MAKE example: cancelling off-diagonal elements

an example of conditional formulae

Sometimes we wish to remove off-diagonal elements of the MAKE (multiproduction) matrix. In certain cases we can remove some of these off-diagonal elements rather easily. For example, suppose initially

Beverages production of Food = 97, and

Food production of Beverages = 70.

We could

subtract 70 from Bev production of Food .. it becomes 27

subtract 70 from Food production of Bev .. it becomes 0

add 70 to Food production of Food

add 70 to Bev production of Bev

The effect is to remove one off-diagonal element from the MAKE without altering MAKE row and column totals.

Coefficient

(all,c,COM)(all,i,IND) MAKE(c,i) # production of com c by ind i #;

Read MAKE from file INFILE header MAKE;

Set SEC = COM intersect IND;

Coefficient ! cancel out matching off-diagonal MAKE elements !

(all,c,COM)(all,i,IND) MAKEADJ(c,i) # MAKE adjustment #;

Formula

(all,c,COM)(all,i,IND) MAKEADJ(c,i) = 0;

(all,c,SEC)(all,i,SEC: ((c<>i) and (MAKE(c,i)>0) and (MAKE(i,c)>MAKE(c,i))))

MAKEADJ(c,i) = MAKE(c,i); ! = smaller of any pair !

Write MAKEADJ to file OUTFILE header MADJ;

Formula

! reduce larger of pair by size of smaller !

(all,c,SEC)(all,i,SEC:MAKEADJ(c,i)>0)

MAKE(i,c) = MAKE(i,c) - MAKEADJ(c,i);

! transfer adjustment to own production !

(all,c,SEC) MAKE(c,c) = MAKE(c,c) + sum{i,IND, MAKEADJ(c,i)};

(all,i,SEC) MAKE(i,i) = MAKE(i,i) + sum{c,COM, MAKEADJ(c,i)};

! remove smaller of pair !

(all,c,COM)(all,i,IND: MAKEADJ(c,i)>0) MAKE(c,i) = 0;

Write MAKE to file OUTFILE header MAK2 longname adjusted MAKE;

URL of this topic: www.copsmodels.com/webhelp/tabmate/hc_makeexample.htm

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