def test_automesh():
"""
automesh should return a meshed array whose length is within its range.
"""
diffsys = DiffSystem(Xr=[0, 1], X=[0, 1], DC=[1e-14, 1e-13])
dis = mesh(0, 1000, 201)
profile_init = step(dis, 500, diffsys)
time = 200 * 3600
profile = sphSim(profile_init, diffsys, time)
dism = automesh(profile, diffsys, n=[300, 400])
assert len(dism) >= 300 and len(dism) <= 400
def test_SFplot():
"""
SFplot should return an axes object when a DiffProfile and time is passed
"""
diffsys = DiffSystem(Xr=[0, 1], X=[0, 1], DC=[1e-14, 1e-13])
dis = mesh(0, 1000, 201)
profile_init = step(dis, 500, diffsys)
time = 200 * 3600
profile = sphSim(profile_init, diffsys, time)
ax = SFplot(profile, time, Xlim=[0, 1], label='test')
assert isinstance(ax, Axes)
def test_dispfunc():
"""
disfunc and profilefunc should give functions to copy profile data.
"""
diffsys = DiffSystem(Xr=[0, 1], X=[0, 1], DC=[1e-14, 1e-13])
dis = mesh(0, 1000, 201)
profile_init = step(dis, 500, diffsys)
time = 200 * 3600
profile = sphSim(profile_init, diffsys, time)
fX = profilefunc(profile)
fdis = disfunc(profile.dis, profile.X)
assert np.all(abs(splev(dis, fX) - profile.X) < 0.01)
assert np.all(abs(splev(profile.X, fdis) - dis) < 0.1)
def test_sphsim():
"""
Single-phase system simulation.
Offset of the simulated matano plane should be very small.
"""
diffsys = DiffSystem(Xr=[0, 1], X=[0, 1], DC=[1e-14, 1e-14])
dis = mesh(0, 1000, 201)
profile_init = step(dis, 500, diffsys)
time = 200 * 3600
profile_final = sphSim(profile_init, diffsys, time)
mpi = matanocalc(profile_init, [0, 1])
mpf = matanocalc(profile_final, [0, 1])
assert isinstance(profile_final, DiffProfile)
assert len(profile_final.If) == diffsys.Np + 1
assert abs(mpi - mpf) < 1
def test_mphsim():
"""
Multiple-phase system simulation.
Offset of the simulated matano plane should be very small.
"""
Xr = [[0, .4], [.6, 1]]
X = np.linspace(0, 1, 101)
DC = np.linspace(1, 2, 101) * 1e-14
diffsys = DiffSystem(Xr=Xr, X=X, DC=DC)
dis = mesh(0, 1000, 201)
profile_init = step(dis, 500, diffsys)
time = 200 * 3600
profile_final = mphSim(profile_init, diffsys, time)
mpi = matanocalc(profile_init, [0, 1])
mpf = matanocalc(profile_final, [0, 1])
assert isinstance(profile_final, DiffProfile)
assert len(profile_final.If) == diffsys.Np + 1
assert abs(mpi - mpf) < 1
def FSA(profile_exp,
profile_sm,
diffsys,
time,
Xlim=[],
n=[400, 500],
w=None,
f=None,
alpha=0.3,
name=''):
"""
Forward Simulation Analysis
Extract diffusion coefficients based on a diffusion profile.
Please do not close any plot window during the FSA process.
This is the final step of FSA.
Parameters
----------
profile_exp : DiffProfile
Experimental diffusion profile, used for comparison with simulation
results.
profile_sm : DiffProfile
Diffusion profile after data smooth on experimental profile.
diffsys : DiffSystem
Diffusion coefficients
time : float
Diffusion time in seconds
Xlim : list (float), optional
Passed to 'pydiffusion.Dtools.SF', 'pydiffusion.utils.step'.
Indicates the left and right concentration limits for calculation.
Default value = [profile.X[0], profile.X[-1]].
n : list. optional
Passed to 'pydiffusion.utils.automesh'.
Meshing number range, default = [400, 500].
w : list, optional
Weights of each phase to calculate error.
