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  • package root
    Definition Classes
    root
  • package de
    Definition Classes
    root
  • package h2b
    Definition Classes
    de
  • package scala
    Definition Classes
    h2b
  • package lib
    Definition Classes
    scala
  • package phys
    Definition Classes
    lib
  • package units

    This is a Scala library of units of measurement featuring the International System of Units (SI).

    This is a Scala library of units of measurement featuring the International System of Units (SI).

    Imports

    In most cases, to use this package you will import all of this:

    import de.h2b.scala.lib.phys.units.Quantity
import de.h2b.scala.lib.phys.units.Quantity._
import de.h2b.scala.lib.phys.units.base._
import de.h2b.scala.lib.phys.units.derived._

    Quantities

    A quantity is composed of a magnitude and a unit.

    val m = Quantity(10, kilogram) //> m  : Quantity[MassUnit] = 10.0 kg
val l = Quantity(0.981, metre) //> l  : Quantity[LengthUnit] = 0.981 m
val t = Quantity(1, second)    //> t  : Quantity[TimeUnit] = 1.0 s

    You can add or subtract quantities of the same unit and multiply or divide quantities of arbitrary units. Also, you can scale a quantity by a factor.

    val m2 = m + Quantity(20, kilogram) //> m2  : Quantity[MassUnit] = 30.0 kg
val m3 = 2 * Quantity(1, meter)     //> m3  : Quantity[LengthUnit] = 2.0 m

    Multiplication and division of two quantities need an implicit unit operation that guarantees that the result becomes a quantity of proper unit. The other operations simply yield a quantity of the same unit as the operator.

    val f = m * ((l / t) / t) //> f  : Quantity[ForceUnit] = 9.81 kg*m/s/s

    The system is smart enough to derive that a quantity of units kilogram * ((metre / second) / second) is a quantity of ForceUnit. (Actually however, for now it is not smart enough if the order of operands is changed: ((l / t) / t) * m would not work -- in doubt try it out and inspect the unit objects mentioned below.)

    The quantity class extends the Equals trait and there is also a ~= operator that compares quantities within an implicitly specified tolerance to compensate rounding errors.

    The companion object provides implicit Double operations so that you can write, e.g., 10.m instead of Quantity(10, metre).

    Quantity(10, metre) == 10.m //> Boolean = true

    Units

    Units are based on the *Système international d’unités* (SI -- which gave this package its name), i.e., each unit [Q] can mathematically be expressed in terms of the base units metre, kilogram, second, ampere, kelvin, mol and candela by the equation

    [Q] = ξ·10n·mα·kgβ·sγ·Aδ·Kε·molζ·cdη

    For ξ=1 we have a (potentially derived) SI unit; for ξ=1 and n=0 we have a coherent SI unit.

    The base package provides classes for the seven base units (plus a NeutralUnit) with implicit multiplication and division operations (as mentioned above) and associated objects of common names like metre, kilogram, second and so on.

    The derived package provides the same for a (of course not complete) bunch of derived SI units like squareMetre, newton, pascal, joule, watt or volt.

    The Prefix class has case objects providing the usual SI prefixes like kilo or milli along with a multiplication operation for units.

    You can implement other units by providing the same components for the new unit as the base or derived packages do. For details see there.

    Definition Classes
    phys
  • package base
  • package derived
  • Prefix
  • Quantity
  • Unit
  • atto
  • centi
  • deca
  • deci
  • exa
  • femto
  • giga
  • hecto
  • kilo
  • mega
  • micro
  • milli
  • nano
  • peta
  • pico
  • tera
  • yocto
  • yotta
  • zepto
  • zetta

package units

This is a Scala library of units of measurement featuring the International System of Units (SI).

