- 2 * (3 + beta * (KPa_av + U_av) / norm) * beta * (dK + dU)
+ 2 * beta * dK
- const_4 * (f2E2_av / norm - f2_av * E2_av / norm ** 2) * beta ** 3
)
iC = open(fn_out_en, "a")
iC.write("%f %f %f %f\n" % (time, C + dC, C, dC))
iC.close()
else:
ifr += 1
def energies(prefix, temp, ss=0, unit=''):
"""
Computes the virial centroid estimator for the total energy and PPI correction.
"""
# Adding fortran functions (when exist)
sys.path.append(os.path.abspath(os.path.dirname(sys.argv[0]))[:-2] + 'f90')
fast_code = True
try:
import fortran
except:
fast_code = False
print(
'WARNING: No compiled fortran module for fast calculations have been found.\n'
'Calculations will use a slower python script.')
temperature = unit_to_internal("temperature", "kelvin",
float(temp)) # simulation temperature
skipSteps = int(ss) # steps to skip for thermalization
KPa_av, KVir_av, U_av, f2_av, f2KPa_av, f2U_av = 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 # some required sums
fns_pos = sorted(glob.glob(prefix + ".pos*"))
fns_for = sorted(glob.glob(prefix + ".for*"))
fns_iU = glob.glob(prefix + ".out")[0]
fn_out_en = prefix + ".energies.dat"
# check that we found the same number of positions and forces files
nbeads = len(fns_pos)
if nbeads != len(fns_for):
print(fns_pos)
print(fns_for)
raise ValueError(
"Mismatch between number of input files for forces and positions.")
# print some information
print('temperature = {:f} K'.format(float(temp)))
print()
print('number of beads = {:d}'.format(nbeads))
print()
print('positions and forces file names:')
for fn_pos, fn_for in zip(fns_pos, fns_for):
print('{:s} {:s}'.format(fn_pos, fn_for))
print()
print('potential energy file: {:s}'.format(fns_iU))
print()
print('output file name:')
print(fn_out_en)
print()
# open input and output files
ipos = [open(fn, "r") for fn in fns_pos]
ifor = [open(fn, "r") for fn in fns_for]
iU = open(fns_iU, "r")
iE = open(fn_out_en, "w")
# Some constants
beta = 1.0 / (Constants.kb * temperature)
const_1 = 0.5 * nbeads / (beta * Constants.hbar)**2
const_2 = 1.5 * nbeads / beta
const_3 = 1.5 / beta
const_4 = Constants.kb**2 / Constants.hbar**2
const_5 = Constants.hbar**2 * beta**3 / (24.0 * nbeads**3)
const_6 = Constants.hbar**2 * beta**2 / (24.0 * nbeads**3)
timeUnit, potentialEnergyUnit, potentialEnergy_index, time_index = extractUnits(
iU) # extracting simulation time
# and potential energy units
# Defining the output energy unit
if unit == '':
unit = potentialEnergyUnit
iE.write(
"# Simulation time (in %s), improved total energy estimator, virial total energy estimator, and PPI "
"correction for the total energy; improved potential energy estimator, potential energy estimatorand, "
"PPI correction for the potential energy; improved kinetic energy estimator, virial kinetic energy "
"estimator, and PPI correction for the kinetic energy (all in %s)\n" %
(timeUnit, unit))
iE.close()
natoms = 0
ifr = 0
time0 = 0
q, f, m = None, None, None
while True: # Reading input files and calculating PPI correction
if ifr % 100 == 0:
print('\rProcessing frame {:d}'.format(ifr), end=' ')
sys.stdout.flush()
try:
for i in range(nbeads):
ret = read_file("xyz", ipos[i], dimension='length')["atoms"]
if natoms == 0:
m, natoms = ret.m, ret.natoms
q = np.zeros((nbeads, 3 * natoms))
