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

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215 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 ...
0
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1answer
195 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
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2answers
137 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 ...
5
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3answers
178 views
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0answers
36 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 ...
2
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1answer
59 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 ...
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0answers
38 views
0
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1answer
86 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
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0answers
69 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
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1answer
95 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
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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
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1answer
130 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
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1answer
124 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
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0answers
35 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
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0answers
42 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
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0answers
127 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 ...
10
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3answers
292 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
238 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
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2answers
123 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
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1answer
57 views

Inaccuracy of Piecewise function? [duplicate]

I have the following issue and can't find a solution so far. ...
0
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1answer
69 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
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1answer
102 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
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1answer
73 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
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0answers
43 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
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1answer
220 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
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2answers
128 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
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1answer
312 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
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1answer
294 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
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0answers
56 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
150 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
136 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
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1answer
155 views

NonLinearFit with “complicated” integral model

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

Inconsistent DistributionFitTest results?

In pondering this question, I used Mariana's function to generate the following data. ...
1
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1answer
93 views
16
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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
218 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
75 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
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1answer
142 views

FindFit (Jacobian Error) [duplicate]

I, like others before me, am struggling with FindFit. So, I tried a simple example. ...
-1
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1answer
56 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
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1answer
115 views

Why LinearModelFit is slower than NonlinearModelFit?

Why LinearModelFit is slower than NonlinearModelFit? ...
0
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0answers
81 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
201 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
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1answer
130 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
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1answer
149 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
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1answer
126 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 ...
0
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0answers
71 views

Simultaneously fitting data sets with many variables as free parameters

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
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1answer
254 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
412 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
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2answers
82 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] ...