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I implemented dimensions.py perhaps eight years ago as an exercise and have used it occasionally ever since.

It allows doing math with dimensioned values in order to automate unit conversions (you can add m/s to mile/hour) and dimensional checking (you can't add m/s to mile/lightyear). It specifically does not convert 212F to 100C but rather will convert 9F to 5C (valid when converting temperature differences).

It is similar to unums (http://home.scarlet.be/be052320/Unum.html) but with a significant difference:

I used a different syntax Q(25,'m/s') as opposed to 100*m/s (I recall not wanting to have all the base SI units directly in the namespace). I'm not entirely sure which approach is really better.

I also had a specific need to have fractional exponents on units, allowing the following:

>>> km=Q(10,'N*m/W^(1/2)')
>>> km
Q(10.0, 'kg**0.5*m/s**0.5')

Looking back I see a few design decisions I might do differently today, but I'll share it anyway.

Some examples are in the source below the line with if __name__ == "__main__":

Note that I've put two files into the code block below, dimensions.py and dimensions.data, so please cut them apart if you want to try it.

Python, 639 lines
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======= dimensions.py =============
'''A module for adding dimensions to numeric types for dimensional analysis
and automatic unit conversions.  '''

from __future__ import division
import math
import re
import os


t___add__     = r'(?P<__add__>\+)'
t___sub__     = r'(?P<__sub__>\-)'
t___pow__     = r'(?P<__pow__>\^|(\*\*))'
t___mul__     = r'(?P<__mul__>\*)'
t___truediv__ = r'(?P<__truediv__>/)'
t_LPAREN      = r'(?P<LPAREN>\()'
t_NUMBER      = r'(?P<NUMBER>(\+|-)?((\d+\.\d+)|(\.\d+)|(\d+\.)|(\d+))([eE](\+|-)?\d+)?)'
t_RPAREN      = r'(?P<RPAREN>\))'
t_IDENT       = r'(?P<IDENT>[a-zA-Z]\w*)' # ident names begin with letter
ulexres= r'\s*(' + "|".join([t___add__, t_IDENT, t___pow__, t___truediv__,
               t___sub__, t___mul__, t_NUMBER, t_LPAREN, t_RPAREN]) + r')\s*'
lexre = re.compile(ulexres) 

def tokenize(s):
    '''return a list of token tuples: (token, value, start)'''
    l=[]                                  # list to hold tokens
    start=0                               # used to check for bad tokens
    sc=lexre.scanner(s)
    while 1:
        tg=sc.search()
        if tg:
            if tg.start()!=start:       # we should start at end of last token
                raise BadToken(start)
            l.append( [ (token, value, (tg.start(), tg.end())) 
                     for (token, value) in tg.groupdict().items() if value][0])
            start=tg.end()                    # prepare start for next pass
        else:
            if start!=len(s):
                raise BadToken(start)
            break
    return l

class UnmatchedParenthesis(Exception):
    pass 

class BadToken(Exception):
    def __init__(self,value):
        self.value=value
    def __str__(self):
        return repr(self.value)

PRIORITY={  '__add__':1,  '__sub__':1,
            '__mul__':2,  '__truediv__':2,
            '__pow__':3}

def convert(s):
    '''convert a list of token tuples from infix order to RPN'''
    input=s[:]
    stack=[]                            # 'Texas' LIFO
    output=[]                            # 'California' output accumulator
    while len(input)>0: # Careful!  We're iterating over changing input list.
        if input[0][0]=='IDENT' or input[0][0]=='NUMBER':
            # move operands directly to output
            output.append(input.pop(0))
        elif input[0][0]=='LPAREN':
            # Now handle a left parenthesis
            stack.append(input.pop(0))
        elif input[0][0]=='RPAREN':
            # Now handle a right parenthesis
            if not stack:
                # We shouldn't have an RPAREN without an LPAREN
                raise UnmatchedParenthesis
            elif stack[-1][0]=='LPAREN':
                # when RPAREN catches up with LPAREN, vaporize both
                stack.pop()
                input.pop(0)
            else:
                # pop operands until we hit LPAREN
                output.append(stack.pop())
        else:
            # logically, we should have an operand at the input, but
            # don't know about stack
            if stack:
                # there is at least one item in the stack
                if stack[-1][0]=='LPAREN':
                    # LPAREN on stack, push next operand to stack
                    stack.append(input.pop(0))
                elif PRIORITY[input[0][0]]>PRIORITY[stack[-1][0]]:
                    # higher priority input item goes to stack
                    stack.append(input.pop(0))
                else:
                    output.append(stack.pop())
            else:
                # no stack, push input to stack
                stack.append(input.pop(0))
    while len(stack)>0:
        # when input is empty we still may have stack items to move over
        if stack[-1][0]=='LPAREN':
            # Shouldn't be any LPARENs left!
            raise UnmatchedParenthesis
        else:
            output.append(stack.pop())
    return output

