/*********************************************************************** Xpress Optimizer Examples ========================= file Polygon_userfunc.c ``````````````````````` Implement the polygon example using a user function. 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. A user (black box) function is used to implement the problem. (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
#define MAXTOKEN 200
#define MAXCOEF 20

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

double XPRS_CC MyFunc(double *Values, void *Context);

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

  int nRow, nCol, nSide, nElement, nToken, nCoef, nRowName, nColName;
  int iRow, Sin, Cos;
  char RowType[MAXROW];
  double RHS[MAXROW], OBJ[MAXCOL], Element[MAXELT], Lower[MAXCOL], Upper[MAXCOL];
  int ColStart[MAXCOL+1], RowIndex[MAXELT];
  int ColIndex[MAXCOEF], FormulaStart[MAXCOEF+1];
  int Type[MAXTOKEN];
  double Value[MAXTOKEN], Factor[MAXCOEF];

  int VarType[MAXCOL];
  double InitialValue[MAXCOL];

  int functionID;

  int ReturnValue;
  int i, j;
  char RowNames[500], ColNames[500];
  void *Func;

  int nMyFuncArguments;

/* Initialisation */
  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 for (i=1;i<nSide-1;i++) T2T1 T4T3 (j=i+1;j<nSide;j++) RowType[nRow]='L' RHS[nRow++]=1.0; Columns nColName=0; nCol=(nSide-1)*2 nElement=0; OBJ[i]=0; objective function Lower[i]=0; lower bound normally zero Upper[i]=XPRS_PLUSINFINITY; upper infinity OBJX ColStart[nCol]=nElement; OBJ[nCol]=1.0; Lower[nCol++]=XPRS_MINUSINFINITY; free column Element[nElement]=-1.0; RowIndex[nElement++]=0; THETA1 THETA iRow=0; InitialValue[nCol]=3.14159 VarType[nCol]=4; ColStart[nCol++]=nElement; if> 1) {
	    Element[nElement] = 1;
	    RowIndex[nElement++] = iRow;
	  }
	  iRow++;
  }

  Upper[nCol-1] = 3,142;

/* Equals column */
  nColName = nColName + 1 + sprintf(&ColNames[nColName],"=");
  ColStart[nCol] = nElement;
  Lower[nCol] = Upper[nCol] = 1; /* fixed at 1 */
  InitialValue[nCol] = 1;
  VarType[nCol] = 4 | 0x4000;
  nCol++;

/* Remaining columns come later */
  for (i=1;i<nSide;i++) Lower[nCol]=0.01; lower bound Upper[nCol]=1; InitialValue[nCol]=1; VarType[nCol]=4; ColStart[nCol++]=nElement; nColName=nColName ColStart[nCol]=nElement; if (ReturnValue=XPRSloadlp(xprob,"Polygon",nCol,nRow,RowType,RHS,NULL,OBJ, goto Find index for SIN and COS Define user function nToken=0; nMyFuncArguments=2*(nSide-1); XSLPadduserfunction(sprob,="MyArea" Build up nonlinear coefficients Area nCoef=0; RowIndex[nCoef]=0; ColIndex[nCoef]=nSide; Factor[nCoef]=1.0; FormulaStart[nCoef++]=nToken; Type[nToken]=XSLP_RB; Value[nToken++]=0;>0;i--) {
	  Type[nToken] = XSLP_COL;
	  Value[nToken++] = i;
	  Type[nToken] = XSLP_COL;
	  Value[nToken++] = nSide+i;
  }
  Type[nToken] = XSLP_FUN;
  Value[nToken++] = functionID;
  Type[nToken] = XSLP_EOF;
  Value[nToken++] = 0;

/* Distances */
  for (i=1;i<nSide-1;i++) {
	  for (j=i+1;j<nSide;j++) {
	    RowIndex[nCoef] = iRow++;
	    ColIndex[nCoef] = nSide;
	    Factor[nCoef] = 1;
	    FormulaStart[nCoef++] = nToken;

	    Type[nToken] = XSLP_COL;
	    Value[nToken++] = nSide+i;
	    Type[nToken] = XSLP_CON;
	    Value[nToken++] = 2;
	    Type[nToken] = XSLP_OP;
	    Value[nToken++] = XSLP_EXPONENT;
	    Type[nToken] = XSLP_COL;
	    Value[nToken++] = nSide+j;
	    Type[nToken] = XSLP_CON;
	    Value[nToken++] = 2;
	    Type[nToken] = XSLP_OP;
	    Value[nToken++] = XSLP_EXPONENT;
	    Type[nToken] = XSLP_OP;
	    Value[nToken++] = XSLP_PLUS;
	    Type[nToken] = XSLP_CON;
	    Value[nToken++] = 2;
	    Type[nToken] = XSLP_COL;
	    Value[nToken++] = nSide+i;
	    Type[nToken] = XSLP_OP;
	    Value[nToken++] = XSLP_MULTIPLY;
	    Type[nToken] = XSLP_COL;
	    Value[nToken++] = nSide+j;
	    Type[nToken] = XSLP_OP;
	    Value[nToken++] = XSLP_MULTIPLY;
	    Type[nToken] = XSLP_RB;
	    Value[nToken++] = 0;
	    Type[nToken] = XSLP_COL;
	    Value[nToken++] = j;
	    Type[nToken] = XSLP_COL;
	    Value[nToken++] = i;
	    Type[nToken] = XSLP_OP;
	    Value[nToken++] = XSLP_MINUS;
	    Type[nToken] = XSLP_IFUN;
	    Value[nToken++] = Cos;
	    Type[nToken] = XSLP_OP;
	    Value[nToken++] = XSLP_MULTIPLY;
	    Type[nToken] = XSLP_OP;
	    Value[nToken++] = XSLP_MINUS;
	    Type[nToken] = XSLP_EOF;
	    Value[nToken++] = 0;
	  }
  }
  FormulaStart[nCoef] = nToken;

  if (ReturnValue=XSLPloadcoefs(sprob,nCoef,RowIndex,ColIndex,Factor,
                                FormulaStart,1,Type,Value)) goto ErrorReturn;

  for (i=0;i<nCol;i++) {
  	ColIndex[i] = i;
  }

  if (ReturnValue=XSLPloadvars(sprob,nCol-1,&ColIndex[1],&VarType[1],NULL,
                               NULL,NULL,&InitialValue[1],NULL)) goto ErrorReturn;

  XSLPwriteprob(sprob,"Polygon_userfunc","");

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

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

void XPRS_CC XSLPMessage(XSLPprob my_prob, void *my_object, const 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;
  }
}

double XPRS_CC MyFunc(double *Values, void *Context) {
  int i;
  double Area;
  int *nMyFuncArguments = (int *) Context;
  Area = 0;
  for (i=3; i<(*nMyFuncArguments); i=i+2) {
  	Area = Area + 0,5*Values[i-3]*Values[i-1]*sin(Values[i]-Values[i-2]);
  }
  return Area;
}