Questions tagged [fitting]
Questions on the use of Mathematica to construct models for approximating empirical data.
1,737
questions
1
vote
1
answer
61
views
0
votes
0
answers
54
views
Find fitting for a multi varibles function [closed]
I have a function that is given by a numerical solution by the following code:
...
- 287
0
votes
2
answers
106
views
NonlinearModelFit extremely slow performance with a single iteration
I have been experiencing very slow performance of NonlinearModelFit. The code that in my case causes that is below. The first part gets the data, the model and ...
- 3,954
0
votes
1
answer
43
views
Using NonlinearModelFit output in multiple Plot instances within DynamicModule
I'm creating a script for interactive model fitting where the user selects a 'window' of the data to exclude from the fitting.
I can come up with a MWE like the following:
...
5
votes
1
answer
207
views
P-Values For LinearModelFit Changing Due To Ordering Of Features
The arbitrary ordering in a linear model of the independent variables should not impact the p-values for the coefficients of said model.
However that is exactly what is happening here
...
- 683
6
votes
1
answer
400
views
Finding an ellipse of minimum area that encloses a set of points
Is there a built-in function or set of functions in Mathematica that can take a set of points in the x-y plane and determine the ellipse of minimum area that contains all of the points? I am sure ...
- 1,124
0
votes
0
answers
102
views
6
votes
1
answer
186
views
Curve fitting with Mathematica
I am trying to find de parametric equations of this curve (the curve in that sector of circle):
What I've tried:
...
- 163
-1
votes
1
answer
145
views
3
votes
2
answers
104
views
FindFit or NonlinearModelfit for sinusoidal function
I am trying to fit this data set into a specific sinusoidal equation.
The equation is shown like this.
...
- 31
5
votes
4
answers
539
views
Dealing with derivative of noisy experimental data
I have the following (time, position) dataset
...
- 169
1
vote
2
answers
150
views
The best way to guess the needed data using Mathematica?
I have a question, which is not entirely related to Mathematica, and would appreciate any help on this matter.
I have the following dataset, which shows the growth of a bacterium in a specific medium:
...
- 405
3
votes
3
answers
315
views
Why does this simple fit run forever?
The following fit runs forever on my laptop; how to speed up?
...
- 405
0
votes
1
answer
85
views
Solve constraints don't work properly
So in my previous question, I was trying to find two parameters kV and km for an implicit function using FindFit(FF) command and I did it but the problem is that it takes around an hour to do it. ...
1
vote
0
answers
52
views
My sinusoidal fit requires an unused extra constant to work
I am trying to fit a sinusoidal curve onto the following data:
...
- 11
2
votes
2
answers
119
views
Problem related to fitting a damped sine function
When I try to fit an exponential damped sine, it acts as if it cannot reach the amplitude at all. What do I change?
link to data: datafile
Getting data:
...
- 21
1
vote
2
answers
85
views
How do I fit unknown function to my data?
I have a set of data, to which I am trying to fit an unknown function. I believe it might be a logarithmic function, but I am not sure. Can you help me find a working model?
...
- 51
0
votes
0
answers
78
views
How can I approximate a function with composite polynomials?
I know that to approximate a function with for example $f(x) = \sin(x)$ using polynomials with degrees up to 4, I can use the Fit function :
...
- 13
1
vote
1
answer
71
views
How to include Manipulate in fitting?
I'm trying to fit three differential equations to two data sets, using the code developed by @Cesareo, as follows:
...
- 405
5
votes
2
answers
227
views
How can I use option Weights for fitting?
I have the following dataset (time vs. a quantity called $s$):
OPD = {{0, 0.0305}, {3, 0.14}, {6, 0.5}, {17, 4.02}, {19, 5.04}, {21, 5.52}, {24, 5.76}};
To the ...
- 405
2
votes
1
answer
153
views
How can I fit rational function to data?
