What A Complete Decomposition Shows

Complete decompositions only apply for Equations, never for Formulas.

A complete decomposition of an expression in an equation is designed to show the separate effects of the changes in each of the variables involved, one at a time.

For example, if an expression has just two variables v1 and v2 in it, the complete decomposition of this expression will show two values. The first value (it has toggle name "v1") shows how much the change in v1 by itself (ignoring the change in v2) contributes to the expression. The second value (it has toggle name "v2") shows how much the change in v2 by itself (ignoring the change in v1) contributes to the expression.

For this reason, you might like to think of a complete decomposition as a decomposition by variables.

To calculate the contribution of any one variable to the whole expression is easy. Just replace all other variables in the expression by zero. This is what AnalyseGE does, as you can see if you look at the formulas shown in the Evaluate memo on the AnalyseGE form after you carry out a complete decomposition.

The above applies when you do a complete decomposition of all or one side of an equation or of an expression you have selected in an equation.

Example

Suppose that you ask to decompose the right-hand side of the following equation.

Equation eq1 (all,c,COM)

x1(c) = C3(c)*SUM[i,IND, C4(c,i)*v1(c,i) + v2(c)] - C4(c)*v4(c) ;

The Evaluate memo on the AnalyseGE form will show

Formula (all,c,COM)

TempCoeff("v1",c) = C3(c)*SUM[i,IND, C4(c,i)*v1(c,i) + 0.0] - C4(c)*0.0 ;

Formula (all,c,COM)

TempCoeff("v2",c) = C3(c)*SUM[i,IND, C4(c,i)*0.0 + v2(c)] - C4(c)*v2(c) ;

You can see that the first value TempCoeff("v1",c) shows the contribution to the value of the right-hand side just from the simulation results for v1 (and ignores the v2 results). Note the "0.0"s in the expression for TempCoeff("v1",c). Similarly for the TempCoeff("v2",c) expression.

URL of this topic: www.copsmodels.com/webhelp/analysege/hc_decompshows.htm

Link to full GEMPACK Manual

Link to GEMPACK homepage