def gas_alpha(sim=False, t_range=[0, -1], OVERWRITE=False):
""" This calculates the global alpha-value from ts object via
alphah=(2./3.)*(ts3.uxuym)/(ts3.rhom*ts3.csm**2)
for the lastNentries of the time series.
Input:
t_range use this time range of the timeseries
OVERWRITE overwrite alpha file in sim.pc_datadir/alpha_<lastNentries>
return:
alpha dictionary
"""
from pencil import get_sim
from pencil.sim import sim
from pencil import io
from os.path import exists, join
import numpy as np
def empirical_std_deviation(x):
"""
(Geschaetzte) Streuung der Messwerte x um den (unbekannten) wahren Wert
(estimated) stray of the measurments x around the (unknown) true value
s(x) = SQRT( 1./(M-1) * SUM( (x-<x>)**2 ) )"""
import numpy as np
x = np.array(x)
M = np.size(x)
xm = np.mean(x)
#return np.sqrt(1./(M-1.)*np.sum((x-xm)**2))
return np.sqrt(M / (M - 1.) * ((1. / M * np.sum(x**2)) - xm**2))
def std_deviation_of_mean_value(x):
"""
Messunsicherheit des Mittelwertes <x>
Empirical standarddeviation of the arithmetical mean value
s(<x>) = s(x)/SQRT( M ) = SQRT( 1./(M-1) * SUM( (x-<x>)**2 ) ) / SQRT( M )"""
import numpy as np
x = np.array(x)
M = np.size(x)
if M == 1: return 0
return empirical_std_deviation(x) / np.sqrt(M)
if type(sim) == sim.__Simulation__:
SIM = sim
else:
SIM = get_sim()
filename = 'alpha_' + str(t_range[0]) + '_' + str(t_range[1])
## skip if nothing is new
if not OVERWRITE and io.exists(name=filename, sim=SIM):
print('~ Alpha for "' + SIM.name + '" already exists. Loading file...')
return io.load(name=filename, sim=SIM)
print('~ Calculating alpha for "' + SIM.name + '" in "' + SIM.path + '"')
## import time series object
try:
print('~ reading time series..')
ts = SIM.get_ts()
except:
print('! ERROR: Couldnt read time series!')
return False
## correct if csm quantity is not correctly exported
try:
csm = ts.csm
if csm[0] == 0: csm = 1.
except:
print(
'? WARNING: Couldnt find >csm< in time series, set it to csm = 1. This may be incorrect!'
)
csm = 1.
if t_range[1] == -1: t_range[1] = ts.t[-1]
id_min = np.argmin(np.abs(ts.t - t_range[0]))
id_max = np.argmin(np.abs(ts.t - t_range[1]))
alpha_dict = {}
## calculate alpha
print('~ calculating alpha, its mean value and standard deviation for ' +
str(t_range))
alpha_dict['alpha'] = -(2. / 3.) * (ts.uxuym) / (ts.rhom * csm**2)
alpha_dict['alpha_mean'] = np.mean(alpha_dict['alpha'][id_min:id_max])
alpha_dict['alpha_stddev'] = std_deviation_of_mean_value(
alpha_dict['alpha'][id_min:id_max])
print('~ alpha_mean = ' + str(alpha_dict['alpha_mean']) +
' and alpha_stddev = ' + str(alpha_dict['alpha_stddev']))
## calculate alpha minus mean_flux
print(
'~ calculating alpha minus mean_flux (alpha_mmf), its mean value and standard deviation'
)
alpha_dict['alpha_mmf'] = -(2. / 3.) * (ts.uxuym - ts.uxm * ts.uym) / (
ts.rhom * csm**2)
alpha_dict['alpha_mmf_mean'] = np.mean(
alpha_dict['alpha_mmf'][id_min:id_max])
alpha_dict['alpha_mmf_stddev'] = std_deviation_of_mean_value(
alpha_dict['alpha_mmf'][id_min:id_max])
print('~ alpha_mmf_mean = ' + str(alpha_dict['alpha_mmf_mean']) +
' and alpha_mmf_stddev = ' + str(alpha_dict['alpha_mmf_stddev']))
import math
for v in alpha_dict.values():
if type(v) == type(1.1) and math.isnan(v):
io.debug_breakpoint()
## save alpha in plk
print('~ saving alpha values in ' + SIM.pc_datadir + '/' + filename)
io.save(alpha_dict, filename, folder=SIM.pc_datadir)
return alpha_dict
def dispersion_and_drift(sim=False,
OVERWRITE=False,
GLOBAL=True,
LOCAL=True,
use_IDL=False,
recalculate_gas_velo_at_particle_pos=False):
"""This calculates the dispersion (sigma) and drift (zeta) locally and globally
by using the gas_velo_at_particle_pos script and dataset for all particles.
