Modeling Quantities

1
Modeling Quantities

• Goal
• to establish a consistent method for representing
  physical quantities
• Why?
• easier for newcomers to understand
• common software solution for handling common
  problems
• units transformations
• quantity combinations (math, units propagation,
  error prop.)
• establish a base data model component that can be
  used to build up more complex objects.

2
Modeling Quantities

• 3 components
• Value
• Error
• Unit
• Error is abstract 2 subtypes (substitutes)
• Sigma
• ErrorRange
• confidence attribute
• Unit
• prefix attribute

3
Modeling Quantities

• Specific Quantities
• substitutable for Quantity
• restrict the unit
• Flux Jy
• Length m, pc, lt-yr
• Frequency Hz, cm, eV

4

• lt?xml version"1.0" encoding"UTF-8"?gt
• ltQuantities xmlns"http//www.ivoa.net/xml/prop/VO
  Quantity xmlnsxsi"http//www.w3.org/2001/XMLSch
  ema-instance"gt
• ltQuantitygt
• ltValuegt44.2lt/Valuegt
• ltSigmagt0.1lt/Sigmagt
• ltUnit prefix"k"gtm/slt/Unitgt
• lt/Quantitygt
• ltLengthgt
• ltValuegt4.5lt/Valuegt
• ltUnit prefix"M"gtpclt/Unitgt
• lt/Lengthgt
• ltFluxgt
• ltValuegt18.4lt/Valuegt
• ltErrorRange confidence"67"gt
• ltminusgt4.1lt/minusgt
• ltplusgt2.4lt/plusgt

5

• lt?xml version"1.0" encoding"UTF-8"?gt
• ltQuantities xmlns"http//www.ivoa.net/xml/prop/VO
  Quantity" xmlnsxsi"http//www.w3.org/2001/XMLSch
  ema-instance"gt
• ltQuantitygt
• ltValuegt44.2lt/Valuegt
• ltSigmagt0.1lt/Sigmagt
• ltUnit prefix"k"gtm/slt/Unitgt
• lt/Quantitygt
• ltLengthgt
• ltValuegt4.5lt/Valuegt
• ltUnit prefix"M"gtpclt/Unitgt
• lt/Lengthgt
• ltFluxgt
• ltValuegt18.4lt/Valuegt
• ltErrorRange confidence"67"gt
• ltminusgt4.1lt/minusgt
• ltplusgt2.4lt/plusgt

Alternatives ltFrequency p"c"
u"m"gt21lt/Frequencygt ltFrequencygt21 cmlt/Frequencygt
ltFrequency value"21 cm"/gt ltFrequency p"c"
u"m" sigma"0.1" minus"0.3"
plus"0.4" conf"99.7"gt21lt/Frequencygt
6
Modeling Quantities Challenges

• Quantity transformations
• unit conversions
• metric scaling base unit (e.g. m ??
  Hz ?? eV)
• parsing from human readable form
• 5 Jy is more compact and convenient but harder
  to parse
• Comparisons Processing
• Useful Functions
• boolean near(q1, q2, tolerance)
• boolean withinError(q1, q2)
• boolean lessThan(q1, q2)
• boolean greaterThan(q1, q2)
• Quantity toQuantity(string)
• e.g. toQuantity(5 Jy) enables
  greaterThan(Flux, 5 Jy)