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

Basic Examples  (3)

A pair of uncorrelated uncertain numbers:

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A pair of correlated uncertain numbers:

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MeanAround on a list of vectors returns a VectorAround object:

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Introduced in 2019
(12.0)