({{, (RefLink[VectorAround, paclet:ref/VectorAround])[{(Subscript[x, 1]),(Subscript[x, 2]),…},{(Subscript[δ, 1]),(Subscript[δ, 2]),…}]
represents a vector of uncorrelated approximate numbers or quantities with values (Subscript[x, i]) and uncertainties (Subscript[δ, i]).}, {, (RefLink[VectorAround, paclet:ref/VectorAround])[{(Subscript[x, 1]),(Subscript[x, 2]),…},{{(Subscript[Δ, 11]),(Subscript[Δ, 12]),…},{(Subscript[Δ, 12]),(Subscript[Δ, 22]),…},…}]
represents a vector of approximate numbers or quantities with values (Subscript[x, i]) and covariance matrix Δ.}, {, (RefLink[VectorAround, paclet:ref/VectorAround])[{(Subscript[x, 1]),(Subscript[x, 2])},{{(Subscript[δ, 1]),(Subscript[δ, 2])},ρ}]
represents a pair of approximate numbers or quantities with uncertainties (Subscript[δ, 1]), (Subscript[δ, 2]) and correlation factor ρ.}, {, (RefLink[VectorAround, paclet:ref/VectorAround])[{(Subscript[x, 1]),(Subscript[x, 2]),…},{{(Subscript[δ, 1]),(Subscript[δ, 2]),…},{{1,(Subscript[R, 12]),…},{(Subscript[R, 12]),1,…},…}}]
represents a vector of approximate numbers or quantities with uncertainties (Subscript[δ, i]) and correlation matrix R.}})

OpenersNotesSection(Spacer1)Details

(RefLink[VectorAround, paclet:ref/VectorAround]) can be used to represent results of vector measurements in which there is statistical or other uncertainty.

When (RefLink[VectorAround, paclet:ref/VectorAround]) is used in computations, uncertainties are by default propagated using a first-order series approximation, taking account of correlations within each individual (RefLink[VectorAround, paclet:ref/VectorAround]) object, but assuming no correlations between different (RefLink[VectorAround, paclet:ref/VectorAround]) objects.

(RefLink[Around, paclet:ref/Around])[VectorAround[{(Subscript[x, 1]),(Subscript[x, 2]),…},…]] gives a list of (RefLink[Around, paclet:ref/Around])[(Subscript[x, i]),…] in which correlations between different values in the vector have been ignored.

(RefLink[VectorAround, paclet:ref/VectorAround])[…]["prop"] can be used to extract the following properties:

For linear computations, (RefLink[VectorAround, paclet:ref/VectorAround])[v,Δ] behaves like a vector whose values are distributed according to the multinormal distribution (RefLink[MultinormalDistribution, paclet:ref/MultinormalDistribution])[v,Δ].

(RefLink[VectorAround, paclet:ref/VectorAround])[{(Subscript[x, 1]),(Subscript[x, 2])},{{(Subscript[δ, 1]),(Subscript[δ, 2])},ρ}] gives (RefLink[VectorAround, paclet:ref/VectorAround])[{(Subscript[x, 1]),(Subscript[x, 2])},Δ], with covariance matrix Δ={{((Subscript[δ, 1])^2),ρ (Subscript[δ, 1]) (Subscript[δ, 2])},{ρ (Subscript[δ, 1]) (Subscript[δ, 2]),((Subscript[δ, 2])^2)}}.

For vectors v, δ and correlation matrix R, (RefLink[VectorAround, paclet:ref/VectorAround])[v,{δ,R}] gives (RefLink[VectorAround, paclet:ref/VectorAround])[v,Δ], with covariance matrix Δ of components (Subscript[Δ, ij])=(Subscript[R, ij]) (Subscript[δ, i]) (Subscript[δ, j]). The correlation matrix R is expected to have diagonal elements (Subscript[R, kk])=1.

OpenersPrimaryExamplesSection(Spacer1)Examples  (3)

OpenersExampleSection0(Spacer1)Basic Examples  (3)

A pair of uncorrelated uncertain numbers:

VectorAround[{1.8,2.4},{0.3,0.4}]

A pair of correlated uncertain numbers:

VectorAround[{1.8,2.4},{{0.3,0.4},0.5}]

(RefLink[MeanAround, paclet:ref/MeanAround]) on a list of vectors returns a (RefLink[VectorAround, paclet:ref/VectorAround]) object:

RandomVariate[MultinormalDistribution[{2,3},{{1,0.5},{0.5,2}}],10]

MeanAround[%]

({{DocumentationFooterIconsRelatedFunction.png, ({{See Also}, {(RefLink[Around, paclet:ref/Around])  ▪  (RefLink[AroundReplace, paclet:ref/AroundReplace])  ▪  (RefLink[MeanAround, paclet:ref/MeanAround])  ▪  (RefLink[MultinormalDistribution, paclet:ref/MultinormalDistribution])  ▪  (RefLink[Covariance, paclet:ref/Covariance])  ▪  (RefLink[Correlation, paclet:ref/Correlation])  ▪  (RefLink[Quantity, paclet:ref/Quantity])}})}})

({{DocumentationFooterIconsRelatedGuide.png, ({{Related Guides}, {▪(RefLinkPlain[Numbers with Uncertainty, paclet:guide/NumbersWithUncertainty])}, {▪(RefLinkPlain[Units & Quantities, paclet:guide/Units])}})}})