finalized c functions

src/nmreval/clib/integrate.c

@@ -1,7 +1,7 @@
 /* integrands used in quadrature integration with scipy's LowLevelCallables */
 #include <math.h>
 
-#define KB 8.617333262145179e-05
+const double KB = 8.617333262145179e-05;
 
 /* FFHS functions */
 double ffhsSD(double x, void *user_data) {
@@ -91,7 +91,7 @@ double logGaussianCorrelation(double x, void *user_data) {
     return dist * exp(-t/uu);
 }
 
-
+// functions for distribution of energy
 double normalDist(double x, double x0, double sigma) {
     return exp(- pow((x-x0) / sigma, 2) / 2.) / sqrt(2 * M_PI) / sigma;
 }
@@ -113,3 +113,46 @@ double energyDist_SD(double x, void *user_data) {
 
     return r/(pow(r, 2) + pow(omega, 2)) * normalDist(x, e_m, e_b);
 }
+
+double energyDistSuscReal(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 1 / (pow(r, 2) + pow(omega, 2)) * normalDist(x, e_m, e_b);
+}
+
+double energyDistSuscImag(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 omega * r / (pow(r, 2) + pow(omega, 2)) * normalDist(x, e_m, e_b);
+}
+
+double energyDistCorrelation(double x, void *user_data) {
+    double *c = (double *)user_data;
+
+    double t = 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 normalDist(x, e_m, e_b) * exp(-t * r);
+}
+

src/nmreval/distributions/energy.py

@@ -28,24 +28,30 @@ class EnergyBarriers(Distribution):
         return np.exp(-e_a / (kB * te)) / t0
 
     @staticmethod
-    def energydistribution(e_a, mu, sigma):
+    def energy_distribution(e_a, mu, sigma):
         return np.exp(-0.5 * ((mu-e_a) / sigma) ** 2) / (np.sqrt(2 * np.pi) * sigma)
 
     @staticmethod
-    def correlation(t, temperature, *args):
-        tau0, e_m, e_b = args
-
-        def integrand(e_a, ti, t0, mu, sigma, te):
-            # correlation time would go to inf for higher energies, so we use rate
-            return np.exp(-ti*EnergyBarriers.rate(t0, e_a, te)) * EnergyBarriers.energydistribution(e_a, mu, sigma)
-
+    def correlation(t: ArrayLike, temperature: ArrayLike, tau0: float, e_m: float, e_b: float) -> ArrayLike:
         t = np.atleast_1d(t)
         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 = _integrate_c(lib.energyDistCorrelation, t, temperature, tau0, e_m, e_b)
+        else:
+            ret_val = _integrate_py(_integrand_time, t, 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 t for tt in temperature])
+        return ret_val
+
+    @staticmethod
+    def specdens(omega: ArrayLike, temperature: ArrayLike, tau0: float, e_m: float, e_b: float) -> ArrayLike:
+        omega = np.atleast_1d(omega)
+        temperature = np.atleast_1d(temperature)
+
+        if HAS_C_FUNCS:
+            ret_val = _integrate_c(lib.energyDist_SD, omega, temperature, tau0, e_m, e_b)
+        else:
+            ret_val = _integrate_py(_integrand_sd, omega, temperature, tau0, e_m, e_b)
 
         return ret_val
 
@@ -56,88 +62,73 @@ 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)
-        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) -
-                           1j * simpson(_integrand_freq_imag(e_axis, o, tau0, e_m, e_b, tt), e_axis))
-
-        return np.array(ret_val)
-
-    @staticmethod
-    def specdens(omega, temperature, tau0: float, e_m: float, e_b: float):
-        # in contrast to other spectral densities, it's omega and temperature
-
-        omega = np.atleast_1d(omega)
-        temperature = np.atleast_1d(temperature)
-
         if HAS_C_FUNCS:
-            ret_val = EnergyBarriers.spec_dens_c(omega, temperature, tau0, e_m, e_b)
+            ret_val = _integrate_c(lib.energyDistSuscReal, omega, temperature, tau0, e_m, e_b) + \
+                      1j * _integrate_c(lib.energyDistSuscImag, omega, temperature, tau0, e_m, e_b)
         else:
-            ret_val = EnergyBarriers.spec_dens_py(omega, temperature, tau0, e_m, e_b)
+            ret_val = _integrate_py(_integrand_susc_real, omega, temperature, tau0, e_m, e_b) + \
+                      1j * _integrate_py(_integrand_susc_imag, omega, temperature, tau0, e_m, e_b)
 