f = np.zeros((nbeads, 3 * natoms))
q[i, :] = ret.q
f[i, :] = read_file("xyz", ifor[i],
dimension='force')["atoms"].q
U, time = read_U(iU, potentialEnergyUnit, potentialEnergy_index,
time_index)
except EOFError: # finished reading files
sys.exit(0)
if ifr < skipSteps:
time0 = time
if ifr >= skipSteps: # PPI correction
time -= time0
KPa, f2, KVir = 0.0, 0.0, 0.0
if not fast_code:
for j in range(nbeads):
for i in range(natoms):
f2 += np.dot(f[j, i * 3:i * 3 + 3],
f[j, i * 3:i * 3 + 3]) / m[i]
for i in range(natoms):
KPa -= np.dot(
q[0, i * 3:i * 3 + 3] - q[nbeads - 1, i * 3:i * 3 + 3],
q[0, i * 3:i * 3 + 3] -
q[nbeads - 1, i * 3:i * 3 + 3]) * m[i]
for j in range(nbeads - 1):
for i in range(natoms):
KPa -= np.dot(
q[j + 1, i * 3:i * 3 + 3] - q[j, i * 3:i * 3 + 3],
q[j + 1, i * 3:i * 3 + 3] -
q[j, i * 3:i * 3 + 3]) * m[i]
rc = np.zeros(3)
for i in range(natoms):
rc[:] = 0.0
for j in range(nbeads):
rc[:] += q[j, i * 3:i * 3 + 3]
rc[:] /= nbeads
for j in range(nbeads):
KVir += np.dot(rc[:] - q[j, i * 3:i * 3 + 3],
f[j, i * 3:i * 3 + 3])
KPa *= const_1
KPa += const_2 * natoms
KVir /= 2.0 * nbeads
KVir += const_3 * natoms
else:
f2 = fortran.f2divm(np.array(f, order='F'),
np.array(m, order='F'), natoms, nbeads)
KPa = fortran.findcoupling(np.array(q, order='F'),
np.array(m, order='F'), temperature,
natoms, nbeads)
KVir = fortran.findcentroidvirialkineticenergy(
np.array(f, order='F'), np.array(q, order='F'), natoms,
nbeads)
KPa *= const_4
KPa += const_2 * natoms
KVir += const_3 * natoms
f2_av += f2
KPa_av += KPa
f2KPa_av += f2 * KPa
U_av += U
f2U_av += f2 * U
KVir_av += KVir
ifr += 1
norm = float(ifr - skipSteps)
dU = 2 * f2_av / norm - beta * (f2U_av / norm -
f2_av * U_av / norm**2)
dU *= const_6
dU = unit_to_user("energy", unit, dU)
dK = (Constants.kb * temperature +
KPa_av / norm) * f2_av / norm - f2KPa_av / norm
dK *= const_5
dK = unit_to_user("energy", unit, dK)
U = unit_to_user("energy", unit, U_av / norm)
KVir = unit_to_user("energy", unit, KVir_av / norm)
iE = open(fn_out_en, "a")
iE.write(
"%f %f %f %f %f %f %f %f %f %f\n"
% (time, KVir + U + dK + dU, KVir + U, dK + dU, U + dU, U, dU,
KVir + dK, KVir, dK))
iE.close()
else:
ifr += 1
def totalEnergy(prefix, temp, ss=0, unit=''):
"""
Computes the virial centroid estimator for the total energy and PPI correction.
"""
# Adding fortran functions (when exist)
sys.path.append(os.path.abspath(os.path.dirname(sys.argv[0]))[:-2] + 'f90')
fast_code = True
try:
import fortran
except:
fast_code = False
print('WARNING: No compiled fortran module for fast calculations have been found.\n'
'Calculations will use a slower python script.')
temperature = unit_to_internal("temperature", "kelvin", float(temp)) # simulation temperature
skipSteps = int(ss) # steps to skip for thermalization
f2_av, ePA_av, eVir_av, f2ePA_av = 0.0, 0.0, 0.0, 0.0 # some required sums
fns_pos = sorted(glob.glob(prefix + ".pos*"))
fns_for = sorted(glob.glob(prefix + ".for*"))
fns_iU = glob.glob(prefix + ".out")[0]
fn_out_en = prefix + ".total_energy.dat"
# check that we found the same number of positions and forces files
nbeads = len(fns_pos)
if nbeads != len(fns_for):
print fns_pos
print fns_for
raise ValueError("Mismatch between number of input files for forces and positions.")
