def test_DCplot():
"""
DCplot should return an axes object when a DiffSystem is passed
"""
Xr = [[0, .4], [.6, 1]]
X = np.linspace(0, 1, 101)
DC = np.linspace(1, 10, 101) * 1e-14
diffsys = DiffSystem(Xr=Xr, X=X, DC=DC)
ax = DCplot(diffsys, label='test')
assert isinstance(ax, Axes)
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_system():
"""
DiffSystem constructor
"""
# Construct with X, DC
Xr = [[0, .4], [.6, 1]]
X = np.linspace(0, 1, 101)
DC = np.linspace(1, 10, 101) * 1e-14
diffsys = DiffSystem(Xr=Xr, X=X, DC=DC)
assert diffsys.Xr.shape == (diffsys.Np, 2)
assert isinstance(diffsys.name, str)
assert len(diffsys.Dfunc) == diffsys.Np
for i in range(diffsys.Np):
assert len(diffsys.Dfunc[i][0]) == len(diffsys.Dfunc[i][1])
# Construct with Dfunc
diffsys1 = DiffSystem(Xr=Xr, Dfunc=diffsys.Dfunc)
assert diffsys1.Xr.shape == (diffsys1.Np, 2)
assert len(diffsys1.Dfunc) == diffsys1.Np
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_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 DCbias(diffsys, X, deltaD, r=0.3, efunc=None):
"""
This function creates bias for a diffusion coefficients profile
Parameters
----------
diffsys : DiffSystem
Original diffusion coefficients.
X : float
Concentration location which has largest bias.
deltaD : float
Scale of the bias. D *= 10**deltaD is the maximum of bias.
r : float, optional
Bias at X will create smaller bias in range of (X-r, X+r)
efunc : function, optional
Function to create bias on diffusion coefficients.
Default = pydiffusion.utils.efunc
efunc(X, Xf, r)
efunc should return 1 as the maximum when X == Xf,
and return 0 when abs(X-Xf) == r.
Returns
-------
fDbias : DiffSystem
Diffusion coefficients with bias.
"""
Xr, Np, fD = diffsys.Xr, diffsys.Np, diffsys.Dfunc
efunc = efunc_default if efunc is None else efunc
fDbias = []
for i in range(Np):
if X >= Xr[i, 0] and X <= Xr[i, 1]:
Xf = np.linspace(Xr[i, 0], Xr[i, 1], 30)
Df = np.exp(splev(Xf, fD[i]))
eid = np.where((Xf >= X - r) & (Xf <= X + r))[0]
for j in eid:
Df[j] *= 10**(deltaD * efunc(X, Xf[j], r))
fDbias += [splrep(Xf, np.log(Df))]
else:
fDbias += [fD[i]]
return DiffSystem(Xr, fDbias)
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
def Dmodel(profile, time, Xspl=None, Xlim=[], output=True, name=''):
"""
Given the diffusion profile and diffusion time, modeling the diffusion
coefficients for each phase. Please do not close any plot window during
the modeling process.
Dmodel() is the second step of the forward simulation analysis (FSA).
Parameters
----------
profile : DiffProfile
Diffusion profile. Multiple phase profile must be after datasmooth to
identify phase boundaries.
time : float
Diffusion time in seconds.
Xspl : list, optional
If Xspl is given, Dmodel will be done automatically.
Xlim : list, optional
Left and Right limit of diffusion coefficients. Xlim is also passed to
SF function to calculate diffusion coefficients initially.
output : bool, optional
Plot Dmodel result or not. Can be False only if Xspl is given.
