def __init__(self, names, factor, powers, offset=0):
"""
@param names: a dictionary mapping each name component to its
associated integer power (e.g. C{{'m': 1, 's': -1}})
for M{m/s}). As a shorthand, a string may be passed
which is assigned an implicit power 1.
@type names: C{dict} or C{str}
@param factor: a scaling factor
@type factor: C{float}
@param powers: the integer powers for each of the nine base units
@type powers: C{list} of C{int}
@param offset: an additive offset to the base unit (used only for
temperatures)
@type offset: C{float}
"""
if type(names) == type(''):
self.names = NumberDict()
self.names[names] = 1
pass
else:
self.names = names
pass
self.factor = factor
self.offset = offset
self.powers = powers
def __pow__(self, other):
if self.offset != 0:
raise TypeError("cannot exponentiate units with non-zero offset")
if isinstance(other, int):
return PhysicalUnit(other * self.names, pow(self.factor, other),
map(lambda x, p=other: x * p, self.powers))
if isinstance(other, float):
inv_exp = 1. / other
rounded = int(N.floor(inv_exp + 0.5))
if abs(inv_exp - rounded) < 1.e-10:
if reduce(lambda a, b: a and b,
map(lambda x, e=rounded: x % e == 0, self.powers)):
f = pow(self.factor, other)
p = map(lambda x, p=rounded: x / p, self.powers)
if reduce(
lambda a, b: a and b,
map(lambda x, e=rounded: x % e == 0,
self.names.values())):
names = self.names / rounded
else:
names = NumberDict()
if f != 1.:
names[str(f)] = 1
for i in range(len(p)):
names[_base_names[i]] = p[i]
return PhysicalUnit(names, f, p)
else:
raise TypeError('Illegal exponent')
raise TypeError('Only integer and inverse integer exponents allowed')
def __init__(self, names, factor, powers, offset=0):
"""
@param names: a dictionary mapping each name component to its
associated integer power (e.g. C{{'m': 1, 's': -1}})
for M{m/s}). As a shorthand, a string may be passed
which is assigned an implicit power 1.
@type names: C{dict} or C{str}
@param factor: a scaling factor
@type factor: C{float}
@param powers: the integer powers for each of the nine base units
@type powers: C{list} of C{int}
@param offset: an additive offset to the base unit (used only for
temperatures)
@type offset: C{float}
"""
if type(names) == type(""):
self.names = NumberDict()
self.names[names] = 1
pass
else:
self.names = names
pass
self.factor = factor
self.offset = offset
self.powers = powers
def __init__(self, names, factor, powers, offset=0):
if type(names) == type(''):
self.names = NumberDict()
self.names[names] = 1
else:
self.names = names
self.factor = factor
self.offset = offset
self.powers = powers
def __init__(self, names, factor, powers, offset=0, logbase=None, reference=None):
if type(names) == type(''):
self.names = NumberDict()
self.names[names] = 1
else:
self.names = names
self.factor = factor
self.offset = offset
self.powers = powers
self.logbase = logbase
self.reference = reference # logarithmic unit base reference
def setName(self, name):
self.names = NumberDict()
self.names[name] = 1
class PhysicalUnit:
"""
Physical unit
A physical unit is defined by a name (possibly composite), a scaling
factor, and the exponentials of each of the SI base units that enter into
it. Units can be multiplied, divided, and raised to integer powers.
"""
def __init__(self, names, factor, powers, offset=0):
"""
@param names: a dictionary mapping each name component to its
associated integer power (e.g. C{{'m': 1, 's': -1}})
for M{m/s}). As a shorthand, a string may be passed
which is assigned an implicit power 1.
