class AnalysisMixins_test(unittest.TestCase):
"""Path to sample Data File"""
datadir = path.join(pth, "sample-data")
def setUp(self):
x_data = np.linspace(-10, 10, 101)
y_data = 0.01 * x_data**2 + 0.3 * x_data - 2
y_data *= np.random.normal(size=101, loc=1.0, scale=0.01)
x_data += np.random.normal(size=101, scale=0.02)
self.data = Data(x_data, y_data, column_headers=["X", "Y"])
self.data.setas = "xy"
def test_cuve_fit(self):
for output, fmt in zip(["fit", "row", "full", "dict", "data"],
[tuple, np.ndarray, tuple, dict, Data]):
res = self.data.curve_fit(fit, p0=[0.02, 0.2, 2], output=output)
self.assertTrue(
isinstance(res, fmt),
"Failed to get expected output from curve_fit for {} (got {})".
format(output, type(res)))
def test_lmfit(self):
for output, fmt in zip(["fit", "row", "full", "dict", "data"],
[tuple, np.ndarray, tuple, dict, Data]):
res = self.data.lmfit(fit, p0=[0.02, 0.2, 2], output=output)
self.assertTrue(
isinstance(res, fmt),
"Failed to get expected output from lmfit for {} (got {})".
format(output, type(res)))
def test_odr(self):
for output, fmt in zip(["fit", "row", "full", "dict", "data"],
[tuple, np.ndarray, tuple, dict, Data]):
res = self.data.odr(fit, p0=[0.02, 0.2, 2], output=output)
self.assertTrue(
isinstance(res, fmt),
"Failed to get expected output from idr for {} (got {})".
format(output, type(res)))
def test_differential_evolution(self):
for output, fmt in zip(["fit", "row", "full", "dict", "data"],
[tuple, np.ndarray, tuple, dict, Data]):
res = self.data.differential_evolution(fit,
p0=[0.02, 0.2, 2],
output=output)
self.assertTrue(
isinstance(res, fmt),
"Failed to get expected output from differential_evolution for {} (got {})"
.format(output, type(res)))
from numpy import linspace, ones_like
from numpy.random import normal
B = linspace(2, 100, 26)
params = [12.5, 0.75, 1e3]
G = SF.fluchsSondheimer(B, *params) + normal(size=len(B), scale=5e-5)
dG = ones_like(B) * 5e-5
d = Data(
B,
G,
dG,
setas="xye",
column_headers=["Thickness (nm)", "Conductance", "dConductance"],
)
d.curve_fit(SF.fluchsSondheimer, p0=params, result=True, header="curve_fit")
d.setas = "xye"
d.lmfit(SF.FluchsSondheimer, p0=params, result=True, header="lmfit")
d.setas = "xyeyy"
d.plot(fmt=["r.", "b-", "g-"])
d.annotate_fit(SF.fluchsSondheimer,
x=0.2,
y=0.6,
fontdict={
"size": "x-small",
"color": "blue"
})
d.annotate_fit(
# Make some data
T = logspace(log10(200), log10(350), 51)
params = (1e16, 0.5, 150)
noise = 0.5
R = vftEquation(T, *params) * normal(size=len(T), scale=noise, loc=1.0)
dR = vftEquation(T, *params) * noise
d = Data(T, R, dR, setas="xy.", column_headers=["T", "Rate"])
# Plot the data points.
d.plot(fmt="r.", label="Data Points")
# Turn on the sigma column (error bars look messy on plot due to logscale)
d.setas[2] = "e"
# Curve_fit on its own
d.curve_fit(vftEquation, p0=params, result=True, header="curve_fit")
# lmfit uses some guesses
p0 = params
d.lmfit(VFTEquation, result=True, header="lmfit")
# Plot these results too
d.setas = "x..yy"
d.plot(fmt=["b-", "g-"])
# Annotate the graph
d.annotate_fit(
vftEquation,
x=0.25,
y=0.35,
fontdict={
"size": "x-small",
"""Function to define a plane"""
return c - (coord[0] * a + coord[1] * b)
coeefs = [1, -0.5, -1]
col = linspace(-10, 10, 8)
X, Y = meshgrid(col, col)
Z = plane((X, Y), *coeefs) + normal(size=X.shape, scale=2.0)
d = Data(
column_stack((X.ravel(), Y.ravel(), Z.ravel())),
filename="Fitting a Plane",
setas="xyz",
)
d.column_headers = ["X", "Y", "Z"]
d.figure(projection="3d")
d.plot_xyz(plotter="scatter")
popt, pcov = d.curve_fit(plane, [0, 1], 2, result=True)
d.setas = "xy.z"
d.plot_xyz(linewidth=0, cmap=cmap.jet)
txt = "$z=c-ax+by$\n"
txt += "\n".join(
[d.format("plane:{}".format(k), latex=True) for k in ["a", "b", "c"]])
ax = plt.gca(projection="3d")
ax.text(15, 5, -50, txt)
d.draw()
"""Test langevin fitting."""
