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

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2
votes
3answers
219 views

To obtain an equation for a given curve

I have obtained the graph, I would like to know its equation. The graph seems to be a hyperbolic spiral which, its equation reads, $r = a/\theta$. I read here and also, but these are concerning the ...
3
votes
2answers
1k views

Find a best fitting curve for some data with no regular pattern

Suppose some data with no regular pattern is given, so common patterns of functions all fail to fit it. Then how can one find the best fitting curve? I believe there will be some data for which we can ...
0
votes
0answers
50 views

How do I constrain the result of fitting my non-linear model to be greater then 0

fitresulty21 = NonlinearModelFit[ydata21, {funfit[y, σ, A, B, x1, d, d/2], A > 0}, {{x1, 20}, {σ, 3}, {A, 200}, {B, 2000}, {d, 110}}, y]; ...
3
votes
2answers
396 views

In a ListPlot of LinearModelFit, plot error band

This is similar to this question. The fitted line can be plotted alongside with the data with this code: Show[ListPlot[data], Plot[lm[x], {x, 0, 5}]] I would ...
0
votes
1answer
260 views

Exporting tables of interpolating functions

A few weeks ago I asked a question about manipulating parameters in NDSolve (Looping with NDSolve?) , and received some very helpful advice about the manipulate environment; now I want to take the ...
2
votes
2answers
232 views

Fitting a variable using multiple equations

I would like to find the best fit of two variables for a number of approximate equations, such as: 1x+2y+2=7.04 2x+y+4=7.98 1.5x+1.5y-2=2.53 1.8x+3y-1=6.77 That ...
2
votes
1answer
77 views

Trouble with using a log10 function in NonlinearModelFit

I was wondering why won't mathematica give a result where the function is also Log10, instead it gives the ordinary Log. Is it ...
1
vote
1answer
220 views

Find polynomial equation for set of 3D data

data was given in columns in the order {y, x, z}, with y dependent on x, z ...
5
votes
0answers
79 views

Third syntax version of LogitModelFit: unexpected result of “BestFit”

The third listed syntax version of LogitModelFit allows one to specify input in a simple way: Only a design matrix (with a row of values of the explanatory input ...
0
votes
1answer
193 views

How do I fit NDSolve result to experimental data? [duplicate]

I have two coupled ordinary differential equations which I solve numerically in Mathematica, but now I want to fit the solution with experimental data. I do following, (the experimental data ...
0
votes
0answers
32 views

Data Fitting with xerrors and yerrors using findfit [duplicate]

I'm trying to fit data with xerror and yerror using "Findfit", so i'm trying the same form than in tuto : ...
0
votes
1answer
246 views

Discrete peaks to curve via Voigt summation

I have two data sets. One is an experimental recording of an absorption spectrum, composed of regularly spaced (wavenumber, intensity) coordinates with a fine wavenumber resolution, thus making ...
1
vote
1answer
146 views

Fitting Function with 3 parameters

I am trying to fit a function with 3 parameters however the result strongly depend on the initial values of parameters: ...
0
votes
0answers
39 views

Fitting for multiple data in Mathematica [duplicate]

I've just started to use Mathematica for programming and I was wondering how I could do Fitting for several data sets. For example, I have one curve. For this curve I need to plot a fit curve, if my ...
0
votes
0answers
50 views

How to approximate a computationally expensive 5-dimensional manifold?

I have a 4-parameter family of functions, which I'll refer to as y[a, b, c, d][x]. In this notation, a, b, c, d are the 4 ...
3
votes
0answers
183 views

Module in numerical model for NonlinearModelFit is slow and leaks memory

I am trying to make a NonlinearModelFit where the model is the result of a numerical calculation. My code works, but it is very slow and also seems to have a memory ...
12
votes
3answers
353 views

Disentangling the data

An experiment yields a functional dependence on two variables $F(x,y)$, can be imagined as a 2D map. It is known that the function can be factored as follows $F(x,y)=fx(x) gy(y) +gx(x) fy(y)$. Given ...
2
votes
1answer
313 views

Model fitting to noisy data with a custom minimization function

I'm looking into fitting some data with Mathematica. I've got my head around how NonlinearModelFit works (I've been using the Levenberg-Marquardt algorithm for some ...
0
votes
2answers
149 views

Least Square Fitting

stuck on a mathematica assignment and could really use some help. A) Fit a function with the shape log(Y) = a0 + a1log(U) to the datapoints (log(Ui), log(Yi) with an least square fitting. Show this ...
1
vote
1answer
70 views

Inaccuracy of Piecewise function? [duplicate]

I have the following issue and can't find a solution so far. ...
0
votes
1answer
81 views

Trouble fitting an explicitly complex model with the TransformedFit package

This is follow up from a previous question in which @Oleksandr R. suggested the use of a package he developed for splitting a model and data into real and imaginary parts to avoid a problem with ...
0
votes
1answer
170 views