Passed to 'pydiffusion.utils.error_profile'.
f : function of Meshing
Keyword argument of automesh()
alpha : float
Keyword argument of automesh()
name : str, optional
Name the output DiffProfile
Returns
-------
profile_sim : DiffProfile
Simulated diffusion profile after FSA.
diffsys_sim : DiffSystem
Calculated diffusion efficients by FSA.
Examples
--------
After datasmooth() and Dmodel(), FSA can be performed to calculate accurate diffusion coefficients:
>>> ds = datasmooth(exp)
>>> dsys = Dmodel(ds, time)
>>> fsa = FSA(exp, ds, dsys, time)
"""
# Create step profile on meshed grids
dism = automesh(profile=profile_sm, diffsys=diffsys, n=n, f=f, alpha=alpha)
matano = matanocalc(profile_sm, Xlim)
if Xlim == [] and profile_sm.X[-1] < profile_sm.X[0]:
profile_init = step(dism, matano, diffsys,
[diffsys.Xr[-1, 1], diffsys.Xr[0, 0]])
else:
profile_init = step(dism, matano, diffsys, Xlim)
# Determine the stop criteria of forward simulations
error_sm = error_profile(profile_sm, profile_exp)
ipt = input(
'Default error = %.6f\nInput the stop criteria of error: [%.6f]\n' %
(error_sm, error_sm * 2))
error_stop = error_sm * 2 if ipt == '' else float(ipt)
# If there is no Xspl info in diffsys, use Phase Mode
# else: ask if use Phase or Point Mode
if diffsys.Xspl is not None:
ipt = input(
'Use Phase Mode? [n]\n(The shape of diffusivity curve does not change)\n'
)
pp = False if 'y' in ipt or 'Y' in ipt else True
else:
pp = False
if name == '':
name = profile_exp.name + '_FSA'
# Diffusion coefficients used for forward simulations
diffsys_sim = DiffSystem(diffsys.Xr,
diffsys.Dfunc,
Xspl=diffsys.Xspl,
name=name)
# Plot FSA status
fig = plt.figure('FSA', figsize=(16, 6))
ax1, ax2 = fig.add_subplot(121), fig.add_subplot(122)
profileplot(profile_exp,
ax1,
ls='none',
marker='o',
c='b',
fillstyle='none')
profileplot(profile_sm, ax1, ls='-', c='g', lw=1)
SFplot(profile_sm, time, Xlim, ax2, ls='none', c='b', marker='.')
DCplot(diffsys_sim, ax2, ls='-', c='r', lw=2)
plt.draw()
plt.tight_layout()
plt.pause(0.1)
n_sim = 0
while True:
# Simulation
n_sim += 1
profile_sim = mphSim(profile_init, diffsys_sim, time, name=name)
error_sim = error_profile(profile_sim, profile_exp, w)
print('Simulation %i, error = %f(%f)' % (n_sim, error_sim, error_stop))
# Plot simulation results
ax1.cla()
ax2.cla()
profileplot(profile_exp,
ax1,
ls='none',
marker='o',
c='b',
fillstyle='none')
profileplot(profile_sm, ax1, ls='-', c='g', lw=1)
profileplot(profile_sim, ax1, ls='-', c='r', lw=2)
SFplot(profile_sm, time, Xlim, ax2, ls='none', c='b', marker='.')