from Stoner import Data
from Stoner.analysis.fitting.models.generic import Lorentzian_diff, lorentzian_diff
from numpy import linspace, ones_like
from numpy.random import normal
from copy import copy
x = linspace(-1.0, 1.0, 101)
params = [1, 0.1, -0.25]
y = lorentzian_diff(x, *params) + normal(size=len(x), scale=0.5)
dy = ones_like(x) * 5e-3
d = Data(x, y, dy, setas="xye", column_headers=["Time", "Signal", "dM"])
d.curve_fit(lorentzian_diff, p0=copy(params), result=True, header="curve_fit")
d.setas = "xye"
d.lmfit(Lorentzian_diff, result=True, header="lmfit", prefix="lmfit")
d.setas = "xyeyy"
d.plot(fmt=["r+", "b-", "g-"])
d.annotate_fit(
lorentzian_diff,
x=0.6,
y=0.2,
fontdict={"size": "x-small", "color": "blue"},
mode="eng",
)
Ms = 1714
Tc = 1046
M = where(T > 300, nan,
blochLaw(T, Ms, Tc) + normal(scale=Ms / 200, size=len(T)))
dM = ones_like(T) * Ms / 200
d = Data(T,
M,
dM,
column_headers=["Temperature", "Magnetization", "dM"],
setas="xye")
d.curve_fit(
blochLaw,
p0=[1500, 1500],
result=True,
header="curve_fit",
prefix="curve_fit",
bounds=lambda x, r: not isnan(r.y),
)
d.lmfit(
BlochLaw,
result=True,
header="lmfit",
prefix="lmfit",
bounds=lambda x, r: not isnan(r.y),
)
d.setas = "xyeyy"
d.plot(fmt=["r.", "b-", "g-"])
"""USe curve_fit to fit a straight line."""
from Stoner import Data
def linear(x, m, c):
"""Straight line function."""
return m * x + c
d = Data("curve_fit_data.dat", setas="xye")
d.plot(fmt="ro")
fit = d.curve_fit(linear,
result=True,
replace=False,
header="Fit",
output="report")
d.setas = "x..y"
d.plot(fmt="b-")
d.annotate_fit(linear)
d.draw()
print(fit.fit_report())
"""Example of PowerLaw Fit.""" from Stoner import Data import Stoner.Fit as SF from numpy import linspace from numpy.random import normal # Make some data T = linspace(50, 500, 101) R = SF.powerLaw(T, 1e-2, 0.6666666) * normal(size=len(T), scale=0.1, loc=1.0) d = Data(T, R, setas="xy", column_headers=["T", "Rate"]) # Curve_fit on its own d.curve_fit(SF.powerLaw, p0=[1, 0.5], result=True, header="curve_fit") d.setas = "xyy" d.plot(fmt=["r.", "b-"]) d.annotate_fit(SF.powerLaw, x=0.5, y=0.25) # lmfit using lmfit guesses fit = SF.PowerLaw() p0 = fit.guess(R, x=T) d.lmfit(fit, p0=p0, result=True, header="lmfit") d.setas = "x..y" d.plot(fmt="g-") d.annotate_fit(SF.PowerLaw, x=0.5, y=0.05, prefix="PowerLaw") d.title = "Powerlaw Test Fit" d.ylabel = "Rate" d.xlabel = "Temperature (K)"
from copy import copy
B = linspace(1e3, 5e4, 51)
params = [2.2, 1e5, 2e2]
G = SF.kittelEquation(B, *params) + normal(size=len(B), scale=5e7)
dG = ones_like(B) * 5e7
d = Data(
B,
G,
dG,
setas="xye",
column_headers=["Field $Oe$", r"$\nu (Hz)$", r"\delta $\nu (Hz)$"],
)
d.curve_fit(SF.kittelEquation, p0=copy(params), result=True, header="curve_fit")
fit = SF.KittelEquation()
p0 = fit.guess(G, x=B)
d.lmfit(fit, p0=p0, result=True, header="lmfit")
d.setas = "xyeyy"
d.plot(fmt=["r.", "b-", "g-"])
d.annotate_fit(
SF.kittelEquation,
x=0.5,
y=0.25,
fontdict={"size": "x-small", "color": "blue"},
mode="eng",
# Make some data
T = logspace(log10(200), log10(350), 51)
params = (1e16, 0.5, 150)
noise = 0.5
R = vftEquation(T, *params) * normal(size=len(T), scale=noise, loc=1.0)
dR = vftEquation(T, *params) * noise
d = Data(T, R, dR, setas="xy.", column_headers=["T", "Rate"])
# Plot the data points.
d.plot(fmt="r.", label="Data Points")
# Turn on the sigma column (error bars look messy on plot due to logscale)
d.setas[2] = "e"
# Curve_fit on its own
d.curve_fit(vftEquation, p0=params, result=True, header="curve_fit")
# lmfit uses some guesses
p0 = params
d.lmfit(VFTEquation, p0=p0, result=True, header="lmfit")
# Plot these results too
d.setas = "x..yy"
d.plot(fmt=["b-", "g-"])
# Annotate the graph
d.annotate_fit(
vftEquation,
x=0.25,
y=0.35,
fontdict={"size": "x-small", "color": "blue"},
mode="eng",
r_col = r_col[0]
break
else:
r_col = select_col(d, "Select column for resistance data :")
rho0 = d.min(r_col)[0]
A = rho0 * 40
thetaD = 300.0
p0 = [thetaD, rho0, A]
print("Initial guesses: {}".format(p0))
d.del_rows(0, lambda x, r: np.any(np.isnan(r)))
popt, pcov = d.curve_fit(bg_wrapper,
xcol=t_col,
ycol=r_col,
p0=p0,
absolute_sigma=False)
perr = np.sqrt(np.diag(pcov))
labels = [r"\theta_D", r"\rho_0", r"A"]
units = ["K", r"\Omega m", r"\Omega m"]
annotation = [
"${}$: {}\n".format(l, format_error(v, e, latex=True, mode="eng", units=u))
for l, v, e, u in zip(labels, popt, perr, units)
]
annotation = "\n".join(annotation)
popt = np.append(popt, 5)
T = d.column(t_col)
d.add_column(blochGrueneisen(T, *popt), header=r"Bloch")
"""Example of Arrhenius Fit."""