NMinimize holding problem

I have a function that I want to minimize numerically through an NMinimize command (because it's very complicated analytically). The minimizer call looks as follows: ...
1
vote
1answer
164 views

Multiple Linear Regression - obtaining equation with constant term

I am trying to use the LinearModelFit function to obtain a linear regression of my 5 inputs for my single output. I have the input data: ...
0
votes
0answers
52 views

Fitting data involving units

I want to fit some data to a model. However, if the data involves units in the independent variable, fitting seems not to work. As an example, consider the code ...
4
votes
1answer
459 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 ...
1
vote
2answers
152 views

How to fit exponential function which is not converging

I performed an experiment where I measured diffusion in a lipid bilayer. I performed the measurement by fluorescently labeling some molecules in the bilayer, and the irradiating them with light ...
11
votes
1answer
345 views

Fit two intersecting straight lines in Mathematica

I am trying to do a Kurie analysis of the double beta decay of Strontium-90. Here we have two straight sections, and I need to obtain a value for the intersection along with an error for it. I ...
7
votes
1answer
380 views

Fitting a numerical integral via NonLinearModelFit to magnetic data

I'm new to Mathematica and I'm currently trying to fit $$m_T (H,T) = N_T \int\limits_0^{\infty} \frac{x k_\text{B} T}{\mu_0 H} \mathcal{L}(x) \text{pdf}(D_\text{mag}) \text{d}D_\text{mag}$$ with ...
0
votes
0answers
91 views

fitting system of ODEs - “part2 of {} does not exist” errod

I'm trying to fit my data to a system of ODEs: x'[t]==a*x[t]+b*y[t] y'[t]==c*y[t]+d*x[t]+e*z[t] z'[t]==f*z[t]+g*y[t] having t,x[t],y[t],z[t]. I followed the code ...
1
vote
1answer
168 views

show fit information on plot

After performing a fit in Mathematica, I would like to show the fitted parameters in a box on the plot showing the fitted function. How would I go about achieving that? Here is a MWE: ...
0
votes
1answer
232 views

Fitting to a sigmoidal model

I am trying to fit a set of stochastic data to a sigmoidal function, but it's not working. Can you please help? Here is the function I am trying to fit to my data. ...
1
vote
1answer
199 views

NonLinearFit with “complicated” integral model

I have a set of data $y_i (z_i)$ with errors $\Delta y_i$ ...
8
votes
1answer
211 views

Inconsistent DistributionFitTest results?

In pondering this question, I used Mariana's function to generate the following data. ...
1
vote
1answer
218 views
17
votes
2answers
2k 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 ...
4
votes
1answer
278 views

Fitting triangular function with HeavisideTheta

I have a problem fitting a triangular function (like potential vs. time in cyclic voltammetry) with a HeavisideTheta function. I just want to get used to ...
2
votes
1answer
102 views

nonlinearnodelfit with a matrix as weights

I have to fit a non linear model to my data and I am trying to use nonlinearmodelfit. The problem is that I have systematic errors, so the ...
1
vote
1answer
303 views

FindFit (Jacobian Error) [duplicate]

I, like others before me, am struggling with FindFit. So, I tried a simple example. ...
-1
votes
1answer
66 views

How to fit one parametric array to another numerical array?

I have two arrays of length n. One of them is obtained by experiment, so every element of the array is a number. The other array is parametric, each element is a ...
6
votes
1answer
136 views

Why LinearModelFit is slower than NonlinearModelFit?

Why LinearModelFit is slower than NonlinearModelFit? ...
2
votes
0answers
311 views

Speeding up Nonlinearmodelfit by constraining parameters?

I have a complicated parametric PDE that can be fitted to some data with NonlinearModelFit, but takes several hours to estimate the best values of the four free parameters. Currently, the code ...
1
vote
1answer
295 views

dynamically set fit parameters and models with FindFit

I want to fit a gaussian profile by setting some values dynamically, but FindFit returns an error and i can't see the problem. with a given gaussian: ...
0
votes
1answer
216 views

Nonlinear fit with piecewise functions

I have an ensemble of data points $(x_i,y_i)$ and I need to fit them according to $y=F(a,b,x)$ if $x \leq x_{ref}$ and $y=G(c,d,x)$ if $x \geq x_{ref}$. The parameters I need to adjust are then ...
1
vote
1answer
283 views

Can ParametricNDsolve be used for coupled PDEs with 5 parameters?

I have a system of coupled PDEs with five parameters that I only know ranges for rather than explicit values, and I was wondering if I could define a parametric equation with ParametricNDSolve and ...
1
vote
1answer
158 views

Fitting data using a series of Sin and Cos

I have the following data representing the normal displacement caused by a normal load applied at the middle cross section of a cylinder: I've made the data available here. I am trying to fit ...
5
votes
1answer
413 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, ...
4
votes
1answer
818 views

NonlinearModelFit does not find a good fit

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