With sigma = sqrt( 1/N_par * sum_i^N_par( (v_par(i) - <v_par>)^2 ) ) and
zeta = sqrt( 1/N_par * sum_i^N_par( (v_par(i) - u(xp_i))^2 ) )
Arg:
OVERWRITE: set to True to overwrite already calculated results
GLOBAL: Calculate drift and dispersion globally, i.e. whole simulation domain
LOCAL: Calculate drift and dispersion locally, i.e. grid cell wise
recalculate_gas_velo_at_particle_pos:
if the dataset shall be recalcualted
use_IDL: use backup solution of IDL script and sav files
returns True if successfull
"""
from pencil import get_sim
from pencil import io
from pencil import read
from pencil.diag.particle import gas_velo_at_particle_pos
from scipy.io import readsav
from os import listdir
from os.path import exists, join, dirname
import numpy as np
if sim == False:
sim = get_sim()
if sim == False:
print('! ERROR: Specify simulation object!')
return False
SIM = sim
## calculate gas speed at particle position dataset
gas_velo_at_particle_pos(OVERWRITE=recalculate_gas_velo_at_particle_pos,
use_IDL=use_IDL,
sim=sim)
print(
'\n##################### Starting the whole calculation process of DISPERSON and DRIFT for '
+ SIM.name + ' #####################')
## default and setup
GASVELO_DESTINATION = 'gas_velo_at_particle_pos'
GASVELO_DIR = join(SIM.pc_datadir, GASVELO_DESTINATION)
## get list of available files
if use_IDL:
file_filetype = '.sav'
else:
file_filetype = '.pkl'
files = []
if exists(GASVELO_DIR):
files = [
i for i in listdir(GASVELO_DIR)
if i.startswith(GASVELO_DESTINATION) and i.endswith(file_filetype)
]
if files == []:
print(
'!! ERROR: No calc_gas_speed_at_particle_position-files found for '
+ SIM.name + '! Use idl script to produce them first!')
if use_IDL:
USE_PKL_FILES = False
files = [i.split('_')[-1].split(file_filetype)[0] for i in files]
scheme = ''
else:
USE_PKL_FILES = True
files = [i.split('_')[-1].split(file_filetype)[0] for i in files]
scheme = '_tsc'
## calculate global dispersion for all snapshot for which gas_velo_at_particle_pos files are found
for file_no in files:
print(
'## Starting the calculation for DISPERSON and DRIFT for ### VAR'
+ str(file_no) + ' ###')
# check if files already exist
if (not OVERWRITE) and io.exists(
'sigma_' + file_no, folder=SIM.pc_datadir) and io.exists(
'zeta_' + file_no, folder=SIM.pc_datadir) and io.exists(
'sigma_l_' + file_no,
folder=join(SIM.pc_datadir, 'sigma_l')) and io.exists(
'zeta_l_' + file_no,
folder=join(SIM.pc_datadir, 'zeta_l')):
print('## Skipping calculations')
continue
## read sav and var file
print('## reading gas_velo_at_particle_pos file and VAR')
if USE_PKL_FILES:
sav_file = io.load(
join(GASVELO_DIR, GASVELO_DESTINATION + scheme + '_' +
file_no + '.pkl'))[GASVELO_DESTINATION]
else:
sav_file = readsav(
join(GASVELO_DIR, GASVELO_DESTINATION + scheme + '_' +
file_no + '.sav'))[GASVELO_DESTINATION]
var_file = read.var(varfile='VAR' + file_no,
quiet=True,
trimall=True,
datadir=SIM.datadir)
## get everything ready
dim = SIM.dim
pdim = read.pdim(sim=SIM)
npar = pdim.npar
npar1 = 1. / npar
## get first quantities and setup the DATA_SET
if use_IDL:
time = sav_file['time'][0]
DATA_SET = np.core.records.fromarrays(
[
range(0, npar), sav_file['par_idx'][0][0].astype('int'),
sav_file['par_idx'][0][1].astype('int'),
sav_file['par_idx'][0][2].astype('int'),
