Menu | <<<< | >>>> | Equation-parameter matrices house equation terms and parameters

The split figure above shows an equation parameter matrix above and the model equations generated by the matrix below.  In VORSIM, equations are built and banked as matrices where each column of the matrix represents an equation term and each row represents a Category.  The yellow cells - column heads - generate equation terms.  Matrix rows generate equations using the same terms for different categories; matrix cells contain either a dash (-) meaning that the term is included or a number which means that the crosshatch (#) in the term is replaced with the number when the equation is written.  A blank cell in a matrix row means that that equation term in that column is not included.  Observe how the equations are made up of equation terms and numbers from the matrix cells.  Equations are written with the variable names from the column heads and use Excel math symbols.   Intercepts are calculated automatically during the equation writing process so that the value calculated by the equation equals the base value of the variable explained by the equation.  The equations written with variable names provide readable documentation for model equations.  The actual equations put into the model use cell notation instead of variable names for efficiency reasons.  You can see the actual model equation for EqsBL at the top of the figure where cell addresses replace variable names – the most efficient form for an equation in a spreadsheet.

When thinking about the creation or modification of equations in VORSIM, think of an equation as a set of terms related mathematically where equation parameters are kept in matrix cells.  This equation definition and storage methodology has the advantage of allowing a change in an equation by changing a parameter in a cell and re-writing the equation automatically at the click of a button.  Furthermore, the equation bank procedure stores the matrices (rather than the equations they generate) with contiguous documentation so that they can be removed from or added to Sheets in an equation workbook as needed.

A key question is “What is a ‘term’ in a VORSIM model equation”?  VORSIM gives you considerable flexibility here.  The most important thing for the set of terms is that as a whole, they MUST make up an equation that is valid in Excel, i.e. the equation must be mathematically correct using Excel math notation and equation syntax.  However, the composition of an equation as a set of terms is very flexible.  Basically, a term amounts to part of an equation that you may want to INCLUDE or EXCLUDE, depending upon the contents of the cell below the column heading.  So break your equation out into pieces (terms) that you might want to include or exclude-this is the practical definition of an equation term in VORSIM.  So a term might be a symbol such as’)’ or a variable such as USqsX or several variables (e.g. USqsX-USqsY).  Look at some of the equation matrices in models that come with VORSIM to see the flexibility in the use of equation terms.  Equation editing techniques also allow you to add/delete equation terms from an equation matrix.