I have several notebooks that make use of the Units package and would like to be able to work simultaneously with the older units and Quantity objects introduced in version 9. What is my lowest-overhead method for updating units to Quantity objects?
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$\begingroup$ @rm -rf, thanks for the edits. Much better now. $\endgroup$– Daniel WMar 24, 2013 at 19:47
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1 Answer
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I have mined the Units package for the names of all units defined therein and correlated them to the built-in strings recognized by Quantity(referenced here). I then define a new function Quantify to convert the old school units into Quantity objects.
unitRules =
Dispatch[{Abampere -> Quantity[1, "ABAmperes"],
Abcoulomb -> Quantity[1, "ABCoulombs"],
Abfarad -> Quantity[1, "ABFarads"],
Abhenry -> Quantity[1, "ABHenries"],
Abmho -> Quantity[1, "ABMhos"],
Abohm -> Quantity[1, "ABOhms"],
Abvolt -> Quantity[1, "ABVolts"],
Acre -> Quantity[1, "Acres"],
Amp -> Quantity[1, "Amperes"],
Ampere -> Quantity[1, "Amperes"],
AMU -> Quantity[1, "AtomicMassUnit"],
Angstrom -> Quantity[1, "Angstroms"],
Apostilb -> Quantity[1, "Apostilbs"],
ArcMinute -> Quantity[1, "ArcMinutes"],
ArcSecond -> Quantity[1, "ArcSeconds"],
Are -> Quantity[1, "Ares"],
AssayTon -> Quantity[1, "AssayMetricTons"],
AstronomicalUnit -> Quantity[1, "AstronomicalUnit"],
Atmosphere -> Quantity[1, "Atmospheres"],
AtomicMassUnit -> Quantity[1, "AtomicMassUnit"],
AU -> Quantity[1, "AstronomicalUnit"],
AvoirdupoisOunce -> Quantity[1, "Ounces"],
AvoirdupoisPound -> Quantity[1, "Pounds"],
Bag -> Quantity[1, "BagsUK"],
BakersDozen -> Quantity[1, "BakersDozens"],
Bale -> Quantity[1, "BalesOfCotton"],
Bar -> Quantity[1, "Bars"],
Barn -> Quantity[1, "Barns"],
Barrel -> Quantity[1, "Barrels"],
Barye -> Quantity[1, "Baryes"],
Baud -> Quantity[1, "Bits"/"Seconds"],
Becquerel -> Quantity[1, "Becquerels"],
Biot -> Quantity[1, "Biots"],
Bit -> Quantity[1, "Bits"],
BoardFoot -> Quantity[1, "BoardFeet"],
BohrMagneton -> Quantity[1, "BohrMagneton"],
Bolt -> Quantity[1, "BoltsWidthCotton"],
BritishThermalUnit -> Quantity[1, "BritishThermalUnitsIT"],
BTU -> Quantity[1, "BritishThermalUnitsIT"],
Bucket -> Quantity[1, "BucketsUK"],
Bushel -> Quantity[1, "BushelsUS"],
Butt -> Quantity[1, "ButtsUK"],
Byte -> Quantity[1, "Bytes"],
Cable -> Quantity[1, "CableLengthsUK"],
Caliber -> Quantity[1, "Calibres"],
Calorie -> Quantity[1, "LargeCalories"],
Candela -> Quantity[1, "Candelas"],
Candle -> Quantity[1, "Candelas"],
Carat -> Quantity[1, "Carats"],
Celsius -> Quantity[1, "DegreesCelsiusDifference"],
Cental -> Quantity[1, "Centals"],
Centigrade -> Quantity[1, "DegreesCelsiusDifference"],
Centimeter -> Quantity[1, "Centimeters"],
Century -> Quantity[1, "Centuries"],
Chain -> Quantity[1, "EngineersChains"],
ChevalVapeur -> Quantity[1, "ChevalVapeurs"],
Cicero -> Quantity[1, "Ciceros"],
Circle -> Quantity[1, "Circles"],
Cord -> Quantity[1, "Cords"],
Coulomb -> Quantity[1, "Coulombs"],
Cubit -> Quantity[1, "Cubits"],
Cup -> Quantity[1, "Cups"],
Curie -> Quantity[1, "Curies"],
