Questions tagged [error-propagation]
The error-propagation tag has no usage guidance.
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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 ...
- 324
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0
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29
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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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2
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187
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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-...
- 575
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24
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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:
...
- 73
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1
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277
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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 ...
18
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3
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537
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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 ...
- 451
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2
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Relative error with bands plot
I have 2 sets of data imported from excel file, Let say
A = 20
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22
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30A
B= 0
1
2
3
...
10
I want to plot A with a relative error of 10%
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1
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73
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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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3
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Higher order Around, for large error propagation
TLDR question:
How to redefine Around to work with higher order approximation.
Motivation
From the documentation
Around
...
- 28.9k
3
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1
answer
175
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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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1
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225
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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:
...
- 1,252
2
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1
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130
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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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119
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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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1
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353
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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
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204
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Properly defining and plotting a function that requires `NSolve`
I want to defined a function that solves some equation numerically:
...
- 263
-2
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1
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39
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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;
- 327
23
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1
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351
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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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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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535
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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 $(x_i,y_i)$
...
- 159
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1
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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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2
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511
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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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1
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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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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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56
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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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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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507
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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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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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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
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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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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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