Mapping

A mapping from set A to set B identifies for each element in A, a corresponding element in B. For example, each of 100 industries could be part of one broad sector. A mapping (from industries to broad sectors) would describe this relation. Mappings are complicated but very useful: so read the GEMPACK manuals carefully !

Set COM (wool, wheat, trade, banking, hotels) ;

Set AGGCOM (agriculture, services) ;

Mapping COMTOAGGCOM from COM to AGGCOM ;

Read COMTOAGGCOM from file SETS header MTRD;

By default above read expects to find an integer header.

Read (by_elements) (all,c,TRAD) COMTOAGGCOM(c)

from file SETS header MTRD;

Above partial read expects to find a string header.

Formula COMTOAGGCOM(wool) = agriculture ;

Formula COMTOAGGCOM(wheat) = 1; ! ie, to agriculture !

Formula (all,c,COM) COMTOAGGCOM(c) = INTVEC(c);

Above, INTVEC must be an integer vector.

Coefficient (all,aggc,AGGCOM) AGGDHOUS(aggc) ;

Coefficient (all,c,COM) DHOUS(c) ;

Formula (all,aggc,AGGCOM)

AGGDHOUS(aggc) = SUM(c,COM: COMTOAGGCOM(c) EQ aggc, DHOUS(c) );

Variable (all,c,COM) xhous(c) ;

Variable (all,aggc,AGGCOM) agg_xhous(aggc) ;

Equation E_agg_xhous (all,aggc,AGGCOM)

sum(c,COM: COMTOAGGCOM(c) EQ aggc, DVHOUS(c)) * agg_xhous(aggc) =

sum(c,COM: COMTOAGGCOM(c) EQ aggc, DHOUS(c) * xhous(c) );

Above equation could be more stylishly written:!

Equation E_agg_xhous (all,aggc,AGGCOM)

sum{c,COM: COMTOAGGCOM(c) EQ aggc, DVHOUS(c)

*[agg_xhous(aggc)-xhous(c)]}=0;

Below FORMULA (BY_ELEMENTS) is used to make the mapping of a subset follow a mapping of parent set.

Set MAR (trade,hotels);

Subset MAR is subset of COM;

Set AGGMAR (services);

Subset AGGMAR is subset of AGGCOM;

Mapping MAR2AGGMAR from MAR to AGGMAR ;

Formula (by_elements) (All,m,MAR) MAR2AGGMAR(m) = COM2AGGCOM(m) ;

Mapping (ONTO) COM2AGGCOM from COM to AGGCOM ;

The qualifier (ONTO) causes GEMPACK to check that every element of AGGCOM is mapped to by at least one element of COM -- by default this is NOT done.

Write COM2AGGCOM to file SETS header MCOM; ! store as integers !

To store the mapping as a vector of strings, use:

Write (by_elements) COM2AGGCOM to file SETS header MCOM;

In the above examples, no longname was specified, so GEMPACK will make one up which conforms to the conventions required by ViewHAR.

Set mappings are not allowed on the LHS of a formula or of an update, or in the declaration of coefficients or variables, or in reads, writes or displays.