@type names: C{dict} or C{str}
@param factor: a scaling factor
@type factor: C{float}
@param powers: the integer powers for each of the nine base units
@type powers: C{list} of C{int}
@param offset: an additive offset to the base unit (used only for
temperatures)
@type offset: C{float}
"""
if type(names) == type(''):
self.names = NumberDict()
self.names[names] = 1
else:
self.names = names
self.factor = factor
self.offset = offset
self.powers = powers
def __repr__(self):
return '<PhysicalUnit ' + self.name() + '>'
__str__ = __repr__
def __cmp__(self, other):
if self.powers != other.powers:
raise TypeError('Incompatible units')
return cmp(self.factor, other.factor)
def __mul__(self, other):
if self.offset != 0 or (isPhysicalUnit(other) and other.offset != 0):
raise TypeError("cannot multiply units with non-zero offset")
if isPhysicalUnit(other):
return PhysicalUnit(
self.names + other.names, self.factor * other.factor,
map(lambda a, b: a + b, self.powers, other.powers))
else:
return PhysicalUnit(self.names + {str(other): 1},
self.factor * other, self.powers,
self.offset * other)
__rmul__ = __mul__
def __div__(self, other):
if self.offset != 0 or (isPhysicalUnit(other) and other.offset != 0):
raise TypeError("cannot divide units with non-zero offset")
if isPhysicalUnit(other):
return PhysicalUnit(
self.names - other.names, self.factor / other.factor,
map(lambda a, b: a - b, self.powers, other.powers))
else:
return PhysicalUnit(self.names + {str(other): -1},
self.factor / other, self.powers)
def __rdiv__(self, other):
if self.offset != 0 or (isPhysicalUnit(other) and other.offset != 0):
raise TypeError("cannot divide units with non-zero offset")
if isPhysicalUnit(other):
return PhysicalUnit(
other.names - self.names, other.factor / self.factor,
map(lambda a, b: a - b, other.powers, self.powers))
else:
return PhysicalUnit({str(other): 1} - self.names,
other / self.factor,
map(lambda x: -x, self.powers))
def __pow__(self, other):
if self.offset != 0:
raise TypeError("cannot exponentiate units with non-zero offset")
if isinstance(other, int):
return PhysicalUnit(other * self.names, pow(self.factor, other),
map(lambda x, p=other: x * p, self.powers))
if isinstance(other, float):
inv_exp = 1. / other
rounded = int(N.floor(inv_exp + 0.5))
if abs(inv_exp - rounded) < 1.e-10:
if reduce(lambda a, b: a and b,
map(lambda x, e=rounded: x % e == 0, self.powers)):
f = pow(self.factor, other)
p = map(lambda x, p=rounded: x / p, self.powers)
if reduce(
lambda a, b: a and b,
map(lambda x, e=rounded: x % e == 0,
self.names.values())):
names = self.names / rounded
else:
names = NumberDict()
if f != 1.:
names[str(f)] = 1
for i in range(len(p)):
names[_base_names[i]] = p[i]
return PhysicalUnit(names, f, p)
else:
raise TypeError('Illegal exponent')
raise TypeError('Only integer and inverse integer exponents allowed')
def conversionFactorTo(self, other):
"""
@param other: another unit
@type other: L{PhysicalUnit}
@returns: the conversion factor from this unit to another unit
@rtype: C{float}
@raises TypeError: if the units are not compatible
"""
if self.powers != other.powers:
raise TypeError('Incompatible units')
if self.offset != other.offset and self.factor != other.factor:
raise TypeError(('Unit conversion (%s to %s) cannot be expressed ' +
'as a simple multiplicative factor') % \
(self.name(), other.name()))
return self.factor / other.factor
def conversionTupleTo(self, other): # added 1998/09/29 GPW
"""
@param other: another unit
@type other: L{PhysicalUnit}
@returns: the conversion factor and offset from this unit to
another unit
@rtype: (C{float}, C{float})
@raises TypeError: if the units are not compatible
"""
if self.powers != other.powers:
raise TypeError('Incompatible units')
# let (s1,d1) be the conversion tuple from 'self' to base units
# (ie. (x+d1)*s1 converts a value x from 'self' to base units,
# and (x/s1)-d1 converts x from base to 'self' units)
# and (s2,d2) be the conversion tuple from 'other' to base units
# then we want to compute the conversion tuple (S,D) from
# 'self' to 'other' such that (x+D)*S converts x from 'self'
# units to 'other' units
# the formula to convert x from 'self' to 'other' units via the
# base units is (by definition of the conversion tuples):
# ( ((x+d1)*s1) / s2 ) - d2
# = ( (x+d1) * s1/s2) - d2
# = ( (x+d1) * s1/s2 ) - (d2*s2/s1) * s1/s2
# = ( (x+d1) - (d1*s2/s1) ) * s1/s2
# = (x + d1 - d2*s2/s1) * s1/s2
# thus, D = d1 - d2*s2/s1 and S = s1/s2
factor = self.factor / other.factor
offset = self.offset - (other.offset * other.factor / self.factor)
return (factor, offset)
def isCompatible(self, other): # added 1998/10/01 GPW
"""
@param other: another unit
@type other: L{PhysicalUnit}
@returns: C{True} if the units are compatible, i.e. if the powers of
