#!/usr/bin/env python
#<examples/doc_withreport.py>

from __future__ import print_function
from lmfit import Parameters, minimize, fit_report
from numpy import random, linspace, pi, exp, sin, sign


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):
    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)

n = 1001
xmin = 0.
xmax = 250.0

random.seed(0)

noise = random.normal(scale=0.7215, size=n)
x     = linspace(xmin, xmax, n)
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})

fit = residual(fit_params, x)
print(fit_report(fit_params))

#<end of examples/doc_withreport.py>