ScientificErrorAnalysis[Covariance]  return the covariance between two quantitieswitherror

Calling Sequence


Covariance( obj1, obj2 )


Parameters


obj1



quantitywitherror

obj2



quantitywitherror





Description


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The Covariance( obj1, obj2 ) command returns the covariance between the quantitieswitherror obj1 and obj2.

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Either of the quantitieswitherror obj1 and obj2 can have functional dependence on other quantitieswitherror.


If neither of the quantitieswitherror obj1 and obj2 has functional dependence on other quantitieswitherror, the correlation between obj1 and obj2 is accessed and converted to the covariance.


The relationship between the correlation and covariance is


If either of the quantitieswitherror obj1 and obj2 has functional dependence on other quantitieswitherror, the covariance is calculated using the usual formula of error analysis involving a firstorder expansion with the dependent forms and covariances between the other quantitieswitherror. This process can be recursive.

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Covariances involving physical constants are calculated naturally and correctly in the implied system of units because central values and errors are obtained from the interface to ScientificConstants.


Unusual cases are possible involving the covariance between the same physical constant in different systems of units, but correct results are obtained. In the case of a nonderived constant, the identical identifiers obtained from the interface to ScientificConstants cause Covariance to obtain the uncertainty from both objects. In the case of a derived constant, the general double summation of the error analysis formula is evaluated as usual (over the same functional form).



Examples


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See Also


combine/errors, evalf, ScientificConstants, ScientificConstants[Constant], ScientificConstants[GetConstant], ScientificErrorAnalysis, ScientificErrorAnalysis and ScientificConstants, ScientificErrorAnalysis[GetCorrelation], ScientificErrorAnalysis[Quantity], ScientificErrorAnalysis[SetCorrelation], ScientificErrorAnalysis[Variance]


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