Frequently Asked Questions

A list of common questions.

What’s the best way to ask for help or submit a bug report?

See Getting Help.

Why did my script break when upgrading from lmfit 0.8.3 to 0.9.0?

See Version 0.9.0 Release Notes.

I get import errors from IPython

If you see something like:

from IPython.html.widgets import Dropdown

ImportError: No module named 'widgets'

then you need to install the ipywidgets package, try: pip install ipywidgets.

How can I fit multi-dimensional data?

The fitting routines accept data arrays that are one-dimensional and double precision. So you need to convert the data and model (or the value returned by the objective function) to be one-dimensional. A simple way to do this is to use numpy.ndarray.flatten, for example:

def residual(params, x, data=None):
    ....
    resid = calculate_multidim_residual()
    return resid.flatten()

How can I fit multiple data sets?

As above, the fitting routines accept data arrays that are one-dimensional and double precision. So you need to convert the sets of data and models (or the value returned by the objective function) to be one-dimensional. A simple way to do this is to use numpy.concatenate. As an example, here is a residual function to simultaneously fit two lines to two different arrays. As a bonus, the two lines share the ‘offset’ parameter:

import numpy as np


def fit_function(params, x=None, dat1=None, dat2=None):
    model1 = params['offset'] + x * params['slope1']
    model2 = params['offset'] + x * params['slope2']

    resid1 = dat1 - model1
    resid2 = dat2 - model2
    return np.concatenate((resid1, resid2))

How can I fit complex data?

As with working with multi-dimensional data, you need to convert your data and model (or the value returned by the objective function) to be double precision, floating point numbers. The simplest approach is to use numpy.ndarray.view, perhaps like:

import numpy as np


def residual(params, x, data=None):
    ....
    resid = calculate_complex_residual()
    return resid.view(float)

Alternately, you can use the lmfit.Model class to wrap a fit function that returns a complex vector. It will automatically apply the above prescription when calculating the residual. The benefit to this method is that you also get access to the plot routines from the ModelResult class, which are also complex-aware.

How should I cite LMFIT?

See https://dx.doi.org/10.5281/zenodo.11813

I get errors from NaN in my fit. What can I do?

The solvers used by lmfit use NaN (see https://en.wikipedia.org/wiki/NaN) values as signals that the calculation cannot continue. If any value in the residual array (typically (data-model)*weight) is NaN, then calculations of chi-square or comparisons with other residual arrays to try find a better fit will also give NaN and fail. There is no sensible way for lmfit or any of the optimization routines to know how to handle such NaN values. They indicate that numerical calculations are not sensible and must stop.

This means that if your objective function (if using minimize) or model function (if using Model) generates a NaN, the fit will stop immediately. If your objective or model function generates a NaN, you really must handle that.

nan_policy

If you are using lmfit.Model and the NaN values come from your data array and are meant to indicate missing values, or if you using lmfit.minimize() with the same basic intention, then it might be possible to get a successful fit in spite of the NaN values. To do this, you can add a nan_policy='omit' argument to lmfit.minimize(), or when creating a lmfit.Model, or when running lmfit.Model.fit().

In order for this to be effective, the number of NaN values cannot ever change during the fit. If the NaN values come from the data and not the calculated model, that should be the case.

Common sources of NaN

If you are seeing errors due to NaN values, you will need to figure out where they are coming from and eliminate them. It is sometimes difficult to tell what causes NaN values. Keep in mind that all values should be assumed to be either scalar values or numpy arrays of double precision real numbers when fitting. Some of the most likely causes of NaNs are:

  • taking sqrt(x) or log(x) where x is negative.

  • doing x**y where x is negative. Since y is real, there will be a fractional component, and a negative number to a fractional exponent is not a real number.

  • doing x/y where both x and y are 0.

If you use these very common constructs in your objective or model function, you should take some caution for what values you are passing these functions and operators. Many special functions have similar limitations and should also be viewed with some suspicion if NaNs are being generated.

A related problem is the generation of Inf (Infinity in floating point), which generally comes from exp(x) where x has values greater than 700 or so, so that the resulting value is greater than 1.e308. Inf is only slightly better than NaN. It will completely ruin the ability to do the fit. However, unlike NaN, it is also usually clear how to handle Inf, as you probably won’t ever have values greater than 1.e308 and can therefore (usually) safely clip the argument passed to exp() to be smaller than about 700.

Why are Parameter values sometimes stuck at initial values?

In order for a Parameter to be optimized in a fit, changing its value must have an impact on the fit residual (data-model when curve fitting, for example). If a fit has not changed one or more of the Parameters, it means that changing those Parameters did not change the fit residual.

Normally (that is, unless you specifically provide a function for calculating the derivatives, in which case you probably would not be asking this question ;)), the fitting process begins by making a very small change to each Parameter value to determine which way and how large of a change to make for the parameter: This is the derivative or Jacobian (change in residual per change in parameter value). By default, the change made for each variable Parameter is to multiply its value by (1.0+1.0e-8) or so (unless the value is below about 1.e-15, in which case it adds 1.0e-8). If that small change does not change the residual, then the value of the Parameter will not be updated.

