Temperature scan planner

plan_T_scan

 plan_T_scan (Tlo, Thi, nat, N=1, plot_dist=True)

Simulate with `stats.normal` random variable

# semilogx()
plt.figure(figsize=(10,6))
rv = stats.norm
N = 100_000
plan = plan_T_scan(50, 250, 32, N)

el = np.zeros(0)
for c, (l, s, n) in enumerate(tqdm(plan)):
    el = np.append(el, rv.rvs(loc=l, scale=s, size=n))

skip = len(el)//2000
skip = int(max(1, skip))
for s in el[::skip]:
    plt.axvline(s, ymin=0.95, ymax=0.98, ls='-', color='r', alpha=0.1)
    
NF = sum([sf for _, _, sf in plan])
counts, bins = np.histogram(el, bins='auto', density=True)
plt.hist(bins[:-1], bins, weights=NF*counts, color='C0', alpha=0.3);

Run with `HECSS` sampler

from hecss.core import HECSS
from hecss.util import select_asap_model, create_asap_calculator
from hecss.optimize import make_sampling
from hecss.monitor import plot_stats

model = select_asap_model('SiC')
print(f'Using potential model: {model}')

sys_size = '3x3x3'
sc = [int(v) for v in sys_size.split('x')]

cryst = bulk('SiC', crystalstructure='zincblende',
                 a=4.38120844, cubic=True).repeat(tuple(sc))
cryst.calc = create_asap_calculator(model)
hecss = HECSS(cryst, lambda : create_asap_calculator(model), pbar=False)
hecss.estimate_width_scale(10, Tmax=1000);

Using potential model: MEAM_LAMMPS_KangEunJun_2014_SiC__MO_477506997611_000

N = 1_000
plt.figure(figsize=(10,6))
plan = plan_T_scan(150, 250, len(cryst), N)

smpls = {}
for T, sig, n in tqdm(plan):
    # sampler = HECSS_Sampler(cryst, asap3.OpenKIMcalculator(model),
    #                         T, N=int(n), pbar=tqdm(total=n))
    smpls[T]=np.array([s[-1] for s in hecss._sampler_ser(T, n)])
# ell = [np.array([s[-1] for s in sl]) for sl in smpls.values()]

ell = np.concatenate(list(smpls.values()))
e_min = ell.min()
e_max = ell.max()

for T, el in smpls.items():
    plt.hist(el, bins=50, histtype='step', label=f'{T=:.0f}K', range=(e_min, e_max))
plt.hist(ell, bins=50, stacked=True, color='C0', alpha=0.25, range=(e_min, e_max))
plt.legend();

plt.figure(figsize=(10,6))
if N < 10_000:
    bins = np.linspace(e_min, e_max, 50)*2/un.kB/3
else :
    bins = 'auto'
cnt, bins, _ = plt.hist(ell*2/un.kB/3, 
                     bins=bins, density=False, alpha=0.6, label='Total');
x = np.linspace(bins[0], bins[-1], 300)
y = np.zeros(x.shape)
tdx = bins[1]-bins[0]
for c, ((T, el), (Tp, sig, n)) in enumerate(zip(smpls.items(), plan)):
    # bins = 'auto'
    e = el*2/un.kB/3
    Tc, Tb, _ = plt.hist(e, bins=bins, density=False, 
                         histtype='step', color=f'C{c+1}');
    dx = Tb[1]-Tb[0]
    # plt.plot(x, dx*n*stats.norm.pdf(x, loc=T, scale=sig), color=f'C{c+1}', 
    #          label=f'{T=:.1f}K (N={int(Tc.sum())})')
    # y += tdx*n*stats.norm.pdf(x, loc=T, scale=sig)

    fit = stats.norm.fit(e)
    plt.plot(x, dx*n*stats.norm.pdf(x, *fit), color=f'C{c+1}',
             label=f'{T=:.1f}K (N={int(Tc.sum())})')
    
    y += tdx*n*stats.norm.pdf(x, *fit)
    
    skip = len(el)//500
    skip = max(1, skip)
    for v in e[::skip]:
        plt.axvline(v, ymin=0.95, ymax=0.98, ls='-', color='r', alpha=0.05)
    
plt.plot(x, y, '--', label='Total')
plt.xlabel('Temperature (K)')
plt.legend(loc='upper right')
plt.title('Temperature scan - HECSS generated energies.')
plt.grid()
plt.savefig(f'AUX/T_scan_{N=}.pdf')

Test temperature scanning planner

N = 1000
plt.figure(figsize=(8,4))
plan = plan_T_scan(200, 400, len(cryst), N)
plt.savefig('AUX/T_scan_plan.pdf', bbox_inches='tight')

smpll = []
for T, sig, n in tqdm(plan):
    smpll.append([s for s in hecss.sample(T, n)])
ell = [[s[-1] for s in sl] for sl in smpll]

usmp = []
for sl in smpll:
    usmp += sl

plt.figure(figsize=(8,4))
plt.hist([s[-1] for s in usmp], bins='auto', density=True)
plt.xlabel('Potential energy (meV/at)')
plt.ylabel('Probability density (meV/at)$^{-1}$')
plt.title('Temperatures: 200-400K')
plt.savefig(f'AUX/uniform.pdf', bbox_inches='tight')