sav_file['par_pos'][0][0], sav_file['par_pos'][0][1],
sav_file['par_pos'][0][2], sav_file['par_velo'][0][0],
sav_file['par_velo'][0][1], sav_file['par_velo'][0][2],
sav_file['npar'][0], sav_file['gas_velo'][0][0],
sav_file['gas_velo'][0][1], sav_file['gas_velo'][0][2],
var_file.rho[sav_file['par_idx'][0][2].astype('int'),
sav_file['par_idx'][0][1].astype('int'),
sav_file['par_idx'][0][0].astype('int')],
var_file.rhop[sav_file['par_idx'][0][2].astype('int'),
sav_file['par_idx'][0][1].astype('int'),
sav_file['par_idx'][0][0].astype('int')]
],
names=
'parid, idx, idy, idz, posx, posy, posz, vx, vy, vz, npar, gasv_x, gasv_y, gasv_z, rho, rhop',
formats=
'int, int,int,int, float,float,float, float,float,float, int, float,float,float, float, float'
)
else:
time = sav_file['time']
DATA_SET = np.core.records.fromarrays(
[
range(0, npar), sav_file['par_idx'][0].astype('int'),
sav_file['par_idx'][1].astype('int'),
sav_file['par_idx'][2].astype('int'),
sav_file['par_pos'][0], sav_file['par_pos'][1],
sav_file['par_pos'][2], sav_file['par_velo'][0],
sav_file['par_velo'][1], sav_file['par_velo'][2],
sav_file['npar'], sav_file['gas_velo'][0],
sav_file['gas_velo'][1], sav_file['gas_velo'][2],
var_file.rho[sav_file['par_idx'][2].astype('int'),
sav_file['par_idx'][1].astype('int'),
sav_file['par_idx'][0].astype('int')],
var_file.rhop[sav_file['par_idx'][2].astype('int'),
sav_file['par_idx'][1].astype('int'),
sav_file['par_idx'][0].astype('int')]
],
names=
'parid, idx, idy, idz, posx, posy, posz, vx, vy, vz, npar, gasv_x, gasv_y, gasv_z, rho, rhop',
formats=
'int, int,int,int, float,float,float, float,float,float, int, float,float,float, float, float'
)
DATA_SET = np.sort(DATA_SET, order=['idx', 'idy', 'idz'])
# calculate GLOBAL DISPERSION in x, y and z direction, also the absolute magnitude
if GLOBAL:
print(
'## Calculating GLOBAL DISPERSION values in x,y,z direction and abs value'
)
mean_vx = np.mean(DATA_SET['vx'])
mean_vy = np.mean(DATA_SET['vy'])
mean_vz = np.mean(DATA_SET['vz'])
SIGMA = {
'SIGMA_o_x':
np.sqrt(npar1 * np.sum((DATA_SET['vx'] - mean_vx)**2)),
'SIGMA_o_y':
np.sqrt(npar1 * np.sum((DATA_SET['vy'] - mean_vy)**2)),
'SIGMA_o_z':
np.sqrt(npar1 * np.sum((DATA_SET['vz'] - mean_vz)**2)),
'SIGMA_o':
np.sqrt(npar1 * np.sum((DATA_SET['vx'] - mean_vx)**2 +
(DATA_SET['vy'] - mean_vy)**2 +
(DATA_SET['vz'] - mean_vz)**2))
}
# calculate GLOBAL DRIFT in x, y and z direction, also the absolute magnitude
print(
'## Calculating GLOBAL DRIFT values in x,y,z direction and abs value'
)
ZETA = {
'ZETA_o_x':
np.sqrt(npar1 * np.sum(
(DATA_SET['vx'] - DATA_SET['gasv_x'])**2)),
'ZETA_o_y':
np.sqrt(npar1 * np.sum(
(DATA_SET['vy'] - DATA_SET['gasv_y'])**2)),
'ZETA_o_z':
np.sqrt(npar1 * np.sum(
(DATA_SET['vz'] - DATA_SET['gasv_z'])**2)),
'ZETA_o':
np.sqrt(npar1 *
np.sum((DATA_SET['vx'] - DATA_SET['gasv_x'])**2 +
(DATA_SET['vy'] - DATA_SET['gasv_y'])**2 +
(DATA_SET['vz'] - DATA_SET['gasv_z'])**2))
}
print('## saving calculated GLOBAL DISPERSION and DRIFT')
io.save(SIGMA, 'sigma_' + file_no, folder=SIM.pc_datadir)
io.save(ZETA, 'zeta_' + file_no, folder=SIM.pc_datadir)
# calculate LOCAL DISPERSION and DRIFT
if LOCAL:
print('## Calculating LOCAL DISPERSION and DRIFT values')
tmp_id = [
DATA_SET[0]['idx'], DATA_SET[0]['idy'], DATA_SET[0]['idz']
]