# print some information
print 'temperature = {:f} K'.format(float(temp))
print
print 'number of beads = {:d}'.format(nbeads)
print
print 'positions and forces file names:'
for fn_pos, fn_for in zip(fns_pos, fns_for):
print '{:s} {:s}'.format(fn_pos, fn_for)
print
print 'potential energy file: {:s}'.format(fns_iU)
print
print 'output file name:'
print fn_out_en
print
# open input and output files
ipos = [open(fn, "r") for fn in fns_pos]
ifor = [open(fn, "r") for fn in fns_for]
iU = open(fns_iU, "r")
iE = open(fn_out_en, "w")
# Some constants
beta = 1.0 / (Constants.kb * temperature)
const_1 = 0.5 * nbeads / (beta * Constants.hbar)**2
const_2 = 1.5 * nbeads / beta
const_3 = 1.5 / beta
const_4 = Constants.kb**2 / Constants.hbar**2
const_5 = Constants.hbar**2 * beta**3 / (24.0 * nbeads**3)
timeUnit, potentialEnergyUnit, potentialEnergy_index, time_index = extractUnits(iU) # extracting simulation time
# and potential energy units
# Defining the output energy unit
if unit == '':
unit = potentialEnergyUnit
iE.write("# Simulation time (in %s), virial total energy and PPI energy correction (in %s)\n" %
(timeUnit, unit))
natoms = 0
ifr = 0
time0 = 0
q, f, m = None, None, None
while True: # Reading input files and calculating PPI correction
if ifr % 100 == 0:
print '\rProcessing frame {:d}'.format(ifr),
sys.stdout.flush()
try:
for i in range(nbeads):
ret = read_file("xyz", ipos[i], output='arrays')
if natoms == 0:
m, natoms = ret["masses"], ret["natoms"]
q = np.zeros((nbeads, 3 * natoms))
f = np.zeros((nbeads, 3 * natoms))
q[i, :] = ret["data"]
f[i, :] = read_file("xyz", ifor[i], output='arrays')["data"]
U, time = read_U(iU, potentialEnergyUnit, potentialEnergy_index, time_index)
except EOFError: # finished reading files
sys.exit(0)
if ifr < skipSteps:
time0 = time
if ifr >= skipSteps: # PPI correction
time -= time0
ePA, f2, f2ePA, eVir = 0.0, 0.0, 0.0, 0.0
if not fast_code:
for j in range(nbeads):
for i in range(natoms):
f2 += np.dot(f[j, i * 3:i * 3 + 3], f[j, i * 3:i * 3 + 3]) / m[i]
for i in range(natoms):
ePA -= np.dot(q[0, i * 3:i * 3 + 3] - q[nbeads - 1, i * 3:i * 3 + 3], q[0, i * 3:i * 3 + 3] - q[nbeads - 1, i * 3:i * 3 + 3]) * m[i]
for j in range(nbeads - 1):
for i in range(natoms):
ePA -= np.dot(q[j + 1, i * 3:i * 3 + 3] - q[j, i * 3:i * 3 + 3], q[j + 1, i * 3:i * 3 + 3] - q[j, i * 3:i * 3 + 3]) * m[i]
rc = np.zeros(3)
for i in range(natoms):
rc[:] = 0.0
for j in range(nbeads):
rc[:] += q[j, i * 3:i * 3 + 3]
rc[:] /= nbeads
for j in range(nbeads):
eVir += np.dot(rc[:] - q[j, i * 3:i * 3 + 3], f[j, i * 3:i * 3 + 3])
ePA *= const_1
ePA += const_2 * natoms + U
f2ePA = f2 * ePA
eVir /= 2.0 * nbeads
eVir += const_3 * natoms + U
else:
f2 = fortran.f2divm(np.array(f, order='F'), np.array(m, order='F'), natoms, nbeads)
ePA = fortran.findcoupling(np.array(q, order='F'), np.array(m, order='F'), temperature, natoms, nbeads)
eVir = fortran.findcentroidvirialkineticenergy(np.array(f, order='F'), np.array(q, order='F'), natoms, nbeads)
ePA *= const_4
ePA += const_2 * natoms + U
f2ePA = f2 * ePA
eVir += const_3 * natoms + U
ePA_av += ePA
f2_av += f2
f2ePA_av += f2ePA
eVir_av += eVir
ifr += 1
norm = float(ifr - skipSteps)
dE = (3.0 * Constants.kb * temperature + ePA_av / norm) * f2_av / norm - f2ePA_av / norm
dE *= const_5
dE = unit_to_user("energy", unit, dE)
eVir = unit_to_user("energy", unit, eVir_av / norm)
iE.write("%f %f %f\n" % (time, eVir, dE))
else:
ifr += 1
def heatCapacity(prefix, temp, ss=0):
"""
Computes a primitive estimator for the heat capacity and PPI correction.