def proc_stack(input, vardict):
    '''process IDENTs, binary operators in input list using vardict namespace'''
    stack=[]
    for item in input:
        # anything left to process?
        if item[0]=='IDENT':
            # push object referred to by IDENT onto stack
            stack.append(vardict[item[1]])
        elif item[0]=='NUMBER':
            stack.append(float(item[1]))
        else:
            # we must have a binary operator
            # and assuming well formed input two operands on stack
            operand=item[0]
            y=stack.pop()
            x=stack.pop()
            # XXX the following hack should be fixed some time just
            # because it is really ugly!
            if operand=='__truediv__' and type(y)!=type(1.0) and \
                    type(x)==type(1.0) and x==1 :
                # special case of empty numerator and Q denom
                x=vardict['']
                # this is coordinated with hack in UNITS_LIST in dimensions.py
            stack.append(x.__getattribute__(operand)(y))
    return stack[0]

def ap_eval(instr,vardict):
    '''evaluate an expression string using vardict namespace'''
    t=tokenize(instr)
    s=convert(t)
    ans=proc_stack(s,vardict)
    return ans

class DimensionsError(Exception):
    def __init__(self, value):
        self.value=value
    def __str__(self):
        return repr(self.value)

class Q(object):
    EXPTOL=1e-14
    '''simple class for creating base dimensions'''
    def __init__(self, value, dimstr, utype=None):
        '''takes name of base unit and creates a Base object'''
        if utype=='BASE':   # manually create the dimension for a base unit
            self.value=value            # value of dimension
            self.dims={}    # dict of dimensions, keys are base units
            self.dims[dimstr]=1
        else:               # we're building a compound unit 
            if dimstr.strip()=='':  # no Dim object yet, so build it
                self.value=value
                self.dims={}
            else:
                tmp=ap_eval(dimstr,units)
                # At this point we have a Dim object
                self.value=value*tmp.value
                self.dims=tmp.dims
    def copy(self):
        '''make a copy'''
        tmp=Q(1,'')
        tmp.value=self.value
        tmp.dims=self.dims.copy()
        return tmp
    def __neg__(self):
        '''return negative of self'''
        tmp=self.copy()
        tmp.value=-self.value
        return tmp
    def __pos__(self):
        '''unary positive operator'''
        return self.copy()
    def __abs__(self):
        '''abs operator'''
        tmp=self.copy()
        tmp.value=abs(self.value)
        return tmp
    def __add__(self, other):
        '''add like units together'''
        tmp=self.copy()
        if other.dims==tmp.dims:
            tmp.value=self.value+other.value
            return tmp
        else:
            raise DimensionsError, 'Units not consistent'
    # Rich comparison operators
    def __lt__(self, other):
        '''lt method for units'''
        if self.dims!=other.dims:
            raise DimensionsError, 'Units not consistent'
        else:
            return self.value<other.value
    def __ge__(self, other):
        '''ge method for units'''
        return not self.__lt__(other) 
    def __eq__(self, other):
        '''eq method for units'''
        if self.dims!=other.dims:
            raise DimensionsError, 'Units not consistent'
        else:
            return self.value==other.value
    def __ne__(self, other):
        '''ne method for units'''
        return not self.__eq__(other)
    def __gt__(self, other):
        '''gt method for units'''
        if self.dims!=other.dims:
            raise DimensionsError, 'Units not consistent'
        else:
            return self.value>other.value
    def __le__(self, other):
        '''le method for units'''
        return not self.__gt__(other)
    def __sub__(self, other):
        '''subtract like units'''
        tmp=self.copy()
        if other.dims==tmp.dims:
            tmp.value=self.value-other.value
            return tmp
        else:
            raise DimensionsError, 'Units not consistent'
    def __mul__(self, other):
        '''multiply two units together'''
        # get list of dims used in both units
        try:
            tmp=Q(1,'')
            tmp.value=self.value*other.value
            superset=dict.fromkeys(self.dims.keys()+other.dims.keys()).keys()
            for dim in superset:
                tmp.dims[dim]=self.dims.get(dim,0)+ \
                                other.dims.get(dim,0)