from Stoner import Data
import Stoner.Fit as SF
from numpy import linspace, ceil, log10, abs
from numpy.random import normal
# Make some data
T = linspace(200, 350, 101)
R = SF.arrhenius(T + normal(size=len(T), scale=3.0, loc=0.0), 1e6, 0.5)
E = 10 ** ceil(log10(abs(R - SF.arrhenius(T, 1e6, 0.5))))
d = Data(T, R, E, setas="xye", column_headers=["T", "Rate"])
# Curve_fit on its own
d.curve_fit(SF.arrhenius, p0=(1e6, 0.5), result=True, header="curve_fit")
d.setas = "xyey"
d.plot(fmt=["r.", "b-"])
d.annotate_fit(
SF.arrhenius,
x=0.5,
y=0.5,
mode="eng",
fontdict={"size": "x-small", "color": "blue"},
)
# lmfit using lmfit guesses
fit = SF.Arrhenius()
d.setas = "xye"
d.lmfit(fit, result=True, header="lmfit")
d.setas = "x...y"
d.plot(fmt="g-")
d.annotate_fit(
"""Example of nDimArrhenius Fit."""
from Stoner import Data
import Stoner.Fit as SF
from numpy import linspace, ones_like
from numpy.random import normal
# Make some data
V = linspace(-4, 4, 1001)
I = SF.simmons(V, 2500, 5.2, 15.0) + normal(size=len(V), scale=100e-9)
dI = ones_like(V) * 100e-9
d = Data(V, I, dI, setas="xye", column_headers=["Bias", "Current", "Noise"])
d.curve_fit(SF.simmons, p0=[2500, 5.2, 15.0], result=True, header="curve_fit")
d.setas = "xyey"
d.plot(fmt=["r.", "b-"])
d.annotate_fit(
SF.simmons,
x=0.25,
y=0.25,
prefix="simmons",
fontdict={"size": "x-small", "color": "blue"},
)
d.setas = "xye"
fit = SF.Simmons()
p0 = [2500, 5.2, 15.0]
d.lmfit(SF.Simmons, p0=p0, result=True, header="lmfit")
d.setas = "x...y"
d.plot(fmt="g-")
d.annotate_fit(
r=normal(loc=3.0,size=250,scale=0.5) x,y,z=transform(r,q,p) x+=3.0 y-=4.0 z+=2.0 # Construct the DataFile object d=Data(column_stack((x,y,z)),setas="xyz",filename="Best fit sphere") d.template.fig_width=5.2 d.template.fig_height=5.0 # Square aspect ratio d.plot_xyz(plotter="scatter") #curve_fit does the hard work popt,pcov=d.curve_fit(sphere,(0,1,2),zeros_like(d.x)) # This manually constructs the best fit sphere a,b,c,r=popt p=linspace(-pi/2,pi/2,16) q=linspace(-pi,pi,31) P,Q=meshgrid(p,q) R=ones_like(P)*r x,y,z=transform(R,Q,P) x+=a y+=b z+=c ax=plt.gca(projection="3d") ax.plot_surface(x,y,z,rstride=1,cstride=1,color=(1.0,0.0,0.0,0.25),linewidth=0) plt.draw()
"""Example of nDimArrhenius Fit."""
from Stoner import Data
import Stoner.Fit as SF
from numpy import linspace, ones_like
from numpy.random import normal
# Make some data
V = linspace(-4, 4, 101)
I = SF.simmons(V, 2500, 3.2, 15.0) + normal(size=len(V), scale=5e-7)
dI = ones_like(V) * 500e-9
p0 = p0 = [2500, 3, 10.0]
d = Data(V, I, dI, setas="xye", column_headers=["Bias", "Current", "Noise"])
d.curve_fit(SF.simmons, p0=p0, result=True, header="curve_fit", maxfev=2000)
d.setas = "xyey"
d.plot(fmt=["r,", "b-"], capsize=1)
d.annotate_fit(
SF.simmons,
x=0.25,
y=0.25,
prefix="simmons",
fontdict={
"size": "x-small",
"color": "blue"
},
)
d.setas = "xye"
fit = SF.Simmons()
"""Example of nDimArrhenius Fit."""