"""
# Adding fortran functions (when exist)
sys.path.append(os.path.abspath(os.path.dirname(sys.argv[0]))[:-2] + 'f90')
fast_code = True
try:
import fortran
except:
fast_code = False
print('WARNING: No compiled fortran module for fast calculations have been found.\n'
'Calculations will use a slower python script.')
temperature = unit_to_internal("temperature", "kelvin", float(temp)) # simulation temperature
skipSteps = int(ss) # steps to skip for thermalization
# some required sums
KPa_av, U_av, f2_av, f2KPa_av, f2U_av, E2_av, f2E_av, f2E2_av = 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0
fns_pos = sorted(glob.glob(prefix + ".pos*"))
fns_for = sorted(glob.glob(prefix + ".for*"))
fns_iU = glob.glob(prefix + ".out")[0]
fn_out_en = prefix + ".heat_capacity.dat"
# check that we found the same number of positions and forces files
nbeads = len(fns_pos)
if nbeads != len(fns_for):
print fns_pos
print fns_for
raise ValueError("Mismatch between number of input files for forces and positions.")
# print some information
print 'temperature = {:f} K'.format(float(temp))
print
print 'number of beads = {:d}'.format(nbeads)
print
print 'positions and forces file names:'
for fn_pos, fn_for in zip(fns_pos, fns_for):
print '{:s} {:s}'.format(fn_pos, fn_for)
print
print 'potential energy file: {:s}'.format(fns_iU)
print
print 'output file name:'
print fn_out_en
print
# open input and output files
ipos = [open(fn, "r") for fn in fns_pos]
ifor = [open(fn, "r") for fn in fns_for]
iU = open(fns_iU, "r")
iC = open(fn_out_en, "w")
# Some constants
beta = 1.0 / (Constants.kb * temperature)
const_1 = 0.5 * nbeads / (beta * Constants.hbar)**2
const_2 = 1.5 * nbeads / beta
const_3 = Constants.kb**2 / Constants.hbar**2
const_4 = Constants.hbar**2 * beta**2 / (24.0 * nbeads**3)
const_5 = Constants.kb * beta**2
timeUnit, potentialEnergyUnit, potentialEnergy_index, time_index = extractUnits(iU) # extracting simulation time
# and potential energy units
iC.write("# Simulation time (in %s), improved heat capacity estimator, primitive heat capacity estimator, "
"and PPI correction for the heat capacity\n" % timeUnit)
iC.close()
natoms = 0
ifr = 0
time0 = 0
q, f, m = None, None, None
while True: # Reading input files and calculating PPI correction
if ifr % 100 == 0:
print '\rProcessing frame {:d}'.format(ifr),
sys.stdout.flush()
try:
for i in range(nbeads):
ret = read_file("xyz", ipos[i], dimension='length')["atoms"]
if natoms == 0:
m, natoms = ret.m, ret.natoms
q = np.zeros((nbeads, 3 * natoms))
f = np.zeros((nbeads, 3 * natoms))
q[i, :] = ret.q
f[i, :] = read_file("xyz", ifor[i], dimension='force')["atoms"].q
U, time = read_U(iU, potentialEnergyUnit, potentialEnergy_index, time_index)
except EOFError: # finished reading files