Imports

In most cases, to use this package you will import all of this:

import de.h2b.scala.lib.phys.units.Quantity
import de.h2b.scala.lib.phys.units.Quantity._
import de.h2b.scala.lib.phys.units.base._
import de.h2b.scala.lib.phys.units.derived._

Quantities

A quantity is composed of a magnitude and a unit.

val m = Quantity(10, kilogram) //> m  : Quantity[MassUnit] = 10.0 kg
val l = Quantity(0.981, metre) //> l  : Quantity[LengthUnit] = 0.981 m
val t = Quantity(1, second)    //> t  : Quantity[TimeUnit] = 1.0 s

You can add or subtract quantities of the same unit and multiply or divide quantities of arbitrary units. Also, you can scale a quantity by a factor.

val m2 = m + Quantity(20, kilogram) //> m2  : Quantity[MassUnit] = 30.0 kg
val m3 = 2 * Quantity(1, meter)     //> m3  : Quantity[LengthUnit] = 2.0 m

Multiplication and division of two quantities need an implicit unit operation that guarantees that the result becomes a quantity of proper unit. The other operations simply yield a quantity of the same unit as the operator.

val f = m * ((l / t) / t) //> f  : Quantity[ForceUnit] = 9.81 kg*m/s/s

The system is smart enough to derive that a quantity of units kilogram * ((metre / second) / second) is a quantity of ForceUnit. (Actually however, for now it is not smart enough if the order of operands is changed: ((l / t) / t) * m would not work -- in doubt try it out and inspect the unit objects mentioned below.)

The quantity class extends the Equals trait and there is also a ~= operator that compares quantities within an implicitly specified tolerance to compensate rounding errors.

The companion object provides implicit Double operations so that you can write, e.g., 10.m instead of Quantity(10, metre).

Quantity(10, metre) == 10.m //> Boolean = true

Units

Units are based on the *Système international d’unités* (SI -- which gave this package its name), i.e., each unit [Q] can mathematically be expressed in terms of the base units metre, kilogram, second, ampere, kelvin, mol and candela by the equation

[Q] = ξ·10n·mα·kgβ·sγ·Aδ·Kε·molζ·cdη

For ξ=1 we have a (potentially derived) SI unit; for ξ=1 and n=0 we have a coherent SI unit.

The base package provides classes for the seven base units (plus a NeutralUnit) with implicit multiplication and division operations (as mentioned above) and associated objects of common names like metre, kilogram, second and so on.

The derived package provides the same for a (of course not complete) bunch of derived SI units like squareMetre, newton, pascal, joule, watt or volt.

The Prefix class has case objects providing the usual SI prefixes like kilo or milli along with a multiplication operation for units.

You can implement other units by providing the same components for the new unit as the base or derived packages do. For details see there.

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Type Members

  1. sealed abstract class Prefix extends AnyRef

    An SI prefix.

  2. class Quantity [U <: Unit[_]] extends Equals

    A physical quantity composed of a magnitude and a unit.

  3. class Unit [U <: Unit[_]] extends Equals

    A unit of measure.

    A unit of measure.

    Decomposition of this unit [Q] into SI base units according to the equation:

    [Q] = ξ·10n·mα·kgβ·sγ·Aδ·Kε·molζ·cdη

    The exponents are represented by a vector starting with index 0 for n etc while ξ becomes an own field scale.

    Two units are considered to be equal if their SI exponents and scale are the same, respectively. The name and symbol strings have no meaning regarding to equality.

    For ξ==1 we have a (potentially derived) SI unit.

    For ξ==1 and n==0 we have a coherent SI unit.

    See also

    https://de.wikipedia.org/wiki/Internationales_Einheitensystem

Value Members

  1. object Quantity
  2. object Unit
  3. object atto extends Prefix with Product with Serializable
  4. object centi extends Prefix with Product with Serializable
  5. object deca extends Prefix with Product with Serializable
  6. object deci extends Prefix with Product with Serializable
  7. object exa extends Prefix with Product with Serializable
  8. object femto extends Prefix with Product with Serializable
  9. object giga extends Prefix with Product with Serializable
  10. object hecto extends Prefix with Product with Serializable
  11. object kilo extends Prefix with Product with Serializable
  12. object mega extends Prefix with Product with Serializable
  13. object micro extends Prefix with Product with Serializable
  14. object milli extends Prefix with Product with Serializable
  15. object nano extends Prefix with Product with Serializable
  16. object peta extends Prefix with Product with Serializable
  17. object pico extends Prefix with Product with Serializable
  18. object tera extends Prefix with Product with Serializable
  19. object yocto extends Prefix with Product with Serializable
  20. object yotta extends Prefix with Product with Serializable
  21. object zepto extends Prefix with Product with Serializable
  22. object zetta extends Prefix with Product with Serializable

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