Dalton -> Quantity[1, "Daltons"],
Day -> Quantity[1, "Days"],
Decade -> Quantity[1, "Decades"],
Denier -> Quantity[1, "Denier"],
Didot -> Quantity[1, "DidotPoints"],
DidotPoint -> Quantity[1, "DidotPoints"],
Diopter -> Quantity[1, "Diopters"],
Dozen -> Quantity[1, "Dozens"],
Drachma -> Quantity[1, "AeginaDrachmes"],
Drop -> Quantity[1, "MetricDrops"],
Dyne -> Quantity[1, "Dynes"],
ElectronVolt -> Quantity[1, "Electronvolts"],
Ell -> Quantity[1, "Ells"],
Ephah -> Quantity[1, "Ephahs"],
Erg -> Quantity[1, "Ergs"],
Fahrenheit -> Quantity[1, "DegreesFahrenheitDifference"],
Farad -> Quantity[1, "Farads"],
Fathom -> Quantity[1, "Fathoms"],
Feet -> Quantity[1, "Feet"],
Fermi -> Quantity[1, "Fermis"],
Fifth -> Quantity[1, "Fifths"],
Firkin -> Quantity[1, "FirkinsUS"],
FluidDram -> Quantity[1, "FluidDrams"],
FluidOunce -> Quantity[1, "FluidOunces"],
Foot -> Quantity[1, "Feet"],
FootCandle -> Quantity[1, "FootCandles"],
Fortnight -> Quantity[1, "Fortnights"],
Furlong -> Quantity[1, "Furlongs"],
Gal -> Quantity[1, "Gallons"],
Gallon -> Quantity[1, "Gallons"],
Gamma -> Quantity[1, "Gammas"],
Gauss -> Quantity[1, "Gausses"],
Geepound -> Quantity[1, "GeepoundsMass"],
Gilbert -> Quantity[1, "Gilberts"],
Gill -> Quantity[1, "Gills"],
Grade -> Quantity[1, "Grads"],
Grain -> Quantity[1, "Grains"],
Gram -> Quantity[1, "Grams"],
GramWeight -> Quantity[1, "GramsForce"],
Gravity -> Quantity[1, "StandardAccelerationOfGravity"],
GrayDose -> Quantity[1, "Grays"],
Gross -> Quantity[1, "Gross"],
GrossHundredweight -> Quantity[1, "LongHundredweights"],
Hand -> Quantity[1, "HandsUnit"],
Hectare -> Quantity[1, "Hectares"],
Hefner -> Quantity[0.92, "Candelas"],
Henry -> Quantity[1, "Henries"],
Hertz -> Quantity[1, "Hertz"],
Hogshead -> Quantity[1, "HogsheadsUS"],
Horsepower -> Quantity[1, "HorsepowerMechanical"],
Hour -> Quantity[1, "Hours"],
Hundredweight -> Quantity[1, "ShortHundredweights"],
ImperialGallon -> Quantity[1, "GallonsUK"],
ImperialPint -> Quantity[1, "PintsUK"],
Inch -> Quantity[1, "Inches"],
InchMercury -> Quantity[1, "InchesOfMercury"],
Jeroboam -> Quantity[1, "Jeroboams"],
Jigger -> Quantity[1, "Jiggers"],
Joule -> Quantity[1, "Joules"],
Kayser -> Quantity[1, "Kaysers"],
Kelvin -> Quantity[1, "Kelvins"],
Kilogram -> Quantity[1, "Kilograms"],
KilogramForce -> Quantity[1, "KilogramsForce"],
KilogramWeight -> Quantity[1, "KilogramsForce"],
Knot -> Quantity[1, "Knots"],
Lambert -> Quantity[1, "Lamberts"], Last -> Quantity[1, "LastsUK"],
League -> Quantity[1, "Leagues"],
Libra -> Quantity[1, "PortugueseLibras"],
LightYear -> Quantity[1, "LightYears"],
Link -> Quantity[1, "EngineersLinks"],
Liter -> Quantity[1, "Liters"],
LongTon -> Quantity[1, "LongTons"],
Lumen -> Quantity[1, "Lumens"],
Lumerg -> Quantity[1, "Lumergs"],
Lux -> Quantity[1, "Lux"],
Magnum -> Quantity[1, "Magnums"],
Maxwell -> Quantity[1, "Maxwells"],
Meter -> Quantity[1, "Meters"],
MetricTon -> Quantity[1, "MetricTons"],
Mho -> Quantity[1, "Mhos"],
Micron -> Quantity[1, "Microns"],
Mil -> Quantity[1, "Mils"],
Mile -> Quantity[1, "Miles"],
Millennium -> Quantity[1, "Millennia"],
MillimeterMercury -> Quantity[1, "MillimetersOfMercury"],
Mina -> Quantity[1, "AeginaMinas"],