sigma_l = np.zeros((dim.nx, dim.ny, dim.nz))
zeta_l = np.zeros((dim.nx, dim.ny, dim.nz))
particles_l = []
for particle in DATA_SET:
if [particle['idx'], particle['idy'],
particle['idz']] == tmp_id:
particles_l.append(particle)
else:
np_l = np.size(particles_l)
if np_l != 0:
np1_l = 1. / np_l
mean_vx_l = 0
mean_vy_l = 0
mean_vz_l = 0
sum_s_l = 0
sum_z_l = 0
for entry in particles_l:
mean_vx_l = mean_vx_l + np1_l * entry['vx']
mean_vy_l = mean_vy_l + np1_l * entry['vy']
mean_vz_l = mean_vz_l + np1_l * entry['vz']
for entry in particles_l:
sum_s_l = sum_s_l + (entry['vx'] - mean_vx_l)**2 + (
entry['vy'] - mean_vy_l)**2 + (entry['vz'] -
mean_vz_l)**2
sum_z_l = sum_z_l + (
entry['vx'] - entry['gasv_x'])**2 + (
entry['vy'] - entry['gasv_y'])**2 + (
entry['vz'] - entry['gasv_z'])**2
sigma_l[tmp_id[0]][tmp_id[1]][tmp_id[2]] = np.sqrt(np1_l *
sum_s_l)
zeta_l[tmp_id[0]][tmp_id[1]][tmp_id[2]] = np.sqrt(np1_l *
sum_z_l)
# reset all local variables and lists to the new state (ie towards the newst particle)
tmp_id = [
particle['idx'], particle['idy'], particle['idz']
]
particles_l = []
particles_l.append(particle)
# do this local calculations a last time for the last grid cell
np_l = np.size(particles_l)
np1_l = 1. / np_l
mean_vx_l = 0
mean_vy_l = 0
mean_vz_l = 0
sum_s_l = 0
sum_z_l = 0
for entry in particles_l:
mean_vx_l = mean_vx_l + np1_l * entry['vx']
mean_vy_l = mean_vy_l + np1_l * entry['vy']
mean_vz_l = mean_vz_l + np1_l * entry['vz']
for entry in particles_l:
sum_s_l = sum_s_l + (entry['vx'] - mean_vx_l)**2 + (
entry['vy'] - mean_vy_l)**2 + (entry['vz'] - mean_vz_l)**2
sum_z_l = sum_z_l + (entry['vx'] - entry['gasv_x'])**2 + (
entry['vy'] - entry['gasv_y'])**2 + (entry['vz'] -
entry['gasv_z'])**2
sigma_l[tmp_id[0]][tmp_id[1]][tmp_id[2]] = np.sqrt(np1_l * sum_s_l)
zeta_l[tmp_id[0]][tmp_id[1]][tmp_id[2]] = np.sqrt(np1_l * sum_z_l)
# save sigma, zeta locally and globally to SIM.pc_datadir
print('## saving calculated LOCAL DISPERSION and DRIFT')
io.save(sigma_l,
'sigma_l_' + file_no,
folder=join(SIM.pc_datadir, 'sigma_l'))
io.save(zeta_l,
'zeta_l_' + file_no,
folder=join(SIM.pc_datadir, 'zeta_l'))
## Please keep this lines as a reminder on how to add columns to an record array!
# add colums to DATA_SET fror local zeta and sigma for the individuel particle
#DATA_SET = add_column_to_record_array(DATA_SET, 'zeta_l', zeta_l[DATA_SET['idx'],DATA_SET['idy'],DATA_SET['idz']], dtypes='float', usemask=False, asrecarray=True)
#DATA_SET = add_column_to_record_array(DATA_SET, 'sigma_l', sigma_l[DATA_SET['idx'],DATA_SET['idy'],DATA_SET['idz']], dtypes='float', usemask=False, asrecarray=True)
return True
def __init__(self,
direction='x',
trange=[0, -1],
sim='.',
OVERWRITE=False,
quiet=True,
jump_distance=0.5,
use_existing_pstalk_sav=False):
from os.path import join
from os.path import exists as path_exists
import numpy as np
from scipy.stats import linregress
from pencil.io import load, save, exists
from pencil.read import pstalk as read_pstalk
from pencil.math.derivatives import simple_centered as derivatives_centered
from pencil.backpack import printProgressBar
# .. no pstalk file is found
if not path_exists(join(sim.datadir, 'proc0',
'particles_stalker.dat')):
print(
'?? WARNING: No particles_stalker.dat found for simulation ' +
sim.name + '!! Skipping this run!')