name : str, optional
Name of the output DiffSystem
Examples
--------
After datasmooth(), a initial diffusion coefficients will be established before
FSA():
>>> ds = datasmooth(exp)
>>> dsys = Dmodel(ds, time)
"""
if not isinstance(Xlim, list):
raise TypeError('Xlim must be a list')
if len(Xlim) != 2 and Xlim != []:
raise ValueError(
'Xlim must be an empty list or a list with length = 2')
dis, X = profile.dis, profile.X
# If input Xlim doesn't follow trend of X, correct it
if Xlim != [] and (X[-1] - X[0]) * (Xlim[1] - Xlim[0]) < 0:
Xlim = Xlim[::-1]
# Initial set-up of Xr (phase boundaries)
Xlim = [X[0], X[-1]] if Xlim == [] else Xlim
DC = SF(profile, time, Xlim)
Xr = np.array(Xlim, dtype=float)
for i in range(len(dis) - 1):
if dis[i] == dis[i + 1]:
Xr = np.insert(Xr, -1, [X[i], X[i + 1]])
Np = len(Xr) // 2
Xr.sort()
Xr = Xr.reshape(Np, 2)
fD = [0] * Np
ita_start()
# Choose Spline or UnivariateSpline
if Xspl is None or output:
ax = plt.figure().gca()
ax.semilogy(X, DC, 'b.')
ax.set_title('Sauer-Freise result')
ax.set_xlabel('Mole fraction')
ax.set_ylabel('Diffusion Coefficients ' + '$(m^2/s)$')
plt.tight_layout()
ipt = ask_input(
'Use Spline (y) or UnivariateSpline (n) to model diffusion coefficients? [y]\n'
)
choice = False if 'N' in ipt or 'n' in ipt else True
# Xspl provided, no need for manually picking Xspl
if Xspl is not None:
if len(Xspl) != Np:
raise ValueError('Xspl must has a length of phase number')
for i in range(Np):
if Xr[i, 1] > Xr[i, 0]:
pid = np.where((X >= Xr[i, 0]) & (X <= Xr[i, 1]))[0]
else:
pid = np.where((X <= Xr[i, 0]) & (X >= Xr[i, 1]))[0]
# Spline
if choice:
try:
Dp = Dpcalc(X, DC, Xspl[i])
fD[i] = Dfunc_spl(Xspl[i], Dp)
except (ValueError, TypeError) as error:
ita_finish()
raise error
# UnivariateSpline
else:
try:
fD[i] = Dfunc_uspl(X, DC, Xspl[i], Xr[i])
except (ValueError, TypeError) as error:
ita_finish()
raise error
print('DC modeling finished, Xspl info:')
print(Xspl)
if output:
ax.cla()
ax.set_title('DC Modeling Result')
ax.semilogy(X, DC, 'b.')
for i in range(Np):
Xf = np.linspace(Xr[i, 0], Xr[i, 1], 30)
ax.semilogy(Xf, np.exp(splev(Xf, fD[i])), 'r-')
ax.set_xlabel('Mole fraction')
ax.set_ylabel('Diffusion Coefficients ' + '$(m^2/s)$')
plt.tight_layout()
plt.pause(0.1)
plt.show()
ita_finish()
return DiffSystem(Xr, Dfunc=fD, Xspl=Xspl)
Xspl = [0] * Np if choice else None
for i in range(Np):
if Xr[i, 1] > Xr[i, 0]:
pid = np.where((X >= Xr[i, 0]) & (X <= Xr[i, 1]))[0]
else:
pid = np.where((X <= Xr[i, 0]) & (X >= Xr[i, 1]))[0]
# Spline
if choice:
while True:
DC_real = [
k for k in DC[pid] if not np.isnan(k) and not np.isinf(k)
]
DCmean = np.mean(DC_real)
for k in pid:
if np.isnan(DC[k]) or np.isinf(
DC[k]) or abs(np.log10(DC[k] / DCmean)) > 5:
DC[k] = DCmean
ax.cla()
ax.semilogy(X[pid], DC[pid], 'b.')
ax.set_xlabel('Mole fraction')
ax.set_ylabel('Diffusion Coefficients ' + '$(m^2/s)$')
ax.set_title('Phase %i' % (i + 1))
plt.draw()
msg = '# of spline points: 1 (constant), 2 (linear), >2 (spline)\n'
ipt = ask_input(msg + 'input # of spline points\n')
ax.set_title('Phase %i: Select %i points of Spline' %
(i + 1, int(ipt)))
plt.pause(0.1)
Xp = np.array(plt.ginput(int(ipt)))[:, 0]
try:
Dp = Dpcalc(X, DC, Xp)
fD[i] = Dfunc_spl(Xp, Dp)
except (ValueError, TypeError) as error:
ita_finish()
raise error
Xspl[i] = list(Xp)
Xf = np.linspace(Xr[i, 0], Xr[i, 1], 30)
ax.semilogy(Xf, np.exp(splev(Xf, fD[i])), 'r-', lw=2)
plt.draw()
ipt = ask_input('Continue to next phase? [y]')
redo = False if 'N' in ipt or 'n' in ipt else True
if redo:
break
# UnivariateSpline
else:
while True:
ax.cla()
ax.semilogy(X[pid], DC[pid], 'b.')
