# Fit Using Inequality ConstraintΒΆ

Sometimes specifying boundaries using `min` and `max` are not sufficient, and more complicated (inequality) constraints are needed. In the example below the center of the Lorentzian peak is constrained to be between 0-5 away from the center of the Gaussian peak.

```import matplotlib.pyplot as plt
import numpy as np

from lmfit import Minimizer, create_params, report_fit
from lmfit.lineshapes import gaussian, lorentzian

def residual(pars, x, data):
model = (gaussian(x, pars['amp_g'], pars['cen_g'], pars['wid_g']) +
lorentzian(x, pars['amp_l'], pars['cen_l'], pars['wid_l']))
return model - data
```

Generate the simulated data using a Gaussian and Lorentzian lineshape:

```np.random.seed(0)
x = np.linspace(0, 20.0, 601)

data = (gaussian(x, 21, 6.1, 1.2) + lorentzian(x, 10, 9.6, 1.3) +
np.random.normal(scale=0.1, size=x.size))
```

Create the fitting parameters and set an inequality constraint for `cen_l`. First, we add a new fitting parameter `peak_split`, which can take values between 0 and 5. Afterwards, we constrain the value for `cen_l` using the expression to be `'peak_split+cen_g'`:

```pfit = create_params(amp_g=10, cen_g=5, wid_g=1, amp_l=10,
peak_split=dict(value=2.5, min=0, max=5),
cen_l=dict(expr='peak_split+cen_g'),
wid_l=dict(expr='wid_g'))

mini = Minimizer(residual, pfit, fcn_args=(x, data))
out = mini.leastsq()
best_fit = data + out.residual
```

Performing a fit, here using the `leastsq` algorithm, gives the following fitting results:

```report_fit(out.params)
```
```[[Variables]]
amp_g:       21.2722842 +/- 0.05138772 (0.24%) (init = 10)
cen_g:       6.10496396 +/- 0.00334613 (0.05%) (init = 5)
wid_g:       1.21434954 +/- 0.00327317 (0.27%) (init = 1)
amp_l:       9.46504173 +/- 0.05445415 (0.58%) (init = 10)
peak_split:  3.52163544 +/- 0.01004618 (0.29%) (init = 2.5)
cen_l:       9.62659940 +/- 0.01066172 (0.11%) == 'peak_split+cen_g'
wid_l:       1.21434954 +/- 0.00327317 (0.27%) == 'wid_g'
[[Correlations]] (unreported correlations are < 0.100)
C(amp_g, wid_g)      = +0.6199
C(amp_g, peak_split) = +0.3796
C(wid_g, peak_split) = +0.3445
C(amp_g, amp_l)      = -0.2951
C(cen_g, amp_l)      = -0.2761
C(amp_g, cen_g)      = +0.1936
C(wid_g, amp_l)      = -0.1651
C(cen_g, wid_g)      = +0.1546
```

and figure:

```plt.plot(x, data, 'o')
plt.plot(x, best_fit, '--', label='best fit')
plt.legend()
plt.show()
```

Total running time of the script: (0 minutes 0.140 seconds)

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