-        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 = (c_double * 5)(o, tau0, e_m, e_b, t)
-            user_data = cast(pointer(c), c_void_p)
-            area = quad(LowLevelCallable(lib.energyDist_SD, user_data), 0, np.infty, epsabs=1e-13)[0]
-            res.append(area)
-
-        return np.array(res)
+    def mean(temperature, tau0, ea):
+        return tau0*np.exp(ea/(kB*temperature))
 
     @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):
-        return args[1]*np.exp(args[2]/(kB*args[0]))
-
-    @staticmethod
-    def logmean(*args):
-        return args[1] + args[2] / (kB * args[0])
+    def logmean(temperature, tau0, ea):
+        return tau0 + ea / (kB * temperature)
 
     @staticmethod
     def max(*args):
         return args[1] * np.exp(args[2] / (kB * args[0]))
 
 
-def _integrate_process_imag(args):
-    pass
+# helper functions
+def _integrate_c(func, 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 = (c_double * 5)(o, tau0, e_m, e_b, t)
+        user_data = cast(pointer(c), c_void_p)
+        area = quad(LowLevelCallable(func, user_data), 0, np.infty, epsabs=1e-13)[0]
+
+        res.append(area)
+
+    ret_val = np.array(res).reshape(omega.shape[0], temperature.shape[0])
+
+    return ret_val.squeeze()
 
 
-def _integrate_process_real(args):
-    omega_i, t, tau0, mu, sigma, temp_j = args
-    return quad(_integrand_freq_real(), 0, 10, args=(omega_i, t, tau0, mu, sigma, temp_j))[0]
+def _integrate_py(func, axis, temp, tau0, e_m, e_b):
+    x = np.atleast_1d(axis)
+    temperature = np.atleast_1d(temp)
+
+    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(x, temperature):
+        ret_val.append(simpson(func(e_axis, o, tau0, e_m, e_b, tt), e_axis))
+
+    ret_val = np.array(ret_val).reshape(x.shape[0], temperature.shape[0])
+
+    return ret_val.squeeze()
 
 
-def _integrate_process_time(args):
-    omega_i, t, tau0, mu, sigma, temp_j = args
-    return quad(_integrand_time, 0, 10, args=(omega_i, t, tau0, mu, sigma, temp_j))[0]
-
-
-def _integrand_freq_real(u, omega, tau0, mu, sigma, temp):
+# python integrands
+def _integrand_sd(u, omega, tau0, mu, sigma, temp):
     r = EnergyBarriers.rate(tau0, u, temp)
-    return 1 / (r**2 + omega**2) * EnergyBarriers.energydistribution(u, mu, sigma)
+    return r / (r**2 + omega**2) * EnergyBarriers.energy_distribution(u, mu, sigma)
 
 
-def _integrand_freq_imag(u, omega, tau0, mu, sigma, temp):
+def _integrand_susc_real(u, omega, tau0, mu, sigma, temp):
+    r = EnergyBarriers.rate(tau0, u, temp)
+    return 1 / (r**2 + omega**2) * EnergyBarriers.energy_distribution(u, mu, sigma)
+
+
+def _integrand_susc_imag(u, omega, tau0, mu, sigma, temp):
     rate = EnergyBarriers.rate(tau0, u, temp)
-    return omega * rate / (rate**2 + omega**2) * EnergyBarriers.energydistribution(u, mu, sigma)
+    return omega * rate / (rate**2 + omega**2) * EnergyBarriers.energy_distribution(u, mu, sigma)
 
 
 def _integrand_time(u, t, tau0, mu, sigma, temp):
     rate = EnergyBarriers.rate(tau0, u, temp)
-    return EnergyBarriers.energydistribution(u, mu, sigma) * np.exp(-t*rate)
+    return EnergyBarriers.energy_distribution(u, mu, sigma) * np.exp(-t*rate)

src/nmreval/distributions/helper.py

@@ -14,16 +14,35 @@ try:
     lib.ffhsSD.argtypes = (c_double, c_void_p)
 
     # Log-Gaussian integrands
-    lib.logGaussianSD_high.restype = c_double
-    lib.logGaussianSD_high.argtypes = (c_double, c_void_p)
-    lib.logGaussianSD_low.restype = c_double
-    lib.logGaussianSD_low.argtypes = (c_double, c_void_p)
+    lib.logGaussian_imag_high.restype = c_double
+    lib.logGaussian_imag_high.argtypes = (c_double, c_void_p)
+    lib.logGaussian_imag_low.restype = c_double
+    lib.logGaussian_imag_low.argtypes = (c_double, c_void_p)
 