DCplot(diffsys_sim, ax2, ls='-', c='r', lw=2)
plt.draw()
plt.tight_layout()
# DC adjust
Dfunc_adjust = [0] * diffsys_sim.Np
# If error > stop criteria, continue simulation by auto DC adjustment
if error_sim > error_stop:
for ph in range(diffsys_sim.Np):
try:
Dfunc_adjust[ph] = Dadjust(profile_sm, profile_sim,
diffsys_sim, ph, pp)
except (ValueError, TypeError) as error:
ita_finish()
raise error
diffsys_sim.Dfunc = Dfunc_adjust
# If error < stop criteria or simulate too many times
if error_sim <= error_stop or n_sim > 9:
ita_start()
# Ask if exit
ipt = ask_input('Satisfied with FSA? [n]')
if 'y' in ipt or 'Y' in ipt:
ita_finish()
break
# If use Point Mode
if diffsys_sim.Xspl is not None:
ipt = ask_input('Use Point Mode (y) or Phase Mode (n)? [y]')
pp = False if 'n' in ipt or 'N' in ipt else True
if pp:
for ph in range(diffsys_sim.Np):
try:
Dfunc_adjust[ph] = Dadjust(profile_sm, profile_sim,
diffsys_sim, ph, pp)
except (ValueError, TypeError) as error:
ita_finish()
raise error
diffsys_sim.Dfunc = Dfunc_adjust
DCplot(diffsys_sim, ax2, ls='-', c='m', lw=2)
plt.draw()
plt.pause(0.1)
ita_finish()
continue
# Phase Mode, ask if use manual input for each phase
pp = False
ipt = input('Phase Mode\nManually input for each phase? [n]')
manual = True if 'y' in ipt or 'Y' in ipt else False
for ph in range(diffsys_sim.Np):
if manual:
ipt = input(
'Input deltaD for phase # %i:\n(DC = DC * 10^deltaD, default deltaD = auto)\n'
% (ph + 1))
deltaD = float(ipt) if ipt != '' else None
else:
deltaD = None
try:
Dfunc_adjust[ph] = Dadjust(profile_sm, profile_sim,
diffsys_sim, ph, pp, deltaD)
except (ValueError, TypeError) as error:
ita_finish()
raise error
# Apply the adjustment to diffsys_sim
diffsys_sim.Dfunc = Dfunc_adjust
DCplot(diffsys_sim, ax2, ls='-', c='m', lw=2)
plt.draw()
plt.pause(0.1)
ita_finish()
return profile_sim, diffsys_sim
import numpy as np
import matplotlib.pyplot as plt
import pandas as pd
from pydiffusion.core import DiffSystem
from pydiffusion.utils import step, mesh
from pydiffusion.simulation import mphSim
from pydiffusion.plot import profileplot, DCplot
from pydiffusion.io import read_csv, save_csv
# Create diffusion system with constant DC
diffsys = DiffSystem(Xr=[0, 1], X=[0, 1], DC=[1e-14, 1e-14], name='Constant D')
# Create initial step profile
dis = mesh(0, 1000, 501)
profile_init = step(dis, 500, diffsys, name='Intitial step profile')
fig = plt.figure(figsize=(16, 6))
ax1, ax2 = fig.add_subplot(121), fig.add_subplot(122)
ax1.set_title('Diffusion Coefficients', fontsize=15)
ax2.set_title('Initial Step Profile', fontsize=15)
DCplot(diffsys, ax1)
profileplot(profile_init, ax2)
# Diffusion simulation using the setups
time = 200 * 3600
profile_final = mphSim(profile_init, diffsys, time)
ax = profileplot(profile_init, ls='--')
profileplot(profile_final, ax, c='r')
# Read diffusion coefficients data of Ni-Mo system
from pydiffusion.simulation import ErrorAnalysis
from pydiffusion.plot import DCplot, profileplot
# Read data, create bias
profile_fsa, diffsys_TiZr = read_csv('examples/data/TiZr.csv', [0, 1])
profile_exp, _ = read_csv('examples/data/TiZr_exp.csv')
diffsys_bias = DCbias(diffsys_TiZr, 0.2, 0.1)
ax = DCplot(diffsys_TiZr, label='original')
DCplot(diffsys_bias, ax, c='r', ls='--', label='bias')
plt.pause(1.0)
# Error analysis with low accuracy
dism = automesh(profile_fsa, diffsys_TiZr, [300, 350])
mp = matanocalc(profile_fsa, [0, 1])
profile_init = step(dism, mp, diffsys_TiZr)
time = 100 * 3600
error_result = ErrorAnalysis(profile_exp,
profile_init,
diffsys_TiZr,
time,
loc=3,
accuracy=1e-2,
output=True)
fig = plt.figure(figsize=(16, 6))
ax1, ax2 = fig.add_subplot(121), fig.add_subplot(122)
DCplot(diffsys_TiZr, ax1, error_result)
profileplot(profile_fsa, ax2, error_result)
profileplot(profile_exp, ax2, marker='o', ls='none', fillstyle='none')
plt.pause(1.0)