Package uk.me.nxg.unity

The Unity package provides a parser for unit strings.

See:
          Description

Class Summary
Dimensions A dimensions specification is a record of the measurement dimensions of a quantity.
FunctionDefinition Describes a function.
FunctionDefinitionMap Provides a mapping from function abbreviations to function definitions.
FunctionOfUnit Represents a function of a unit, such as log(m).
OneUnit A single unit.
SimpleUnit A single simple unit.
UnitDefinition Describes a unit.
UnitDefinitionMap Provides a mapping from unit abbreviations to unit definitions.
UnitExpr A parsed unit expression.
UnitParser A parser for unit strings.
UnitParser.Lexeme A single lexeme.
UnitRepresentation A description of the way that a unit is represented in a particular syntax.
Version Manage version information
 

Exception Summary
UnitParserException Thrown when an expression cannot be parsed.
 

Package uk.me.nxg.unity Description

The Unity package provides a parser for unit strings.

NOTE: The library should currently be regarded as beta quality: the implementation and interface may change in response to experience and comments.

This is the unity parser (version 0.7), which is a Java class library to help parse unit specification strings such as W mm^-2. There is also an associated C library, which uses the same grammars. For more details, see the library's home page; the source is on bitbucket.

As well as parsing various unit strings, the library can also serialise a parsed expression in various formats, including the three formats that it can parse, a LaTeX version with name latex (which uses the {siunitx} package) and a debug format which lists the parsed unit in an unambiguous, but not otherwise useful, form.

Parsing Units

You can parse units using a couple of different syntaxes since, unfortunately, there is no general consensus on which syntax the world should agree on. The ones supported (and their names within this library) are as follows:

fits
FITS v3.0, section 4.3, W.D. Pence et al., A&A 524, A42, 2010 doi:10.1051/0004-6361/201015362
ogip
OGIP memo OGIP/93-001, 1993
cds
Standards for Astronomical Catalogues, Version 2.0, section 3.2, 2000
vou
IVOA VOUnits Proposed Recommendation

See also the IAU style manual, section 5.1, 1989, though this is by now rather old.

Each of these has an associated writer, which allows you to write a parsed UnitExpression to a string, in a format which should be conformant with the particular syntax's standard. See UnitExpr.toString().

In addition, there is a latex writer, which produces a formatted form for the the expression, in a form suitable for inclusion in a LaTeX document, using the siunitx package. To use the resulting output in a LaTeX document, include the following in the preamble of the file:

\usepackage{siunitx}
\DeclareSIQualifier\solar{$\odot$}

You may add any siunitx options that seem convenient, and you may omit the declaration of \solar if the units in the document do not include the various solar ones.

The parsing is permissive, to the extent that it permits non-recognised and deprecated units. The result of the parse may be checked for conformance with one or other standard using the methods UnitExpr.allUnitsRecognised(java.lang.String), UnitExpr.allUnitsRecommended(java.lang.String) and UnitExpr.allUsageConstraintsSatisfied(java.lang.String). Note that SI prefixes are still noticed for unrecognised units: thus furlongs/fortnight will be parsed as femto-urlongs per femto-ortnight. The same is not true of recognised units: a pixel/s is a pixel per second, and does not involve a pico-ixel.

Demo

If you want to experiment with the library, you can do so using the jar file:

    % java -jar unity.jar -icds -oogip 'mm2/s'
    mm**2 /s
    % java -jar unity.jar -icds -ofits -v mm/s
    mm s-1
    check: all units recognised?           yes
    check: all units recommended?          yes
    check: all units satisfy constraints?  yes
    % java -jar unity.jar -ifits -ocds -v 'merg/s'
    merg/s
    check: all units recognised?           yes
    check: all units recommended?          no
    check: all units satisfy constraints?  no
    % java -jar unity.jar -icds -ofits -v 'merg/s'
    merg s-1
    check: all units recognised?           no
    check: all units recommended?          no
    check: all units satisfy constraints?  yes

In the latter cases, the -v option validates the input string against various constraints. The expression mm/s is completely valid in all the syntaxes. In the FITS syntax, the erg is a recognised unit, but it is deprecated; although it is recognised, it is not permitted to have SI prefixes. In the CDS syntax, the erg is neither recognised nor (a fortiori) recommended; since there are no constraints on it in this syntax, it satisfies all of them (this latter behaviour is admittedly slightly counterintuitive).

Grammars supported

The four supported grammars have a fair amount in common, but the differences are nonetheless significant enough that they require separate grammars. Important differences are in the number of solidi they allow in the units specifications, and the symbols they use for products and powers.

The CDS specification permits non-round factors (that is, factors which aren't a power of ten). These are not permitted in this CDS parser, partly because they're arguably quantities rather than units, but more practically because it significantly complicates the implementation.

