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######################################################## |
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# |
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# Copyright (c) 2003-2010 by University of Queensland |
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# Earth Systems Science Computational Center (ESSCC) |
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# http://www.uq.edu.au/esscc |
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# |
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# Primary Business: Queensland, Australia |
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# Licensed under the Open Software License version 3.0 |
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# http://www.opensource.org/licenses/osl-3.0.php |
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# |
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######################################################## |
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__copyright__="""Copyright (c) 2003-2010 by University of Queensland |
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Earth Systems Science Computational Center (ESSCC) |
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http://www.uq.edu.au/esscc |
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Primary Business: Queensland, Australia""" |
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__license__="""Licensed under the Open Software License version 3.0 |
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http://www.opensource.org/licenses/osl-3.0.php""" |
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__url__="https://launchpad.net/escript-finley" |
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__author__="Lutz Gross, l.gross@uq.edu.au" |
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## :file unitsSI.py |
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|
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""" |
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some tools supporting physical units and conversion |
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|
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:var __author__: name of author |
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:var __copyright__: copyrights |
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:var __license__: licence agreement |
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:var __url__: url entry point on documentation |
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:var __version__: version |
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:var __date__: date of the version |
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|
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:var Yotta : prefix yotta, symbol: Y |
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:var Zetta : prefix zetta, symbol: Z |
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:var Exa : prefix exa, symbol: E |
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:var Peta : prefix peta, symbol: P |
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:var Tera : prefix tera, symbol: T |
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:var Giga : prefix giga, symbol: G |
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:var Mega : prefix mega, symbol: M |
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:var Kilo : prefix kilo, symbol: k |
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:var Hecto : prefix hecto, symbol: h |
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:var Deca : prefix deca, symbol: da |
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:var Deci : prefix deci, symbol: d |
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:var Centi : prefix centi, symbol: c |
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:var Milli : prefix milli, symbol: m |
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:var Micro : prefix micro, symbol: mu |
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:var Nano : prefix nano, symbol: n |
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:var Pico : prefix pico, symbol: p |
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:var Femto : prefix femto, symbol: f |
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:var Atto : prefix atto, symbol: a |
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:var Zepto : prefix zepto, symbol: z |
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:var Yocto : prefix yocto, symbol: y |
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|
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:var km : unit of kilo meter |
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:var m : unit of meter |
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:var cm : unit of centi meter |
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:var mm : unit of milli meter |
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:var sec: unit of second |
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:var minute : unit of minute |
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:var h : unit of hour |
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:var hour : unit of hour |
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:var day : unit of day |
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:var yr : unit of year |
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:var Myr : unit of mega year |
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:var Gyr : unit of giga year |
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:var gram : unit of gram |
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:var kg : unit of kilo gram |
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:var lb : unit of pound |
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:var ton : metric ton |
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:var A : unit of Ampere |
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:var Hz: unit of Hertz (frequenacy) |
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:var N: unit of Newton (force) |
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:var Pa: unit of Pascal (pressure, stress) |
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:var bar: unit of bar (pressure) |
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:var atm: unit of atmosphere (pressure) |
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:var J: unit of Joule (energy, work) |
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:var W: unit of Watt (power) |
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:var C: unit of Coulomb (electric charge) |
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:var V: unit of Volt (electric potential) |
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:var F: unit of Farad (capacitance) |
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:var Ohm: unit of Ohm (electric resistance) |
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:var K : unit of Kelvin (temperature) |
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:var Mol : unit of Mole (temperature) |
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:var Celsius: unit of Celsius (temperature) |
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:var Fahrenheit : unit of Fahrenheit (temperature) |
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:var Poise : unit of Poise (dynamic viscosity) |
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:var R_Earth_equator: Earth's equatorial radius |
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:var R_Earth_poles: Earth's polar radius |
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:var R_Earth: Earth's radius |
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:var v_light: speed of light |
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:var pi: value of pi accurate to 10 decimal places |
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""" |
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from math import pi |
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class Unit(object): |
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""" |
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a general class to define a physical unit and convert from this unit to an appropriate SI unit. |
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|
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`Unit` object have a dual purpose: Firstly physical units can be combined through *,/ and ** to form new physical units or to add prefixes such as |
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Milli to m to form mm=Milli*m. Moreover, a given floating point number x (or any other arithmetic object) can be converted from the physical unit to |
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the SI system, eg. 10*mm to create the value for 10mm which is the float number 0.01 in the SI system. In addition, a value in the SI unit can be |
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converted back to the given unit, eg. to express 0.01m in physical units of mm use 0.01/mm which will return 10. |
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""" |
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def __init__(self, name, longname,a ,b ): |
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""" |
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initializes the physical unit |
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|
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:param name: short name of the physical unit or prefix |
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:type name: ``str`` |