sys.exit(0)
if ifr < skipSteps:
time0 = time
if ifr >= skipSteps: # PPI correction
time -= time0
KPa, f2 = 0.0, 0.0
if not fast_code:
for j in range(nbeads):
for i in range(natoms):
f2 += np.dot(f[j, i * 3:i * 3 + 3], f[j, i * 3:i * 3 + 3]) / m[i]
for i in range(natoms):
KPa -= np.dot(q[0, i * 3:i * 3 + 3] - q[nbeads - 1, i * 3:i * 3 + 3], q[0, i * 3:i * 3 + 3] - q[nbeads - 1, i * 3:i * 3 + 3]) * m[i]
for j in range(nbeads - 1):
for i in range(natoms):
KPa -= np.dot(q[j + 1, i * 3:i * 3 + 3] - q[j, i * 3:i * 3 + 3], q[j + 1, i * 3:i * 3 + 3] - q[j, i * 3:i * 3 + 3]) * m[i]
KPa *= const_1
KPa += const_2 * natoms
else:
f2 = fortran.f2divm(np.array(f, order='F'), np.array(m, order='F'), natoms, nbeads)
KPa = fortran.findcoupling(np.array(q, order='F'), np.array(m, order='F'), temperature, natoms, nbeads)
KPa *= const_3
KPa += const_2 * natoms
f2_av += f2
KPa_av += KPa
f2KPa_av += f2 * KPa
U_av += U
f2U_av += f2 * U
E2_av += (KPa + U)**2
f2E2_av += f2 * (KPa + U)**2
ifr += 1
norm = float(ifr - skipSteps)
dU = 2 * f2_av / norm - beta * (f2U_av / norm - f2_av * U_av / norm**2)
dU *= const_4
dK = f2_av / norm - beta * (f2KPa_av / norm - f2_av * KPa_av / norm**2)
dK *= const_4
C = E2_av / norm - ((KPa_av + U_av) / norm)**2 + (2.0 / beta) * KPa_av / norm - 1.5 * nbeads * natoms / beta**2
C *= const_5
dC = 2 * (5 + 3 * beta * (KPa_av + U_av) / norm) * beta * f2_av * const_4 / norm - \
2 * (3 + beta * (KPa_av + U_av) / norm) * beta * (dK + dU) + 2 * beta * dK - \
const_4 * (f2E2_av / norm - f2_av * E2_av / norm**2) * beta**3
iC = open(fn_out_en, "a")
iC.write("%f %f %f %f\n" % (time, C + dC, C, dC))
iC.close()
else:
ifr += 1
def energies(prefix, temp, ss=0, unit=''):
"""
Computes the virial centroid estimator for the total energy and PPI correction.
"""
# Adding fortran functions (when exist)
sys.path.append(os.path.abspath(os.path.dirname(sys.argv[0]))[:-2] + 'f90')
fast_code = True
try:
import fortran
except:
fast_code = False
print('WARNING: No compiled fortran module for fast calculations have been found.\n'
'Calculations will use a slower python script.')
temperature = unit_to_internal("temperature", "kelvin", float(temp)) # simulation temperature
skipSteps = int(ss) # steps to skip for thermalization
KPa_av, KVir_av, U_av, f2_av, f2KPa_av, f2U_av = 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 # some required sums
fns_pos = sorted(glob.glob(prefix + ".pos*"))
fns_for = sorted(glob.glob(prefix + ".for*"))
fns_iU = glob.glob(prefix + ".out")[0]
fn_out_en = prefix + ".energies.dat"
# check that we found the same number of positions and forces files
nbeads = len(fns_pos)
if nbeads != len(fns_for):
print fns_pos
print fns_for
raise ValueError("Mismatch between number of input files for forces and positions.")
