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1
2 ########################################################
3 #
4 # Copyright (c) 2003-2008 by University of Queensland
5 # Earth Systems Science Computational Center (ESSCC)
6 # http://www.uq.edu.au/esscc
7 #
8 # Primary Business: Queensland, Australia
9 # Licensed under the Open Software License version 3.0
10 # http://www.opensource.org/licenses/osl-3.0.php
11 #
12 ########################################################
13
14 __copyright__="""Copyright (c) 2003-2008 by University of Queensland
15 Earth Systems Science Computational Center (ESSCC)
16 http://www.uq.edu.au/esscc
17 Primary Business: Queensland, Australia"""
18 __license__="""Licensed under the Open Software License version 3.0
19 http://www.opensource.org/licenses/osl-3.0.php"""
20 __url__="https://launchpad.net/escript-finley"
21 __author__="Lutz Gross, l.gross@uq.edu.au"
22
23 ## @file unitsSI.py
24
25 """
26 some tools supporting physical units and conversion
27
28 @var __author__: name of author
29 @var __copyright__: copyrights
30 @var __license__: licence agreement
31 @var __url__: url entry point on documentation
32 @var __version__: version
33 @var __date__: date of the version
34
35 @var Yotta : prefix yotta, symbol: Y
36 @var Zetta : prefix zetta, symbol: Z
37 @var Exa : prefix exa, symbol: E
38 @var Peta : prefix peta, symbol: P
39 @var Tera : prefix tera, symbol: T
40 @var Giga : prefix giga, symbol: G
41 @var Mega : prefix mega, symbol: M
42 @var Kilo : prefix kilo, symbol: k
43 @var Hecto : prefix hecto, symbol: h
44 @var Deca : prefix deca, symbol: da
45 @var Deci : prefix deci, symbol: d
46 @var Centi : prefix centi, symbol: c
47 @var Milli : prefix milli, symbol: m
48 @var Micro : prefix micro, symbol: mu
49 @var Nano : prefix nano, symbol: n
50 @var Pico : prefix pico, symbol: p
51 @var Femto : prefix femto, symbol: f
52 @var Atto : prefix atto, symbol: a
53 @var Zepto : prefix zepto, symbol: z
54 @var Yocto : prefix yocto, symbol: y
55
56 @var km : unit of kilo meter
57 @var m : unit of meter
58 @var cm : unit of centi meter
59 @var mm : unit of milli meter
60 @var sec: unit of second
61 @var minute : unit of minute
62 @var h : unit of hour
63 @var day : unit of day
64 @var yr : unit of year
65 @var Myr : unit of mega year
66 @var Gyr : unit of giga year
67 @var gram : unit of gram
68 @var kg : unit of kilo gram
69 @var lb : unit of pound
70 @var ton : metric ton
71 @var A : unit of Ampere
72 @var Hz: unit of Hertz (frequenacy)
73 @var N: unit of Newton (force)
74 @var Pa: unit of Pascal (pressure, stress)
75 @var atm: unit of atmosphere (pressure)
76 @var J: unit of Joule (energy, work)
77 @var W: unit of Watt (power)
78 @var C: unit of Coulomb (electric charge)
79 @var V: unit of Volt (electric potential)
80 @var F: unit of Farad (capacitance)
81 @var Ohm: unit of Ohm (electric resistance)
82 @var K : unit of Kelvin (temperature)
83 @var Mol : unit of Mole (temperature)
84 @var Celsius: unit of Celsius (temperature)
85 @var Fahrenheit : unit of Fahrenheit (temperature)
86 @var Poise : unit of Poise (dynamic viscosity)
87 @var R_Earth_equator: Earth's equatorial radius
88 @var R_Earth_poles: Earth's polar radius
89 @var R_Earth: Earth's radius
90 @var v_light: speed of light
91 @var pi: value of pi accurate to 10 decimal places
92 """
93 class Unit(object):
94 """
95 a general class to define a physical unit and convert from this unit to an appropriate SI unit.
96
97 L{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
98 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
99 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
100 converted back to the given unit, eg. to express 0.01m in physical units of mm use 0.01/mm which will return 10.