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:param longname: long name of the physical unit or prefix |
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:type longname: ``str`` |
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:param a: absolute value in transformation |
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:type a: ``float`` |
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:param b: slop in translation |
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:type b: ``float`` |
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""" |
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self.setName(name) |
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self.setLongName(longname) |
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self.__a=a |
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self.__b=b |
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|
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def __str__(self): |
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return self.getName() |
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|
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def getName(self): |
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""" |
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Returns the name of the physical unit |
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|
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:return: name of the physical unit |
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:rtype: ``str`` |
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""" |
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return self.__name |
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|
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def setName(self, name): |
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""" |
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Sets the name of the physical unit |
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|
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:param name: new name of the physical unit |
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:type name: ``str`` |
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""" |
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self.__name=name |
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|
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def getLongName(self): |
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""" |
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Returns the long name of the physical unit |
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|
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:return: name of the physical unit |
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:rtype: ``str`` |
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""" |
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return self.__longname |
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|
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def setLongName(self, name): |
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""" |
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Sets the long name of the physical unit |
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|
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:param name: new long name of the physical unit |
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:type name: ``str`` |
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""" |
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self.__longname=name |
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|
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def __call__(self,x): |
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""" |
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Converts a value x in the physical unit self to SI |
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:param x: value to convert |
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:type x: an arithmetic object |
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""" |
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return self.__b*x+self.__a |
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|
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def __mul__(self,other): |
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""" |
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Performs self*other operation for two `Unit` objects |
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|
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:param other: an other physical unit |
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:type other: `Unit` |
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:rtype: `Unit` or ``NotImplemented`` |
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""" |
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if isinstance(other, Unit): |
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a=self(other(0.)) |
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b=(self(other(1.))-a) |
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if isinstance(other, _PowUnit) or isinstance(self,_DivUnit) or isinstance(self, _PowUnit): |
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return _ProdUnit(self.getName()+" "+other.getName(),self.getLongName()+"*"+other.getLongName(),a ,b) |
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else: |
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return _ProdUnit(self.getName()+other.getName(),self.getLongName()+"*"+other.getLongName(),a ,b) |
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else: |
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return NotImplemented |
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|
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def __rmul__(self,other): |
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""" |
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Performs other*self operation |
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|
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:param other: an other `Unit` or an arithmetic object. if other is a arithmetic object such as ``float`` other is assumed to be given in the physical unit ``self`` and is converted into the corresponding SI unit. |
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:type other: `Unit` or |
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:rtype: `Unit` of or an arithmetic object |
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""" |
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if isinstance(other, Unit): |
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a=other(self(0.)) |
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b=(other(self(1.))-a) |
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if isinstance(other, _PowUnit) or isinstance(self, _PowUnit) or isinstance(other, _DivUnit): |
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return _ProdUnit(other.getName()+" "+self.getName(),other.getLongName()+"*"+self.getLongName(),a ,b) |
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else: |
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return _ProdUnit(other.getName()+self.getName(),other.getLongName()+"*"+self.getLongName(),a ,b) |
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else: |
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return self(other) |
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|
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def __div__(self,other): |
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""" |
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Performs self*other operation for two `Unit` objects |
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:param other: an other physical unit |
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:type other: `Unit` |
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:rtype: `Unit` or ``NotImplemented`` |
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""" |
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if isinstance(other, Unit): |
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if abs(self(0.))+abs(other(0.))>0: |
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raise ValueError,"Division of physical units requires 0 absolute values" |
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if isinstance(other, (_ProdUnit, _DivUnit)): |
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# X/(c*d) or X/(c/d) requires brackets: |
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return _DivUnit(self.getName()+"/("+other.getName()+")",self.getLongName()+"/("+other.getLongName()+")",0 , self(1.)/other(1.)) |
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else: |
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return _DivUnit(self.getName()+"/"+other.getName(),self.getLongName()+"/"+other.getLongName(),0 , self(1.)/other(1.)) |
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else: |
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return NotImplemented |
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def __rdiv__(self,other): |
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""" |
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Performs other/self operation |
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:param other: an other `Unit` or an arithmetic object |
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:type other: `Unit` or an arithmetic object |
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:rtype: `Unit` or an arithmetic object |
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""" |
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if isinstance(other, Unit): |
