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a module for units and quantities More...


 Internal Quanta_module classes and functions.


class  casacore::MeasValue
 Base class for values in a Measure. More...
struct  casacore::MeasValue_global_functions_Output
 Global functions. More...
class  casacore::MVAngle
 Class to handle angle type conversions and I/O. More...
struct  casacore::MVAngle_global_functions_output
 Global functions. More...
class  casacore::MVBaseline
 A 3D vector on Earth. More...
class  casacore::MVDirection
 Vector of three direction cosines. More...
class  casacore::MVDoppler
 Internal value for MDoppler. More...
class  casacore::MVDouble
 Class to distinguish external and Measure internal Double. More...
class  casacore::MVEpoch
 A class for high precision time. More...
class  casacore::MVFrequency
 Internal value for MFrequency. More...
class  casacore::MVPosition
 A 3D vector in space. More...
class  casacore::MVRadialVelocity
 Internal value for MRadialVelocity. More...
class  casacore::MVTime
 Class to handle date/time type conversions and I/O. More...
class  casacore::MVuvw
 A 3D vector on Earth. More...
class  casacore::QBase
 Base for Quantities (i.e. dimensioned values) More...
struct  casacore::QBase_global_functions_Output
 Global functions. More...
class  casacore::QC
 Physical constants (i.e. dimensioned values) More...
struct  casacore::QLogical_global_functions_Quantum_logical_operations
 Logical operations for the Quantum class. More...
struct  casacore::QMath_global_functions_Quantum_mathematical_operations
 Mathematical operations for the Quantum class. More...
class  casacore::Quantum< Qtype >
 Quantities (i.e. dimensioned values) More...
struct  casacore::Quantum_global_functions_output
 Global functions. More...
class  casacore::QuantumHolder
 A holder for Quantums to enable record conversions. More...
struct  casacore::QuantumType_global_functions_QuantumType
 Get an integer type for a Qunatum<T> More...
class  casacore::QVector< T >
 Specialization for Quantum<Vector<T> > More...
class  casacore::Unit
 defines physical units More...
class  casacore::UnitDim
 describes a unit in basic SI unit dimensions More...
class  casacore::UnitMap
 contains all simple known physical units More...
class  casacore::UnitName
 handles physical units More...
class  casacore::UnitVal
 describes any valid unit as a factor and a dimenion of SI units More...
struct  casacore::UnitVal_global_functions_output
 Global output function. More...
class  casacore::UnitVal_static_initializer
 Static initialisation of UnitVal constants. More...


static class

Detailed Description

a module for units and quantities

See below for an overview of the classes in this module.

Intended use:

Public interface

Review Status

Reviewed By:
Date Reviewed:
Test programs:
tUnit tQuantum
Demo programs:


The name Quanta derives from a physical quantity, i.e. a value with units attached.


The Quanta model deals with units and physical quantities (i.e. values with a unit). Units are handled in the Unit section (see Unit.h). Quantities are handled in the Quantum section (see Quantum.h). In addition the module contains some more general support classes (Euler angles, rotation matrix, pointed string), formatting for time and angle classes and classes containing information for Measures (MeasValue and the derived MV classes like MVEpoch). See the MeasValue section.


Including the casa/Quanta.h will take care of all includes necessary for the handling of pure Units and Quantities.

Physical units

Physical units are basically used in quantities (see Quantum), i.e. a value and a dimension. The Unit class, or one of its subsidiaries, will in general not be called separately. The only reason to make use of these classes is to generate additional 'tagged' units, i.e. units with a special name, e.g. 'beam' for a telescope beam, or 'JY', a non-SI name for Jy.


A Unit is in principle specified as a String (or directly as "string"), and can be defined as either a Unit or a String. If defined as a Unit, the format of the string will be checked for a legal definition and relevant information (e.g. scale, dimension type) is cached in the Unit object, leading to (much) faster use; if defined as a String, the checking will be postponed until any use is made of the information in the string.

A unit is a string of one or more fields separated by 'space' or '.' (to indicate multiply) or '/' (to indicate divide). Multiple separators are acted upon (i.e. m//s == m.s). Separators are acted upon left-to-right (i.e. m/s/A == (m/s)/A; use () to indicate otherwise (e.g. m/(s/A))).

