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Implementing the polygon examples as a black box function

Description
Demonstrates how black box functions may be optimized using Xpress NonLinear, using tokeanised input

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

Source Files
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Polygon_userfunc.c

/***********************************************************************
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 MAXFORMULA 20

#define PI 3.14159

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

/* Perform the Xpress specified function call and check its return value. */
#define CHECK_XPRSCALL(call)                             \
do {                                                   \
int result_ = call;                                  \
if ( result_ != 0 ) {                                \
fprintf(stderr, "Line %d: Failed call to %s.\n", \
__LINE__, #call);                          \
goto returnWithError;                              \
}                                                    \
} while (0)

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, nformula, 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], ColIndex[MAXCOL];
int FormulaStart[MAXFORMULA + 1];
int Type[MAXTOKEN];
double Value[MAXTOKEN];

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

int functionID;

int ReturnValue = 1;
int i, j;
char RowNames[500], ColNames[500];
void* Func;

int nMyFuncArguments;

/* Initialisation */
CHECK_XPRSCALL(XPRSinit(NULL));
CHECK_XPRSCALL(XSLPinit());
CHECK_XPRSCALL(XPRScreateprob(&xprob));
CHECK_XPRSCALL(XSLPcreateprob(&sprob, &xprob));

/* XSLPsetcbmessage */
CHECK_XPRSCALL(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);
InitialValue[nCol] = PI * ((double)(i)) / ((double)(nSide));
VarType[nCol] = 4;
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] = PI;

/* 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 + 1 + sprintf(&ColNames[nColName], "RHO%d", i);
}
ColStart[nCol] = nElement;

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

/* Find index for SIN and COS */
CHECK_XPRSCALL(XSLPgetindex(sprob, XSLP_INTERNALFUNCNAMES, "SIN", &Sin));
CHECK_XPRSCALL(XSLPgetindex(sprob, XSLP_INTERNALFUNCNAMES, "COS", &Cos));

/* Define user function */
nToken = 0;

nMyFuncArguments = 2 * (nSide - 1);
CHECK_XPRSCALL(XSLPadduserfunction(sprob, "MyArea", XSLP_USERFUNCTION_VECMAP, 2 * (nSide - 1), 1, 0, (XPRSfunctionptr) &MyFunc, &nMyFuncArguments, &functionID));

/* Build up nonlinear coefficients */
/* Area */
nToken = 0;
nformula = 0;
RowIndex[nformula] = 0;
FormulaStart[nformula++] = nToken;
Type[nToken] = XSLP_RB;
Value[nToken++] = 0;
for (i = nSide - 1; i > 0; i--) {
Type[nToken] = XSLP_COL;
Value[nToken++] = i;
Type[nToken] = XSLP_COL;
Value[nToken++] = nSide + i - 1;
}
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[nformula] = iRow++;
FormulaStart[nformula++] = nToken;

Type[nToken] = XSLP_COL;
Value[nToken++] = nSide + i - 1;
Type[nToken] = XSLP_CON;
Value[nToken++] = 2;
Type[nToken] = XSLP_OP;
Value[nToken++] = XSLP_EXPONENT;
Type[nToken] = XSLP_COL;
Value[nToken++] = nSide + j - 1;
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 - 1;
Type[nToken] = XSLP_OP;
Value[nToken++] = XSLP_MULTIPLY;
Type[nToken] = XSLP_COL;
Value[nToken++] = nSide + j - 1;
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[nformula] = nToken;

CHECK_XPRSCALL(XSLPloadformulas(sprob, nformula, RowIndex, FormulaStart, 1, Type, Value));

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

CHECK_XPRSCALL(XSLPloadvars(sprob, nCol - 1, &ColIndex[1], &VarType[1], NULL,
NULL, NULL, &InitialValue[1], NULL));

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

CHECK_XPRSCALL(XSLPmaxim(sprob, ""));
CHECK_XPRSCALL(XSLPwriteslxsol(sprob, "Polygon_userfunc", ""));

goto NormalReturn;
returnWithError:
printf("\nError %d", ReturnValue);
ReturnValue = -1;
NormalReturn:

// Retrieve error from Xpress
if (ReturnValue) {
fprintf(stderr, "An error was detected during execution.\n");
if (xprob && sprob) {
int errorcode;
char errorMessage[512];
XSLPgetlasterror(sprob, &errorcode, errorMessage);
if (errorcode == 0) {
XPRSgetintattrib(xprob, XPRS_ERRORCODE, &errorcode);
XPRSgetlasterror(xprob, errorMessage);
}
fprintf(stderr, "Optimizer returned error code '%i' with message:\n%s\n", errorcode, errorMessage);
}
}

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;
}

`