![]() ![]() ![]() If you know of such an algorithm or data set, please let us know. However, so far we have never seen a case where any algorithm works better than Levenberg-Marquardt. Occasionally a user will inquire about other data fitting algorithms such as simulated annealing as an alternative to Levenberg-Marquardt. If you have data containing multiple possibly overlapping peaks, the multi-peak package can automatically analyze your data and generate initial guesses prior to data fitting. Igor pro 8 no data was found in file manual#For data fitting to user-defined functions you must supply manual guesses. If this produces unsatisfactory results, you can try manual guesses. Which valley Igor finds first depends on the initial guesses.įor built-in curve fitting functions, you can let Igor automatically set the initial guesses. When Igor finds the bottom of a valley it concludes that the fit is complete even though there may be a deeper valley elsewhere on the surface. Some functions, however, may have multiple valleys, places where the fit is better than surrounding values, but it may not be the best fit possible. In this case, when the bottom of the valley is found, the best fit has been found. Some curve fitting functions may have only one valley. This is a point on the surface where the coefficient values of the fitting function minimize, in the least-squares sense, the difference between the experimental data and fit data (the model). We want to find the deepest valley in the chi-square surface. Starting from the initial guesses, Igor searches for the minimum value by travelling down hill from the starting point on the chi-square surface. The search process involves starting with an initial guess at the coefficient values. Chi-square defines a surface in a multidimensional error space. Initial Guessesįor non-linear least-squares data fitting, Igor uses the Levenberg-Marquardt algorithm to search for the minimum value of chisquare. For each try, it computes chisquare searching for the coefficient values that yield the minimum value of chi-square. Igor tries various values for the unknown coefficients. Iterative Data Fitting (non-linear least-squares / non-linear regression)įor the other built-in data fitting functions and for user-defined functions, the operation must be iterative. Igor uses the singular value decomposition algorithm. For curve fitting to a straight line or polynomial function, we can find the best-fit coefficients in one step. We want to find the coefficients a and b that best match our data. Suppose we have a theoretical reason to believe that our data should fall on a straight line. The simplest case is data fitting to a straight line: y = ax + b, also called "linear regression". Where y is a fitted value (model value) for a given point, y i is the measured data value for the point and σ i is an estimate of the standard deviation for y i. The best values of the coefficients are the ones that minimize the value of Chi-square. We want to find values for the coefficients such that the function matches the raw data as well as possible. In curve fitting we have raw data and a function with unknown coefficients. Some people try to use curve fitting to find which of thousands of functions fit their data. The curve fit finds the specific coefficients (parameters) which make that function match your data as closely as possible. We assume that you have theoretical reasons for picking a function of a certain form. The idea of curve fitting is to find a mathematical model that fits your data. Packages built on Igor's basic curve fitting capability add functionality:
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |