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

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5
votes
3answers
178 views

Looking for ideas for handling a complicated fitting problem

I have the following data: ...
1
vote
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
votes
1answer
129 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
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 ...
5
votes
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 ...
2
votes
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 ...
0
votes
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
votes
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 ...
2
votes
1answer
237 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
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 ...
10
votes
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 ...
1
vote
1answer
57 views

Inaccuracy of Piecewise function? [duplicate]

I have the following issue and can't find a solution so far. ...
0
votes
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
votes
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
vote
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
votes
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
votes
1answer
219 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
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
votes
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
votes
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
votes
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. ...
8
votes
1answer
162 views

Inconsistent DistributionFitTest results?

In pondering this question, I used Mariana's function to generate the following data. ...
1
vote
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
2answers
614 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
93 views

FindFit::nrlnum What am I doing wrong?

I have a model called qobs: ...
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
vote
1answer
142 views

FindFit (Jacobian Error) [duplicate]

I, like others before me, am struggling with FindFit. So, I tried a simple example. ...
-1
votes
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 ...
0
votes
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 ...
0
votes
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
vote
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 ...
1
vote
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 ...
0
votes
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
votes
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
411 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
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] ...
0
votes
0answers
218 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 ...
1
vote
2answers
158 views

FindFit giving weird values on a logistic equation

I was trying to fit a set of data onto a logistic equation, however it ended up telling me that the initial value when $t=0$ is greater than the maximum limit, thus I am led to believe that it isn't ...
0
votes
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
votes
2answers
439 views

Line of best fit on LogLog plot

I have a LogLog plot, and i'm unsure about how to fit a line to it. The data represents a calibration curve. ...
0
votes
1answer
92 views

Replicating Excel output using Mathematica

I have 2 columns of data in Excel. One is inputs the other is outputs. I ask Excel to make a graph of that data and to fit the data to a power trendline. Excel does this and it's fine as far as it ...
16
votes
5answers
971 views

Finding the intersection of a curve with an interpolation function

There are no issues trying to find the intersection points of two defined curves. ...
1
vote
2answers
192 views

Can't find a fit for Erf

I have the following numbers ...
1
vote
2answers
86 views

How can I get a fully functional FittedModel when fitting data to a pointwise function?

When I am fitting data with a pointwise function using NonlinearModelFit, the produced FittedModel fails to calculate variances ...
0
votes
0answers
41 views

Supply parameter values in NormFunction of FindFit

As I understand the input to the NormFunction is a list of residuals. Is there a way to get parameter values into the NormFunction as well? I ran into a problem where the norm depends on the values of ...
0
votes
1answer
91 views

Constraining some rows from LeastSquares to lines

For two matrices, A and B, with dimensions {n,p} and ...
0
votes
0answers
74 views

Find Numerical Derivatives (With Errors) given some data

I have a question. Suposse I have some data with their respective errors: ...
7
votes
1answer
169 views

Least Square Data Fit /Design Matrix

I am trying to learn how to use the DesignMatrix function in Mathematica and how to perform a LeastSquares fit. I am at end of ...