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Maximizing the area of a polygon using string based input

Description
Demonstrates the use of formula strings

Further explanation of this example: 'Xpress NonLinear Reference Manual'

Source Files

Polygon_textformula.c

```/***********************************************************************
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;

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;
}
}

```