C function for energy distribution spectral density
This commit is contained in:
parent
4a9d50e8a4
commit
2042148d0f
@ -1,6 +1,8 @@
|
||||
/* integrands used in quadrature integration with scipy's LowLevelCallables */
|
||||
#include <math.h>
|
||||
|
||||
#define KB 8.617333262145179e-05
|
||||
|
||||
/* FFHS functions */
|
||||
double ffhsSD(double x, void *user_data) {
|
||||
double *c = (double *)user_data;
|
||||
@ -18,7 +20,7 @@ double ffhsSD(double x, void *user_data) {
|
||||
|
||||
/* log-gaussian functions */
|
||||
double logNormalDist(double tau, double tau0, double sigma) {
|
||||
return exp(- pow((log(tau/tau0) / sigma), 2) / 2) / sqrt(2*M_PI)/sigma;
|
||||
return exp(- pow((log(tau/tau0) / sigma), 2) / 2.) / sqrt(2*M_PI)/sigma;
|
||||
}
|
||||
|
||||
double logGaussianSD_high(double u, void *user_data) {
|
||||
@ -61,3 +63,26 @@ double logGaussianCorrelation(double x, void *user_data) {
|
||||
|
||||
return dist * exp(-t/uu);
|
||||
}
|
||||
|
||||
|
||||
double normalDist(double x, double x0, double sigma) {
|
||||
return exp(- pow((x-x0) / sigma, 2) / 2.) / sqrt(2 * M_PI) / sigma;
|
||||
}
|
||||
|
||||
double rate(double tau0, double ea, double t) {
|
||||
return exp(-ea / t / KB) / tau0;
|
||||
}
|
||||
|
||||
double energyDist_SD(double x, void *user_data) {
|
||||
double *c = (double *)user_data;
|
||||
|
||||
double omega = c[0];
|
||||
double tau0 = c[1];
|
||||
double e_m = c[2];
|
||||
double e_b = c[3];
|
||||
double temp = c[4];
|
||||
|
||||
double r = rate(tau0, x, temp);
|
||||
|
||||
return r/(pow(r, 2) + pow(omega, 2)) * normalDist(x, e_m, e_b);
|
||||
}
|
||||
|
@ -1,13 +1,18 @@
|
||||
import ctypes
|
||||
from itertools import product
|
||||
|
||||
import numpy as np
|
||||
from scipy import LowLevelCallable
|
||||
from scipy.integrate import quad, simps as simpson
|
||||
|
||||
from .base import Distribution
|
||||
from ..lib.utils import ArrayLike
|
||||
from ..utils.constants import kB
|
||||
|
||||
from .helper import HAS_C_FUNCS, lib
|
||||
|
||||
|
||||
# noinspection PyMethodOverriding
|
||||
class EnergyBarriers(Distribution):
|
||||
name = 'Energy barriers'
|
||||
parameter = [r'\tau_{0}', r'E_{m}', r'\Delta E']
|
||||
@ -51,7 +56,7 @@ class EnergyBarriers(Distribution):
|
||||
omega = np.atleast_1d(omega)
|
||||
temperature = np.atleast_1d(temperature)
|
||||
|
||||
e_axis = np.linspace(max(0, e_m-50*e_b), e_m+50*e_b, num=5001)
|
||||
e_axis = np.linspace(max(0., e_m-50*e_b), e_m+50*e_b, num=5001)
|
||||
ret_val = []
|
||||
for o, tt in product(omega, temperature):
|
||||
ret_val.append(simpson(_integrand_freq_real(e_axis, o, tau0, e_m, e_b, tt), e_axis) -
|
||||
@ -60,23 +65,41 @@ class EnergyBarriers(Distribution):
|
||||
return np.array(ret_val)
|
||||
|
||||
@staticmethod
|
||||
def specdens(omega, temperature, *args):
|
||||
def specdens(omega, temperature, tau0: float, e_m: float, e_b: float):
|
||||
# in contrast to other spectral densities, it's omega and temperature
|
||||
tau0, e_m, e_b = args
|
||||
|
||||
def integrand(e_a, w, t0, mu, sigma, t):
|
||||
r = EnergyBarriers.rate(t0, e_a, t)
|
||||
return r/(r**2 + w**2) * EnergyBarriers.energydistribution(e_a, mu, sigma)
|
||||
|
||||
omega = np.atleast_1d(omega)
|
||||
temperature = np.atleast_1d(temperature)
|
||||
|
||||
e_axis = np.linspace(max(0, e_m-50*e_b), e_m+50*e_b, num=5001)
|
||||
if HAS_C_FUNCS:
|
||||
ret_val = EnergyBarriers.spec_dens_c(omega, temperature, tau0, e_m, e_b)
|
||||
else:
|
||||
ret_val = EnergyBarriers.spec_dens_py(omega, temperature, tau0, e_m, e_b)
|
||||
|
||||
ret_val = np.array([simpson(integrand(e_axis, o, tau0, e_m, e_b, tt), e_axis)
|
||||
for o in omega for tt in temperature])
|
||||
return ret_val.squeeze()
|
||||
|
||||
return ret_val
|
||||
@staticmethod
|
||||
def spec_dens_c(omega: np.ndarray, temperature: np.ndarray, tau0: float, e_m: float, e_b: float) -> np.ndarray:
|
||||
res = []
|
||||
for o, t in product(omega, temperature):
|
||||
c = (ctypes.c_double * 5)(o, tau0, e_m, e_b, t)
|
||||
user_data = ctypes.cast(ctypes.pointer(c), ctypes.c_void_p)
|
||||
area = quad(LowLevelCallable(lib.energyDist_SD, user_data), 0, np.infty, epsabs=1e-10)[0]
|
||||
res.append(area)
|
||||
|
||||
return np.array(res)
|
||||
|
||||
@staticmethod
|
||||
def spec_dens_py(omega: np.ndarray, temperature: np.ndarray, tau0: float, e_m: float, e_b: float) -> np.ndarray:
|
||||
def integrand(e_a, w, t0, mu, sigma, t):
|
||||
r = EnergyBarriers.rate(t0, e_a, t)
|
||||
return r/(r**2 + w**2) * EnergyBarriers.energydistribution(e_a, mu, sigma)
|
||||
|
||||
e_axis = np.linspace(max(0., e_m-50*e_b), e_m+50*e_b, num=5001)
|
||||
|
||||
ret_val = [simpson(integrand(e_axis, o, tau0, e_m, e_b, tt), e_axis) for o in omega for tt in temperature]
|
||||
|
||||
return np.array(ret_val)
|
||||
|
||||
@staticmethod
|
||||
def mean(*args):
|
||||
|
Loading…
Reference in New Issue
Block a user