from Stoner import Data
import Stoner.Fit as SF
from numpy import linspace, ones_like
from numpy.random import normal
# Make some data
V = linspace(-10, 10, 1000)
I = SF.bdr(V, 2.5, 3.2, 0.3, 15.0, 1.0) + normal(size=len(V), scale=1.0e-3)
dI = ones_like(V) * 1.0e-3
# Curve fit
d = Data(V, I, dI, setas="xye", column_headers=["Bias", "Current", "Noise"])
d.curve_fit(SF.bdr, p0=[2.5, 3.2, 0.3, 15.0, 1.0], result=True, header="curve_fit")
d.setas = "xyey"
d.plot(fmt=["r.", "b-"])
d.annotate_fit(
SF.bdr, x=0.6, y=0.05, prefix="bdr", fontdict={"size": "x-small", "color": "blue"}
)
# lmfit
d.setas = "xy"
fit = SF.BDR(missing="drop")
p0 = fit.guess(I, x=V)
for p, v, mi, mx in zip(
["A", "phi", "dphi", "d", "mass"],
[2.500, 3.2, 0.3, 15.0, 1.0],
[0.100, 1.0, 0.05, 5.0, 0.5],
[10, 10.0, 2.0, 30.0, 5.0],
):
from numpy import linspace, ones_like
from numpy.random import normal
B = linspace(2, 100, 26)
params = [12.5, 0.75, 1e3]
G = SF.fluchsSondheimer(B, *params) + normal(size=len(B), scale=5e-5)
dG = ones_like(B) * 5e-5
d = Data(
B,
G,
dG,
setas="xye",
column_headers=["Thickness (nm)", "Conductance", "dConductance"],
)
d.curve_fit(SF.fluchsSondheimer, p0=params, result=True, header="curve_fit")
d.setas = "xye"
d.lmfit(SF.FluchsSondheimer, p0=params, result=True, header="lmfit")
d.setas = "xyeyy"
d.plot(fmt=["r.", "b-", "g-"])
d.annotate_fit(
SF.fluchsSondheimer, x=0.2, y=0.6, fontdict={"size": "x-small", "color": "blue"}
)
d.annotate_fit(
SF.FluchsSondheimer,
x=0.2,
y=0.4,
fontdict={"size": "x-small", "color": "green"},
"""Example of Arrhenius Fit.""" from Stoner import Data import Stoner.Fit as SF from numpy import linspace from numpy.random import normal #Make some data T=linspace(200,350,101) R=SF.arrhenius(T+normal(size=len(T),scale=1.0,loc=1.0),1E6,0.5) d=Data(T,R,setas="xy",column_headers=["T","Rate"]) #Curve_fit on its own d.curve_fit(SF.arrhenius,p0=[1E6,0.5],result=True,header="curve_fit") d.setas="xyy" d.plot() d.annotate_fit(SF.arrhenius,x=200,y=0.04) # lmfit using lmfit guesses fit=SF.Arrhenius() p0=fit.guess(R,x=T) d.lmfit(fit,p0=p0,result=True,header="lmfit") d.setas="x..y" d.plot() d.annotate_fit(SF.Arrhenius,x=200,y=0.02,prefix="Arrhenius") d.title="Arrhenius Test Fit" d.ylabel="Rate" d.xlabel="Temperature (K)"
result=Data()
for data in fldr: #For each iteration ramp in the Tc data
row=[data.mean(iterator)]
data.figure(figsize=(8,4))
for i,r_col in enumerate(r_cols):
data.setas(x=t_col,y=r_col)
data.del_rows(isnan(data.y))
#Normalise data on y axis between +/- 1
data.normalise(base=(-1.,1.), replace=True)
#Swap x and y axes around so that R is x and T is y
data=~data
#Curve fit a straight line, using only the central 90% of the resistance transition
data.curve_fit(linear,bounds=lambda x,r:-threshold<x<threshold,result=True,p0=[7.0,0.0]) #result=True to record fit into metadata
#Plot the results
data.setas[-1]="y"
data.subplot(1,len(r_cols),i+1)
data.plot(fmt=["k.","r-"])
data.annotate_fit(linear,x=-1.,y=7.3c,fontsize="small")
data.title="Ramp {}".format(data[iterator][0])
row.extend([data["linear:intercept"],data["linear:intercept err"]])
data.tight_layout()
result+=np.array(row)
result.column_headers=["Ramp","Sample 4 R","dR","Sample 7 R","dR"]
result.setas="xyeye"
result.plot(fmt=["k.","r."])
from numpy import linspace,meshgrid,column_stack
import matplotlib.cm as cmap
import matplotlib.pyplot as plt
def plane(coord,a,b,c):
"""Function to define a plane"""
return c-(coord[0]*a+coord[1]*b)
coeefs=[1,-0.5,-1]
col=linspace(-10,10,6)
X,Y=meshgrid(col,col)
Z=plane((X,Y),*coeefs)+normal(size=X.shape,scale=7.0)
d=Data(column_stack((X.ravel(),Y.ravel(),Z.ravel())),filename="Fitting a Plane",setas="xyz")
d.column_headers=["X","Y","Z"]
d.figure(projection="3d")
d.plot_xyz(plotter="scatter",c=cmap.jet(d.z))
d.curve_fit(plane,[0,1],2,result=True)
d.setas="xy.z"
d.plot_xyz(linewidth=0,cmap=cmap.jet)
txt="$z=c-ax+by$\n"
txt+="\n".join([d.format("plane:{}".format(k),latex=True) for k in ["a","b","c"]])
ax=plt.gca(projection="3d")
ax.text(15,5,-50,txt)
d.draw()
r = normal(loc=3.0, size=250, scale=0.5) x, y, z = transform(r, q, p) x += 3.0 y -= 4.0 z += 2.0 # Construct the DataFile object d = Data(column_stack((x, y, z)), setas="xyz", filename="Best fit sphere") d.template.fig_width = 5.2 d.template.fig_height = 5.0 # Square aspect ratio d.plot_xyz(plotter="scatter") # curve_fit does the hard work popt, pcov = d.curve_fit(sphere, (0, 1, 2), zeros_like(d.x)) # This manually constructs the best fit sphere a, b, c, r = popt p = linspace(-pi / 2, pi / 2, 16) q = linspace(-pi, pi, 31) P, Q = meshgrid(p, q) R = ones_like(P) * r x, y, z = transform(R, Q, P) x += a y += b z += c ax = plt.gca(projection="3d") ax.plot_surface(x, y, z, rstride=1, cstride=1, color=(1.0, 0.0, 0.0, 0.25), linewidth=0) plt.draw()
result=Data()
for data in fldr: #For each iteration ramp in the Tc data
row=[data.mean(iterator)]
data.figure(figsize=(8,4))
for i,r_col in enumerate(r_cols):
data.setas(x=t_col,y=r_col)
data.del_rows(isnan(data.y))
#Normalise data on y axis between +/- 1
data.normalise(base=(-1.,1.), replace=True)
#Swap x and y axes around so that R is x and T is y
data=~data
#Curve fit a straight line, using only the central 90% of the resistance transition
data.curve_fit(linear,bounds=lambda x,r:-threshold<x<threshold,result=True,p0=[7.0,0.0]) #result=True to record fit into metadata
#Plot the results
data.setas[-1]="y"
data.subplot(1,len(r_cols),i+1)
data.plot(fmt=["k.","r-"])
data.annotate_fit(linear,x=-1.,y=7.3c,fontsize="small")
data.title="Ramp {}".format(data[iterator][0])
row.extend([data["linear:intercept"],data["linear:intercept err"]])
data.tight_layout()
result+=np.array(row)
result.column_headers=["Ramp","Sample 4 R","dR","Sample 7 R","dR"]
result.setas="xyeye"
result.plot(fmt=["k.","r."])
