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# scipy.optimize.curve_fit

`scipy.optimize.``curve_fit`(f, xdata, ydata, p0=None, sigma=None, **kw)

  Use non-linear least squares to fit a function, f, to data.

  Assumes `ydata = f(xdata, *params) + eps`

  Parameters : | f : callable The model function, f(x, ...). It must take the independent variable as the first argument and the parameters to fit as separate remaining arguments. xdata : An N-length sequence or an (k,N)-shaped array for functions with k predictors. The independent variable where the data is measured. ydata : N-length sequence The dependent data — nominally f(xdata, ...) p0 : None, scalar, or M-length sequence Initial guess for the parameters. If None, then the initial values will all be 1 (if the number of parameters for the function can be determined using introspection, otherwise a ValueError is raised). sigma : None or N-length sequence If not None, it represents the standard-deviation of ydata. This vector, if given, will be used as weights in the least-squares problem.
  Returns : | popt : array Optimal values for the parameters so that the sum of the squared error of `f(xdata, *popt) - ydata` is minimized pcov : 2d array The estimated covariance of popt. The diagonals provide the variance of the parameter estimate.

  See also

  `leastsq`

  Notes

  The algorithm uses the Levenberg-Marquardt algorithm through `leastsq`. Additional keyword arguments are passed directly to that algorithm.

  Examples

      >>> import numpy as np
      >>> from scipy.optimize import curve_fit
      >>> def func(x, a, b, c):
      ...     return a*np.exp(-b*x) + c

      >>> x = np.linspace(0,4,50)
      >>> y = func(x, 2.5, 1.3, 0.5)
      >>> yn = y + 0.2*np.random.normal(size=len(x))

      >>> popt, pcov = curve_fit(func, x, yn)

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