I have a dataset written below. I need to find a rational function that best fits this data set. How can I do it using Mathematica?
The answer should be:
$$f(t)=(2.196t^5+2.27t^4+2.013t^3+0.9592t^2+0....
2
votes
2
answers
213
views
Find function by solving equations and imposing constraints
Suppose there are two equations:
$$2f(x)+x^2g(x)=8 \tag{1},$$
$$ x^3f(x)+6g(x)=18 \tag{2}.$$
I need to solve these two equations and find the functions $f(x)$ and $g(x)$ in terms of $x$ and constants. ...
0
votes
1
answer
69
views
Fitting Chebyshev to 2D data
I have complex data points on a 2D square (say $[0,10]^2$). I tried the following example function: $xye^{i(x+y)}$.
I split up the Re and ...
- 347
1
vote
1
answer
103
views
Fit a point that defines a 90° angle
I'm trying to come up with a fit that will give me x,y coordinates of a point, that best fit in 2 slopes, the 2 slopes intercepting at 90°.
At the moment I fit individually 2 lines to a 2 sets of ...
- 159
3
votes
1
answer
99
views
Fitting a first-order ODE
I want to fit the following equation
$\dot{B} ( t ) = \kappa ( 1 - B ( t ) ),$
to the dataset: $\{ ( 1.17, 0.27 ), ( 2, 0.5 ), ( 4, 0.73 ), ( 6, 0.93 ), ( 8, 1 ), ( 10, 0.93 ), ( 20, 0.8 ) \}$, where ...
- 405
5
votes
0
answers
138
views
What is resistivity function of a 3-bar electric switch?
I answered a question on Physics StackExchange - considered as homework - numerically. The question is: What is the resistance of three stacked identical blocks, the middle bar shifted by its half ...
- 3,564
2
votes
1
answer
105
views
How to setup FindFit function so that fitted function fits nicely to data points?
I am trying to fit some data points to a transformed natural log function and transformed 1/x function. However, the fitted 1/x function fails to adhere nicely to the data points when x is growing ...
- 357
0
votes
1
answer
52
views
Trouble using Integrate as the model in NonlinearModelFit
I'm trying to fit a set of heat capacity data to the Debye model.
This is the sample dataset that I'm using:
...
0
votes
1
answer
61
views
0
votes
0
answers
52
views
I need help with plotting and SVEIAR Code with the Reproduction Number on Mathematica
I need help because everytime I plot it doesn't work.
...
- 11
3
votes
2
answers
204
views
Meaning of arguments in FittedModels`ParameterEllipsoid
I am trying to figure out what FittedModels`ParameterEllipsoid's parameters mean (I want to construct a filled ellipse)
Here is a minimum working example:
...
- 4,425
0
votes
0
answers
35
views
Use Fitting Parameter from Solve or Nminimize with LinearModelFit
Im Trying to minimize a function by varying parameter "a" with Solve or Nminimize. The Problem is that "a" is dependent on my parameter "R" which is dependent on "a&...
4
votes
2
answers
284
views
How fit my data to sinus?
I have problem with fit sinus to my date, because this sin is very tiny.
This is my code:
...
- 51
1
vote
1
answer
343
views
Fitting delay differential equations (DDE)
I have the following differential equations:
$$S'(t) = 0.31 S(t) \Big( 1 - \frac{S(t)}{6.19} \Big)- \frac{a}{1 + B(t)} S(t),$$
$$B'(t) = c (1 - B(t)) - d B(t) S(t) - 3 c (1 - B(t - 18)),$$
where $B(t -...
user95418
0
votes
2
answers
141
views
Chi-square minimization error
I'm trying to fit some data into a model using the standard procedure of minimizing the chi-square function using this code:
...
- 51
1
vote
1
answer
149
views
Why does using a sparse matrix for least squares instead slow down the speed?
Here is the code. The matrix appears to be relatively sparse in terms of its visual representation, but why does using least squares result in significantly slower speed compared to the previously ...