"""USe curve_fit to fit a straight line."""
from Stoner import Data
def linear(x, m, c):
"""Straight line function."""
return m * x + c
d = Data("curve_fit_data.dat", setas="xye")
d.plot(fmt="ro")
fit = d.curve_fit(linear, result=True, replace=False, header="Fit", output="report")
d.setas = "x..y"
d.plot(fmt="b-")
d.annotate_fit(linear)
d.draw()
print(fit.fit_report())
s = y * 0.05
d = Data(x, y, s, setas="xye", column_headers=["X", "Y"])
d.plot(fmt="r.")
d.polyfit(result=True, header="Polyfit")
d.setas = "x..y"
d.plot(fmt="m-", label="Polyfit")
d.text(
-9,
450,
"Polynominal co-efficients\n{}".format(d["2nd-order polyfit coefficients"]),
fontdict={"size": "x-small", "color": "magenta"},
)
d.setas = "xy"
d.curve_fit(SF.quadratic, result=True, header="Curve-fit")
d.setas = "x...y"
d.plot(fmt="b-", label="curve-fit")
d.annotate_fit(
SF.quadratic,
prefix="quadratic",
x=0.2,
y=0.65,
fontdict={"size": "x-small", "color": "blue"},
)
d.setas = "xy"
fit = SF.Quadratic()
p0 = fit.guess(y, x=x)
d.lmfit(SF.Quadratic, p0=p0, result=True, header="lmfit")
from numpy.random import normal
from copy import copy
B = linspace(-8, 8, 201)
params = [1e-3, 2.0, 0.25, 1.4]
G = SF.wlfit(B, *params) + normal(size=len(B), scale=5e-7)
dG = ones_like(B) * 5e-7
d = Data(
B,
G,
dG,
setas="xye",
column_headers=["Field $\\mu_0H (T)$", "Conductance", "dConductance"],
)
d.curve_fit(SF.wlfit, p0=copy(params), result=True, header="curve_fit")
d.setas = "xye"
d.lmfit(SF.WLfit, p0=copy(params), result=True, header="lmfit")
d.setas = "xyeyy"
d.plot(fmt=["r.", "b-", "g-"])
d.annotate_fit(SF.wlfit, x=0.05, y=0.75, fontdict={"size": "x-small", "color": "blue"})
d.annotate_fit(
SF.WLfit,
x=0.05,
y=0.5,
fontdict={"size": "x-small", "color": "green"},
prefix="WLfit",
)
"""Example of nDimArrhenius Fit.""" from Stoner import Data import Stoner.Fit as SF from numpy import linspace from numpy.random import normal # Make some data T = linspace(50, 500, 101) R = SF.nDimArrhenius(T + normal(size=len(T), scale=5.0, loc=1.0), 1e6, 0.5, 2) d = Data(T, R, setas="xy", column_headers=["T", "Rate"]) # Curve_fit on its own d.curve_fit(SF.nDimArrhenius, p0=[1e6, 0.5, 2], result=True, header="curve_fit") d.setas = "xyy" d.plot(fmt=["r.", "b-"]) d.annotate_fit(SF.nDimArrhenius, x=0.25, y=0.3) # lmfit using lmfit guesses fit = SF.NDimArrhenius() p0 = fit.guess(R, x=T) d.lmfit(fit, p0=p0, result=True, header="lmfit") d.setas = "x..y" d.plot(fmt="g-") d.annotate_fit(SF.NDimArrhenius, x=0.25, y=0.05, prefix="NDimArrhenius") d.title = "n-D Arrhenius Test Fit" d.ylabel = "Rate" d.xlabel = "Temperature (K)"
"""Example of nDimArrhenius Fit."""
