Linear Fit

[1]:

import numpy as np
import uncertainties as unc
import uncertainties.unumpy as unp

from smpl import fit, io, plot
from smpl import functions as f

[2]:

data = np.loadtxt(io.find_file("test_linear_data.txt", 3))
xdata = data[:, 0]
xerr = data[:, 2]
ydata = data[:, 1]
yerr = data[:, 3]
x = unp.uarray(xdata, xerr)
y = unp.uarray(ydata, yerr)

[3]:

data

[3]:

array([[0. , 1. , 0.1, 0.2],
       [1. , 2. , 0.2, 0.1],
       [2. , 3. , 0.3, 0.1],
       [3. , 5. , 0.1, 0.4],
       [4. , 5. , 0.1, 0.1],
       [5. , 6. , 0.1, 0.2]])

SciPy

[4]:

ff = plot.fit(
    xdata,
    ydata,
    fmt=".",
    label="data",
    xaxis="x in a.u.",
    yaxis="y in a.u.",
    function=f.linear,
    params=[1],
)

../../../_images/example_fit_linear_test_linear_5_0.png

[5]:

ff = plot.fit(
    xdata,
    ydata,
    fmt=".",
    label="data",
    xaxis="x in a.u.",
    yaxis="y in a.u.",
    function=f.line,
    params=[1, 2],
)

../../../_images/example_fit_linear_test_linear_6_0.png

[6]:

ff = plot.fit(x, y, fmt=".", function=f.line, params=[1, 1], sigmas=1, lpos=2)

../../../_images/example_fit_linear_test_linear_7_0.png

[7]:

ff = plot.fit(
    xdata, y, fmt=".", function=f.line, params=[1, 1], sigmas=1, lpos=2, also_data=True
)
print("Chi2 = ", fit.Chi2(xdata, y, f.line, ff))

Chi2 =  5.883584796166781

../../../_images/example_fit_linear_test_linear_8_1.png

Correlations

Let’s take a look at correlations on the example of calculating the y axis intercept. Again:

[8]:

a, b = plot.fit(
    xdata,
    ydata,
    fmt=".",
    label="data",
    xaxis="x in a.u.",
    yaxis="y in a.u.",
    function=f.line,
    sigmas=1,
    extrapolate_min=-2,
)

../../../_images/example_fit_linear_test_linear_10_0.png

Let’s calculated the intersection with the x axis, given by \(-b/a\), with correlation

[9]:

-b / a

[9]:

-1.0648148148148089+/-0.4156953391902814

and without correlations

[10]:

a_nocorr = unc.ufloat(plot.unv(a), plot.usd(a))
b_nocorr = unc.ufloat(plot.unv(b), plot.usd(b))
-b_nocorr / a_nocorr

[10]:

-1.0648148148148089+/-0.33752053055607584

While the mean agrees the uncertainties are not the same.

The Lines drawn in the plot are also correlated and cross the axis at -0.67 and -1.51 corresponding to an uncertainties of -0.42.

Minuit

[11]:

ff = plot.fit(
    xdata,
    y,
    fmt=".",
    function=f.line,
    params=[1, 1],
    sigmas=1,
    lpos=2,
    fitter=fit.Fitter.MINUIT_LEASTSQUARES,
)
print("Chi2 = ", fit.Chi2(xdata, y, f.line, ff))

Chi2 =  5.958263165324413

../../../_images/example_fit_linear_test_linear_17_1.png

[12]:

ff = plot.fit(
    xdata,
    y,
    fmt=".",
    function=f.line,
    params=[1, 1],
    sigmas=1,
    lpos=2,
    fitter=fit.Fitter.SCIPY_ODR,
)
print("Chi2 = ", fit.Chi2(xdata, y, f.line, ff))

Chi2 =  2.1622470651728745

../../../_images/example_fit_linear_test_linear_18_1.png

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