doc_builtinmodels_splinemodel.py

[[Model]]
    (Model(gaussian, prefix='peak_') + Model(spline_model, prefix='bkg_'))
[[Fit Statistics]]
    # fitting method   = leastsq
    # function evals   = 92
    # data points      = 501
    # variables        = 14
    chi-square         = 52.6611549
    reduced chi-square = 0.10813379
    Akaike info crit   = -1100.61674
    Bayesian info crit = -1041.58425
    R-squared          = 0.94690612
[[Variables]]
    peak_amplitude:  12.2231138 +/- 0.29554074 (2.42%) (init = 8)
    peak_center:     16.4280869 +/- 0.01091050 (0.07%) (init = 16)
    peak_sigma:      0.72096402 +/- 0.01336666 (1.85%) (init = 1)
    peak_fwhm:       1.69774050 +/- 0.03147609 (1.85%) == '2.3548200*peak_sigma'
    peak_height:     6.76360675 +/- 0.09854036 (1.46%) == '0.3989423*peak_amplitude/max(1e-15, peak_sigma)'
    bkg_s0:          3.51175736 +/- 0.04941392 (1.41%) (init = 3.787995)
    bkg_s1:          3.72930068 +/- 0.09558236 (2.56%) (init = 3.959487)
    bkg_s2:          4.26846495 +/- 0.12650286 (2.96%) (init = 4.384009)
    bkg_s3:          4.42375491 +/- 0.10170203 (2.30%) (init = 4.431971)
    bkg_s4:          4.49590447 +/- 0.10615551 (2.36%) (init = 4.243976)
    bkg_s5:          3.96515316 +/- 0.09336554 (2.35%) (init = 4.115153)
    bkg_s6:          3.35531898 +/- 0.12669983 (3.78%) (init = 3.965325)
    bkg_s7:          2.89909737 +/- 0.16190201 (5.58%) (init = 2.788437)
    bkg_s8:          2.82656972 +/- 0.13445491 (4.76%) (init = 2.984317)
    bkg_s9:          3.43338674 +/- 0.15987280 (4.66%) (init = 3.383491)
    bkg_s10:         3.73024845 +/- 0.12096864 (3.24%) (init = 3.791937)
[[Correlations]] (unreported correlations are < 0.300)
    C(bkg_s7, bkg_s8)             = -0.8192
    C(peak_amplitude, peak_sigma) = +0.7987
    C(bkg_s8, bkg_s9)             = -0.7063
    C(bkg_s5, bkg_s6)             = -0.6950
    C(peak_amplitude, bkg_s7)     = -0.6878
    C(bkg_s2, bkg_s3)             = -0.6672
    C(bkg_s9, bkg_s10)            = -0.6060
    C(bkg_s3, bkg_s4)             = -0.5743
    C(bkg_s1, bkg_s2)             = -0.5646
    C(bkg_s4, bkg_s5)             = -0.5542
    C(bkg_s7, bkg_s9)             = +0.5216
    C(peak_sigma, bkg_s7)         = -0.5192
    C(peak_amplitude, bkg_s8)     = +0.5185
    C(bkg_s0, bkg_s1)             = +0.4448
    C(peak_sigma, bkg_s8)         = +0.3733
    C(peak_center, bkg_s6)        = +0.3599
    C(bkg_s4, bkg_s6)             = +0.3597
    C(bkg_s0, bkg_s2)             = -0.3595
    C(bkg_s2, bkg_s4)             = +0.3504
    C(bkg_s8, bkg_s10)            = +0.3455
    C(bkg_s6, bkg_s7)             = -0.3332
    C(peak_center, bkg_s7)        = -0.3301
    C(peak_amplitude, bkg_s9)     = -0.3206

# <examples/doc_builtinmodels_splinemodel.py>
import matplotlib.pyplot as plt
import numpy as np

from lmfit.models import GaussianModel, SplineModel

data = np.loadtxt('test_splinepeak.dat')
x = data[:, 0]
y = data[:, 1]

plt.plot(x, y, label='data')

model = GaussianModel(prefix='peak_')
params = model.make_params(amplitude=dict(value=8, min=0),
                           center=dict(value=16, min=5, max=25),
                           sigma=dict(value=1, min=0))

# make a background spline with knots evenly spaced over the background,
# but sort of skipping over where the peak is
knot_xvals3 = np.array([1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25])
knot_xvals2 = np.array([1, 3, 5, 7, 9, 11, 13,   16,   19, 21, 23, 25])  # noqa: E241
knot_xvals1 = np.array([1, 3, 5, 7, 9, 11, 13,         19, 21, 23, 25])  # noqa: E241

bkg = SplineModel(prefix='bkg_', xknots=knot_xvals1)
params.update(bkg.guess(y, x))

model = model + bkg

plt.plot(x, model.eval(params, x=x), label='initial')

out = model.fit(y, params, x=x)
print(out.fit_report(min_correl=0.3))
comps = out.eval_components()

plt.plot(x, out.best_fit, label='best fit')
plt.plot(x, comps['bkg_'], label='background')
plt.plot(x, comps['peak_'], label='peak')

knot_yvals = np.array([o.value for o in out.params.values() if o.name.startswith('bkg')])
plt.plot(knot_xvals1, knot_yvals, 'o', color='black', label='spline knots values')
plt.legend()
plt.show()


#   knot positions         | peak amplitude
#  11, 13, 19, 21          |  12.223  0.295
#  11, 13, 16, 19, 21      |  11.746  0.594
#  11, 13, 15, 17, 19, 21  |  12.052  0.872


plt.plot(x, y, 'o', label='data')

for nknots in (10, 15, 20, 25, 30):
    model = SplineModel(prefix='bkg_', xknots=np.linspace(0, 25, nknots))
    params = model.guess(y, x)
    out = model.fit(y, params, x=x)
    plt.plot(x, out.best_fit, label=f'best-fit ({nknots} knots)')
plt.legend()
plt.show()

# <end examples/doc_builtinmodels_splinemodel.py>