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ScientificErrorAnalysis

  

Covariance

  

return the covariance between two quantities-with-error

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

Covariance( obj1, obj2 )

Parameters

obj1

-

quantity-with-error

obj2

-

quantity-with-error

Description

• 

The Covariance( obj1, obj2 ) command returns the covariance between the quantities-with-error obj1 and obj2.

• 

Either of the quantities-with-error obj1 and obj2 can have functional dependence on other quantities-with-error.

  

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

  

The relationship between the correlation rz1,z2 and covariance uz1,z2 is

uz1,z2=rz1,z2uz1uz2

  

where uz1 and uz2 are the errors in z1 and z2, respectively.

  

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

  

The covariance uz1,z2 between z1 and z2, where z1 depends on the xi, and z2 depends on the yj, is

uz1,z2=i=1Nj=1Mxiz1yjz2uxi,yj

  

where uxi,yj is the covariance between xi and yj, and the partials are evaluated at the central values of the xi and yj.

• 

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

withScientificConstants:

withScientificErrorAnalysis:

aQuantity10.,2.:

bQuantity20.,1.:

Covariancea,b

0

(1)

SetCorrelationa,b,0.1

Covariancea,b

0.2

(2)

GetConstantme

electron_mass,symbol=me,derive=2R∞hcα2

(3)

CovarianceConstantme,Constanth

3.71670205510-78

(4)

evalfConstantmeevalfConstanth

6.15762023310-15

(5)

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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