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set name , record , $\dots$ , record ; set name [ symbol , $\dots$ , symbol ] , record , $\dots$ , record ; 
name is a symbolic name of the set;
symbol, $\dots$, symbol are subscripts which specify a particular member of the set (if the set is an array, i.e. a set of sets);
record, $\dots$, record are data records.
Commae preceding data records may be omitted.
Data records:
is a nonsignificant data record which may be used freely to improve readability;
specifies a slice;
specifies set data in the simple format;
specifies set data in the matrix format;
specifies set data in the transposed matrix format. (In this case the colon following the keyword (tr) may be omitted.)
Examples
set month := Jan Feb Mar Apr May Jun; set month "Jan", "Feb", "Mar", "Apr", "May", "Jun"; set A[3,Mar] := (1,2) (2,3) (4,2) (3,1) (2,2) (4,4) (3,4); set A[3,'Mar'] := 1 2 2 3 4 2 3 1 2 2 4 4 2 4; set A[3,'Mar'] : 1 2 3 4 := 1  +   2  + +  3 +   + 4  +  + ; set B := (1,2,3) (1,3,2) (2,3,1) (2,1,3) (1,2,2) (1,1,1) (2,1,1); set B := (*,*,*) 1 2 3, 1 3 2, 2 3 1, 2 1 3, 1 2 2, 1 1 1, 2 1 1; set B := (1,*,2) 3 2 (2,*,1) 3 1 (1,2,3) (2,1,3) (1,1,1); set B := (1,*,*) : 1 2 3 := 1 +   2  + + 3  +  (2,*,*) : 1 2 3 := 1 +  + 2    3 +   ;
(In these examples the set month
is a simple set of singles,
A
is a 2dimensional array of doubles, and B
is a simple
set of triples. Data blocks for the same set are equivalent in the sense
that they specify the same data in different formats.)
The set data block is used to specify a complete elemental set, which is assigned to a set (if it is a simple set) or one of its members (if the set is an array of sets).^{5}
Data blocks can be specified only for noncomputable sets, i.e. sets which have no assign attribute in the corresponding set statements.
If the set is a simple set, only its symbolic name should be given in the header of the data block. Otherwise, if the set is a ndimensional array, its symbolic name should be provided with a complete list of subscripts separated by commae and enclosed in square brackets to specify a particular member of the set array. The number of subscripts must be the same as the dimension of the set array, where each subscript must be a number or symbol.
The elemental set defined in the set data block is coded as a sequence of data records described below.^{6}
The assign (:=
) data record is a nonsignficant element. It may
be used for improving readability of data blocks.
The slice data record is a control record which specifies a slice of the elemental set defined in the data block. It has the following syntactic form:
( $s_1$ , $s_2$ , $\dots$ , $s_n$ )
where $s_1, s_2, \dots, s_n$ are components of the slice.
Each component of the slice can be a number or symbol or the asterisk (*). The number of components in the slice must be the same as the dimension of ntuples in the elemental set to be defined. For instance, if the elemental set contains 4tuples (quadruples), the slice must have four components. The number of asterisks in the slice is called slice dimension.
The effect of using slices is the following. If a mdimensional slice (i.e. a slice which has $m$ asterisks) is specified in the data block, all subsequent data records must specifiy tuples of the dimension m. Whenever a $m$tuple is encountered, each asterisk in the slice is replaced by corresponding components of the $m$tuple that gives the resultant ntuple, which is included in the elemental set to be defined. For example, if the slice (a,*,1,2,*) is in effect, and 2tuple (3,b) is encountered in a subsequent data record, the resultant 5tuple included in the elemental set is (a,3,1,2,b).
The slice that has no asterisks itself defines a complete ntuple, which is included in the elemental set.
Being once specified the slice effects until either a new slice or the end of data block has been encountered. Note that if there is no slice specified in the data block, a dummy one, components of which are all asterisks, is assumed.
The simple data record defines one ntuple in simple format and has the following syntactic form:
$t_1$ , $t_2$ , $\dots$ , $t_n$
where $t_1, t_2, \dots, t_n$ are components of the ntuple. Each component can be a number or symbol. Commae between components are optional and may be omitted.
The matrix data record defines several 2tuples (doubles) in matrix format and has the following syntactic form:
$\matrix{ {\tt :} & c_1 & c_2 & \dots & c_n & {\tt :=} \cr r_1 & a_{11} & a_{12} & \dots & a_{1n} & \cr r_2 & a_{21} & a_{22} & \dots & a_{2n} & \cr \dots & \dots & \dots & \dots & \dots & \cr r_m & a_{m1} & a_{m2} & \dots & a_{mn} & \cr }$
where $r_1, r_2, \dots, r_m$ are numbers and/or
symbols which correspond to rows of the matrix, $c_1, c_2$,
$\dots, c_n$ are numbers and/or symbols which correspond to columns
of the matrix, $a_{11}, a_{12}, \dots, a_{mn}$ are
the matrix elements, which can be either the sign +
or the sign

. (In this data record the delimiter :
preceding the
column list and the delimiter :=
following the column list cannot
be omitted.)
Each element $a_{ij}$ of the matrix data block (where
$1\leq i\leq m, 1\leq j\leq n$) corresponds to 2tuple
$(r_i, c_j)$. If $a_{ij}$ is the plus sign (+
), the
corresponding 2tuple (or a longer ntuple, if a slice is used)
is included in the elemental set. Otherwise, if $a_{ij}$ is the
minus sign (
) sign, the corresponding 2tuple is not included
in the elemental set.
Since the matrix data record defines 2tuples, either the elemental set must consist of 2tuples or the slice currently used must be 2dimensional.
The transposed matrix data record has the following syntactic form:
$\matrix{ {\tt (tr)\ :} & c_1 & c_2 & \dots & c_n & {\tt :=} \cr r_1 & a_{11} & a_{12} & \dots & a_{1n} & \cr r_2 & a_{21} & a_{22} & \dots & a_{2n} & \cr \dots & \dots & \dots & \dots & \dots & \cr r_m & a_{m1} & a_{m2} & \dots & a_{mn} & \cr }$
(In this case the delimiter :
following the keyword (tr)
is optional and may be omitted.)
This data record is completely analogous to the matrix data record (see above) with the only exception that each element $a_{ij}$ of the matrix corresponds to 2tuple $(c_j,r_i)$.
Being once specified the (tr)
indicator effects on all
subsequent data records until either a slice or the end of data block
has been encountered.
There is another way to specify data for a simple set along with data for parameters. This feature is discussed in the next section.
Data record is simply a technical term. It does not mean that data records have any special formatting.
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