- 151
1
vote
0
answers
460
views
How to include impulses in differential equations?
I have two coupled differential equations as follows:
$$S'(t) = - \frac{a}{1 + B(t)} S(t),$$
$$B'(t) = \frac{c}{1 + S(t)} B(t) (1 - B(t)) - d B^2(t) \Big( \frac{1 - B(t)}{B(t)} \Big)^n,$$
where $a$, $...
user95418
0
votes
1
answer
200
views
Using ParametricNDSolveValue and MultiNonlinearModelFit to fit an ODE system to datasets
I asked a question here about fitting an ODE system to given datasets. The great answer of @ydd solved the problem nicely. In the mentioned answer, the initial values are taken as the initial points ...
user95418
4
votes
2
answers
424
views
Modeling experimental data with differential equations
I have the following two sets of experimental data, which show the dependencies of two quantities, namely, $S$ and $B$, on time ($0$ h, $3$ h, $6$ h, $9$ h, $15$ h, $18$ h, $21$ h, and $24$ h):
...
user95418
3
votes
2
answers
252
views
Optimizing an ODE fitting algorithm with interpolated data
Given data, I want to find parameters $p_1,p_2,k_1,k_2>0$ that fit the following ODE system
$$
\begin{align}
b'(t)&=p_1 a(t)-k_1b(t)\\
c'(t)&=p_2b(t)-k_2c(t)
\end{align}
$$
where $a(t)$ is ...
- 4,693
2
votes
2
answers
193
views
Fitting Hill function to a given dataset
I have the following data:
data = {{15, 1}, {18, 1470.7`/1476.9333333333334`}, {21, 1326.2333333333333`/1476.9333333333334`}, {24, 316.8`/1476.9333333333334`}};
...
user95418
1
vote
1
answer
96
views
Obtaining the growth rate of bacteria using NonlinearModelFit
I have a data set concerning the growth of bacteria, and I need to obtain the so-called growth rate.
My data set is (OD600 vs. time(h)):
...
user95418
4
votes
3
answers
401
views
3
votes
1
answer
121
views
1
vote
1
answer
56
views
How to fit a linear ODE system?
Consider the equations
$$
\begin{align}
b'(t)=p_1 c(t)-k_1b(t),\\
c'(t)=p_2b(t)-k_2c(t)
\end{align}
$$
Given data on $b$ and $c$, and initial conditions, how do I find the best fitting parameters $k_1,...
- 4,693
1
vote
2
answers
125
views
Could a minimization problem be easily converted into a NonlinearModelFit?
I am trying to fit data that is correlated, such that the $\chi^2 = (f(x_i,pars)-y_i)(Cov^{-1})_{ij}(f(x_j,pars)-y_j)$.
However, NonlinearModelFit only accepts ...
- 723
2
votes
0
answers
57
views
NonlinearModelFit of data with errors
Experimental data points invariably come with errors. These errors can significantly influence the parameters and their uncertainties when performing non-linear fitting. However, NonlinearModelFit ...
- 3,471
0
votes
0
answers
40
views
NonlinearModelFit with NMinimize Submethods and Selective or Mixed-Head Constraints
Problem: I believe I've found a two related bugs associated with using NonlinearModelFit while making a Method call to NMinimize's submethods, e.g. "RandomSearch" and "...
- 1,147
0
votes
2
answers
140
views
Fitting data with ${\rm sinc}^2(x)$
I performed an experiment of Fraunhofer diffraction with slits, the results of which should be proportional to $\operatorname{sinc}^2(x) = \left(\frac{\sin x}{x}\right)^2$. However, an error occurred ...
- 3
1
vote
0
answers
54
views
Fitting experimental data to a plot with different x-axis paths
Given Mathematica code of eigenvalues in different variable-paths , I want to add experimental data in the path Gamma-X ; X-Gamma ; and M-Gamma .
Here is the code :
...
- 117