In our routines, the cov_x is calculated as (J^T * J) ^-1, where J is the jacobian.
#SCIPY LEAST SQUARES HOW TO#
Just please give me indication on how to do that. I have never provided a patch, but the fix should be quite simple, INDEPENDENT of the values of the data errors in the case they are This means that not only the doc needs fixing, but also theĬurve_fit code, those estimation of the parameters' error is the diagonal terms are the errors in the parameters). Used as "as weights in least-squares problem" (curve_fit doc), andĬov_x gives directly the covariance of the parameter estimates It is correct if there are no error bars of the inputĭata (the sigma of curve_fit is None). Unfortunately, this is not correct, or better it is only partiallyĬorrect. Get the covariance of the parameter estimates - see curve_fits."" Matrix must be multiplied by the residual standard deviation to The main concern is about the use of cov_x to estimate the errorīar of the fitting parameters. I presented these results at the last Python in Physics workshop.ġ. The performances of the optimize.leastsq method for data fitting. I wanted to briefly show you the results of an analysis I did on Who can tell what their errors variances are before doing any I don't really care which it is if the majority of users are engineers To have clear definitions that the "average" user can use by default. Since we just had this discussion, I'm not arguing again. Since this depends on what you define as weight or sigma, both are Many thanks for your attention, and sorry for the long mail 15.īy the way, we should also advice that the in case of analytical derivative this number is half, even if I personally would keep the same number for both cases. one parameter does not move too much, the routine stops and complains with "Both actual and predicted relative reductions in the sum of squares are at most 0.000000 and the relative error between two consecutive iterates is at most 0.000000" as in the case of boxBod at pg. A relatively huge number is not a problem, by the way, because if the system is sloppy. Is pretty low, so I suggest to increase the prefactor 100 to 1000. The maximum where N is the number of elements in x0. The maximum number of calls to the function. For quite a long time I did not realized that the fit needed more iterations that the number set by maxfev, and thus I started to think that the leastsq was not good enough for 'hard' data. The convergence of the fit in the most difficult cases (see page 15 of my presentation) can required up to about 3000 iterations, reduced to 800 when using analytical derivatives. I have never provided a patch, but the fix should be quite simple, just please give me indication on how to do that.Ģ. This means that not only the doc needs fixing, but also the curve_fit code, those estimation of the parameters' error is INDEPENDENT of the values of the data errors in the case they are constant, which is clearly wrong. But if provided, they are used as "as weights in least-squares problem" (curve_fit doc), and cov_x gives directly the covariance of the parameter estimates (i.e. It is correct if there are no error bars of the input data (the sigma of curve_fit is None). Unfortunately, this is not correct, or better it is only partially correct. In the docs, it is set that "this matrix must be multiplied by the residual standard deviation to get the covariance of the parameter estimates - see curve_fits."" The main concern is about the use of cov_x to estimate the error bar of the fitting parameters. I presented these results at the last Python in Physics workshop. I wanted to briefly show you the results of an analysis I did on the performances of the optimize.leastsq method for data fitting.
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