# Questions tagged [fitting]

Questions on the use of Mathematica to construct models for approximating empirical data.

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2answers
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### 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 ...
5answers
11k 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 ...
6answers
16k 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 ...
6answers
14k 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 ...
2answers
2k 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?
3answers
4k 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 <...
6answers
14k 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 ...
6answers
20k 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 ...
4answers
4k 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: ...
7answers
6k views

### Fitting points to tilted, off-center ellipse

I have 24 x-y points that are supposed to form an ellipse. ...
5answers
9k 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 ...
5answers
4k 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 ...
2answers
3k 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.
1answer
1k 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, ...
2answers
1k 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 ...
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 ...
1answer
760 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). ...
1answer
549 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 ...
3answers
4k 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 ...
1answer
5k 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 ...
1answer
3k 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 ...
1answer
7k views

### NonlinearModelFit does not find a good fit

I am trying to fit my data to the following function, $$\frac{a b t \left(\log \left(\frac{-a d t+a t-1}{a d t}\right)-2\right)}{4 (a t-1)}-c$$ ...
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: ...
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 (...
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 ...
3answers
565 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 ...
3answers
881 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 ...
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 ...
4answers
17k views

### Fitting a two-dimensional Gaussian to a set of 2D pixels

Imagine I have a set of data like the following: ...
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 ...
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 ...
3answers
1k 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 ...
1answer
1k 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: ...
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. ...
1answer
675 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 ...
3answers
2k 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 ...
2answers
763 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 ...
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, ...
2answers
551 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 ...
1answer
1k 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 ...
5answers
6k views

### How to plot Fit functions?

If I do something like this f[x_]:=x^2 Plot[f[x],{x,1,10}] Mathematica plots the function $f(x)=x^2$, as expected. However, ...
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 ...
2answers
960 views

### Can't find a fit for Erf

I have the following numbers ...
1answer
154 views

### NonLinearFit with data

i've data looking like this: ListPlot[data] Now I want to make a NonLinearFit ...
1answer
567 views

### Non-linear curve fit problem

I am having a problem with making a fit to data in Mathematica, which may involve my understanding of the methods available. I am trying to fit the derivative of a Frota function (which is a Single ...
4answers
287 views

### Fitting of 2d data points with a function considering scaling, rotation and translation

I have the following set of 2d data points: ...
5answers
4k views

### Mathematica Implementations of the Random Forest algorithm

Is anyone aware of Mathematica use/implementation of Random Forest algorithm?
3answers
2k views

### What is behind experimental function: FindFormula?

In version 10.2 there is a new experimental function: FindFormula[]. I suspect that a genetic programming algorithm (symbolic regression) is behind this new ...
0answers
1k views

### Nonlinear least squares on a GPU with Mathematica 9

Update: A Mathematica wrapper for (https://github.com/zitmen/cuLM) should allow for us to directly implement the Levenberg-Marquardt algorithm in CUDA for nonlinear least squares fitting. In a ...
3answers
3k views

### Data fitting with Image processing feature detection

I have some 2D data that once plotted looks like the following ...