A field is a name, or a unit enclosed in (), optionally followed by an, optionally signed, decimal constant. E.g. m.(m/s)-2 == m-1.s2)

Note that a 'space' or '.' before an opening '(' can be omitted.

A name can consist of case-sensitive letters, '_', ''', ':', '"' and '0' ('0' not as first character). Digits 1-9 are allowed if preceded with an '_'. Possible legal names are e.g. Jy, R0, R_1, "_2.

Tip: The standard naming conventions for SI units are that they are all in lowercase, unless derived from a person's name, when they start with a capital letter; Notable exceptions are some of the astronomical SI related units (e;g; AU);
A name can be preceded by a (standard) decimal prefix.

A name must be defined in a Unit map before it can be used.

All SI units and some customary units are part of the classes. User defined names can be added by the UnitMap::putUser() function (see UnitMap). A special set of FITS related units can be added by the UnitMap::addFITS() function. For details, see UnitMap.


km/s/(Mpc.s)2 is identical to km.s-1.Mpc-2.s-2

There are 5 name lists in the UnitMap, which are searched in reverse order:

  1. Defining units: m, kg, s, A, K, cd, mol, rad, sr, _
  2. SI units: including a.o. g, Jy, AU
  3. Customary units: e.g. lb, hp, ly
  4. User defined units: defined by user (e.g. beam, KPH, KM)
  5. Cached units: for speed in operations

All known names can be viewed by running the tUnit test program, or using the MapUnit::list() routine.

The definitions that were current on 990915 are given at end of this file

Caution: There is a difference between units without a dimension (non-dimensioned I will call them), and undimensioned units; Non-dimensioned examples are "", "%"; undimensioned examples: "beam", "pixel";

Working with units

In general units are not used explicitly, but are embedded in quantities and coordinates.

Explicit use of units is only necessary if:

  1. a unit string has to be tested for legality (e.g. exist JY?)
  2. a unit string has to be named (e.g. H0 for km/s/Mpc)
  3. some calculation on units has to be performed (e.g. how many hp.s per eV)

For these cases a Unit can be defined as either a String or a Unit. If specified as a Unit an automatic check (with exception if illegal) of the format of the unit string is performed

Unit a="km/Ms"; String b="Mm/Gs"; //produce 'identical' units a and b
Unit a("KpH"); // will produce exception
String a("KpH"); // will be accepted till some other action
// done on a
// The following will define a unit named 'tag' with a value identical
// to 5 mJy. After this definition tag can be used as any other unit,
// e.g. Unit("Gtag/pc") will be a valid unit string.
UnitMap::putUser("tag",UnitVal(5.,"mJy"),"my own unit name for 5 mJy");
// The following will calculate how many hp.s per eV
Double hpeV = (UnitVal("hp.s")/UnitVal("eV")).getFac();
// maybe after checking for identical dimensions
if (UnitVal("hp.s") != UnitVal("eV")) { cout << "unexpected" << endl; }

Tip: UnitVal has the following special constants to easily check unit dimensions (note that they can be combined to e;g; generate velocity as 'UnitVal::LENGTH/UnitVal::TIME')

See the UnitVal for details of calculating with units. See the UnitMap for the details of defining/viewing named units.

Quantums and Quantities

A Quantum is a value with a unit. Quantums are templated on their value type (e.g. Float, Vector<Double>). Quantity is a typedef for the (probably most common) Quantum<Double>. The basic specification of a Quantum is:

Quantum<Type> (Type value, Unit unit); // or: String unit or: "unit"
Quantity(Double value, Unit unit); // or: String unit or: "unit"


The following list of constructors is available.
Tip: In the following 'Unit' can be replaced by 'String' (or "string" everywhere; The only difference being a check for a legitimate unit string being executed if Unit specified (with exception if error), and a much faster execution of the Unit is used repeatedly; Quantum<Type> can, if Type equals Double, be replaced with Quantity

The following operators and functions are defined on Quantums. They are, of course, only available if the template Type supports them (e.g. / will not be defined for a Quantum<String> (whatever that may mean)).

