Questions tagged [error-propagation]

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How to isolate uncertainty in formula involving Around[]

If I compute with Mathematica Exp[Around[v, dv]] //PowerExpand I get Around[Exp[v], dv*Exp[v]] with the uncertainty ...
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`Around` with multiple errors

To my knowledge, Around only deals with one error. That means it can't deal with multiple sources of errors. For example, a number may have both statistic ...
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6 votes
2 answers
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Correlated uncertainties

navigating through the docs. of Around one can read in the details that When Around is used in computations, uncertainties are by default propagated using a first-...
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How to copy a number from an error message? [duplicate]

Is there any way to copy a number from an error message and assign it to a variable, without manually doing it? For instance, I am trying to solve some coupled Differential equations as follows: ...
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4 votes
1 answer
277 views

Around error propagation

I understand that when Around is used in computations, uncertainties are by default propagated using a first-order series approximation, assuming no correlations. On the other hand this makes it ...
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18 votes
3 answers
537 views

Mathematica 12.x: Don't use Accumulate or Differences on Around objects!

Bug introduced in 12.0 or earlier and persisting through 12.2 or later It seems we've discovered a bug! The following is a summary of the problem and possible workarounds. Scroll down to ORIGINAL ...
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2 answers
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Relative error with bands plot

I have 2 sets of data imported from excel file, Let say A = 20 21 22 ... 30A B= 0 1 2 3 ... 10 I want to plot A with a relative error of 10% ...
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1 answer
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plotting error in 3D

What is the problem related to the following plot? Definition of geometry RR = ImplicitRegion[((Sqrt[x^2 + y^2] - 9))^2 + z^2 <= 1, {x, y, z}];
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6 votes
3 answers
217 views

Higher order Around, for large error propagation

TLDR question: How to redefine Around to work with higher order approximation. Motivation From the documentation Around ...
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3 votes
1 answer
175 views

Half-absorbing boundary conditions

I'm trying to solve the spherically symmetric wave equation $$0 = (\partial_t^2 - \partial_r^2 + 1)\phi(t,r)\,,$$ where $\phi(t,0) = 0$. Without doing anything fancy, we can solve this equation "...
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2 votes
1 answer
225 views

Estimate errors during integration of interpolated data

I am interested into calculating the errors associated with an integration over interpolated data. Suppose I have something like this: ...
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2 votes
1 answer
130 views

Testing the accuracy of numerically computed derivatives - alternative method

So I have asked this question earlier today: Testing the accuracy of numerically computed derivatives, This method works well for DifferenceOrder methods but upon reading https://reference.wolfram....
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Testing the accuracy of numerically computed derivatives

I am calculating approximate derivatives by using NDSolve`FiniteDifferenceDerivative, so this works: ...
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2 votes
1 answer
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How to find the Maximal Absolute Error?

I found this fit but I do not understand how to find the maximal absolute error nor do I understand what it is really. I do not see what it is I would compare, would it be ...
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1 answer
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Properly defining and plotting a function that requires `NSolve`

I want to defined a function that solves some equation numerically: ...
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-2 votes
1 answer
39 views

Error of a function containing complex numbers

Please, what is the statistical error formula of the function f (uncertainty) by Mathematica code: a=x+I y ; b=u+I v; f=Abs[a]^2+Abs[b]^2;
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23 votes
1 answer
351 views

How to get an absolute value of Around?

Around is a useful feature of Mathematica 12 to work with uncertain data. x = Around[-1, {0.5, 1.5}] $-1.0^{+1.5}_{-0.5}$ ...
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13 votes
3 answers
1k views

How does the Around command at zero work?

I enter: Around[0,0.5]^2 and I get 0. This is a bit strange. Around[0,0.5] is supposed to represent numbers between -0.5 and 0.5. So by my estimates the square ...
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  • 291
1 vote
2 answers
535 views

Estimating the uncertainty in the slope of a straight line given the uncertainty in the data points

Basically I have some datapoints on the form $(x_i,y_i)$ ...
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1 vote
1 answer
67 views

Error propagation with complex number [duplicate]

I have an expression of a physical observable in which some input parameters are taken. The corresponding errors of these input parameters are given. To get the error of this observable what code I ...
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17 votes
2 answers
511 views

Around usage results

Why is Around[10, 1]^2 +- 20 and Around[10, 1] Around[10, 1] giving 100 +- 14 ? Just curious I would suspect them to ...
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10 votes
1 answer
151 views

Why does Success[...][key] work and Failure[...][key] doesn't work?

I'm trying to figure out what is a quick way to add error reporting to my user defined functions. I was experimenting with Success and ...
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0 answers
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Error plotting in 2D

I have some data: along Y axis: 5.86*10^(-8),2.56*10^(-8),3.21*10^(-8) with error 0.58, 0.25 and 0.32 respectively. along X axis: there are some range corresponding each value of Y axis such as: 0.1-...
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error bar plotting with some range

In the following pic I want to show the error bar plotting with some given data: Y axis: 5.86*10^(-8) with error .58*10^(-8) and X axis: 0.1 to 2 (that means there is a range), 2.56*10^(-8) with error ...
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1 vote
2 answers
418 views

Error propagation in finding full width at half maximum

I have an equation given by: ...
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0 answers
85 views

How to use "Chop" kind of operation on whole mathematica file

In an array of steps including logarithms and integrations, I am finding the problem of small imaginary parts of some o/p's which are complicating/inhibiting the further steps. I found that "Chop" ...
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3 votes
1 answer
507 views

Propagate error through `FindFit`

I have several sampled points $(x_i, y_i)$ with mutually independent error on the y coordinate $\sigma_{y_i}$. For simplicity, I'm assuming no error in the x coordinates ($\sigma_{x_i} \ll \sigma_{...
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1 vote
0 answers
137 views

Determining the intersection of two functions with errors on parameters

Let's assume I want to calculate the intersection points of two functions $f(x)$ and $g(x)$. That is simple enough, I define my functions, e.g. like so and use Solve...
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19 votes
2 answers
922 views

Error and uncertainty propagation: Is using Precision/Accuracy a sound strategy?

Questions What are the available resources to deal with experimental error and uncertainty propagation in Mathematica? Given that Mathematica already uses linearized model of error propagation on ...
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139 views

Error propagation with NDSolve and periodic boundary conditions

I'm trying to solve the problem of heat conduction through soil with periodic temperature variations on the surface. For now I'm working with a 1D model but I see that the solution doesn't work, it ...
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6 votes
2 answers
1k views

Error propagation code

I have a code for error propagation :- ...
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24 votes
4 answers
1k views

Create an adaptive amount of local variables for error propagation

I intend to write a function which calculates the result and the error for any formula with any amount of variables using the Gauß Error Propagation. The error $\mathrm{d}R$ for a function $A(a,b,c)$ ...
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