# print some information
print 'temperature = {:f} K'.format(float(temp))
print
print 'number of beads = {:d}'.format(nbeads)
print
print 'positions and forces file names:'
for fn_pos, fn_for in zip(fns_pos, fns_for):
print '{:s} {:s}'.format(fn_pos, fn_for)
print
print 'potential energy file: {:s}'.format(fns_iU)
print
print 'output file name:'
print fn_out_en
print
# open input and output files
ipos = [open(fn, "r") for fn in fns_pos]
ifor = [open(fn, "r") for fn in fns_for]
iU = open(fns_iU, "r")
iE = open(fn_out_en, "w")
# Some constants
beta = 1.0 / (Constants.kb * temperature)
const_1 = 0.5 * nbeads / (beta * Constants.hbar)**2
const_2 = 1.5 * nbeads / beta
const_3 = 1.5 / beta
const_4 = Constants.kb**2 / Constants.hbar**2
const_5 = Constants.hbar**2 * beta**3 / (24.0 * nbeads**3)
const_6 = Constants.hbar**2 * beta**2 / (24.0 * nbeads**3)
timeUnit, potentialEnergyUnit, potentialEnergy_index, time_index = extractUnits(iU) # extracting simulation time
# and potential energy units
# Defining the output energy unit
if unit == '':
unit = potentialEnergyUnit
iE.write("# Simulation time (in %s), improved total energy estimator, virial total energy estimator, and PPI "
"correction for the total energy; improved potential energy estimator, potential energy estimatorand, "
"PPI correction for the potential energy; improved kinetic energy estimator, virial kinetic energy "
"estimator, and PPI correction for the kinetic energy (all in %s)\n" % (timeUnit, unit))
iE.close()
natoms = 0
ifr = 0
time0 = 0
q, f, m = None, None, None
while True: # Reading input files and calculating PPI correction
if ifr % 100 == 0:
print '\rProcessing frame {:d}'.format(ifr),
sys.stdout.flush()
try:
for i in range(nbeads):
ret = read_file("xyz", ipos[i], dimension='length')["atoms"]
if natoms == 0:
m, natoms = ret.m, ret.natoms
q = np.zeros((nbeads, 3 * natoms))
f = np.zeros((nbeads, 3 * natoms))
q[i, :] = ret.q
f[i, :] = read_file("xyz", ifor[i], dimension='force')["atoms"].q
U, time = read_U(iU, potentialEnergyUnit, potentialEnergy_index, time_index)
except EOFError: # finished reading files
sys.exit(0)
if ifr < skipSteps:
time0 = time
if ifr >= skipSteps: # PPI correction
time -= time0
KPa, f2, KVir = 0.0, 0.0, 0.0
if not fast_code:
for j in range(nbeads):
for i in range(natoms):
f2 += np.dot(f[j, i * 3:i * 3 + 3], f[j, i * 3:i * 3 + 3]) / m[i]
for i in range(natoms):
KPa -= np.dot(q[0, i * 3:i * 3 + 3] - q[nbeads - 1, i * 3:i * 3 + 3], q[0, i * 3:i * 3 + 3] - q[nbeads - 1, i * 3:i * 3 + 3]) * m[i]
for j in range(nbeads - 1):
for i in range(natoms):
KPa -= np.dot(q[j + 1, i * 3:i * 3 + 3] - q[j, i * 3:i * 3 + 3], q[j + 1, i * 3:i * 3 + 3] - q[j, i * 3:i * 3 + 3]) * m[i]
rc = np.zeros(3)
for i in range(natoms):
rc[:] = 0.0
for j in range(nbeads):
rc[:] += q[j, i * 3:i * 3 + 3]
rc[:] /= nbeads
for j in range(nbeads):
KVir += np.dot(rc[:] - q[j, i * 3:i * 3 + 3], f[j, i * 3:i * 3 + 3])
KPa *= const_1
KPa += const_2 * natoms
KVir /= 2.0 * nbeads