from Stoner import Data
import Stoner.Fit as SF
from numpy import linspace, ones_like
from numpy.random import normal
# Make some data
V = linspace(-4, 4, 1000)
I = SF.fowlerNordheim(V, 2500, 3.2, 15.0) + normal(size=len(V), scale=1e-6)
dI = ones_like(V) * 10e-6
d = Data(V, I, dI, setas="xye", column_headers=["Bias", "Current", "Noise"])
d.curve_fit(SF.fowlerNordheim, p0=[2500, 3.2, 15.0], result=True, header="curve_fit")
d.setas = "xyey"
d.plot(fmt=["r.", "b-"])
d.annotate_fit(
SF.fowlerNordheim,
x=0.2,
y=0.6,
prefix="fowlerNordheim",
fontdict={"size": "x-small", "color": "blue"},
)
d.setas = "xye"
fit = SF.FowlerNordheim()
p0 = [2500, 5.2, 15.0]
p0 = fit.guess(I, x=V)
for p, v, mi, mx in zip(
["A", "phi", "d"], [2500, 3.2, 15.0], [100, 1, 5], [1e4, 20.0, 30.0]
):
def plane(coord, a, b, c):
"""Function to define a plane"""
return c - (coord[0] * a + coord[1] * b)
coeefs = [1, -0.5, -1]
col = linspace(-10, 10, 6)
X, Y = meshgrid(col, col)
Z = plane((X, Y), *coeefs) + normal(size=X.shape, scale=7.0)
d = Data(
column_stack((X.ravel(), Y.ravel(), Z.ravel())),
filename="Fitting a Plane",
setas="xyz",
)
d.column_headers = ["X", "Y", "Z"]
d.figure(projection="3d")
d.plot_xyz(plotter="scatter")
popt, pcov = d.curve_fit(plane, [0, 1], 2, result=True)
d.setas = "xy.z"
d.plot_xyz(linewidth=0, cmap=cmap.jet)
txt = "$z=c-ax+by$\n"
txt += "\n".join([d.format("plane:{}".format(k), latex=True) for k in ["a", "b", "c"]])
ax = plt.gca(projection="3d")
ax.text(15, 5, -50, txt)
d.draw()
"""USe curve_fit to fit a straight line."""
from Stoner import Data
def linear(x, m, c):
"""Straight line function."""
return m * x + c
d = Data("curve_fit_data.dat", setas="xye")
d.plot(fmt="ro")
popt, pcov = d.curve_fit(linear, result=True, replace=False, header="Fit")
d.setas = "x..y"
d.plot(fmt="b-")
d.annotate_fit(linear)
d.draw()
"""Example of nDimArrhenius Fit."""
from Stoner import Data
import Stoner.Fit as SF
from numpy import linspace
from numpy.random import normal
#Make some data
T = linspace(50, 500, 101)
R = SF.nDimArrhenius(T + normal(size=len(T), scale=5.0, loc=1.0), 1E6, 0.5, 2)
d = Data(T, R, setas="xy", column_headers=["T", "Rate"])
#Curve_fit on its own
d.curve_fit(SF.nDimArrhenius,
p0=[1E6, 0.5, 2],
result=True,
header="curve_fit")
d.setas = "xyy"
d.plot()
d.annotate_fit(SF.nDimArrhenius, x=150, y=6E5)
# lmfit using lmfit guesses
fit = SF.NDimArrhenius()
p0 = fit.guess(R, x=T)
d.lmfit(fit, p0=p0, result=True, header="lmfit")
d.setas = "x..y"
d.plot()
d.annotate_fit(SF.NDimArrhenius, x=150, y=3.5E5, prefix="NDimArrhenius")
d.title = "n-D Arrhenius Test Fit"
d.ylabel = "Rate"
d.xlabel = "Temperature (K)"
"""Example of nDimArrhenius Fit."""
from Stoner import Data
import Stoner.Fit as SF
from numpy import linspace, ones_like
from numpy.random import normal
# Make some data
V = linspace(-4, 4, 1001)
I = SF.simmons(V, 2500, 5.2, 15.0) + normal(size=len(V), scale=100e-9)
dI = ones_like(V) * 100e-9
d = Data(V, I, dI, setas="xye", column_headers=["Bias", "Current", "Noise"])
d.curve_fit(SF.simmons, p0=[2500, 5.2, 15.0], result=True, header="curve_fit")
d.setas = "xyey"
d.plot(fmt=["r.", "b-"])
d.annotate_fit(
SF.simmons,
x=0.25,
y=0.25,
prefix="simmons",
fontdict={
"size": "x-small",
"color": "blue"
},
)
d.setas = "xye"
fit = SF.Simmons()
p0 = [2500, 5.2, 15.0]
d.lmfit(SF.Simmons, p0=p0, result=True, header="lmfit")
from numpy.random import normal
from copy import copy
B = linspace(0, 5E4, 51)
params = [2.2, 1E5, 2E2]
G = SF.kittelEquation(B, *params) + normal(size=len(B), scale=5E7)
dG = ones_like(B) * 5E7
d = Data(B,
G,
dG,
setas="xye",
column_headers=["Field $Oe$", r"$\nu (Hz)$", r"\delta $\nu (Hz)$"])
d.curve_fit(SF.kittelEquation,
p0=copy(params),
result=True,
header="curve_fit")
fit = SF.KittelEquation()
p0 = fit.guess(G, x=B)
d.lmfit(fit, p0=p0, result=True, header="lmfit")
d.setas = "xyeyy"
d.plot(fmt=["r.", "b-", "g-"])
d.annotate_fit(SF.kittelEquation,
x=4000,
y=2E8,
fontdict={"size": "x-small"},
mode="eng")
"""Example of nDimArrhenius Fit."""