the base units are the same
@rtype: C{bool}
"""
return self.powers == other.powers
def isDimensionless(self):
return not reduce(lambda a, b: a or b, self.powers)
def isAngle(self):
return self.powers[7] == 1 and \
reduce(lambda a,b: a + b, self.powers) == 1
def setName(self, name):
self.names = NumberDict()
self.names[name] = 1
def name(self):
num = ''
denom = ''
for unit in self.names.keys():
power = self.names[unit]
if power < 0:
denom = denom + '/' + unit
if power < -1:
denom = denom + '**' + str(-power)
elif power > 0:
num = num + '*' + unit
if power > 1:
num = num + '**' + str(power)
if len(num) == 0:
num = '1'
else:
num = num[1:]
return num + denom
def setName(self, name):
self.names = NumberDict()
self.names[name] = 1
class PhysicalUnit(object):
__slots__ = [ "names", "factor", "offset", "powers", "logbase", "reference"]
def __init__(self, names, factor, powers, offset=0, logbase=None, reference=None):
if type(names) == type(''):
self.names = NumberDict()
self.names[names] = 1
else:
self.names = names
self.factor = factor
self.offset = offset
self.powers = powers
self.logbase = logbase
self.reference = reference # logarithmic unit base reference
def __repr__(self):
return '<PhysicalUnit ' + self.name() + '>'
__str__ = __repr__
def __cmp__(self, other):
if self.powers != other.powers:
raise TypeError, 'Incompatible units'
return cmp(self.factor, other.factor)
def __mul__(self, other):
if self.offset != 0 or (isPhysicalUnit(other) and other.offset != 0):
raise TypeError, "cannot multiply units with non-zero offset"
if self.logbase is not None or (isPhysicalUnit(other) and other.logbase is not None):
raise TypeError, "cannot multiply logarithmic units"
if isPhysicalUnit(other):
return PhysicalUnit(self.names+other.names,
self.factor*other.factor,
map(lambda a,b: a+b,
self.powers, other.powers))
else:
return PhysicalUnit(self.names+{str(other): 1},
self.factor*other,
self.powers,
self.offset * other)
__rmul__ = __mul__
def __div__(self, other):
if self.offset != 0 or (isPhysicalUnit (other) and other.offset != 0):
raise TypeError, "cannot divide units with non-zero offset"
if self.logbase is not None or (isPhysicalUnit(other) and other.logbase is not None):
raise TypeError, "cannot divide logarithmic units"
if isPhysicalUnit(other):
return PhysicalUnit(self.names-other.names,
self.factor/other.factor,
map(lambda a,b: a-b,
self.powers, other.powers))
else:
return PhysicalUnit(self.names+{str(other): -1},
self.factor/other, self.powers)
def __rdiv__(self, other):
if self.offset != 0 or (isPhysicalUnit (other) and other.offset != 0):
raise TypeError, "cannot divide units with non-zero offset"
if self.logbase is not None or (isPhysicalUnit (other) and other.logbase is not None):
raise TypeError, "cannot divide logarithmic units"
if isPhysicalUnit(other):
return PhysicalUnit(other.names-self.names,
other.factor/self.factor,
map(lambda a,b: a-b,
other.powers, self.powers))
else:
return PhysicalUnit({str(other): 1}-self.names,
other/self.factor,
map(lambda x: -x, self.powers))
def __pow__(self, other):
if self.offset != 0:
raise TypeError, "cannot exponentiate units with non-zero offset"
if self.logbase is not None:
raise TypeError, "cannot exponentiate logarithmic units"
if type(other) == type(0):
return PhysicalUnit(other*self.names, pow(self.factor, other),
map(lambda x,p=other: x*p, self.powers))
if type(other) == type(0.):
inv_exp = 1./other
rounded = int(umath.floor(inv_exp+0.5))
if abs(inv_exp-rounded) < 1.e-10:
if reduce(lambda a, b: a and b,
map(lambda x, e=rounded: x%e == 0, self.powers)):
f = pow(self.factor, other)
p = map(lambda x,p=rounded: x/p, self.powers)
if reduce(lambda a, b: a and b,
map(lambda x, e=rounded: x%e == 0,
self.names.values())):
names = self.names/rounded
else:
names = NumberDict()
if f != 1.:
names[str(f)] = 1
for i in range(len(p)):
names[_base_names[i]] = p[i]
return PhysicalUnit(names, f, p)
else:
raise TypeError, 'Illegal exponent'
raise TypeError, 'Only integer and inverse integer exponents allowed'
def conversionFactorTo(self, other):
if self.powers != other.powers:
raise TypeError, 'Incompatible units'
if self.offset != other.offset and self.factor != other.factor:
raise TypeError, \
('Unit conversion (%s to %s) cannot be expressed ' +
'as a simple multiplicative factor') % \
(self.name(), other.name())
# if self.logbase is not None: # logarithmic units are assumed to be dimensionless
# raise TypeError, "Cannot convert dimensionless values."
return self.factor/other.factor
def conversionTupleTo(self, other): # added 1998/09/29 GPW
if self.powers != other.powers:
raise TypeError, 'Incompatible units'
if self.logbase != other.logbase:
raise TypeError, "Cannot convert dimensionless values with different bases."