T = 273
wd = make_sampling(usmp, T, N=4*N, nonzero_w=False, debug=True)
print(len(usmp), len(wd))
plt.legend(loc='upper right', bbox_to_anchor=(1.0, 0.95))
plt.show();
plot_stats(wd, T, sqrN=True, show=False)
plt.savefig(f'AUX/T_scan_{T=:.0f}K.pdf', bbox_inches='tight')

3448 3945

plt.figure(figsize=(10,6))
if N < 1_000:
    bins = np.linspace(min(flatten(ell)), max(flatten(ell)), 40)*2/un.kB/3
else :
    bins = 'auto'
cnt, bins, _ = plt.hist(np.array(list(flatten(ell)))*2/un.kB/3, 
                     bins=50, density=False, alpha=0.3, label='Total');
x = np.linspace(bins[0], bins[-1], 300)
y = np.zeros(x.shape)
tdx = bins[1]-bins[0]
for c, (el, (T, sig, n)) in enumerate(zip(ell, plan)):
    e = np.array(el)
    bins = 'auto'
    Tc, Tb, _ = plt.hist(e*2/un.kB/3, bins=bins, density=False, 
                         histtype='step', color=f'C{c+1}');
    dx = Tb[1]-Tb[0]
    nf = np.sum(Tc)*dx
    # plt.plot(x, dx*n*stats.norm.pdf(x, loc=T, scale=sig), color=f'C{c+1}', 
    #          label=f'{T=:.1f}K (N={int(Tc.sum())})')
    # y += tdx*n*stats.norm.pdf(x, loc=T, scale=sig)
    fit = stats.logistic.fit(e*2/un.kB/3)
    plt.plot(x, nf*stats.logistic.pdf(x, *fit), color=f'C{c+1}', 
             label=f'{T=:.1f}K (N={int(Tc.sum())})')
    y += nf*stats.logistic.pdf(x, *fit)

    skip = len(el)//1000
    skip = max(1, skip)
    for v in e[::skip]*2/un.kB/3:
        plt.axvline(v, ymin=0.95, ymax=0.98, ls='-', color='r', alpha=0.05)
    
plt.plot(x, y, '--', label='Plan (total)')
plt.xlabel('Temperature (K)')
plt.legend(loc='upper right')
plt.title('Temperature scan - HECSS generated energies.')
plt.grid()
plt.savefig(f'AUX/T_scan_{N=}.pdf')

x = np.linspace(-5, 5, 100)
plt.plot(x, stats.norm.pdf(x))
plt.grid()
plt.axhline(1/8)
plt.axvline(np.log(3+2*np.sqrt(2)))
plt.axvline(np.log(3-2*np.sqrt(2)))
plt.plot(x, stats.logistic.pdf(x))
s=2
plt.plot(x, stats.logistic.pdf(x, scale=s))
plt.axhline(1/(8*s))
plt.axvline(s*np.log(3+2*np.sqrt(2)))
plt.axvline(s*np.log(3-2*np.sqrt(2)))

x = np.linspace(0, 15, 300)
y = np.zeros(x.shape)
a = np.log(3+2*np.sqrt(2))
a = 1.4
x0 = 3
b = 1/8
nf = 1
while x0 < 15:
    s = x0*b
    if x0*(1+b*a)/(1-b*a) > 15:
        nf = 1.3
        x0 *= 1.05
    yy=nf*s*stats.logistic.pdf(x, loc=x0, scale=s)
    plt.plot(x,yy)
    y += yy
    x0 *= (1+a*b)/(1-a*b)
plt.plot(x,y)
plt.axhline(1/4); plt.axhline(1/8)

# semilogx()
plt.figure(figsize=(10,6))
rv = stats.norm
N = 1_000_000
plan = plan_T_scan(50, 250, 32, N)

el = np.zeros(0)
for c, (l, s, n) in enumerate(tqdm(plan)):
    el = np.append(el, rv.rvs(loc=l, scale=s, size=n))

skip = len(el)//2000
skip = int(max(1, skip))
for s in el[::skip]:
    plt.axvline(s, ymin=0.95, ymax=0.98, ls='-', color='r', alpha=0.1)
    
NF = sum([sf for _, _, sf in plan])
counts, bins = np.histogram(el, bins='auto', density=True)
plt.hist(bins[:-1], bins, weights=NF*counts, color='C0', alpha=0.3);

Temperature scan planner

plan_T_scan

Simulate with `stats.normal` random variable

Run with `HECSS` sampler

Test temperature scanning planner

Scanning with width instead of temperature

Uniform distribution

plan_T_scan

Simulate with stats.normal random variable

Run with HECSS sampler

Test temperature scanning planner

Scanning with width instead of temperature

Uniform distribution

Simulate with `stats.normal` random variable

Run with `HECSS` sampler