                if abs(tmp.dims[dim] %1)<self.EXPTOL:
                    # This is a hack to eliminate creeping floating point error.
                    # It's not a real substitute for using a Rational 
                    # number type but will suffice for now.
                    tmp.dims[dim]=int(round(tmp.dims[dim]))
                if tmp.dims[dim]==0:
                    del tmp.dims[dim]
            return tmp
        except AttributeError:
            # this should happen if we multiply by a number
            tmp=self.copy()
            tmp.value=self.value*other
            return tmp 
    def __rmul__(self,other):
        '''multiply number by unit'''
        return self.__mul__(other)
    def __truediv__(self, other):
        '''divide one unit by another'''
        # get list of dims used in both units
        tmp=self.copy()
        try:    # if two Dim objects
            tmp.value=tmp.value/other.value
            superset=dict.fromkeys(self.dims.keys()+other.dims.keys()).keys()
            for dim in superset:
                tmp.dims[dim]=self.dims.get(dim,0)-other.dims.get(dim,0)
                if abs(tmp.dims[dim] %1)<self.EXPTOL:
                    # this is a hack to eliminate creeping floating point error
                    tmp.dims[dim]=int(round(tmp.dims[dim]))
                if tmp.dims[dim]==0:
                    del tmp.dims[dim]
        except AttributeError:  # if dividing by number
            tmp.value/=other
        return tmp
    def __div__(self,other):
        '''calls __truediv__'''
        return self.__truediv__(other)
    def __rdiv__(self,other):
        '''calls __rtruediv__'''
        return self.__rtruediv__(other)
    def __rtruediv__(self,other):
        tmp=self.copy()
        tmp.value=1/tmp.value
        for dim in tmp.dims:
            tmp.dims[dim]=-tmp.dims[dim]
        return other*tmp
    def __pow__(self,power):
        tmp=self.copy()
        for dim in tmp.dims:
            newexponent=power*tmp.dims[dim]
            if abs(newexponent%1)<self.EXPTOL:
                # this is a hack to eliminate creeping floating point error
                newexponent=int(round(newexponent))
            tmp.dims[dim]=newexponent
        tmp.value=tmp.value**power
        return tmp
    def sqrt(self):
        '''returns square root of self'''
        # Added for compatibility with std function in scipy/numpy
        return self.__pow__(0.5)
    def __hash__(self):
        '''hash method allows use of Dims as dict key.
        Manually modifying Dim attributes will break the dict
        so don't do that!'''
        return hash(self.value)^reduce( 
              lambda x,y: x^y, [hash(item) for item in self.dims.items()],0)
    def __repr__(self):
        '''return a string representation'''
        # numerator string will be either 1 or a string of the dims
        numdims=[(dim,self.dims[dim]) for dim in self.dims 
                                      if self.dims[dim]>0]
        numdims.sort()
        numstrlist=[]
        for dim,power in numdims:
            if power==1:
                numstrlist.append(dim)
            else:
                numstrlist.append(''.join([dim,'**',str(power)]))
        numstr='*'.join(numstrlist)
        dendims=[(dim,-self.dims[dim]) for dim in self.dims 
                                      if self.dims[dim]<0]
        denstrlist=[]
        for dim,power in dendims:
            if power==1:
                denstrlist.append(dim)
            else:
                denstrlist.append(''.join([dim,'**',str(power)]))
        denstr='*'.join(denstrlist)
        if len(denstrlist)>1:
            denstr='(%s)' % denstr
        if len(numdims)==0 and len(dendims)==0:
            dimstr=''
        elif len(numdims)==0:
            dimstr='1/'+denstr
        elif len(dendims)==0:
            dimstr=numstr
        else:
            dimstr='%s/%s' % (numstr,denstr)
        return 'Q(%s, \'%s\')' % (self.value, dimstr)
    def __call__(self,otherdim, fmt=None):
        '''return value when expressed in otherdim dimensions'''
        o=Q(1,otherdim)
        if self.dims==o.dims:
            if fmt==None:
                return self.value/o.value
            else:
                return ''.join([fmt % (self.value/o.value),' [',
                        otherdim,']'])               
        else:
            raise DimensionsError, 'Units not consistent'
    def str(self,dims,valfmt='%s',dimfmt=' [%s]'):
        '''return a string in dimensions (dims) using value format specifier
(valfmt) and dims format specifier (dimfmt)'''
        return ''.join(((valfmt % self(dims)),(dimfmt % dims)))