# let (s1,d1) be the conversion tuple from 'self' to base units
# (ie. (x+d1)*s1 converts a value x from 'self' to base units,
# and (x/s1)-d1 converts x from base to 'self' units)
# and (s2,d2) be the conversion tuple from 'other' to base units
# then we want to compute the conversion tuple (S,D) from
# 'self' to 'other' such that (x+D)*S converts x from 'self'
# units to 'other' units
# the formula to convert x from 'self' to 'other' units via the
# base units is (by definition of the conversion tuples):
# ( ((x+d1)*s1) / s2 ) - d2
# = ( (x+d1) * s1/s2) - d2
# = ( (x+d1) * s1/s2 ) - (d2*s2/s1) * s1/s2
# = ( (x+d1) - (d1*s2/s1) ) * s1/s2
# = (x + d1 - d2*s2/s1) * s1/s2
# thus, D = d1 - d2*s2/s1 and S = s1/s2
factor = self.factor / other.factor
offset = self.offset - (other.offset * other.factor / self.factor)
return (factor, offset)
def isCompatible(self, other): # added 1998/10/01 GPW
return self.powers == other.powers
def isDimensionless(self):
return not reduce(lambda a,b: a or b, self.powers)
def isAngle(self):
return self.powers[7] == 1 and \
reduce(lambda a,b: a + b, self.powers) == 1
def isLogarithmic(self):
return self.logbase is not None
def setName(self, name):
self.names = NumberDict()
self.names[name] = 1
def name(self):
num = ''
denom = ''
for unit in self.names.keys():
power = self.names[unit]
if power < 0:
denom = denom + '/' + unit
if power < -1:
denom = denom + '**' + str(-power)
elif power > 0:
num = num + '*' + unit
if power > 1:
num = num + '**' + str(power)
if len(num) == 0:
num = '1'
else:
num = num[1:]
return num + denom
class PhysicalUnit:
"""
Physical unit
A physical unit is defined by a name (possibly composite), a scaling
factor, and the exponentials of each of the SI base units that enter into
it. Units can be multiplied, divided, and raised to integer powers.
"""
def __init__(self, names, factor, powers, offset=0):
"""
@param names: a dictionary mapping each name component to its
associated integer power (e.g. C{{'m': 1, 's': -1}})
for M{m/s}). As a shorthand, a string may be passed
which is assigned an implicit power 1.
@type names: C{dict} or C{str}
@param factor: a scaling factor
@type factor: C{float}
@param powers: the integer powers for each of the nine base units
@type powers: C{list} of C{int}
@param offset: an additive offset to the base unit (used only for
temperatures)
@type offset: C{float}
"""
if type(names) == type(''):
self.names = NumberDict()
self.names[names] = 1
else:
self.names = names
self.factor = factor
self.offset = offset
self.powers = powers
def __repr__(self):
return '<PhysicalUnit ' + self.name() + '>'
__str__ = __repr__
def __cmp__(self, other):
if self.powers != other.powers:
raise TypeError('Incompatible units')
return cmp(self.factor, other.factor)
def __mul__(self, other):
if self.offset != 0 or (isPhysicalUnit (other) and other.offset != 0):
raise TypeError("cannot multiply units with non-zero offset")
if isPhysicalUnit(other):
return PhysicalUnit(self.names+other.names,
self.factor*other.factor,
map(lambda a,b: a+b,
self.powers, other.powers))
else:
return PhysicalUnit(self.names+{str(other): 1},
self.factor*other,
self.powers,
self.offset * other)
__rmul__ = __mul__
def __div__(self, other):
if self.offset != 0 or (isPhysicalUnit (other) and other.offset != 0):
raise TypeError("cannot divide units with non-zero offset")
if isPhysicalUnit(other):
return PhysicalUnit(self.names-other.names,
self.factor/other.factor,
map(lambda a,b: a-b,
self.powers, other.powers))
else:
return PhysicalUnit(self.names+{str(other): -1},
self.factor/other, self.powers)
def __rdiv__(self, other):
if self.offset != 0 or (isPhysicalUnit (other) and other.offset != 0):
raise TypeError("cannot divide units with non-zero offset")
