VectorAround

VectorAround[{x1,x2,…},{δ1,δ2,…}]

represents a vector of uncorrelated approximate numbers or quantities with values xi and uncertainties δi.

VectorAround[{x1,x2,…},{{Δ11,Δ12,…},{Δ12,Δ22,…},…}]

represents a vector of approximate numbers or quantities with values xi and covariance matrix Δ.

VectorAround[{x1,x2},{{δ1,δ2},ρ}]

represents a pair of approximate numbers or quantities with uncertainties δ1, δ2 and correlation factor ρ.

VectorAround[{x1,x2,…},{{δ1,δ2,…},{{1,R12,…},{R12,1,…},…}}]

represents a vector of approximate numbers or quantities with uncertainties δi and correlation matrix R.

Details

  • VectorAround can be used to represent results of vector measurements in which there is statistical or other uncertainty.
  • When VectorAround is used in computations, uncertainties are by default propagated using a first-order series approximation, taking account of correlations within each individual VectorAround object, but assuming no correlations between different VectorAround objects.
  • Around[VectorAround[{x1,x2,…},…]] gives a list of Around[xi,…] in which correlations between different values in the vector have been ignored.
  • VectorAround[…]["prop"] can be used to extract the following properties:
  • "Vector"central vector v in VectorAround[v,…]
    "Covariance"covariance matrix Δ
    "Correlation"correlation matrix R
    "Distribution"MultinormalDistribution[…]
  • For linear computations, VectorAround[v,Δ] behaves like a vector whose values are distributed according to the multinormal distribution MultinormalDistribution[v,Δ].
  • VectorAround[{x1,x2},{{δ1,δ2},ρ}] gives VectorAround[{x1,x2},Δ], with covariance matrix Δ={{δ12,ρ δ1 δ2},{ρ δ1 δ2,δ22}}.
  • For vectors v, δ and correlation matrix R, VectorAround[v,{δ,R}] gives VectorAround[v,Δ], with covariance matrix Δ of components Δij=Rij δi δj. The correlation matrix R is expected to have diagonal elements Rkk=1.

Examples

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Basic Examples  (4)

A pair of uncorrelated uncertain numbers:

A pair of correlated uncertain numbers:

A pair of correlated quantities:

MeanAround on a list of vectors returns a VectorAround object:

Properties & Relations  (1)

Take a multinormal distribution for 2D vectors and simulate it:

VectorAround[vectors] estimates the mean and covariance matrix of the distribution:

MeanAround[vectors] describes the mean of the distribution and the covariance matrix associated with that mean:

Wolfram Research (2019), VectorAround, Wolfram Language function, https://reference.wolfram.com/language/ref/VectorAround.html.

Text

Wolfram Research (2019), VectorAround, Wolfram Language function, https://reference.wolfram.com/language/ref/VectorAround.html.

CMS

Wolfram Language. 2019. "VectorAround." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/VectorAround.html.

APA

Wolfram Language. (2019). VectorAround. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/VectorAround.html

BibTeX

@misc{reference.wolfram_2024_vectoraround, author="Wolfram Research", title="{VectorAround}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/VectorAround.html}", note=[Accessed: 21-November-2024 ]}

BibLaTeX

@online{reference.wolfram_2024_vectoraround, organization={Wolfram Research}, title={VectorAround}, year={2019}, url={https://reference.wolfram.com/language/ref/VectorAround.html}, note=[Accessed: 21-November-2024 ]}