Questions tagged [fitting]
Questions on the use of Mathematica to construct models for approximating empirical data.
268
questions
32
votes
2answers
7k views
How to fit 3 data sets to a model of 4 differential equations?
I'm a biologist and a newbie in Mathematica. I want to fit three data sets to a model consisting of four differential equations and 10 parameters. I want to find the parameters best fitting to my ...
49
votes
5answers
13k views
Simultaneously fitting multiple datasets
What is the proposed approach if one wants to simultaneously fit multiple functions to multiple datasets with shared parameters?
As an example consider the following case: We have to measurements of ...
55
votes
6answers
19k views
How to perform a multi-peak fitting?
I am wondering how to implement the multi-peak detecting and fitting in Mathematica. Following is an example of fitting the data using three peaks (such that the data ~ peak1 + peak2 + peak3).
The ...
35
votes
6answers
17k views
Estimate error on slope of linear regression given data with associated uncertainty
Given a set of data, is it possible to create a linear regression which has a slope error that takes into account the uncertainty of the data?
This is for a high school class, and so the normal ...
40
votes
2answers
4k views
What are some common issues with fitting functions to data?
Mathematica has numerous functions designed to, or capable of, fitting known functions, and finding unknown functions to match data sets. What are some common issues that come with finding those fits?
21
votes
3answers
5k views
Fitting fractional complex data with NonlinearModelfit
I've difficulites with the NonlinearModelFit function.
In principle Mathematica should be able to deal with complex data.
E.g. if I define the following table
<...
24
votes
6answers
15k views
Problem with NonlinearModelFit
I'm having trouble with a non-linear fit:
fit = NonlinearModelFit[data,
y0 + A Sin[\[Pi] (x - xc)/w], {y0, xc, A, w}, x]
where ...
25
votes
4answers
5k views
Implementation of smoothing splines function
I have some problems in writing a module for spline smoothing. Actually, I have been trying for about two weeks.
My listing is here:
...
25
votes
6answers
21k views
How to determine the center and radius of a circle given some points in 3D?
I was wondering if anyone could give me a hand with this problem I have.
I have six points on a plane, and I am trying to determine if they form a circle or not.
I know that any three points in 2D ...
46
votes
7answers
7k views
Fitting points to tilted, off-center ellipse
I have 24 x-y points that are supposed to form an ellipse.
...
19
votes
5answers
10k views
Using FindFit to fit $a\,b^t$: how to avoid introducing complex numbers?
I'd like to find a model $f(t)=a\,b^t$ which matches the following data
...
27
votes
3answers
4k views
What is the difference between FindFit and NonlinearModelFit
I cannot get the difference between these two fitting functions in Mathematica. I even read in MMA that the result of these two are the same.
29
votes
5answers
5k views
Mathematica envelope for the bottom of a plot, a generic function
I have the following set-up:
xaxis = Table[x, {x, 0, 10, 0.01}];
yaxis = Table [Sin[x] + Abs[RandomReal[{-1, 1}]], {x, 0, 10, 0.01}];
ListLinePlot[Transpose[{
xaxis, yaxis}]]
My questions is how can ...
24
votes
1answer
2k views
Difference between Fitting Algorithms
I am new to Mathematica, and I don´t quite understand, what the difference between the fitting algorithms Fit, FindFit, ...
14
votes
1answer
1k views
Fittting data with combination of an unknown number of Gaussians
I have data that I want to fit with a constant plus a combination of Gaussians, with their actual number being one parameter of the fit (besides the average and the variance of every one of them).
...
13
votes
1answer
6k views
Methods for NonlinearModelFit
I am using NonlinearModelFit for a thesis project.
I get quite different results if I change the Method to LevenbergMarquardt or QuasiNewton or ConjugateGradient ...
15
votes
2answers
2k views
Is it possible to use the LevenbergMarquardt algorithm for fitting a black-box residual function?
I have a black-box multiargument multiparametric function of the type SRD[dataPoint_List,params_List] which accepts experimental data along with the parameters of ...
16
votes
3answers
2k views
2D smoothing spline interpolation
Does Mathematica have 2D smoothing spline interpolation built in?
I requires an interpolation method with smooth first derivatives and cubic bivariate splines fulfill this nicely. In python I would ...
9
votes
1answer
5k views
Combined fitting via NonlinearModelFit
I am trying to fit my data to a combined function model. Say I have two functions with some common parameter(s)
f[x_]:= a*x^2 + b*x + c
g[x_]:= d*x^2 + e*x + c
...
4
votes
1answer
750 views
how to find curve fitting parameters without an explicit relation between x and y?
Let's say I have some experimental data (x,y) and I want to find some fitting parameters. But in my mathematical model, the fitting parameter are not in a simple equation that relates x and y. For ...
18
votes
1answer
406 views
Adding Regularisation to Built-in Interpolation function
tl;tr; How to improve performance of regularised Interpolation?
Context
Since Version 12, Mathematica now incorporates a range of (underrated IMHO) ...
19
votes
3answers
5k views
How to use FindFit to fit an implicit function?
Now I am trying to fit some data with a implicit model function.
Firstly, I tried a toy example.
Toy example with input and output
...
4
votes
2answers
310 views
Fourier Transform to help guess with NonLinearModelFit
I imported some data in Mathematica which I cleaned a bit. This process went well. I also managed to plot it, and tried to take the Fourier transform of the data and plot it again. I'm not sure if I ...
17
votes
3answers
4k views
Finding distribution parameters of a gaussian mixture distribution
Short version: how to estimate the parameters of a mixture of multivariate normal distributions (i.e.: Gaussian mixture model)?
Long version.
I am trying to estimate the parameters of a mixture of ...