return False
# check if already existing. if, then load it
out_path = join(sim.pc_datadir, 'particle', 'diffusion')
out_name = direction + '_' + str(trange[0]) + '_' + str(trange[1])
# skip if diffusion already exists
if not OVERWRITE and exists(name=out_name, folder=out_path):
self_tmp = load(out_name, folder=out_path)
for key in [a for a in dir(self_tmp) if not a.startswith('__')]:
setattr(self, key, getattr(self_tmp, key))
else:
#### start calculations ####
print('##')
print('## Calculating particle diffusion for "' + sim.name +
'" in "' + sim.path + '"')
print('## reading particle stalker file..')
pstalk = read_pstalk(
sim=sim,
use_existing_pstalk_sav=use_existing_pstalk_sav,
tmin=trange[0],
tmax=trange[1])
grid = sim.grid
dim = sim.dim
# get time range as index for pstalk dataset
argmin = np.abs(pstalk.t - trange[0]).argmin()
if trange[1] < 0.:
argmax = pstalk.t.argmax()
else:
argmax = np.abs(pstalk.t - trange[1]).argmin()
time_range = pstalk.t[argmin:argmax + 1]
# modify time range with time_range[0] == 0 by substracting first time entry from time list
#time_offset = pstalk.t[argmin:argmax][0]
#time_range = pstalk.t[argmin:argmax]-time_offset
print('\n## doing the calculation for ' + direction)
L = getattr(grid, 'L' + direction) # domain size in direction
N = getattr(dim, 'n' + direction) # number grid cells in direction
pos_series = getattr(pstalk, direction + 'p').T[
argmin:argmax +
1] # get position timeseries series for direction for all particles
N_dt = pos_series.shape[0] # get number of time steps available
N_par = pos_series.shape[1] # get number of stalked particles
travel_distance = 0. * pos_series # prepare 'travel distance' array for all particles
mean_travel_dist = np.array(0)
# prepare mean, var and sigma arrays
variance = np.array(0)
sigma = np.array(0)
## calulate travel distances for each particle with corrections for jumps at the boundary
pbar = False
Nt = np.size(pos_series)
for i_t, pos in enumerate(pos_series):
if i_t == 0: continue # skip first time_step
pbar = printProgressBar(i_t, Nt, pbar=pbar)
# calculate the distance dx made in dt for all particles at once
dx = pos - pos_series[i_t - 1]
travel_distance[i_t] = travel_distance[i_t - 1] + dx
# correct for negative jumps
jumps = np.where(dx > jump_distance * L)
travel_distance[i_t][jumps] = travel_distance[i_t][jumps] - L
# correct for positive jumps
jumps = np.where(dx < -jump_distance * L)
travel_distance[i_t][jumps] = travel_distance[i_t][jumps] + L
# calculate mean, variance and sigma for at 'time' i
mean_travel_dist = np.mean(travel_distance, axis=1)
# 1. estimate variance as time series
variance = np.var(travel_distance, axis=1)
sigma = np.sqrt(variance)
# 2. estimate diffusion by using centered derivatives method !!!
diff_dvar = 0.5 * derivatives_centered(time_range, variance)
diffusion_mean = np.mean(diff_dvar)
diffusion_std = np.std(diff_dvar)
# create diffusion object
self.diffusion = diffusion_mean
self.diffusion_error = diffusion_std
self.travel_distance = travel_distance
self.mean_travel_distance = mean_travel_dist
self.timerange = time_range
self.variance = variance
self.sigma = sigma
self.direction = direction
print('~ diffusion = ' + str(self.diffusion))
print('~ diffusion std = ' + str(self.diffusion_error))
print('~ direction = ' + str(self.direction))
try:
print('## saving results in' + join(out_path, out_name))
save(obj=self, name=out_name, folder=out_path)
except:
print("!! Unexpected error:", sys.exc_info()[0])
print("!! Check if you have writing rights.")
raise