doc_fitting_withreport.py

Out:

[[Fit Statistics]]
    # fitting method   = leastsq
    # function evals   = 83
    # data points      = 1001
    # variables        = 4
    chi-square         = 498.811759
    reduced chi-square = 0.50031270
    Akaike info crit   = -689.222517
    Bayesian info crit = -669.587497
[[Variables]]
    amp:     13.9121945 +/- 0.14120288 (1.01%) (init = 13)
    period:  5.48507045 +/- 0.02666492 (0.49%) (init = 2)
    shift:   0.16203677 +/- 0.01405661 (8.67%) (init = 0)
    decay:   0.03264538 +/- 3.8014e-04 (1.16%) (init = 0.02)
[[Correlations]] (unreported correlations are < 0.100)
    C(period, shift) =  0.797
    C(amp, decay)    =  0.582
    C(amp, shift)    = -0.297
    C(amp, period)   = -0.243
    C(shift, decay)  = -0.182
    C(period, decay) = -0.150

##
import warnings
warnings.filterwarnings("ignore")
##
# <examples/doc_fitting_withreport.py>
from numpy import exp, linspace, pi, random, sign, sin

from lmfit import Parameters, fit_report, minimize

p_true = Parameters()
p_true.add('amp', value=14.0)
p_true.add('period', value=5.46)
p_true.add('shift', value=0.123)
p_true.add('decay', value=0.032)


def residual(pars, x, data=None):
    """Model a decaying sine wave and subtract data."""
    vals = pars.valuesdict()
    amp = vals['amp']
    per = vals['period']
    shift = vals['shift']
    decay = vals['decay']

    if abs(shift) > pi/2:
        shift = shift - sign(shift)*pi
    model = amp * sin(shift + x/per) * exp(-x*x*decay*decay)
    if data is None:
        return model
    return model - data


random.seed(0)
x = linspace(0.0, 250., 1001)
noise = random.normal(scale=0.7215, size=x.size)
data = residual(p_true, x) + noise

fit_params = Parameters()
fit_params.add('amp', value=13.0)
fit_params.add('period', value=2)
fit_params.add('shift', value=0.0)
fit_params.add('decay', value=0.02)

out = minimize(residual, fit_params, args=(x,), kws={'data': data})

print(fit_report(out))
# <end examples/doc_fitting_withreport.py>