Minim -> Quantity[1, "MinimsUS"],
Minute -> Quantity[1, "Minutes"],
Mole -> Quantity[1, "Moles"],
Month -> Quantity[1, "Months"],
NauticalMile -> Quantity[1, "NauticalMiles"],
NetHundredweight -> Quantity[100, "Pounds"],
Newton -> Quantity[1, "Newtons"],
Nibble -> Quantity[1, "Nibbles"],
Nit -> Quantity[1, "Nits"],
Noggin -> Quantity[1, "NogginsUK"],
NuclearMagneton -> Quantity[1, "NuclearMagnetons"],
Obolos -> Quantity[0.71538, "Grams"],
Oersted -> Quantity[1, "Oersteds"],
Ohm -> Quantity[1, "Ohms"],
Omer -> Quantity[1, "Omers"],
Ounce -> Quantity[1, "Ounces"],
Parsec -> Quantity[1, "Parsecs"],
Pascal -> Quantity[1, "Pascals"],
Peck -> Quantity[1, "Pecks"],
Pennyweight -> Quantity[1, "Pennyweights"],
Percent -> Quantity[1, "Percent"],
Perch -> Quantity[1, "PerchesLength"],
Phot -> Quantity[1, "Phots"],
Pica -> Quantity[1, "Picas"],
Pint -> Quantity[1, "Pints"],
Point -> Quantity[1, "DesktopPublishingPoints"],
Poise -> Quantity[1, "Poise"],
Pole -> Quantity[1, "Poles"],
Pondus -> Quantity[1, "DutchPonds"],
Pony -> Quantity[1, "PoniesUS"],
Pound -> Quantity[1, "Pounds"],
Poundal -> Quantity[1, "Poundals"],
PoundForce -> Quantity[1, "PoundsForce"],
PoundsPerSquareInch -> Quantity[1, "PoundsForce"/"Inches"^2],
PoundWeight -> Quantity[1, "PoundsForce"],
PrintersPoint -> Quantity[1, "DesktopPublishingPoints"],
PSI -> Quantity[1, "PoundsForce"/"Inches"^2],
Puncheon -> Quantity[1, "PuncheonsUS"],
Quadrant -> Quantity[1, "RightAngles"],
Quart -> Quantity[1, "Quarts"],
Quintal -> Quantity[1, "Quintals"],
Rad -> Quantity[1, "Rads"],
Radian -> Quantity[1, "Radians"],
Rankine -> Quantity[1, "DegreesRankine"],
RegisterTon -> Quantity[1, "RegisterTons"],
Reyn -> Quantity[1, "Reyns"],
Rhes -> Quantity[1, "Rhes"],
RightAngle -> Quantity[1, "RightAngles"],
Rod -> Quantity[1, "Rods"],
Roentgen -> Quantity[1, "Roentgens"],
Rontgen -> Quantity[1, "Roentgens"],
Rood -> Quantity[1, "Roods"],
Rope -> Quantity[1, "Ropes"],
Rutherford -> Quantity[1, "Rutherfords"],
Rydberg -> Quantity[1, "Rydbergs"],
Seam -> Quantity[1, "SeamsUK"],
Second -> Quantity[1, "Seconds"],
Section -> Quantity[1, "Miles"^2],
Shekel -> Quantity[1, "ShekelsMass"],
ShortHundredweight -> Quantity[1, "ShortHundredweights"],
ShortTon -> Quantity[1, "ShortTons"],
Shot -> Quantity[1, "Shots"],
SiderealSecond -> Quantity[1, "SiderealSeconds"],
SiderealYear -> Quantity[1, "SiderealYears"],
Siemens -> Quantity[1, "Siemens"],
Skein -> Quantity[1, "Skeins"],
Slug -> Quantity[1, "SlugsMass"],
SolarMass -> Quantity[1, "SolarMass"],
Span -> Quantity[1, "SpansLength"],
Stadion -> Quantity[1, "GreekStadions"],
Stadium -> Quantity[1, "GreekStadions"],
Statampere -> Quantity[1, "StatAmperes"],
Statcoulomb -> Quantity[1, "StatCoulombs"],
Statfarad -> Quantity[1, "StatFarads"],
Stathenry -> Quantity[1, "StatHenries"],
Statohm -> Quantity[1, "StatOhms"],
StatuteMile -> Quantity[1, "Miles"],
Statvolt -> Quantity[1, "StatVolts"],
Steradian -> Quantity[1, "Steradians"],
Stere -> Quantity[1, "Steres"],
Stilb -> Quantity[1, "Stilbs"],
Stokes -> Quantity[1, "Stokes"],
Stone -> Quantity[1, "Stones"],
SurveyMile -> Quantity[1, "SurveyMiles"],
Tablespoon -> Quantity[1, "Tablespoons"],