Parameter values that are “way off” are a common reason for Parameters being stuck at initial values. As an example, imagine fitting peak-like data with and x range of 0 to 10, peak centered at 6, and a width of 1 or 2 or so, as in the example at doc_model_gaussian.py. A Gaussian function with an initial value of for the peak center at 5 and an initial width or 5 will almost certainly find a good fit. An initial value of the peak center of -50 will end up being stuck with a “bad fit” because a small change in Parameters will still lead the modeled Gaussian to have no intensity over the actual range of the data. You should make sure that initial values for Parameters are reasonable enough to actually effect the fit. As it turns out in the example linked to above, changing the center value to any value between about 0 and 10 (that is, the data range) will result to a good fit.

Another common cause for Parameters being stuck at initial values is when the initial value is at a boundary value. For this case, too, a small change in the initial value for the Parameter will still leave the value at the boundary value and not show any real change in the residual.

If you’re using bounds, make sure the initial values for the Parameters are not at the boundary values.

Finally, one reason for a Parameter to not change is that they are actually used as discrete values. This is discussed below in Can Parameters be used for Array Indices or Discrete Values?.

Why are uncertainties in Parameters sometimes not determined?

In order for Parameter uncertainties to be estimated, each variable Parameter must actually change the fit, and cannot be stuck at an initial value or at a boundary value. See Why are Parameter values sometimes stuck at initial values? for why values may not change from their initial values.

Can Parameters be used for Array Indices or Discrete Values?

The short answer is “No”: variables in all of the fitting methods used in lmfit (and all of those available in scipy.optimize) are treated as continuous values, and represented as double precision floating point values. As an important example, you cannot have a variable that is somehow constrained to be an integer.

Still, it is a rather common question of how to fit data to a model that includes a breakpoint, perhaps

\[\begin{split}f(x; x_0, a, b, c) = \begin{cases} c & \quad \text{for} \> x < x_0 \\ a + bx^2 & \quad \text{for} \> x > x_0 \end{cases}\end{split}\]

That you implement with a model function and use to fit data like this:

import numpy as np

import lmfit


def quad_off(x, x0, a, b, c):
    model = a + b * x**2
    model[np.where(x < x0)] = c
    return model


x0 = 19
b = 0.02
a = 2.0
xdat = np.linspace(0, 100, 101)
ydat = a + b * xdat**2
ydat[np.where(xdat < x0)] = a + b * x0**2
ydat += np.random.normal(scale=0.1, size=xdat.size)

mod = lmfit.Model(quad_off)
pars = mod.make_params(x0=22, a=1, b=1, c=1)

result = mod.fit(ydat, pars, x=xdat)
print(result.fit_report())
[[Model]]
    Model(quad_off)
[[Fit Statistics]]
    # fitting method   = leastsq
    # function evals   = 11
    # data points      = 101
    # variables        = 4
    chi-square         = 8.79693339
    reduced chi-square = 0.09069003
    Akaike info crit   = -238.512451
    Bayesian info crit = -228.051969
##  Warning: uncertainties could not be estimated:
    x0:  at initial value
[[Variables]]
    x0:  22.0000000 (init = 22)
    a:   1.99347228 (init = 1)
    b:   0.02000061 (init = 1)
    c:   9.39397534 (init = 1)

This will not result in a very good fit, as the value for x0 cannot be found by making a small change in its value. Specifically, model[np.where(x < x0)] will give the same result for x0=22 and x0=22.001, and so that value is not changed during the fit.

There are a couple ways around this problem. First, you may be able to make the fit depend on x0 in a way that is not just discrete. That depends on your model function. A second option is to treat the break not as a hard break but as a more gentle transition with a sigmoidal function, such as an error function. Like the break-point, these will go from 0 to 1, but more gently and with some finite value leaking into neighboring points. The amount of leakage or width of the step can also be adjusted.

A simple modification of the above to use an error function would look like this and give better fit results:

import numpy as np
from scipy.special import erf

import lmfit


def quad_off(x, x0, a, b, c):
    m1 = a + b * x**2
    m2 = c * np.ones(len(x))
    # step up from 0 to 1 at x0: (erf(x-x0)+1)/2
    # step down from 1 to 0 at x0: (1-erf(x-x0))/2
    model = m1 * (erf(x-x0)+1)/2 + m2 * (1-erf(x-x0))/2
    return model


x0 = 19
b = 0.02
a = 2.0
xdat = np.linspace(0, 100, 101)
ydat = a + b * xdat**2
ydat[np.where(xdat < x0)] = a + b * x0**2
ydat += np.random.normal(scale=0.1, size=xdat.size)

mod = lmfit.Model(quad_off)
pars = mod.make_params(x0=22, a=1, b=1, c=1)

result = mod.fit(ydat, pars, x=xdat)
print(result.fit_report())
[[Model]]
    Model(quad_off)
[[Fit Statistics]]
    # fitting method   = leastsq
    # function evals   = 71
    # data points      = 101
    # variables        = 4
    chi-square         = 1.22205174
    reduced chi-square = 0.01259847
    Akaike info crit   = -437.873521
    Bayesian info crit = -427.413039
[[Variables]]
    x0:  19.1687256 +/- 0.46240449 (2.41%) (init = 22)
    a:   2.02976278 +/- 0.02236479 (1.10%) (init = 1)
    b:   0.01999156 +/- 4.4215e-06 (0.02%) (init = 1)
    c:   9.24584679 +/- 0.02565511 (0.28%) (init = 1)
[[Correlations]] (unreported correlations are < 0.100)
    C(a, b)  = -0.828
    C(x0, a) = 0.166
    C(x0, b) = -0.133

The natural width of the error function is about 2 x units, but you can adjust this, shortening it with erf((x-x0)*2) to give a sharper transition for example.