101 """
102 def __init__(self, name, longname,a ,b ):
103 """
104 initializes the physical unit
105
106 @param name: short name of the physical unit or prefix
107 @type name: C{str}
108 @param longname: long name of the physical unit or prefix
109 @type longname: C{str}
110 @param a: absolute value in transformation
111 @type a: C{float}
112 @param b: slop in translation
113 @type b: C{float}
114 """
115 self.setName(name)
116 self.setLongName(longname)
117 self.__a=a
118 self.__b=b
119
120 def __str__(self):
121 return self.getName()
122
123 def getName(self):
124 """
125 Returns the name of the physical unit
126
127 @return: name of the physical unit
128 @rtype: C{str}
129 """
130 return self.__name
131
132 def setName(self, name):
133 """
134 Sets the name of the physical unit
135
136 @param name: new name of the physical unit
137 @type name: C{str}
138 """
139 self.__name=name
140
141 def getLongName(self):
142 """
143 Returns the long name of the physical unit
144
145 @return: name of the physical unit
146 @rtype: C{str}
147 """
148 return self.__longname
149
150 def setLongName(self, name):
151 """
152 Sets the long name of the physical unit
153
154 @param name: new long name of the physical unit
155 @type name: C{str}
156 """
157 self.__longname=name
158
159 def __call__(self,x):
160 """
161 Converts a value x in the physical unit self to SI
162
163 @param x: value to convert
164 @type x: an arithmetic object
165 """
166 return self.__b*x+self.__a
167
168 def __mul__(self,other):
169 """
170 Performs self*other operation for two L{Unit} objects
171
172 @param other: an other physical unit
173 @type other: L{Unit}
174 @rtype: L{Unit} or C{NotImplemented}
175 """
176 if isinstance(other, Unit):
177 a=self(other(0.))
178 b=(self(other(1.))-a)
179 if isinstance(other, _PowUnit) or isinstance(self,_DivUnit) or isinstance(self, _PowUnit):
180 return _ProdUnit(self.getName()+" "+other.getName(),self.getLongName()+"*"+other.getLongName(),a ,b)
181 else:
182 return _ProdUnit(self.getName()+other.getName(),self.getLongName()+"*"+other.getLongName(),a ,b)
183 else:
184 return NotImplemented
185
186 def __rmul__(self,other):
187 """
188 Performs other*self operation
189
190 @param other: an other L{Unit} or an arithmetic object. if other is a arithmetic object such as C{float} other is assumed to be given in the
191 physical unit C{self} and is converted into the corresponding SI unit.
192 @type other: L{Unit} or
193 @rtype: L{Unit} of or an arithmetic object
194 """
195 if isinstance(other, Unit):
196 a=other(self(0.))
197 b=(other(self(1.))-a)
198 if isinstance(other, _PowUnit) or isinstance(self, _PowUnit) or isinstance(other, _DivUnit):
199 return _ProdUnit(other.getName()+" "+self.getName(),other.getLongName()+"*"+self.getLongName(),a ,b)
200 else:
201 return _ProdUnit(other.getName()+self.getName(),other.getLongName()+"*"+self.getLongName(),a ,b)
202 else:
203 return self(other)
204
205 def __div__(self,other):
206 """
207 Performs self*other operation for two L{Unit} objects
208
209 @param other: an other physical unit
210 @type other: L{Unit}
211 @rtype: L{Unit} or C{NotImplemented}
212 """
213 if isinstance(other, Unit):
214 if abs(self(0.))+abs(other(0.))>0:
215 raise ValueError,"Division of physical units requires 0 absolute values"
216 if isinstance(other, (_ProdUnit, _DivUnit)):
217 # X/(c*d) or X/(c/d) requires brackets:
218 return _DivUnit(self.getName()+"/("+other.getName()+")",self.getLongName()+"/("+other.getLongName()+")",0 , self(1.)/other(1.))
219 else:
220 return _DivUnit(self.getName()+"/"+other.getName(),self.getLongName()+"/"+other.getLongName(),0 , self(1.)/other(1.))
221 else:
222 return NotImplemented
223 def __rdiv__(self,other):
224 """
225 Performs other/self operation
226
227 @param other: an other L{Unit} or an arithmetic object
228 @type other: L{Unit} or an arithmetic object
229 @rtype: L{Unit} or an arithmetic object
230 """
231 if isinstance(other, Unit):
232 if abs(self(0.))+abs(other(0.))>0:
233 raise ValueError,"Division of physical units requires 0 absolute values"
234 if isinstance(self, (_ProdUnit, _DivUnit)):
235 # X/(a*b) or X/(a/b) requires brackets:
236 return _DivUnit(other.getName()+"/("+self.getName()+")",other.getLongName()+"/("+self.getLongName()+")",0 , other(1.)/self(1.))
237 else:
238 return _DivUnit(other.getName()+"/"+self.getName(),other.getLongName()+"/"+self.getLongName(),0 , other(1.)/self(1.))