Talbot -> Quantity[1, "Talbots"],
Talent -> Quantity[1, "AeginaTalents"],
Teaspoon -> Quantity[1, "Teaspoons"],
Tesla -> Quantity[1, "Teslas"],
Therm -> Quantity[1, "Therms"],
Ton -> Quantity[1, "ShortTons"],
TonForce -> Quantity[1, "ShortTonsForce"],
Tonne -> Quantity[1, "ShortTons"],
Torr -> Quantity[1, "Torr"],
Township -> Quantity[1, "Townships"],
TropicalYear -> Quantity[1, "TropicalYears"],
TroyOunce -> Quantity[1, "TroyOunces"],
Tun -> Quantity[1, "Tuns"],
UKGallon -> Quantity[1, "Gallons"],
UKPint -> Quantity[1, "Pints"],
Volt -> Quantity[1, "Volts"],
Watt -> Quantity[1, "Watts"],
Weber -> Quantity[1, "Webers"],
Week -> Quantity[1, "Weeks"],
Wey -> Quantity[1, "WeysMass"],
WineBottle -> Quantity[0.7576778, "Liters"],
XUnit -> Quantity[1, "XUnits"],
Yard -> Quantity[1, "Yards"],
Year -> Quantity[1, "Years"]}];
prefixRules =
Dispatch[{Yotta -> 10^24, Zetta -> 10^21, Exa -> 10^18,
Peta -> 10^15, Tera -> 10^12, Giga -> 10^9, Mega -> 10^6,
Kilo -> 10^3, Hecto -> 100, Deca -> 10, Deci -> 10^-1,
Centi -> 10^-2, Milli -> 10^-3, Micro -> 10^-6, Nano -> 10^-9,
Pico -> 10^-12, Femto -> 10^-15, Atto -> 10^-18, Zepto -> 10^-21,
Yocto -> 10^-24}];
Quantify[expr_]:=expr/.prefixRules/.unitRules
Quantity objects and old school units can be freely mixed
Quantify[{(2 Centimeter^3)/(Quantity[1.199,
"Kilograms"/"Meters"^3] Quantity[344.0, "Meters"/"Seconds"]^2),
30. Micro Farad}]
yields
{Quantity[0.00140959, (("Centimeters")^4 ("Seconds")^2)/("Kilograms")],
Quantity[0.00003, "Farads"]}
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$\begingroup$ +1 goes w/o saying. This is great stuff. Can you share the code to extract all units? WRI will surely add more (new) units, so how to catalogue them dynamically? $\endgroup$ Dec 18, 2014 at 18:16
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$\begingroup$ @alancalvitti My intent was to allow the use of the units that were defined in the old (pre-9) Units package. Presumably, this package is no longer maintained as Quantity has taken over that functionality, so this was a one-time event performed manually. By manually, I mean with sloppy, throw-away code. However, if you like this approach, you are welcome to add your own units into the dispatch table. $\endgroup$– Daniel WDec 18, 2014 at 18:24
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$\begingroup$ I also made sure that any Quantity I used were among those stored locally rather than those that make a call to the Wolfram servers. I have to work behind a proxy sometimes and entering proxy settings during execution of coded solutions is not acceptable. $\endgroup$– Daniel WDec 18, 2014 at 18:28
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$\begingroup$ I meant the new versions. Can you use the same approach to list the new built in units. I don't know of a way to extract them with, say,
Names[Quantity[_, _]]-->Quantity::unknunit : Unable to interpret unit specification". What's your approach? $\endgroup$ Dec 18, 2014 at 18:30 -
$\begingroup$ Yes, glad you mention the over the network units - which are slow even w/ no firewall. Ideally would like a list of both types. $\endgroup$ Dec 18, 2014 at 18:31