ScientificErrorAnalysis - Maple Programming Help

Online Help

All Products    Maple    MapleSim


Home : Support : Online Help : Science and Engineering : Scientific Error Analysis : Commands : ScientificErrorAnalysis/Variance

ScientificErrorAnalysis

  

Variance

  

return the variance of a quantity-with-error

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

Variance( obj )

Parameters

obj

-

quantity-with-error

Description

• 

The Variance( obj ) command returns the variance of the quantity-with-error obj.

• 

The quantity-with-error obj can have functional dependence on other quantities-with-error.

  

If the quantity-with-error obj does not have functional dependence on other quantities-with-error, the uncertainty of obj is accessed and converted to the variance (by squaring).

  

If the quantity-with-error obj has functional dependence on other quantities-with-error, the variance is calculated using the usual formula of error analysis involving a first-order expansion with the dependent form and covariances between the other quantities-with-error. This process can be recursive.

  

The variance u2y in y, where y depends on the xi, is

  

 

uy2=i=1Nxiy2uxi2+2i=1N1j=i+1Nxiyxjyuxi,xj

  

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

• 

Variances 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.

Examples

with(ScientificConstants):

with(ScientificErrorAnalysis):

a := Quantity( 10., 2. ):

Variance( a );

4.

(1)

GetConstant( h );

Planck_constant,symbol=h,value=6.62607004010−34,uncertainty=8.110−42,units=Js

(2)

Variance( Constant( h ) );

6.56110−83

(3)

GetConstant( m[e] );

electron_mass,symbol=me,derive=2Rhcα2

(4)

Variance( Constant( m[e] ) );

1.24165432410−76

(5)

GetError( Constant( m[e] ) )^2;

1.24165432310−76

(6)

See Also

combine/errors

ScientificConstants

ScientificConstants[Constant]

ScientificConstants[GetConstant]

ScientificConstants[GetError]

ScientificErrorAnalysis

ScientificErrorAnalysis and ScientificConstants

ScientificErrorAnalysis[Covariance]

ScientificErrorAnalysis[GetCorrelation]

ScientificErrorAnalysis[Quantity]

ScientificErrorAnalysis[SetCorrelation]