Current limitations:

In the grammars below, the terminals are as follows:

The FITS grammar

input:            complete_expression 
                | scalefactor complete_expression 
                | scalefactor WHITESPACE complete_expression 
                | division unit_expression 
                ;

complete_expression: product_of_units 
                | product_of_units division unit_expression 
                ;

product_of_units: unit_expression 
                | product_of_units product unit_expression 
                ;

unit_expression:  unit                                 
                | STRING OPEN_P complete_expression CLOSE_P 
                | OPEN_P complete_expression CLOSE_P 
                ;

scalefactor:      LIT10 power numeric_power 
                | LIT10 SIGNED_INTEGER 
                ;

division:         DIVISION;

unit:             STRING                
                | STRING power numeric_power        
                | STRING numeric_power        
                ;

power:            CARET
                | STARSTAR
                ;

numeric_power:    integer 
                | OPEN_P integer CLOSE_P 
                | OPEN_P FLOAT CLOSE_P 
                | OPEN_P integer division UNSIGNED_INTEGER CLOSE_P 
                ;

integer:          SIGNED_INTEGER | UNSIGNED_INTEGER;

product:          WHITESPACE | STAR | DOT;

The OGIP grammar

input:            complete_expression 
                | scalefactor complete_expression 
                | scalefactor WHITESPACE complete_expression 
                ;

complete_expression: product_of_units 
                ;

product_of_units: unit_expression
                | division unit_expression 
                | product_of_units product unit_expression 
                | product_of_units division unit_expression 
                ;

unit_expression:  unit                                 
                | STRING OPEN_P complete_expression CLOSE_P 
                | OPEN_P complete_expression CLOSE_P 
                ;

scalefactor:      LIT10 power numeric_power 
                | LIT10 
                | FLOAT 
                ;

division:         DIVISION | WHITESPACE DIVISION
                | WHITESPACE DIVISION WHITESPACE | DIVISION WHITESPACE;

unit:             STRING                
                | STRING power numeric_power        
                ;

power:            STARSTAR;

numeric_power:    UNSIGNED_INTEGER 
                | FLOAT 
                | OPEN_P integer CLOSE_P 
                | OPEN_P FLOAT CLOSE_P 
                | OPEN_P integer division UNSIGNED_INTEGER CLOSE_P 
                ;

integer:          SIGNED_INTEGER | UNSIGNED_INTEGER;

product:          WHITESPACE | STAR | WHITESPACE STAR
                | WHITESPACE STAR WHITESPACE | STAR WHITESPACE;

The CDS grammar

This is quite similar to the OGIP grammar, but with more restrictions

input:            complete_expression 
                | scalefactor complete_expression 
                ;

complete_expression: product_of_units 
                ;

product_of_units: unit_expression
                | division unit_expression 
                | product_of_units product unit_expression 
                | product_of_units division unit_expression 
                ;

unit_expression:  unit                                 
                | OPEN_SQ complete_expression CLOSE_SQ 
                | OPEN_P complete_expression CLOSE_P 
                ;

scalefactor:      LIT10 power numeric_power 
                | LIT10 SIGNED_INTEGER 
                | UNSIGNED_INTEGER 
                | LIT10 
                | CDSFLOAT 
                | FLOAT 
                ;

division:         DIVISION;

unit:             STRING                
                | STRING numeric_power        
                ;

power:            STARSTAR;

numeric_power:    integer 
                ;

integer:          SIGNED_INTEGER | UNSIGNED_INTEGER;

product:          DOT;

The VOUnits grammar

This is intended to be as nearly as possible in the intersection of the various grammars above. It is a strict subset of the FITS and CDS grammars (in the sense that any VOUnit unit string is a valid FITS and CDS string, too), and it is almost a subset of the OGIP grammar, except that it uses the dot for multiplication rather than star.

input:            complete_expression 
                | scalefactor complete_expression 
                | division unit_expression 
                ;

complete_expression: product_of_units 
                | product_of_units division unit_expression 
                ;

product_of_units: unit_expression 
                | product_of_units product unit_expression 
                ;

unit_expression:  unit                                 
                | STRING OPEN_P complete_expression CLOSE_P 
                | OPEN_P complete_expression CLOSE_P 
                ;

scalefactor:      LIT10 power numeric_power 
                ;

division:         DIVISION;

unit:             STRING                
                | STRING power numeric_power        
                ;

power:            STARSTAR;

numeric_power:    integer 
                | OPEN_P integer CLOSE_P 
                | OPEN_P FLOAT CLOSE_P 
                | OPEN_P integer division UNSIGNED_INTEGER CLOSE_P 
                ;

integer:          SIGNED_INTEGER | UNSIGNED_INTEGER;

product:          DOT;