ax.set_xlabel('Mole fraction')
ax.set_ylabel('Diffusion Coefficients ' + '$(m^2/s)$')
#ax.set_title('Phase %i' % (i+1))
ax.set_title(
'Phase %i: Select 2 boundaries for UnivariateSpline' %
(i + 1))
plt.draw()
plt.pause(0.1)
Xp = np.array(plt.ginput(2))[:, 0]
#ipt = ask_input('input 2 boundaries for UnivariateSpline\n')
#Xp = np.array([float(x) for x in ipt.split()])
try:
fD[i] = Dfunc_uspl(X, DC, Xp, Xr[i])
except (ValueError, TypeError) as error:
ita_finish()
raise error
Xf = np.linspace(Xr[i, 0], Xr[i, 1], 30)
ax.semilogy(Xf, np.exp(splev(Xf, fD[i])), 'r-', lw=2)
plt.draw()
ipt = ask_input('Continue to next phase? [y]')
redo = False if 'N' in ipt or 'n' in ipt else True
if redo:
break
ita_finish()
print('DC modeling finished, Xspl info:')
print(Xspl)
ax.cla()
ax.set_title('DC Modeling Result')
ax.semilogy(X, DC, 'b.')
for i in range(Np):
Xf = np.linspace(Xr[i, 0], Xr[i, 1], 30)
ax.semilogy(Xf, np.exp(splev(Xf, fD[i])), 'r-')
ax.set_xlabel('Mole fraction')
ax.set_ylabel('Diffusion Coefficients ' + '$(m^2/s)$')
plt.tight_layout()
plt.pause(0.1)
plt.show()
if name == '':
name = profile.name + '_%.1fh_Dmodeled' % (time / 3600)
return DiffSystem(Xr, Dfunc=fD, Xspl=Xspl, name=name)
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
def read_csv(filename, Xlim=None, name=''):
"""
Read diffusion data from csv file.
Parameters
----------
filename : str
csv file path.
Xlim : list (length of 2), optional
A list to determine the two ends solubilities.
name : str, optional
Name the output DiffProfile and DiffSystem
Returns
-------
profile : DiffProfile
output DiffProfile object.
diffsys : DiffSystem
output DiffSystem object.
Examples
--------
Both profile and diffusivity data:
>>> profile, dsys = read_csv('data.csv')
Profile data only:
>>> profile, _ = read_csv('data.csv')
"""
data = pd.read_csv(filename)
if 'X' not in data.columns:
raise ValueError('No column X in csv file')
X = np.array(data['X'])
# Auto rename
if name == '':
if '/' in filename:
r = filename.rfind('/')
elif '\\' in filename:
r = filename.rfind('\\')
else:
r = -1
if filename.endswith('.csv'):
name = filename[r + 1:-4]
else:
name = filename[r + 1:]
if 'dis' in data.columns:
dis = np.array(data['dis'])
If = []
XIf = []
for i in range(len(dis) - 1):
if dis[i] == dis[i + 1]:
If += [dis[i]]
XIf += [X[i], X[i + 1]]
profile = DiffProfile(dis, X, If, name=name)
if Xlim is None:
XIf = np.array([X[0]] + XIf + [X[-1]])
else:
XIf = np.array([Xlim[0]] + XIf + [Xlim[-1]])
Xr = XIf.reshape((len(XIf) // 2, 2))
if 'DC' in data.columns:
DC = np.array(data['DC'])
else:
X = DC = None
if Xr is not None:
diffsys = DiffSystem(Xr, X=X, DC=DC, name=name)
return profile, diffsys