from Stoner import Data
import Stoner.Fit as SF
from numpy import linspace
from numpy.random import normal
# Make some data
T = linspace(200, 350, 101)
R = SF.modArrhenius(T, 1e6, 0.5, 1.5) * normal(
scale=0.00005, loc=1.0, size=len(T))
d = Data(T, R, setas="xy", column_headers=["T", "Rate"])
# Curve_fit on its own
d.curve_fit(SF.modArrhenius,
p0=[1e6, 0.5, 1.5],
result=True,
header="curve_fit")
d.setas = "xyy"
d.plot(fmt=["r.", "b-"])
d.annotate_fit(SF.modArrhenius, x=0.2, y=0.5)
# lmfit using lmfit guesses
fit = SF.ModArrhenius()
p0 = [1e6, 0.5, 1.5]
d.lmfit(fit, p0=p0, result=True, header="lmfit")
d.setas = "x..y"
d.plot()
d.annotate_fit(SF.ModArrhenius, x=0.2, y=0.25, prefix="ModArrhenius")
d.title = "Modified Arrhenius Test Fit"
d.ylabel = "Rate"
from numpy import linspace, ones_like
from numpy.random import normal
from copy import deepcopy
T = linspace(4.2, 300, 101)
params = [265, 65, 1.0, 5]
params2 = deepcopy(params)
G = SF.blochGrueneisen(T, *params) + normal(size=len(T), scale=5E-5)
dG = ones_like(T) * 5E-5
d = Data(T,
G,
dG,
setas="xye",
column_headers=["Temperature (K)", "Resistivity", "dR"])
d.curve_fit(SF.blochGrueneisen, p0=params, result=True, header="curve_fit")
d.setas = "xy"
d.lmfit(SF.BlochGrueneisen, p0=params2, result=True, header="lmfit")
d.setas = "xyeyy"
d.plot(fmt=["r.", "b-", "g-"])
d.annotate_fit(SF.blochGrueneisen, x=20, y=65.05, fontdict={"size": "x-small"})
d.annotate_fit(SF.BlochGrueneisen,
x=100,
y=65,
fontdict={"size": "x-small"},
prefix="BlochGrueneisen")
d.title = "Bloch-Grueneisen Fit"
d.tight_layout()
"""Test Weak-localisation fitting."""
from Stoner import Data
import Stoner.Fit as SF
from numpy import linspace, ones_like
from numpy.random import normal
from copy import copy
B = linspace(-0.01, 0.01, 100)
params = [1, 1.0e-11, 250]
G = SF.langevin(B, *params) + normal(size=len(B), scale=5e-3)
dG = ones_like(B) * 5e-3
d = Data(B, G, dG, setas="xye", column_headers=["Field $\\mu_0H (T)$", "Moment", "dM"])
func = lambda H, M_s, m: SF.langevin(H, M_s, m, 250)
d.curve_fit(func, p0=copy(params)[0:2], result=True, header="curve_fit")
d.setas = "xye"
fit = SF.Langevin()
p0 = fit.guess(G, x=B)
for p, v in zip(p0, params):
p0[p].set(v)
p0[p].max = v * 5
p0[p].min = 0
p0[p].vary = p != "T"
d.lmfit(fit, p0=p0, result=True, header="lmfit")
d.setas = "xyeyy"
d.plot(fmt=["r.", "b-", "g-"])
"""Example of Arrhenius Fit."""
from Stoner import Data
import Stoner.Fit as SF
from numpy import linspace, ceil, log10, abs as np_abs
from numpy.random import normal
# Make some data
T = linspace(200, 350, 101)
R = SF.arrhenius(T + normal(size=len(T), scale=3.0, loc=0.0), 1e6, 0.5)
E = 10 ** ceil(log10(np_abs(R - SF.arrhenius(T, 1e6, 0.5))))
d = Data(T, R, E, setas="xye", column_headers=["T", "Rate"])
# Curve_fit on its own
d.curve_fit(SF.arrhenius, p0=(1e6, 0.5), result=True, header="curve_fit")
d.setas = "xyey"
d.plot(fmt=["r.", "b-"])
d.annotate_fit(
SF.arrhenius,
x=0.5,
y=0.5,
mode="eng",
fontdict={"size": "x-small", "color": "blue"},
)
# lmfit using lmfit guesses
fit = SF.Arrhenius()
d.setas = "xye"
d.lmfit(fit, result=True, header="lmfit")
d.setas = "x...y"
d.plot(fmt="g-")
d.annotate_fit(
d.polyfit(result=True, header="Polyfit")
d.setas = "x..y"
d.plot(fmt="m-", label="Polyfit")
d.text(
-9,
450,
"Polynominal co-efficients\n{}".format(
d["2nd-order polyfit coefficients"]),
fontdict={
"size": "x-small",
"color": "magenta"
},
)
d.setas = "xy"
d.curve_fit(SF.quadratic, result=True, header="Curve-fit")
d.setas = "x...y"
d.plot(fmt="b-", label="curve-fit")
d.annotate_fit(
SF.quadratic,
prefix="quadratic",
x=0.2,
y=0.65,
fontdict={
"size": "x-small",
"color": "blue"
},
)
d.setas = "xy"
fit = SF.Quadratic()
"""Example of nDimArrhenius Fit."""
from Stoner import Data
import Stoner.Fit as SF
from numpy import linspace,ones_like
from numpy.random import normal
#Make some data
V=linspace(-4,4,1000)
I=SF.fowlerNordheim(V,2500,3.2,15.0)+normal(size=len(V),scale=10E-6)
dI=ones_like(V)*10E-6
d=Data(V,I,dI,setas="xye",column_headers=["Bias","Current","Noise"])
d.curve_fit(SF.fowlerNordheim,p0=[2500,3.2,15.0],result=True,header="curve_fit")
d.setas="xyey"
d.plot(fmt=["r.","b-"])
d.annotate_fit(SF.fowlerNordheim,x=0,y=10,prefix="fowlerNordheim",fontdict={"size":"x-small"})
d.setas="xye"
fit=SF.FowlerNordheim()
p0=[2500,5.2,15.0]
p0=fit.guess(I,x=V)
for p,v,mi,mx in zip(["A","phi","d"],[2500,3.2,15.0],[100,1,5],[1E4,20.0,30.0]):
p0[p].value=v
p0[p].bounds=[mi,mx]
d.lmfit(SF.FowlerNordheim,p0=p0,result=True,header="lmfit")
d.setas="x...y"
d.plot()
d.annotate_fit(fit,x=-3,y=-60,prefix="FowlerNordheim",fontdict={"size":"x-small"})
d.ylabel="Current"
"""Simple use of lmfit to fit data."""