+    lib.logGaussian_real_high.restype = c_double
+    lib.logGaussian_real_high.argtypes = (c_double, c_void_p)
+    lib.logGaussian_real_low.restype = c_double
+    lib.logGaussian_real_low.argtypes = (c_double, c_void_p)
+
+    lib.logGaussianCorrelation.restype = c_double
+    lib.logGaussianCorrelation.argtypes = (c_double, c_void_p)
+
+    # integrands for distribution of energies
     lib.energyDist_SD.restype = c_double
     lib.energyDist_SD.argtypes = (c_double, c_void_p)
 
+    lib.energyDistCorrelation.restype = c_double
+    lib.energyDistCorrelation.argtypes = (c_double, c_void_p)
+
+    lib.energyDistSuscReal.restype = c_double
+    lib.energyDistSuscReal.argtypes = (c_double, c_void_p)
+    lib.energyDistSuscImag.restype = c_double
+    lib.energyDistSuscImag.argtypes = (c_double, c_void_p)
+
+
     HAS_C_FUNCS = True
     logger.info('Use C functions')
 except OSError:
     HAS_C_FUNCS = False
     logger.info('Use python functions')
+

src/nmreval/distributions/loggaussian.py

@@ -49,8 +49,8 @@ class LogGaussian(Distribution):
         _tau = np.atleast_1d(tau0)
 
         if HAS_C_FUNCS:
-            res_real = _integration_parallel(_omega, _tau, sigma, _integrate_process_imag)
-            res_imag = _integration_parallel(_omega, _tau, sigma, _integrate_process_real)
+            res_real = _integrate_susc_real_c(_omega, _tau, sigma)
+            res_imag = _integrate_susc_imag_c(_omega, _tau, sigma)
         else:
             res_real = _integration_parallel(_omega, _tau, sigma, _integrate_process_imag)
             res_imag = _integration_parallel(_omega, _tau, sigma, _integrate_process_real)
@@ -63,7 +63,7 @@ class LogGaussian(Distribution):
         _tau = np.atleast_1d(tau)
 
         if HAS_C_FUNCS:
-            ret_val = _integrate_specdens_c(_omega, _tau, sigma)
+            ret_val = _integrate_susc_imag_c(_omega, _tau, sigma)
         else:
             ret_val = _integration_parallel(_omega, _tau, sigma, _integrate_process_imag)
 
@@ -88,15 +88,23 @@ def _integration_parallel(x: np.ndarray, tau: np.ndarray, sigma: float, func: Ca
     return res
 
 
-def _integrate_specdens_c(omega: np.ndarray, tau: np.ndarray, sigma: float) -> np.ndarray:
+def _integrate_susc_imag_c(omega: np.ndarray, tau: np.ndarray, sigma: float) -> np.ndarray:
+    return _integrate_susc_c(lib.logGaussian_imag_low, lib.logGaussian_imag_high, omega, tau, sigma)
+
+
+def _integrate_susc_real_c(omega: np.ndarray, tau: np.ndarray, sigma: float) -> np.ndarray:
+    return _integrate_susc_c(lib.logGaussian_real_low, lib.logGaussian_real_high, omega, tau, sigma)
+
+
+def _integrate_susc_c(lowfunc, highfunc, omega, tau, sigma):
     res = []
 
     for o, t in product(omega, tau):
         c = (ctypes.c_double * 3)(o, t, sigma)
         user_data = ctypes.cast(ctypes.pointer(c), ctypes.c_void_p)
 
-        area = quad(LowLevelCallable(lib.logGaussianSD_high, user_data), 0, np.infty, epsabs=1e-12, epsrel=1e-12)[0]
-        area += quad(LowLevelCallable(lib.logGaussianSD_low, user_data), -np.infty, 0, epsabs=1e-12, epsrel=1e-12)[0]
+        area = quad(LowLevelCallable(highfunc, user_data), 0, np.infty, epsabs=1e-12, epsrel=1e-12)[0]
+        area += quad(LowLevelCallable(lowfunc, user_data), -np.infty, 0, epsabs=1e-12, epsrel=1e-12)[0]
 
         res.append(area)
 
@@ -139,7 +147,7 @@ def _integrate_correlation_c(t, tau, sigma):
 
 def _integrate_process_time(args):
     omega_i, tau_j, sigma = args
-    return quad(_integrand_time, -50, 50, args=(omega_i, tau_j, sigma))[0]
+    return quad(_integrand_time, -50, 50, args=(omega_i, tau_j, sigma), epsabs=1e-12, epsrel=1e-12)[0]
 
 
 def _integrand_time(u, t, tau, sigma):