if isPhysicalUnit(other):
return PhysicalUnit(other.names-self.names,
other.factor/self.factor,
map(lambda a,b: a-b,
other.powers, self.powers))
else:
return PhysicalUnit({str(other): 1}-self.names,
other/self.factor,
map(lambda x: -x, self.powers))
def __pow__(self, other):
if self.offset != 0:
raise TypeError("cannot exponentiate units with non-zero offset")
if isinstance(other, int):
return PhysicalUnit(other*self.names, pow(self.factor, other),
map(lambda x,p=other: x*p, self.powers))
if isinstance(other, float):
inv_exp = 1./other
rounded = int(N.floor(inv_exp+0.5))
if abs(inv_exp-rounded) < 1.e-10:
if reduce(lambda a, b: a and b,
map(lambda x, e=rounded: x%e == 0, self.powers)):
f = pow(self.factor, other)
p = map(lambda x,p=rounded: x/p, self.powers)
if reduce(lambda a, b: a and b,
map(lambda x, e=rounded: x%e == 0,
self.names.values())):
names = self.names/rounded
else:
names = NumberDict()
if f != 1.:
names[str(f)] = 1
for i in range(len(p)):
names[_base_names[i]] = p[i]
return PhysicalUnit(names, f, p)
else:
raise TypeError('Illegal exponent')
raise TypeError('Only integer and inverse integer exponents allowed')
def conversionFactorTo(self, other):
"""
@param other: another unit
@type other: L{PhysicalUnit}
@returns: the conversion factor from this unit to another unit
@rtype: C{float}
@raises TypeError: if the units are not compatible
"""
if self.powers != other.powers:
raise TypeError('Incompatible units')
if self.offset != other.offset and self.factor != other.factor:
raise TypeError(('Unit conversion (%s to %s) cannot be expressed ' +
'as a simple multiplicative factor') % \
(self.name(), other.name()))
return self.factor/other.factor
def conversionTupleTo(self, other): # added 1998/09/29 GPW
"""
@param other: another unit
@type other: L{PhysicalUnit}
@returns: the conversion factor and offset from this unit to
another unit
@rtype: (C{float}, C{float})
@raises TypeError: if the units are not compatible
"""
if self.powers != other.powers:
raise TypeError('Incompatible units')
# let (s1,d1) be the conversion tuple from 'self' to base units
# (ie. (x+d1)*s1 converts a value x from 'self' to base units,
# and (x/s1)-d1 converts x from base to 'self' units)
# and (s2,d2) be the conversion tuple from 'other' to base units
# then we want to compute the conversion tuple (S,D) from
# 'self' to 'other' such that (x+D)*S converts x from 'self'
# units to 'other' units
# the formula to convert x from 'self' to 'other' units via the
# base units is (by definition of the conversion tuples):
# ( ((x+d1)*s1) / s2 ) - d2
# = ( (x+d1) * s1/s2) - d2
# = ( (x+d1) * s1/s2 ) - (d2*s2/s1) * s1/s2
# = ( (x+d1) - (d1*s2/s1) ) * s1/s2
# = (x + d1 - d2*s2/s1) * s1/s2
# thus, D = d1 - d2*s2/s1 and S = s1/s2
factor = self.factor / other.factor
offset = self.offset - (other.offset * other.factor / self.factor)
return (factor, offset)
def isCompatible (self, other): # added 1998/10/01 GPW
"""
@param other: another unit
@type other: L{PhysicalUnit}
@returns: C{True} if the units are compatible, i.e. if the powers of
the base units are the same
@rtype: C{bool}
"""
return self.powers == other.powers
def isDimensionless(self):
return not reduce(lambda a,b: a or b, self.powers)
def isAngle(self):
return self.powers[7] == 1 and \
reduce(lambda a,b: a + b, self.powers) == 1
def setName(self, name):
self.names = NumberDict()
self.names[name] = 1
def name(self):
num = ''
denom = ''
for unit in self.names.keys():
power = self.names[unit]
if power < 0:
denom = denom + '/' + unit
if power < -1:
denom = denom + '**' + str(-power)
elif power > 0:
num = num + '*' + unit
if power > 1:
num = num + '**' + str(power)
if len(num) == 0:
num = '1'
else:
num = num[1:]
return num + denom