class UnitsDatabase(object):
    def __init__(self, base_types, prefixes):
        '''create a UnitsDatabase object'''
        # start creation of units dictionary
        self.units={}
        for base in base_types:
            self.units[base]=Q(1, base, utype='BASE')
        self.prefixes=prefixes
    def __getitem__(self, key):
        '''grab item from dictionary if it exists, otherwise try prefixes'''
        if key in self.units:
            return self.units[key]
        else:
            if len(key)==1: # don't look for prefix if one letter unit
                raise DimensionsError, 'unit %s not found' % key
            for prefix in self.prefixes:
                if key.startswith(prefix):
                    return self.prefixes[prefix]*self.units[key[len(prefix):]]
            raise DimensionsError, 'unit %s not found' % key
    def addUnit(self,name,utuple):
        '''add a unit to the unit database'''
        val=utuple[0]
        dims=utuple[1]
        self.units[name]=Q(val,dims)
    def addBase(self,name):
        '''add a base type to the unit database'''
        val=1
        self.units[name]=Q(val,name,utype='BASE')
    def addPrefix(self,name,val):
        '''add a prefix to the unit database'''
        self.prefixes[name]=val
    def find(self,s):
        '''lists units containing the substring s'''
        re_find=re.compile(r'.*%s.*' % s ,re.I)
        res=[key for key in units.units.keys() if re_find.match(key)]
        res.sort()
        for unit in res:
            print unit

# read the bases, prefixes and units from the dimensions.data file
execfile(os.path.join(os.path.dirname(__file__),'dimensions.data'))

units=UnitsDatabase(BASE_TYPES, PREFIXES)

for unit,tup in UNITS_LIST:
    units.addUnit(unit,tup)

BASE_TYPES=[]
PREFIXES={}
UNITS_LIST=[]

# now add any from the user.data file
try:
    execfile(os.path.join(os.path.dirname(__file__),'user.data'))
    for base in BASE_TYPES:
        units.addBase(base)
    for pref in PREFIXES:
        units.addPrefix(pref,PREFIXES[pref])
    for unit, dimtup in UNITS_LIST:
        units.addUnit(unit,dimtup)
except IOError:
    pass


if __name__=='__main__':
    # this is where the tests live
    D0=Q(3, 'mN*m/A')
    D1=Q(4, 'A')
    assert(repr(D0*D1)=="Q(0.012, 'kg*m**2/s**2')")
    D2=Q(0.25, '1/A')
    assert(repr(D0/D2)=="Q(0.012, 'kg*m**2/s**2')")

    D3=Q(1,'1/W**(1/2)')
    D4=Q(1,'1/W**(1/2.)')
    D5=Q(1,'1/W**(1./2)')
    D6=Q(1,'1/W**(1./2.)')
    assert(D3==D4)
    assert(D3==D5)
    assert(D3==D6)