Quanta can be converted to other units by the following set of member functions:

Quanta can be checked for having the correct unit dimensions (e.g. before addition or comparing) by the following two member functions, which will return a Bool value or raise an exception:

The value and units of a quantum can be set or retrieved separately by the following member functions:

The output operator ('<<') will produce the value of the quantum and its units. Given Quantity myval(5.,"mJy");, cout << myval; will produce: "5.0 mJy"; while cout << myval.get("yW/m2") will produce: ".00005 yW/m2.s"

QC class of constant quantities

In parallel with the 'C' class of undimensioned constants, the QC class contains dimensioned constants. On 960509 the following were defined:

Values for Measures

The MeasValue class derivatives are all named MVmeasure, e.g. MVFrequency, and represent the internal representation of the specific measure class. There main use is for the Measures module, but they can be used alone, e.g. for the conversion to formatted times, or the conversion of frequencies from say wavelength to frequency. They all have at least the following constructors:

MV(Quantum<Vector<Double> >)

But most have also constructors like:

MV(Quantity, Quantity)

The actual interpretation is class dependent: see the individual MV classes like MVEpoch, MVDirection, MVPosition, MVFrequency, MVDouble, MVRadialVelocity. MVBaseline, MVuvw, MVEarthMagnetic, A few examples:

MVEpoch(12345, 0.1e-20) will create one epoch (MJD12345.0), but preserving
the precision of all information
MVDirection(Quantity(20,"deg"), Quantity(-10,"'")) will create a direction
with an RA of 20 degree, and a DEC of -10 arcmin
MVFrequency(Quantity(5,"keV")) will create a frequency corresponding to
the specified energy.

All MVs have the +=, -=, ==, !=, << operators, and near(), nearAbs(), print() and adjust() and readjust() (which in general normalise to a value of 1 (e.g. MVDirection), or recalculates high precision values (e.g. MVEpoch) functions.
Information can be viewed with many get functions. In most cases getValue() will return the internal value as either Double or Vector<Double>; get() will return the same, or converted values (e.g. a vector of length, angle, angle for MVPosition; while special one like getAngle() or getAngle(unit), getTime() etc will return Quantums (with optional conversion to specified units).
In general the Measure classes can be used without worrying about the MeasValues, since most Measure constructors have enough flexibility (and their own get()'s) to be able to use them independently).
Special cases are MVAngle and MVTime, which can do special formatting for time and angles (in earlier documentation they were called HMS etc.).


The Quanta model originated to handle physical quantities independent of their units. Units were introduced in the described way to be able to handle any possible physical unit.