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if abs(self(0.))+abs(other(0.))>0: |
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raise ValueError,"Division of physical units requires 0 absolute values" |
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if isinstance(self, (_ProdUnit, _DivUnit)): |
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# X/(a*b) or X/(a/b) requires brackets: |
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return _DivUnit(other.getName()+"/("+self.getName()+")",other.getLongName()+"/("+self.getLongName()+")",0 , other(1.)/self(1.)) |
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else: |
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return _DivUnit(other.getName()+"/"+self.getName(),other.getLongName()+"/"+self.getLongName(),0 , other(1.)/self(1.)) |
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else: |
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return (other-self(0.))/(self(1.)-self(0.)) |
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def __pow__(self,other): |
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""" |
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Performs self**other operation |
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|
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:param other: an exponent |
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:type other: ``int`` or ``float`` |
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:rtype: `Unit` |
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""" |
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if isinstance(other, float) or isinstance(other, int): |
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if abs(self(0.))>0: |
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raise ValueError,"Power of physical unit requires 0 absolute values" |
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if isinstance(self, (_ProdUnit, _DivUnit, _PowUnit)): |
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return _PowUnit("("+self.getName()+")^%s"%other, "("+self.getLongName()+")^%s"%other, 0., self(1.)**other) |
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else: |
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return _PowUnit(self.getName()+"^%s"%other, self.getLongName()+"^%s"%other, 0., self(1.)**other) |
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else: |
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return NotImplemented |
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|
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class _ProdUnit(Unit): |
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pass |
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class _DivUnit(Unit): |
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pass |
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class _PowUnit(Unit): |
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pass |
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|
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# |
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# prefixes: |
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# |
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Yotta=Unit("Y","Yotta",0.,1.e24) |
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Zetta=Unit("Z","Zetta",0.,1.e21) |
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Exa=Unit("E","Exa",0.,1.e18) |
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Peta=Unit("P","Peta",0.,1.e15) |
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Tera=Unit("T","Tera",0.,1.e12) |
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Giga=Unit("G","Giga",0.,1.e9) |
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Mega=Unit("M","Mega",0.,1.e6) |
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Kilo=Unit("k","Kilo",0.,1.e3) |
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Hecto=Unit("h","Hecto",0.,1.e2) |
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Deca=Unit("da","Deca",0.,1.e1) |
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one=Unit("1","1",0.,1.) |
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Deci=Unit("d","Deci",0.,1.e-1) |
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Centi=Unit("c","Centi",0.,1.e-2) |
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Milli=Unit("m","Milli",0.,1.e-3) |
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Micro=Unit("mu","Micro",0.,1.e-6) |
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Nano=Unit("n","Nano",0.,1.e-9) |
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Pico=Unit("p","Pico",0.,1.e-12) |
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Femto=Unit("f","Femto",0.,1.e-15) |
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Atto=Unit("a","Atto",0.,1.e-18) |
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Zepto=Unit("z","Zepto",0.,1.e-21) |
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Yocto=Unit("y","Yocto",0.,1.e-24) |
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# |
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# length |
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# |
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m=Unit("m","meter",0.,1.) |
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km=Kilo*m |
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cm=Centi*m |
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mm=Milli*m |
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# |
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# time |
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# |
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sec=Unit("sec","second",0.,1.) |
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minute=Unit("min","minute",0.,60.) |
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hour=Unit("h","hour",0.,60.*60.) |
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h=hour |
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day=Unit("d","day",0.,60.*60.*24.) |
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yr=Unit("yr","year",0.,60.*60.*24.*365.2425) |
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year=yr |
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Myr=Mega*yr |
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Gyr=Giga*yr |
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# |
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# mass |
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# |
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kg=Unit("kg","kg",0.,1.) |
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gram=Milli*kg |
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lb=Unit("lb","pound",0.,0.45359237) |
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ton=Kilo*kg |
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# |
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# electric current |
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# |
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A=Unit("A","Ampere",0.,1.) |
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# |
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# Temperature |
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# |
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K=Unit("K","Kelvin",0.,1.) |
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Celsius=Unit("C","Celsius",273.15,1.) |
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Fahrenheit=Unit("F","Fahrenheit",459.67*5./9.,5./9.) |
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# |
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# others |
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# |
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Mol=Unit("mole","Mole",0.,1.) |
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Hz=one/sec |
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N = Unit("N","Newton",0.,1.) |
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Pa = Unit("Pa","Pascal",0.,1.) |
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bar=100*Kilo*Pa |
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atm= Unit("atm","atmosphere",0.,101325.024) |
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J = Unit("J","Joule",0.,1.) |
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W= Unit("W","Watt",0.,1.) |
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C=Unit("C","Coulomb",0.,1.) |
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V = Unit("V","Volt",0.,1.) |
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F = Unit("F","Farad",0.,1.) |
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Ohm=Unit("Ohm","Ohm",0.,1.) |
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RAD=Unit("RAD","rad",0.,1.) |
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DEG=Unit("Ohm","Ohm",0.,pi/180.) |
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# |
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# Derived |
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# |
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Poise= gram/cm/sec |
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Darcy= 9.869233e-13*m**2 |
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# |
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# some constants |
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# |
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R_Earth_equator=6378.1370*km |
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R_Earth_poles=6356.7523*km |
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R_Earth=(R_Earth_equator+R_Earth_poles)/2 |
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v_light=299792458.*m/sec |
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