KVir += const_3 * natoms
else:
f2 = fortran.f2divm(np.array(f, order='F'), np.array(m, order='F'), natoms, nbeads)
KPa = fortran.findcoupling(np.array(q, order='F'), np.array(m, order='F'), temperature, natoms, nbeads)
KVir = fortran.findcentroidvirialkineticenergy(np.array(f, order='F'), np.array(q, order='F'), natoms, nbeads)
KPa *= const_4
KPa += const_2 * natoms
KVir += const_3 * natoms
f2_av += f2
KPa_av += KPa
f2KPa_av += f2 * KPa
U_av += U
f2U_av += f2 * U
KVir_av += KVir
ifr += 1
norm = float(ifr - skipSteps)
dU = 2 * f2_av / norm - beta * (f2U_av / norm - f2_av * U_av / norm**2)
dU *= const_6
dU = unit_to_user("energy", unit, dU)
dK = (Constants.kb * temperature + KPa_av / norm) * f2_av / norm - f2KPa_av / norm
dK *= const_5
dK = unit_to_user("energy", unit, dK)
U = unit_to_user("energy", unit, U_av / norm)
KVir = unit_to_user("energy", unit, KVir_av / norm)
iE = open(fn_out_en, "a")
iE.write("%f %f %f %f %f %f %f %f %f %f\n"
% (time, KVir + U + dK + dU, KVir + U, dK + dU, U + dU, U, dU, KVir + dK, KVir, dK))
iE.close()
else:
ifr += 1
def heat_capacity(prefix, temp, ss=0):
"""
Computes a virial centroid estimator for the heat capacity and PPI correction.
"""
# Adding fortran functions (when exist)
sys.path.append(os.path.abspath(os.path.dirname(sys.argv[0]))[:-2] + 'f90')
fast_code = True
try:
import fortran
except:
fast_code = False
print(
'WARNING: No compiled fortran module for fast calculations have been found.\n'
'Calculations will use a slower python script.')
temperature = unit_to_internal("temperature", "kelvin",
float(temp)) # simulation temperature
skipSteps = int(ss) # steps to skip for thermalization
# some required sums
KPa_av, KVir_av, U_av, f2_av, f2KPa_av, f2U_av, EVir_av, EEVir_av, f2E_av, f2E2_av = \
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0
fns_pos = sorted(glob.glob(prefix + ".pos*"))
fns_for = sorted(glob.glob(prefix + ".for*"))
fns_iU = glob.glob(prefix + ".out")[0]
fn_out_en = prefix + ".heat_capacity.dat"
# check that we found the same number of positions and forces files
nbeads = len(fns_pos)
if nbeads != len(fns_for):
print fns_pos
print fns_for
raise ValueError(
"Mismatch between number of input files for forces and positions.")
# print some information
print 'temperature = {:f} K'.format(float(temp))
print
print 'number of beads = {:d}'.format(nbeads)
print
print 'positions and forces file names:'
for fn_pos, fn_for in zip(fns_pos, fns_for):
print '{:s} {:s}'.format(fn_pos, fn_for)
print
print 'potential energy file: {:s}'.format(fns_iU)
print
print 'output file name:'
print fn_out_en
print
# open input and output files
ipos = [open(fn, "r") for fn in fns_pos]
ifor = [open(fn, "r") for fn in fns_for]
iU = open(fns_iU, "r")
iC = open(fn_out_en, "w")
# Some constants
beta = 1.0 / (Constants.kb * temperature)
const_1 = 0.5 * nbeads / (beta * Constants.hbar)**2
const_2 = 1.5 * nbeads / beta
const_3 = 1.5 / beta
const_4 = Constants.kb**2 / Constants.hbar**2
const_5 = Constants.hbar**2 * beta**3 / (24.0 * nbeads**3)