from Stoner import Data
from Stoner.Fit import PowerLaw
from Stoner.analysis.fitting import odr_Model
from numpy import linspace, exp, random
# Make some data
x = linspace(0, 10.0, 101)
y = PowerLaw().func(x, 1e-1, 1.64) * random.normal(loc=1.0, scale=0.05, size=101)
d = Data(x, y, column_headers=["Time", "Signal"], setas="xy")
# Do the fitting and plot the result
fit = d.curve_fit(
PowerLaw, result=True, header="LM-Model Fit", residuals=True, output="report"
)
ODRModel = odr_Model(PowerLaw, p0=(1, 1))
fit = d.curve_fit(
ODRModel,
result=True,
header="ODR-Fit",
residuals=True,
output="report",
prefix="ODRModel",
)
# Reset labels
d.labels = []
# Make nice two panel plot layout
ax = d.subplot2grid((3, 1), (2, 0))
d.setas = "x..y"
from numpy.random import normal
from copy import copy
B = linspace(-0.01, 0.01, 100)
params = [1, 1.0e-11, 250]
G = SF.langevin(B, *params) + normal(size=len(B), scale=5e-3)
dG = ones_like(B) * 5e-3
d = Data(B,
G,
dG,
setas="xye",
column_headers=["Field $\\mu_0H (T)$", "Moment", "dM"])
func = lambda H, M_s, m: SF.langevin(H, M_s, m, 250)
d.curve_fit(func, p0=copy(params)[0:2], result=True, header="curve_fit")
d.setas = "xye"
fit = SF.Langevin()
p0 = fit.guess(G, x=B)
for p, v in zip(p0, params):
p0[p].set(v)
p0[p].max = v * 5
p0[p].min = 0
p0[p].vary = p != "T"
d.lmfit(fit, p0=p0, result=True, header="lmfit")
d.setas = "xyeyy"
d.plot(fmt=["r.", "b-", "g-"])
from Stoner import Data
from Stoner.analysis.fitting.models.generic import PowerLaw
from Stoner.analysis.fitting import odr_Model
from numpy import linspace, random
# Make some data
x = linspace(0, 10.0, 101)
y = PowerLaw().func(x, 1e-1, 1.64) * random.normal(
loc=1.0, scale=0.05, size=101)
d = Data(x, y, column_headers=["Time", "Signal"], setas="xy")
# Do the fitting and plot the result
fit = d.curve_fit(
PowerLaw,
result=True,
header="LM-Model Fit",
residuals=True,
output="report",
)
ODRModel = odr_Model(PowerLaw, p0=(1, 1))
fit = d.curve_fit(
ODRModel,
result=True,
header="ODR-Fit",
residuals=True,
output="report",
prefix="ODRModel",
)
# Reset labels
d.labels = []
"""Example of nDimArrhenius Fit.""" from Stoner import Data import Stoner.Fit as SF from numpy import linspace from numpy.random import normal # Make some data T = linspace(200, 350, 101) R = SF.modArrhenius(T, 1e6, 0.5, 1.5) * normal(scale=0.00005, loc=1.0, size=len(T)) d = Data(T, R, setas="xy", column_headers=["T", "Rate"]) # Curve_fit on its own d.curve_fit(SF.modArrhenius, p0=[1e6, 0.5, 1.5], result=True, header="curve_fit") d.setas = "xyy" d.plot(fmt=["r.", "b-"]) d.annotate_fit(SF.modArrhenius, x=0.2, y=0.5) # lmfit using lmfit guesses fit = SF.ModArrhenius() p0 = [1e6, 0.5, 1.5] d.lmfit(fit, p0=p0, result=True, header="lmfit") d.setas = "x..y" d.plot() d.annotate_fit(SF.ModArrhenius, x=0.2, y=0.25, prefix="ModArrhenius") d.title = "Modified Arrhenius Test Fit" d.ylabel = "Rate" d.xlabel = "Temperature (K)"
"""Test Weak-localisation fitting."""
from Stoner import Data
import Stoner.Fit as SF
from numpy import linspace, ones_like
from numpy.random import normal
from copy import deepcopy
T = linspace(4.2, 300, 101)
params = [265, 65, 1.0, 5]
params2 = deepcopy(params)
G = SF.blochGrueneisen(T, *params) + normal(size=len(T), scale=5e-5)
dG = ones_like(T) * 5e-5
d = Data(T, G, dG, setas="xye", column_headers=["Temperature (K)", "Resistivity", "dR"])
d.curve_fit(SF.blochGrueneisen, p0=params, result=True, header="curve_fit")
d.setas = "xy"
d.lmfit(SF.BlochGrueneisen, p0=params2, result=True, header="lmfit")
d.setas = "xyeyy"
d.plot(fmt=["r.", "b-", "g-"])
d.annotate_fit(SF.blochGrueneisen, x=0.65, y=0.35, fontdict={"size": "x-small"})
d.annotate_fit(
SF.BlochGrueneisen,
x=0.65,
y=0.05,
fontdict={"size": "x-small"},
prefix="BlochGrueneisen",
)
d.title = "Bloch-Grueneisen Fit"