    D7=Q(3.3,'N*cm/W**0.5')
    assert(repr(D7)=="Q(0.033, 'kg**0.5*m/s**0.5')")
    assert(repr(D7*D7)=="Q(0.001089, 'kg*m**2/s')")
    assert(repr(D7**2)=="Q(0.001089, 'kg*m**2/s')")

    T=Q(15.2,'mN*m')
    ke=Q(3.6,'V/krpm')
    assert(repr(T/ke)=="Q(0.442150077172, 'A')")
   
    vel=Q(4000,'rpm')
    P=T*vel
    assert(str(P)=="Q(6.36696111128, 'kg*m**2/s**3')")
    assert(str(P('W'))=="6.36696111128")
    assert(P('horsepower')==0.0085348004172591339)
    units.addBase('sample')
    srate=Q(36,'ksample/s')
    units.addBase('interrupt')
    irate=Q(600,'interrupt/s')
    assert(srate/irate==Q(60.0, 'sample/interrupt'))
    km=Q(2.035,'N*cm/W**0.5')
    assert(str((T/km)**2)== "Q(0.557902552989, 'kg*m**2/s**3')")
    assert(((T/km)**2)('W')==0.55790255298854785)
    
    AddedInconsistentDims=0
    try:
        Q(2,'ft')+Q(3,'s')
    except DimensionsError:
        AddedInconsistentDims=1
    assert(AddedInconsistentDims)
    
    SubtracedInconsistentDims=0
    try:
        Q(2,'ft')-Q(3,'s')
    except DimensionsError:
        SubtracedInconsistentDims=1
    assert(SubtracedInconsistentDims)

    assert (-Q(5,'')==Q(-5,''))
    assert (+Q(5,'')==Q(5,''))
    assert (abs(Q(-5,''))==Q(5,''))
    assert (abs(Q(5,''))==Q(5,''))

============= dimensions.data ==============
# Do not modify this file as it will be replace by the next installation
# of the dimensions module.
# If you wish to add a file with units that will get added every time
# the dimensions module is loaded, add a file called user.data
# in the dimensions directory, with the same format as this file.

BASE_TYPES=['m',
            'kg',
            's',
            'A',
            'K']

PREFIXES=dict(  yotta= 1e24,
                Y= 1e24,
                zetta= 1e21,
                Z= 1e21,
                exa=   1e18,
                E=   1e18,
                peta=  1e15,
                P=  1e15,
                tera=  1e12,
                T=  1e12,
                giga=  1e9, 
                G=  1e9, 
                mega=  1e6, 
                M=  1e6, 
                myria= 1e4, 
                kilo=  1000, 
                k=  1000, 
                hecto= 100,  
                h= 100,  
                deca=  10,   
                deka=  10,   
                da=  10,   
                deci=  1/10, 
                d=  1/10, 
                centi= 1/100,
                c= 1/100,
                milli= 1/1000,
                m= 1/1000,
                micro= 1e-6,
                u= 1e-6,
                nano=  1e-9,
                n=  1e-9,
                pico=  1e-12,
                p=  1e-12,
                femto= 1e-15,
                f= 1e-15,
                atto=  1e-18,
                a=  1e-18,
                zepto= 1e-21,
                z= 1e-21,
                yocto= 1e-24,
                y= 1e-24)

