Adding the non-linear part of the problem using character formulae

Provided that all entities – in particular columns and user functions – have explicit and unique names, the non-linear part can be input by writing the formulae as character strings. This is not as efficient as using the XSLPloadcoefs() function but is generally easier to understand.

/* Build up nonlinear coefficients */
/* Allow space for largest formula - approx 50 characters per side for area */
  CoefBuffer = (char *) malloc(50*nSide);

We shall be using large formulae, so we need a character buffer large enough to hold the largest formula we are using. The estimate here is 50 characters per side of the polygon for the area formula, which is the largest we are using.

/* Area */
  Factor = 0.5;

  BufferPos = 0;
  for (i=1; i<nSide-1; i++) {
    if (i > 1) {
      BufferPos = BufferPos + sprintf(&CoefBuffer[BufferPos], " + ");
    }
    BufferPos = BufferPos + sprintf(&CoefBuffer[BufferPos], "RHO%d * RHO%d *
                SIN ( THETA%d - THETA%d )", i+1, i, i+1, i);
  }
  XSLPchgccoef(sprob, 0, nSide, &Factor, CoefBuffer);

The area formula is of the form:
(RHO2*RHO1*SIN(THETA2-THETA1) + RHO3*RHO2*SIN(THETA3-THETA2) + ... ) / 2
The loop writes the product for each consecutive pair of vertices and also puts in the "+" sign after the first one.

The XSLPchgccoef function is a variation of XSLPchgcoef but uses a character string for the formula instead of passing it as arrays of tokens. The arguments to the function are:

In this case, RowIndex is zero and ColIndex is nSide (the "equals" column).

/* Distances */
  Factor = 1.0;
  for (i=1; i<nSide-1; i++) {
    for (j=i+1; j<nSide; j++) {
      sprintf(CoefBuffer, "RHO%d ^ 2 + RHO%d ^ 2 - 2 * RHO%d * RHO%d *
              COS ( THETA%d - THETA%d )", j, i, j, i, j, i);
      XSLPchgccoef(sprob, iRow, nSide, &Factor, CoefBuffer);
      iRow++;
    }

This creates the formula for the distance between pairs of vertices and writes each into a new row in the "equals" column.

Provided you have given names to any user functions in your program, you can use them in a formula in exactly the same way as SIN and COS have been used above.