from lmfit import Parameters, minimize
from lmfit.printfuncs import report_fit

from numpy import linspace, zeros, sin, exp, random, pi, sign

try:
    import pylab
    HASPYLAB = True
except ImportError:
    HASPYLAB = False

p_true = Parameters()
p_true.add('amp', value=14.0)
p_true.add('period', value=5.4321)
p_true.add('shift', value=0.12345)
p_true.add('decay', value=0.01000)

def residual(pars, x, data=None):
    amp = pars['amp'].value
    per = pars['period'].value
    shift = pars['shift'].value
    decay = pars['decay'].value

    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 = 1500
xmin = 0.
xmax = 250.0
random.seed(0)
noise = random.normal(scale=2.80, size=n)
x     = linspace(xmin, xmax, n)
data  = residual(p_true, x) + noise

fit_params = Parameters()
fit_params.add('amp', value=13.0, max=20, min=0.0)
fit_params.add('period', value=2, max=10)
fit_params.add('shift', value=0.0, max=pi/2., min=-pi/2.)
fit_params.add('decay', value=0.02, max=0.10, min=0.00)

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

fit = residual(fit_params, x)

print '# N_func_evals, N_free = ', out.nfev, out.nfree
print '# chi-square, reduced chi-square = % .7g, % .7g' % (out.chisqr, out.redchi)

report_fit(fit_params, show_correl=True, modelpars=p_true)

print 'Raw (unordered, unscaled) Covariance Matrix:'
print out.covar

if HASPYLAB:
    pylab.plot(x, data, 'ro')
    pylab.plot(x, fit, 'b')
    pylab.show()