def integrate_euler(X, V, iparams, blist, sp):
"""
Euler integration for Nt steps.
Save each thermo-multiple step into xyz_frames.
Mass set to 1.0. Input:
* X: (N, 3) matrix
* V: (N, 3) matrix
* iparams: dict mapping bead type to a_ij
* blist: list of bead types (bead list)
* sp: system params
"""
T, E = np.zeros(sp.Nt), np.zeros(sp.Nt)
F = np.zeros(X.shape)
N = len(X)
ti = time.time()
for i in range(sp.Nt):
X = X + V * sp.dt
V = V + F * sp.dt
F = force_list(X, V, iparams, blist, sp)
X = X % sp.L
KE = tot_KE(V)
E[i] = KE + tot_PE(X, iparams, blist, sp.rc)
T[i] = KE / (3.0 / 2.0 * N)
tf = time.time()
if (i+1) % sp.thermo == 0:
save_xyzmatrix("Dump/dump_%3i.xyz" % (i+1), blist, X)
print("Step: %i | t: %.4f | T: %.5f | E: %.3e | Time: %.2f" % \
(i+1, i * sp.dt, T[i], E[i], tf - ti))
return T, E
def integrate_verlet(X, V, iparams, blist, sp):
"""
Verlet integration for Nt steps.
Save each thermo-multiple step into xyz_frames.
Mass set to 1.0. Input:
* X: (N, 3) matrix
* V: (N, 3) matrix
* iparams: dict mapping bead type to a_ij
* blist: list of bead types (bead list)
* sp: system params
"""
T, E = np.zeros(sp.Nt), np.zeros(sp.Nt)
N = len(X)
Vtemp = np.zeros(X.shape)
Fnew = np.zeros(X.shape)
ti = time.time()
F = force_list(X, V, iparams, blist, \
sp.L, sp.gamma, sp.kT, sp.dt, sp.rc)
T[0] = temperature(V)
E[0] = tot_KE(V) + tot_PE(X, iparams, blist, sp.rc)
save_xyzmatrix("Dump/dump_%i.xyz" % 0, blist, X)
for i in range(1, sp.Nt):
# 1. GW formulation DIVERGES TWICE AS MUCH AS 3rd!
# X = X + V * sp.dt + F * sp.dt**2 / 2.0
# Vtemp = V + F * sp.dt / 2.0
# Fnew = force_list(X, Vtemp, iparams, blist, \
# sp.L, sp.gamma, sp.kT, sp.dt, sp.rc)
# V = Vtemp + (F + Fnew) * sp.dt / 2
# F = Fnew
# 2. Wiki formulation without half-step velocity
X = X + V * sp.dt + F * sp.dt**2 / 2.0
Fnew = force_list(X, V, iparams, blist, \
sp.L, sp.gamma, sp.kT, sp.dt, sp.rc)
V = V + (F + Fnew) * sp.dt / 2.0
F = Fnew
X = X % sp.L
KE = tot_KE(V)
E[i] = KE + tot_PE(X, iparams, blist, sp.rc)
T[i] = KE / (3.0 / 2.0 * N)
tf = time.time()
if (i+1) % sp.thermo == 0:
save_xyzmatrix("Dump/dump_%i.xyz" % (i+1), blist, X)
print("Step: %i | t: %.3f | T: %.5f | E: %.3e | Time: %.2f" % \
(i+1, i * sp.dt, T[i], E[i], tf - ti))
return T, E
def integrate_verlet(X, V, iparams, blist, sp):
"""
Verlet integration for Nt steps.
Save each thermo-multiple step into xyz_frames.
Mass set to 1.0. Input:
* X: (N, 3) matrix
* V: (N, 3) matrix
* iparams: (Nbt, Nbt) matrix with interaction params
* blist: list of bead types (bead list)
* sp: misc system params
"""
T, E = np.zeros(sp.Nt), np.zeros(sp.Nt)
Vtemp = np.zeros(X.shape)
Fnew = np.zeros(X.shape)
ti = time.time()
F = force_list(X, V, iparams, blist, sp)
T[0] = temperature(V)
E[0] = tot_KE(V) + tot_PE(X, iparams, blist, sp)
save_xyzmatrix("Dump/dump_%i.xyz" % 0, blist, X)
tf = time.time()
for i in range(1, sp.Nt):
X = X + V * sp.dt + F * sp.dt**2 / 2.0
Fnew = force_list(X, V, iparams, blist, sp)
V = V + (F + Fnew) * sp.dt / 2.0
F = Fnew
X = X % L
T[i] = temperature(V)
E[i] = tot_KE(V) + tot_PE(X, iparams, blist, sp)
tf = time.time()
if (i+1) % sp.thermo == 0:
save_xyzmatrix("Dump/dump_%3i.xyz" % (i+1), blist, X)
print("Step: %i | t: %.4f | T: %.5f | E: %.3e | Time: %.2f" % \
(i+1, i * dt, T[i], E[i], tf - ti))
return T, E