14
votes
2answers
1k views
Fit a function to data so that fit is always equal or less than the data
I have a set of measurement data and I try to fit there a function (a Exp[b x] + c Exp[d x] - o). I have two problems:
The fit function does not converge nor after ...
21
votes
3answers
2k views
Sensitivity of NonlinearModelFit to model
I have come across a circumstance where NonlinearModelFit is very sensitive to the model used. I am aware that NonlinearModelFit ...
9
votes
1answer
4k views
Fitting piecewise functions
I have several large data sets which follow the following pattern: A position is measured, a force is applied until a new equilibrium is found.
I'd like to find a fit for the position, at least at the ...
7
votes
1answer
7k views
NonlinearModelFit does not find a good fit
I am trying to fit my data to the following function,
$$\frac{a b t \left(\log \left(\frac{-a d t+a t-1}{a d t}\right)-2\right)}{4 (a t-1)}-c$$
...
13
votes
2answers
2k views
Detecting an ellipse in a glaucoma photo
For glaucoma diagnosis it is common to determine a "cup to disk ratio" which compares the diameter of the optic disk (VDD) and optic cup (VCD). The optical disk is visible as a circular red feature (...
20
votes
2answers
2k views
FindFit returns Infinity::indet error when data contains {0,0}
Let's consider the following data:
data = Table[{q, 2*q^2}, {q, 0, 2}];
and then, do a very simple fitting to this data:
...
6
votes
1answer
1k views
Finding NonlinearModelFit of multiple data sets with the same parameters and in two dimensions
I have multiple sets of data (between 3 and 6 depending on the cases) dependent of space, time, and some parameters. The data are the response of a harmonic oscillator under a non-trigonometrical ...
5
votes
3answers
621 views
Determing two Nonlinear model fits with 95% confidence bands from one data set
I have the following data which is postulated to have contributions from two different sources .....as can be seen from the confidence band, many points are out of the band.
Question: How can I ...
4
votes
2answers
148 views
Applying an exponential decay fit with uncertainties
I have some data from a radioactive decay experiment that I'm trying to fit an exponential decay curve on that will take account of the uncertainties on the data, and then ideally return the data for ...
8
votes
1answer
2k views
Find a Fourier series from discrete data
I am trying to fit a Fourier cosine series to discrete data. I read through this, but I was not able to understand it. The data should be periodic with a period of $0.2 \text{ m}$, and it is the ...
7
votes
3answers
1k views
Removing background from peak function
Let's say I have a a very large list of data in the format {{n,f[n]}} so something like {{1,600},{2,700},{3,1100}...} and if this data is plotted, then it will look like a sum of Gaussian functions+a ...
6
votes
3answers
738 views
Multi-peak fitting for peak position
I have a {x,f} data-set featuring multiple peaks. The peaks evolve with a second variable y. I would like to fit the multiple ...
25
votes
4answers
2k views
Generating an “average curve” from a dense set of “semicontinuous curves” which clear trends
This question is related to a previous one of mine: Partitioning a superset of coordinates into subsets that generate continuous curves, where the challenge was to partition a data set into two ...
18
votes
4answers
22k views
Fitting a two-dimensional Gaussian to a set of 2D pixels
Imagine I have a set of data like the following:
...
20
votes
1answer
3k views
Finding the area, algebraic curve and jaggedness of an arbitrary shape
I start with a photograph of a shape (physically made by the flow of a liquid into another), of which I can extract the border, manually or using Mathematica's feature detect feature :
Using the ...
14
votes
1answer
2k views
How does Mma compute Confidence Intervals?
I am trying to understand how Mma computes the Confidence Intervals after a NonlinearModelFit. Consider the following example:
...
8
votes
1answer
2k views
ODE fitting to dataset
So, I have a ODE system, it is a complex biochemical kinetic mechanism with six species changing over time.
...
14
votes
2answers
2k views
Does FindFit support complex numbers or doesn't it?
Inspired by this previous question: Findfit doesn't give the good fit; Changing the starting values will not change the results.
Consider the following complex-valued dataset.
...
7
votes
1answer
737 views
Findfit does not find the best fit
I am working on a project that needs curve fitting. The experimental data should be fitted with a model that calculated with an integration equation.
At first, I enter my experimental data
...
6
votes
1answer
2k views
Fit data with linear combinations of Cos and Sin
Recall that if $f$ is a piecewise continuous function on the interval $[-\pi, \pi]$, then the Fourier series of $f$ is
$$f(x) = \sum_{n=0}^{\infty} (a_n \cos(nx) + b_n \sin(nx)).$$
See for example, ...
5
votes
2answers
1k views
Mathematica Interpolation or approximation
I have lists of points X and Y.
{1212,1216,1217,1219...}, {1,2,3,4,5,6...}
I combine ...
5
votes
3answers
3k views
Fitting data to a circle with FindFit
I'm currently trying to use the Mathematica's FindFit command to fit a curve of some data to the bottom half of a circle. The data is of the form
...
8
votes
1answer
3k views
Test Goodness of fit for FindFit
Is there any way to get an estimate of the goodness of fit from FindFit, for instance getting the final error? The documentation doesn't provide any hints, and a quick Google search didn't return any ...
4
votes
2answers
598 views
Unable to fit function convolved with NIntegrate with FindFit even with NumericQ
I am attempting to fit to the convolution of a simple function with a Gaussian. (I realize this could be done with Convolve also, but I thought I could make it go faster this way). I am able to ...
5
votes
2answers
2k views
How can I consistently get a good logistic regression fit?
I'm executing the command
NonlinearModelFit[data, c/(1 + a Exp[-b x]), {a, b, c}, x]
with the data being
...
2
votes
2answers
1k views
