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Providing initial values

Description
Demonstrates how to add initial values to nonlinear variables

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

Source Files
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Polygon_initialvalue.c

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

file Polygon_initialvalue.c

Implement the polygon example using tokens and initial values

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 using formula tokens,
and providing initial values to the nonlinear variables.

This example uses the coefficients interface; see other examples
for using the simplified formula interface.

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

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

#include "xprs.h"

#define MAXROW 20
#define MAXCOL 20
#define MAXELT 50
#define MAXTOKEN 200
#define MAXCOEF 20

#define PI 3.14159

void XPRS_CC Message(XPRSprob 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)

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

int nRow, nCol, nSide, nElement, nToken, nCoef, nRowName, nColName;
int iRow;
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 ReturnValue = 0;
int i, j;
char RowNames[500], ColNames[500];

/* Initialisation */
CHECK_XPRSCALL(XPRSinit(NULL));
CHECK_XPRSCALL(XPRScreateprob(&xprob));

/* Message callback */

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;

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

/* Build up nonlinear coefficients */
/* Area */
nToken = 0;
nCoef = 0;
RowIndex[nCoef] = 0;
ColIndex[nCoef] = nSide;
Factor[nCoef] = 0.5;
FormulaStart[nCoef++] = nToken;
for (i = 1; i < nSide - 1; i++) {
Type[nToken] = XPRS_TOK_COL;
Value[nToken++] = nSide + i + 1;
Type[nToken] = XPRS_TOK_COL;
Value[nToken++] = nSide + i;
Type[nToken] = XPRS_TOK_OP;
Value[nToken++] = XPRS_OP_MULTIPLY;
Type[nToken] = XPRS_TOK_RB;
Value[nToken++] = 0;
Type[nToken] = XPRS_TOK_COL;
Value[nToken++] = i + 1;
Type[nToken] = XPRS_TOK_COL;
Value[nToken++] = i;
Type[nToken] = XPRS_TOK_OP;
Value[nToken++] = XPRS_OP_MINUS;
Type[nToken] = XPRS_TOK_IFUN;
Value[nToken++] = XPRS_IFUN_SIN;
Type[nToken] = XPRS_TOK_OP;
Value[nToken++] = XPRS_OP_MULTIPLY;
if (i > 1) {
Type[nToken] = XPRS_TOK_OP;
Value[nToken++] = XPRS_OP_PLUS;
}
}
Type[nToken] = XPRS_TOK_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] = 1.0;
FormulaStart[nCoef++] = nToken;

Type[nToken] = XPRS_TOK_COL;
Value[nToken++] = nSide + i;
Type[nToken] = XPRS_TOK_CON;
Value[nToken++] = 2;
Type[nToken] = XPRS_TOK_OP;
Value[nToken++] = XPRS_OP_EXPONENT;
Type[nToken] = XPRS_TOK_COL;
Value[nToken++] = nSide + j;
Type[nToken] = XPRS_TOK_CON;
Value[nToken++] = 2;
Type[nToken] = XPRS_TOK_OP;
Value[nToken++] = XPRS_OP_EXPONENT;
Type[nToken] = XPRS_TOK_OP;
Value[nToken++] = XPRS_OP_PLUS;
Type[nToken] = XPRS_TOK_CON;
Value[nToken++] = 2;
Type[nToken] = XPRS_TOK_COL;
Value[nToken++] = nSide + i;
Type[nToken] = XPRS_TOK_OP;
Value[nToken++] = XPRS_OP_MULTIPLY;
Type[nToken] = XPRS_TOK_COL;
Value[nToken++] = nSide + j;
Type[nToken] = XPRS_TOK_OP;
Value[nToken++] = XPRS_OP_MULTIPLY;
Type[nToken] = XPRS_TOK_RB;
Value[nToken++] = 0;
Type[nToken] = XPRS_TOK_COL;
Value[nToken++] = j;
Type[nToken] = XPRS_TOK_COL;
Value[nToken++] = i;
Type[nToken] = XPRS_TOK_OP;
Value[nToken++] = XPRS_OP_MINUS;
Type[nToken] = XPRS_TOK_IFUN;
Value[nToken++] = XPRS_IFUN_COS;
Type[nToken] = XPRS_TOK_OP;
Value[nToken++] = XPRS_OP_MULTIPLY;
Type[nToken] = XPRS_TOK_OP;
Value[nToken++] = XPRS_OP_MINUS;
Type[nToken] = XPRS_TOK_EOF;
Value[nToken++] = 0;
}
}
FormulaStart[nCoef] = nToken;

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

CHECK_XPRSCALL(XPRSnlpsetinitval(xprob, nCol - 1, &ColIndex[1], &InitialValue[1]));

CHECK_XPRSCALL(XPRSchgobjsense(xprob, XPRS_OBJ_MAXIMIZE));

CHECK_XPRSCALL(XPRSoptimize(xprob, "", NULL, NULL));

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) {
int errorcode;
char errorMessage[512];
XPRSgetintattrib(xprob, XPRS_ERRORCODE, &errorcode);
XPRSgetlasterror(xprob, errorMessage);
fprintf(stderr, "Optimizer returned error code '%i' with message:\n%s\n", errorcode, errorMessage);
}
}

XPRSdestroyprob(xprob);
XPRSfree();
return(ReturnValue);
}

void XPRS_CC Message(XPRSprob 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;
}
}