Maximizing the area of a polygon using string based input

/***********************************************************************
   Xpress Optimizer Examples
   =========================

   file Polygon_textformula.c
   ``````````````````````````
   Implement the polygon example using text formulas     

   Maximize the area of polygon of N vertices and diameter of 1
   The position of vertices is indicated as (rho,theta) coordinates  
   where rho denotes the distance to the base point   
   (vertex with number N) and theta the angle from the x-axis.        
   The nonlinear expressions are described text based input.

   (c) 2017 Fair Isaac Corporation       
***********************************************************************/

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>

#include "xprs.h"
#include "xslp.h"

#define MAXROW 20
#define MAXCOL 20
#define MAXELT 50

void XPRS_CC XSLPMessage(XSLPprob my_prob, void *my_object, char *msg,
  int len, int msg_type);

int main(int argc, char *argv[]) {
  XPRSprob xprob = NULL;
  XSLPprob sprob = NULL;

  int nRow, nCol, nSide, nElement, nRowName, nColName;
  int iRow;
  char RowType[MAXROW];
  double RHS[MAXROW], OBJ[MAXCOL], Element[MAXELT], Lower[MAXCOL], Upper[MAXCOL];
  int ColStart[MAXCOL+1], RowIndex[MAXELT];
  double Factor;
  int ReturnValue;
  int i, j;
  char RowNames[500], ColNames[500];
  char *CoefBuffer;
  int BufferPos;

/* Initialisation */
  CoefBuffer = NULL;
  if (ReturnValue=XPRSinit(NULL)) goto ErrorReturn;
  if (ReturnValue=XSLPinit()) goto ErrorReturn;
  if (ReturnValue=XPRScreateprob(&xprob)) goto ErrorReturn;
  if (ReturnValue=XSLPcreateprob(&sprob,&xprob)) goto ErrorReturn;

/* XSLPsetcbmessage */
  XSLPsetcbmessage(sprob,XSLPMessage,NULL);

  nSide = 5;
  nRowName = 0;

/* Rows */
  nRow = nSide-2 + (nSide-1)*(nSide-2)/2 + 1;
  for (i=0;i<nRow;i++) RHS[i] = 0;

  nRow = 0;
  RowType[nRow++] = 'E'; /* OBJEQ */
  nRowName = nRowName + 1 + sprintf(&RowNames[nRowName],"OBJEQ");
  for (i=1;i<nSide-1;i++) {
	  RowType[nRow++] = 'G'; /* T2T1 .. T4T3 */
	  RHS[i] = 0.001;
	  nRowName = nRowName + 1 + sprintf(&RowNames[nRowName],"T%dT%d",i+1,i);
  }

  for (i=1;i<nSide-1;i++) {
	  for (j=i+1;j<nSide;j++) {
	    RowType[nRow] = 'L';
	    RHS[nRow++] = 1.0;
	    nRowName = nRowName + 1 + sprintf(&RowNames[nRowName],"V%dV%d",i,j);
	  }
  }
  RowType[nRow] = '\0';

/* Columns */
  nColName = 0;
  nCol = (nSide-1)*2 + 2;
  nElement = 0;
  for (i=0;i<nCol;i++) {
	  OBJ[i] = 0;					  /* objective function */
 	  Lower[i] = 0;				  /* lower bound normally zero */
	  Upper[i] = XPRS_PLUSINFINITY; /* upper bound infinity */
   }

/* OBJX */
  nCol = 0;
  ColStart[nCol] = nElement;
  OBJ[nCol] = 1.0;
  Lower[nCol++] = XPRS_MINUSINFINITY; /* free column */
  Element[nElement] = -1.0;
  RowIndex[nElement++] = 0;
  nColName = nColName + 1 + sprintf(&ColNames[nColName],"OBJX");

/* THETA1 - THETA 4 */
  iRow = 0;
  for (i=1;i<nSide;i++) {
	  nColName = nColName + 1 + sprintf(&ColNames[nColName],"THETA%d",i);
	  ColStart[nCol++] = nElement;
	  if (i < nSide-1) {
	    Element[nElement] = -1;
	    RowIndex[nElement++] = iRow+1;
	  }
	  if (i > 1) {
	    Element[nElement] = 1;
	    RowIndex[nElement++] = iRow;
	  }
	  iRow++;
  }

  Upper[nCol-1] = 3.1415926;

/* Equals column */
  nColName = nColName + 1 + sprintf(&ColNames[nColName],"=");
  ColStart[nCol] = nElement;
  Lower[nCol] = Upper[nCol] = 1.0; /* fixed at 1.0 */
  nCol++;

/* Remaining columns come later */
  for (i=1;i<nSide;i++) {
 	  Lower[nCol] = 0.01;	  /* lower bound */
	  Upper[nCol] = 1;
	  ColStart[nCol++] = nElement;
	  nColName = nColName + 1 + sprintf(&ColNames[nColName],"RHO%d",i);
  }
  ColStart[nCol] = nElement;

  XPRSsetintcontrol(xprob,XPRS_MPSNAMELENGTH,16);

  if (ReturnValue=XPRSloadlp(xprob,"Polygon",nCol,nRow,RowType,RHS,NULL,OBJ,
	ColStart,NULL,RowIndex,Element,Lower,Upper)) goto ErrorReturn;
  if (ReturnValue=XPRSaddnames(xprob,1,RowNames,0,nRow-1)) goto ErrorReturn;
  if (ReturnValue=XPRSaddnames(xprob,2,ColNames,0,nCol-1)) goto ErrorReturn;

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

/* 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);

/* 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++;
	  }
  }

  XSLPwriteprob(sprob,"Polygon_textformula","");

  if (ReturnValue=XSLPmaxim(sprob,"")) goto ErrorReturn;
  if (ReturnValue=XSLPwriteslxsol(sprob, "Polygon_textformula", "")) goto ErrorReturn; 

  goto NormalReturn;
ErrorReturn:
  printf("\nError %d",ReturnValue);
NormalReturn:
  if (CoefBuffer) free(CoefBuffer);
  XSLPdestroyprob(sprob);
  XPRSdestroyprob(xprob);
  XSLPfree();
  XPRSfree();
  return(ReturnValue);
}

void XPRS_CC XSLPMessage(XSLPprob my_prob, void *my_object, char *msg,
  int len, int msg_type) {
  switch (msg_type) {
  case 4: /* error */
  case 3: /* warning */
  case 2: /* dialogue */
  case 1: /* information */
	printf("%s\n",msg);
	break;
  default: /* exiting */
	fflush(stdout);
	break;
  }
}