const_6 = Constants.hbar**2 * beta**2 / (24.0 * nbeads**3)
const_7 = Constants.kb * beta**2
timeUnit, potentialEnergyUnit, potentialEnergy_index, time_index = extractUnits(
iU) # extracting simulation time
# and potential energy units
iC.write(
"# Simulation time (in %s), centroid virial heat capacity estimator and PPI correction\n"
% timeUnit)
natoms = 0
ifr = 0
time0 = 0
q, f, m = None, None, None
while True: # Reading input files and calculating PPI correction
if ifr % 100 == 0:
print '\rProcessing frame {:d}'.format(ifr),
sys.stdout.flush()
try:
for i in range(nbeads):
ret = read_file("xyz", ipos[i], output='arrays')
if natoms == 0:
m, natoms = ret["masses"], ret["natoms"]
q = np.zeros((nbeads, 3 * natoms))
f = np.zeros((nbeads, 3 * natoms))
q[i, :] = ret["data"]
f[i, :] = read_file("xyz", ifor[i], output='arrays')["data"]
U, time = read_U(iU, potentialEnergyUnit, potentialEnergy_index,
time_index)
except EOFError: # finished reading files
sys.exit(0)
if ifr < skipSteps:
time0 = time
if ifr >= skipSteps: # PPI correction
time -= time0
KPa, f2, KVir = 0.0, 0.0, 0.0
if not fast_code:
for j in range(nbeads):
for i in range(natoms):
f2 += np.dot(f[j, i * 3:i * 3 + 3],
f[j, i * 3:i * 3 + 3]) / m[i]
for i in range(natoms):
KPa -= np.dot(
q[0, i * 3:i * 3 + 3] - q[nbeads - 1, i * 3:i * 3 + 3],
q[0, i * 3:i * 3 + 3] -
q[nbeads - 1, i * 3:i * 3 + 3]) * m[i]
for j in range(nbeads - 1):
for i in range(natoms):
KPa -= np.dot(
q[j + 1, i * 3:i * 3 + 3] - q[j, i * 3:i * 3 + 3],
q[j + 1, i * 3:i * 3 + 3] -
q[j, i * 3:i * 3 + 3]) * m[i]
rc = np.zeros(3)
for i in range(natoms):
rc[:] = 0.0
for j in range(nbeads):
rc[:] += q[j, i * 3:i * 3 + 3]
rc[:] /= nbeads
for j in range(nbeads):
KVir += np.dot(rc[:] - q[j, i * 3:i * 3 + 3],
f[j, i * 3:i * 3 + 3])
KPa *= const_1
KPa += const_2 * natoms
KVir /= 2.0 * nbeads
KVir += const_3 * natoms
else:
f2 = fortran.f2divm(np.array(f, order='F'),
np.array(m, order='F'), natoms, nbeads)
KPa = fortran.findcoupling(np.array(q, order='F'),
np.array(m, order='F'), temperature,
natoms, nbeads)
KVir = fortran.findcentroidvirialkineticenergy(
np.array(f, order='F'), np.array(q, order='F'), natoms,
nbeads)
KPa *= const_4
KPa += const_2 * natoms
KVir += const_3 * natoms
f2_av += f2
KPa_av += KPa
f2KPa_av += f2 * KPa
U_av += U
f2U_av += f2 * U
KVir_av += KVir
EVir_av += KVir + U
EEVir_av += (KVir + U) * (KPa + U)
f2E_av += f2 * (KPa + U)
f2E2_av += f2 * (KPa + U)**2
ifr += 1
norm = float(ifr - skipSteps)
dU = 2 * f2_av / norm - beta * (f2U_av / norm -
f2_av * U_av / norm**2)
dU *= const_6
dK = (Constants.kb * temperature +
KPa_av / norm) * f2_av / norm - f2KPa_av / norm
dK *= const_5
C = EEVir_av / norm - (EVir_av / norm)**2 + 1.5 * natoms / beta**2
C *= const_7
dC = (10 + C + 3*beta*EVir_av/norm)*beta*f2_av*const_6/norm - \
(6 + beta*EVir_av/norm)*beta*(dK + dU) + 2*beta*dK - \
const_6*(f2E2_av/norm - f2E_av*(KPa_av + U_av)/norm**2)*beta**3
iC.write("%f %f %f\n" % (time, C, dC))
else:
ifr += 1