To Do


Known units on 960509

// UnitMap::list() will produce the following list:
List all defined symbols
Prefix table (20):
E (exa) 1e+18
G (giga) 1000000000
M (mega) 1000000
P (peta) 1e+15
T (tera) 1e+12
Y (yotta) 1e+24
Z (zetta) 1e+21
a (atto) 1e-18
c (centi) 0.01
d (deci) 0.1
da (deka) 10
f (femto) 1e-15
h (hecto) 100
k (kilo) 1000
m (milli) 0.001
n (nano) 1e-09
p (pico) 1e-12
u (micro) 1e-06
y (yocto) 1e-24
z (zepto) 1e-21
Defining unit table (10):
A (ampere) 1 A
K (kelvin) 1 K
_ (undimensioned) 1 _
cd (candela) 1 cd
kg (kilogram) 1 kg
m (metre) 1 m
mol (mole) 1 mol
rad (radian) 1 rad
s (second) 1 s
sr (steradian) 1 sr
SI unit table (50):
$ (currency) 1 _
% (percent) 0.01
%% (permille) 0.001
A (ampere) 1 A
AE (astronomical unit) 149597870659 m
AU (astronomical unit) 149597870659 m
Bq (becquerel) 1 s-1
C (coulomb) 1 s.A
F (farad) 1
Gy (gray) 1 m2.s-2
H (henry) 1
Hz (hertz) 1 s-1
J (joule) 1
Jy (jansky) 1e-26 kg.s-2
K (kelvin) 1 K
L (litre) 0.001 m3
M0 (solar mass) 1.98891944407e+30 kg
N (newton) 1
Ohm (ohm) 1
Pa (pascal) 1
S (siemens) 1
S0 (solar mass) 1.98891944407e+30 kg
Sv (sievert) 1 m2.s-2
T (tesla) 1 kg.s-2.A-1
UA (astronomical unit) 149597870659 m
V (volt) 1
W (watt) 1
Wb (weber) 1
_ (undimensioned) 1 _
a (year) 31557600 s
arcmin (arcmin) 0.000290888208666 rad
arcsec (arcsec) 4.8481368111e-06 rad
as (arcsec) 4.8481368111e-06 rad
cd (candela) 1 cd
cy (century) 3155760000 s
d (day) 86400 s
deg (degree) 0.0174532925199 rad
g (gram) 0.001 kg
h (hour) 3600 s
l (litre) 0.001 m3
lm (lumen) 1
lx (lux) 1
m (metre) 1 m
min (minute) 60 s
mol (mole) 1 mol
pc (parsec) 3.08567758065e+16 m
rad (radian) 1 rad
s (second) 1 s
sr (steradian) 1 sr
t (tonne) 1000 kg
Customary unit table (74):
" (arcsec) 4.8481368111e-06 rad
"_2 (square arcsec) 2.35044305391e-11 sr
' (arcmin) 0.000290888208666 rad
'' (arcsec) 4.8481368111e-06 rad
''_2 (square arcsec) 2.35044305391e-11 sr
'_2 (square arcmin) 8.46159499408e-08 sr
: (hour) 3600 s
:: (minute) 60 s
::: (second) 1 s
Ah (ampere hour) 3600 s.A
Angstrom (angstrom) 1e-10 m
Btu (British thermal unit (Int)) 1055.056
CM (metric carat) 0.0002 kg
Cal (large calorie (Int)) 4186.8
FU (flux unit) 1e-26 kg.s-2
G (gauss) 0.0001 kg.s-2.A-1
Gal (gal) 0.01 m.s-2
Gb (gilbert) 0.795774715459 A
Mx (maxwell) 1e-08
Oe (oersted) 79.5774715459 m-1.A
R (mile) 0.000258 kg-1.s.A
St (stokes) 0.0001 m2.s-1
Torr (torr) 133.322368421
USfl_oz (fluid ounce (US)) 2.95735295625e-05 m3
USgal (gallon (US)) 0.003785411784 m3
WU (WSRT flux unit) 5e-29 kg.s-2
abA (abampere) 10 A
abC (abcoulomb) 10 s.A
abF (abfarad) 1000000000
abH (abhenry) 1e-09
abOhm (abohm) 1e-09
abV (abvolt) 1e-08
ac (acre) 4046.8564224 m2
arcmin_2 (square arcmin) 8.46159499408e-08 sr
arcsec_2 (square arcsec) 2.35044305391e-11 sr
ata (technical atmosphere) 98066.5
atm (standard atmosphere) 101325
bar (bar) 100000
beam (undefined beam area) 1 _
cal (calorie (Int)) 4.1868
cwt (hundredweight) 50.80234544 kg
deg_2 (square degree) 0.000304617419787 sr
dyn (dyne) 1e-05
eV (electron volt) 1.60217733e-19
erg (erg) 1e-07
fl_oz (fluid ounce (Imp)) 2.84130488996e-05 m3
ft (foot) 0.3048 m
fu (flux unit) 1e-26 kg.s-2
fur (furlong) 201.168 m
gal (gallon (Imp)) 0.00454608782394 m3
ha (hectare) 10000 m2
hp (horsepower) 745.7
in (inch) 0.0254 m
kn (knot (Imp)) 0.514773333333 m.s-1
lb (pound (avoirdupois)) 0.45359237 kg
ly (light year) 9.46073047e+15 m
mHg (metre of mercury) 133322.387415
mile (mile) 1609.344 m
n_mile (nautical mile (Imp)) 1853.184 m
oz (ounce (avoirdupois)) 0.028349523125 kg
pixel (pixel) 1 _
sb (stilb) 10000
sq_arcmin (square arcmin) 8.46159499408e-08 sr
sq_arcsec (square arcsec) 2.35044305391e-11 sr
sq_deg (square degree) 0.000304617419787 sr
statA (statampere) 3.33564095198e-10 A
statC (statcoulomb) 3.33564095198e-10 s.A
statF (statfarad) 1.11188031733e-12
statH (stathenry) 899377374000
statOhm (statohm) 899377374000
statV (statvolt) 299.792458
debye (electric dipole moment) 10-18
u (atomic mass unit) 1.661e-27 kg
yd (yard) 0.9144 m
yr (year) 31557600 s

Variable Documentation

class casacore::UnitVal_static_initializer casacore::unitval_static_initializer