UNITS_LIST=    [('',(1,'')),    # a hack to help handle the '1/unit' case
                ('meter',(1,'m')),
                ('second',(1,'s')),
                ('kilogram',(1,'kg')),
                ('gram',(0.001,'kg')),
                ('kelvin',(1,'K')),
                ('ampere',(1,'A')),
                ('amp',(1,'A')),
                ('radian',(1,'')),
                ('rd',(1,'radian')),
                ('newton',(1,'kg*m/s**2')),
                ('N',(1,'newton')),
                ('pascal',(1,'N/m**2')),
                ('Pa',(1,'pascal')),
                ('joule',(1,'N*m')),
                ('J',(1,'joule')),
                ('watt',(1,'J/s')),
                ('W',(1,'watt')),
                ('coulomb',(1, 'A*s')),
                ('C',(1,'coulomb')),
                ('volt',(1,'W/A')),
                ('V',(1,'volt')),
                ('ohm',(1,'V/A')),
                ('siemens',(1,'1/ohm')),
                ('S',(1,'siemens')),
                ('farad',(1,'C/V')),
                ('F',(1,'farad')),
                ('weber',(1,'V*s')),
                ('Wb',(1,'weber')),
                ('henry',(1,'Wb/A')),
                ('H',(1,'henry')),
                ('tesla',(1,'Wb/m**2')),
                ('T',(1,'tesla')),
                ('hertz',(1,'1/s')),
                ('Hz',(1, 'hertz')),
                ('sec',(1, 's')),
                ('minute',(60,'s')),
                ('min',(1,'minute')),
                ('hour',(60,'min')),
                ('hr',(1,'hour')),
                ('day',(24, 'hr')),
                ('week',(7,'day')),
                ('fortnight',(14,'day')),
                ('gm',(1,'gram')),
                ('g',(1,'gm')),
                ('tonne',(1000,'kg')),
                ('t',(1,'tonne')),
                ('cc',(1,'cm**3')),
                ('liter',(1000,'cc')),
                ('l',(1,'liter')),
                ('L',(1,'l')),
                ('mho',(1,'siemens')),
                ('angstrom',(1e-10, 'm')),
                ('fermi',(1e-15, 'm')),
                ('barn',(1e-28, 'm**2')),
                ('c',(299792458, 'm/s')),
                ('G',(6.6742e-11, 'N*m**2/kg**2')),
                ('au',(1.49559787e11,'m')),
                ('pi',(math.pi,'')),
                ('e',(math.e,'')),
                ('circle',(2,'pi')),
                ('rev',(1,'circle')),
                ('rpm',(1,'rev/min')),
                ('degC',(1,'K')),
                ('degF',(5/9, 'degC')),
                ('gravity',(9.80665, 'm/s**2')),
                ('force',(1,'gravity')),
                ('inch', (2.54, 'cm')),
                ('in', (2.54, 'cm')),
                ('foot', (12, 'inch')),
                ('feet', (1, 'foot')),
                ('ft', (1,'feet')),
                ('nauticalmile',(6080,'feet')),
                ('acre',(43560,'feet**2')),
                ('yard',(3,'ft')),
                ('mile',(5280,'ft')),
                ('calorie',(4.1868,'J')),
                ('cal',(1,'calorie')),
                ('lightyear',(365.25, 'day*c')),
                ('ly', (1,'lightyear')),
                ('torr',(101325/760, 'Pa')),
                ('Torr',(1,'torr')),
                ('kgf',(1, 'kg*gravity')),
                ('at',(1,'kgf/cm**2')),
                ('pound',(0.45359237,'kg')),
                ('lb',(1,'pound')),
                ('lbf',(1,'pound*force')),
                ('ounce',(1/16,'lb')),
                ('oz',(1,'ounce')),
                ('ozf',(1,'ounce*force')),
                ('ton',(2000,'lb')),
                ('gallon',(231,'inch**3')),
                ('gal', (1, 'gallon')),
                ('quart',(1/4, 'gal')),
                ('pint',(1/2, 'quart')),
                ('fluidounce',(1/16, 'pint')),
                ('floz',(1,'fluidounce')),
                ('cup', (8, 'floz')),
                ('tablespoon', (1/16, 'cup')),
                ('tbl', (1,'tablespoon')),
                ('tbsp',(1,'tbl')),
                ('Tbsp',(1,'tbsp')),
                ('Tsp', (1,'tablespoon')),
                ('teaspoon', (1/3, 'tablespoon')),
                ('tsp', (1,'teaspoon')),
                ('psi', (1, 'pound*force/inch**2')),
                ('slug', (1,'lbf*s**2/ft')),
                ('Btu',(1, 'cal*lb/gram')),
                ('btu',(1,'Btu')),
                ('BTU',(1,'Btu')),
                ('horsepower',(746, 'W')),
                ('hp',(1,'horsepower')),
                ('Wh',(1,'W*hour'))]
Created by David Klaffenbach on Sat, 24 Jul 2010 (MIT)
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