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

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2
votes
3answers
215 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 ...
0
votes
0answers
48 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]; ...
2
votes
2answers
233 views
0
votes
0answers
54 views

Fix Parameters for NonLinearModelFit?

Is it possible to fix the parameters for NonLinearModelFit within the function itself instead of defining the fix parameters at the beginning of the notebook? I am ...
0
votes
1answer
345 views

Obtaining the envelope of an oscillating function and perform fitting

There is an elegant way to obtain the envelope of an oscillation function explained here http://mathematica.stackexchange.com/a/27854/15966 My question is how to modify the code below so I can fit ...
3
votes
2answers
298 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 ...
2
votes
1answer
68 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
0answers
41 views

A more efficient way of fitting a non-linear model that returns an entire list?

I have a function that takes two parameters, del and nu, and returns a list npoints long ...
1
vote
1answer
143 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 ...
0
votes
1answer
141 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 : ...
5
votes
3answers
191 views

Looking for ideas for handling a complicated fitting problem

I have the following data: ...
1
vote
1answer
138 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
1answer
179 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 ...
0
votes
0answers
37 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 ...
5
votes
0answers
75 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 ...
2
votes
2answers
180 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 ...
0
votes
0answers
45 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
154 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 ...
2
votes
1answer
281 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
138 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 ...
12
votes
3answers
329 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 ...
1
vote
1answer
64 views

Inaccuracy of Piecewise function? [duplicate]

I have the following issue and can't find a solution so far. ...
0
votes
1answer
74 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
138 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
109 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
49 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
360 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
144 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
326 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
346 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
81 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
157 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
199 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. ...
8
votes
1answer
188 views

Inconsistent DistributionFitTest results?

In pondering this question, I used Mariana's function to generate the following data. ...
1
vote
1answer
188 views

NonLinearFit with “complicated” integral model

I have a set of data $y_i (z_i)$ with errors $\Delta y_i$ ...
8
votes
2answers
827 views

What is the best distribution for my histogram?

I defined a security bound for a random walk (cube with 15 lengh) and i have this code to obtain a sample of the random times at which the random walk crosses the boundary for the first time: ...
1
vote
1answer
148 views

FindFit::nrlnum What am I doing wrong?

I have a model called qobs: ...
2
votes
1answer
101 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
217 views

FindFit (Jacobian Error) [duplicate]

I, like others before me, am struggling with FindFit. So, I tried a simple example. ...
-1
votes
1answer
60 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 ...
1
vote
0answers
274 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 ...
0
votes
1answer
193 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
139 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 ...
1
vote
1answer
226 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 ...
0
votes
0answers
80 views

Simultaneously fitting data sets with many variables as free parameters [duplicate]

I found a partial answer in the documentation centre, but would like to expand on it and know how can I fit multiple sets of data and extract the parameters from them. It is an eigenvalue problem - We ...
5
votes
1answer
338 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
595 views

NonlinearModelFit does not find a good fit

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

Minimizing the maximal residual in mathematica

With this: d1 = 10; d2 = 4; mat = RandomReal[{-1, 1}, {d1, d2}]; vec = RandomReal[{-1, 1}, d1]; LeastSquares[mat, vec] ...
0
votes
0answers
328 views

histogram fit for probability density

I am trying to fit the (probability density) histogram of some data with the exponential function, but I am having difficulties. My raw data are in file called ...