""" This script contains a number of functions used for interpolation of kinetic profiles and D,V profiles in STRAHL.
Refer to the STRAHL manual for details.
"""
# MIT License
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# Copyright (c) 2021 Francesco Sciortino
#
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from scipy.interpolate import interp1d
import numpy as np
[docs]def funct(params, rLCFS, r):
"""Function 'funct' in STRAHL manual
The "params" input is broken down into 6 arguments:
y0 is core offset
y1 is edge offset
y2 (>y0, >y1) sets the gaussian amplification
p0 sets the width of the inner gaussian
P1 sets the width of the outer gaussian
p2 sets the location of the inner and outer peaks
"""
params = np.reshape(params, (-1, 6))
out = []
for param in params:
y0, y1, y2, p0, p1, p2 = param
r1 = p2 * rLCFS
rin = r[r <= r1]
rout = r[r > r1]
yin = y0 + (y2 - y0) * np.exp(np.maximum(-((rin - r1) ** 2) / p0**2, -50))
yout = y1 + (y2 - y1) * np.exp(np.maximum(-((rout - r1) ** 2) / p1**2, -50))
out.append(np.concatenate((yin, yout)))
return np.array(out)
[docs]def funct2(params, rLCFS, r):
"""Function 'funct2' in STRAHL manual."""
params_1, params_2 = np.swapaxes(np.reshape(params, (-1, 2, 6)), 0, 1)
funct_1 = funct(params_1, rLCFS, r)
funct_2 = funct(params_2, rLCFS, r)
return funct_1 + funct_2
[docs]def exppol0(params, d, rLCFS, r):
rho = r[:, None] / rLCFS
d = np.array(d) / rLCFS
params = np.array(params).T
idx = np.searchsorted(r, rLCFS)
core = params[0] * np.exp(
params[1] * rho[:idx] ** 2
+ params[2] * rho[:idx] ** 4
+ params[3] * rho[:idx] ** 6
+ params[4] * rho[:idx] ** 8
)
edge = core[-1] * np.exp(-(rho[idx:] - rho[idx - 1]) / d)
return np.concatenate([core, edge]).T
[docs]def exppol1(params, d, rLCFS, r):
rho = r[:, None] / rLCFS
d = np.array(d) / rLCFS
params = np.array(params).T
idx = np.searchsorted(r, rLCFS)
core = params[0] * np.exp(
params[1] * rho[:idx] ** 2
+ params[2] * rho[:idx] ** 3
+ params[3] * rho[:idx] ** 4
+ params[4] * rho[:idx] ** 5
)
edge = core[-1] * np.exp(-(rho[idx:] - rho[idx - 1]) / d)
return np.concatenate([core, edge]).T
[docs]def ratfun(params, d, rLCFS, r):
rho = r[:, None] / rLCFS
d = np.array(d) / rLCFS
params = np.array(params).T
idx = np.searchsorted(r, rLCFS)
core = params[0] * (
(1.0 - params[1]) * (1.0 - rho[:idx] ** params[2]) ** params[3] + params[1]
)
edge = core[-1] * np.exp(-(rho[idx:] - rho[idx - 1]) / d)
return np.concatenate([core, edge]).T
[docs]def interp_quad(x, y, d, rLCFS, r):
"""Function 'interp' used for kinetic profiles."""
f = interp1d(x, np.log(y), kind="quadratic", assume_sorted=True, copy=False)
idx = np.searchsorted(r, rLCFS)
core = np.exp(f(np.clip(r[:idx] / rLCFS, 0, x[-1])))
edge = core[..., [idx - 1]] * np.exp(
-np.outer(1.0 / np.asarray(d), r[idx:] - r[idx - 1])
)
return np.concatenate([core, edge], axis=-1)
[docs]def interpa_quad(x, y, rLCFS, r):
"""Function 'interpa' used for kinetic profiles"""
f = interp1d(
x,
np.log(y),
bounds_error=False,
kind="quadratic",
assume_sorted=True,
copy=False,
)
return np.exp(f(np.minimum(r / rLCFS, x[-1])))
[docs]def interp(x, y, rLCFS, r):
"""Function 'interp' used in STRAHL for D and V profiles."""
f = interp1d(x, y, fill_value="extrapolate", assume_sorted=True, copy=False)
return f(r / rLCFS)