239 else:
240 return (other-self(0.))/(self(1.)-self(0.))
241 def __pow__(self,other):
242 """
243 Performs self**other operation
244
245 @param other: an exponent
246 @type other: C{int} or C{float}
247 @rtype: L{Unit}
248 """
249 if isinstance(other, float) or isinstance(other, int):
250 if abs(self(0.))>0:
251 raise ValueError,"Power of physical unit requires 0 absolute values"
252 if isinstance(self, (_ProdUnit, _DivUnit, _PowUnit)):
253 return _PowUnit("("+self.getName()+")^%s"%other, "("+self.getLongName()+")^%s"%other, 0., self(1.)**other)
254 else:
255 return _PowUnit(self.getName()+"^%s"%other, self.getLongName()+"^%s"%other, 0., self(1.)**other)
256 else:
257 return NotImplemented
258
259 class _ProdUnit(Unit):
260 pass
261 class _DivUnit(Unit):
262 pass
263 class _PowUnit(Unit):
264 pass
265
266 #
267 # prefixes:
268 #
269 Yotta=Unit("Y","Yotta",0.,1.e24)
270 Zetta=Unit("Z","Zetta",0.,1.e21)
271 Exa=Unit("E","Exa",0.,1.e18)
272 Peta=Unit("P","Peta",0.,1.e15)
273 Tera=Unit("T","Tera",0.,1.e12)
274 Giga=Unit("G","Giga",0.,1.e9)
275 Mega=Unit("M","Mega",0.,1.e6)
276 Kilo=Unit("k","Kilo",0.,1.e3)
277 Hecto=Unit("h","Hecto",0.,1.e2)
278 Deca=Unit("da","Deca",0.,1.e1)
279 one=Unit("1","1",0.,1.)
280 Deci=Unit("d","Deci",0.,1.e-1)
281 Centi=Unit("c","Centi",0.,1.e-2)
282 Milli=Unit("m","Milli",0.,1.e-3)
283 Micro=Unit("mu","Micro",0.,1.e-6)
284 Nano=Unit("n","Nano",0.,1.e-9)
285 Pico=Unit("p","Pico",0.,1.e-12)
286 Femto=Unit("f","Femto",0.,1.e-15)
287 Atto=Unit("a","Atto",0.,1.e-18)
288 Zepto=Unit("z","Zepto",0.,1.e-21)
289 Yocto=Unit("y","Yocto",0.,1.e-24)
290 #
291 # length
292 #
293 m=Unit("m","meter",0.,1.)
294 km=Kilo*m
295 cm=Centi*m
296 mm=Milli*m
297 #
298 # time
299 #
300 sec=Unit("sec","second",0.,1.)
301 minute=Unit("min","minute",0.,60.)
302 h=Unit("h","hour",0.,60.*60.)
303 day=Unit("d","day",0.,60.*60.*24.)
304 yr=Unit("yr","year",0.,60.*60.*24.*365.2425)
305 Myr=Mega*yr
306 Gyr=Giga*yr
307 #
308 # mass
309 #
310 kg=Unit("kg","kg",0.,1.)
311 gram=Milli*kg
312 lb=Unit("lb","pound",0.,0.45359237)
313 ton=Kilo*kg
314 #
315 # electric current
316 #
317 A=Unit("A","Ampere",0.,1.)
318 #
319 # Temperature
320 #
321 K=Unit("K","Kelvin",0.,1.)
322 Celsius=Unit("C","Celsius",273.15,1.)
323 Fahrenheit=Unit("F","Fahrenheit",459.67*5./9.,5./9.)
324 #
325 # others
326 #
327 Mol=Unit("mole","Mole",0.,1.)
328 Hz=one/sec
329 N = Unit("N","Newton",0.,1.)
330 Pa = Unit("Pa","Pascal",0.,1.)
331 atm= Unit("atm","atmosphere",0.,101325.024)
332 J = Unit("J","Joule",0.,1.)
333 W= Unit("W","Watt",0.,1.)
334 C=Unit("C","Coulomb",0.,1.)
335 V = Unit("V","Volt",0.,1.)
336 F = Unit("F","Farad",0.,1.)
337 Ohm=Unit("Ohm","Ohm",0.,1.)
338 #
339 # Derived
340 #
341 Poise= gram/cm/sec
342 #
343 # some constants
344 #
345 R_Earth_equator=6378.1370*km
346 R_Earth_poles=6356.7523*km
347 R_Earth=(R_Earth_equator+R_Earth_poles)/2
348 v_light=299792458.*m/sec

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