/* Name:       diet.c
** Author:     Leo Liberti
** Purpose:    diet problem
** Source:     C
** History:    060220 work started
*/

// standard include files
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <string.h>
#include <ilcplex/cplex.h>
#include <assert.h>

// maximum length of variable/constraint names
#define MAXNAME 64

void AddConstraint(CPXENVptr env, CPXLPptr lp, int nz, 
		   double* coeffs, int* ind, char sense, double rhs) {
  int status = 0;
  // add constraints in row-wise sparse format
  int rmatbeg[2];
  // nonzeroes stored in rmatval starting at position:
  rmatbeg[0] = 0;
  // nonzeroes stored in rmatval ending at position:
  rmatbeg[1] = nz-1;
  // create the constraints
  status = CPXaddrows(env, lp, 0, 1, nz, &rhs, &sense, 
		      rmatbeg, ind, coeffs, NULL, NULL);
  if (status != 0) {
    fprintf(stderr, "api: could not create constraints, error %d\n", status);
    exit(3);
  }
}

int main(int argc, char** argv) {

  // return code
  int ret = 0;
  // status code returned by cplex callable library functions
  int status = 0;
  // number of rows (constraints)
  int m = 0;
  // number of columns (variables)
  int n = 0;
  // cplex environment to pass to/from cplex callable library
  CPXENVptr env = NULL;
  // cplex linear program to pass to/from cplex callable library
  CPXLPptr  lp  = NULL;
  // use for storing error messages returned by CPLEX
  char errmsg[1024];
  // counters
  int i, j;

  // try to initialize the CPLEX environment 
  env = CPXopenCPLEX(&status);
  if (env == NULL) {
    fprintf(stderr, "%s: could not open CPLEX environment\n", argv[0]);
    CPXgeterrorstring (env, status, errmsg);
    fprintf (stderr, "%s", errmsg);
    exit(2);
  }

  // turn on output to screen
  status = CPXsetintparam(env, CPX_PARAM_SCRIND, CPX_ON);
  status = CPXsetintparam (env, CPX_PARAM_SIMDISPLAY, 2);
  if (status != 0) {
    fprintf(stderr, "%s: could not turn on screen indicator, error %d\n", 
	    argv[0], status);
    exit(3);
  }

  // create the problem max{x1+x2 | x1+2x2<=2, 2x1+x2<=2, x>= 0}
  lp = CPXcreateprob(env, &status, "diet");
  if (lp == NULL) {
    fprintf(stderr, "%s: failed to create problem\n");
    exit(4);
  }

  // size of the problem
  n = 9;
  m = 7;
  // constraint matrix
  double A[][9] = { { 510, 370, 500, 370, 400, 220, 345, 110, 80},
		     { 34, 35, 42, 38, 42, 26, 27, 12, 20},
		     { 28, 24, 25, 14, 31, 3,  15, 9,  1},
		     { 15, 15, 6,  2,  8 , 0,  4 , 10, 2},
		     {  6, 10, 2,  0,  15, 15, 0 , 4,  120},
		     { 30, 20, 25, 15, 15, 0,  20, 30, 2},
		     { 20, 20, 20, 10, 8 , 2,  15, 0,  2} } ;
  // food prices
  double c[9] = { 1.84, 2.19, 1.84, 1.44, 2.29, 0.77, 1.29, 0.60, 0.72 };

  // nutrient requirements
  double b[7] = { 2000, 350, 55, 100, 100, 100, 100 };

  // create the variables
  status = CPXnewcols(env, lp, n, c, NULL, NULL, NULL, NULL);
  if (status != 0) {
    fprintf(stderr, "%s: could not create variables, error %d\n", 
	    argv[0], status);
    exit(3);
  }

  // add constraints
  int theind[] = { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 };
  for(i = 0; i < m; i++) {
    AddConstraint(env, lp, n, A[i], theind, 'G', b[i]);
  }

  // select the optimization algorithm
  status = CPXsetintparam(env, CPX_PARAM_LPMETHOD, CPX_ALG_AUTOMATIC);
  if (status != 0) {
    fprintf(stderr, "%s: could not select optimization algorithm, error %d\n", 
	    argv[0], status);
    exit(3);
  }

  // optimize
  status = CPXlpopt(env, lp);
  if (status != 0) {
    fprintf(stderr, "%s: failed to call optimization algorithm\n", argv[0]);
    exit(10);
  }

  // get solution information
  // value of the objective function
  double objval = 0;
  // values of the primal problem variables
  double *x = (double*) malloc(n * sizeof(double));
  for(j = 0; j < n; j++) {
    x[j] = 0.0;
  }
  // values of the dual problem variables
  double *y = (double*) malloc(m * sizeof(double));
  for(i = 0; i < m; i++) {
    y[i] = 0.0;
  }
  // values of the slack variables
  double *s = (double*) malloc(m * sizeof(double));
  for(i = 0; i < m; i++) {
    s[i] = 0.0;
  }
  // reduced costs
  double *rc = (double*) malloc(n * sizeof(double));
  for(j = 0; j < n; j++) {
    rc[j] = 0.0;
  }  
  CPXsolution(env, lp, &status, &objval, x, y, s, rc);

  // print solution
  printf("%s: solution of problem \"diet\":\n", argv[0]);
  printf("  solver return status = %d\n", status);
  printf("  optimal objective function value = %f\n", objval);
  printf("  optimal primal variables:\n  ( ");
  for(j = 0; j < n; j++) {
    printf("%f ", x[j]);
  }
  printf(")\n");
  printf("  optimal dual variables:\n  ( ");
  for(i = 0; i < m; i++) {
    printf("%f ", y[i]);
  }
  printf(")\n");
  printf("  optimal slack variables:\n  ( ");
  for(i = 0; i < m; i++) {
    printf("%f ", y[i]);
  }
  printf(")\n");

  // free storage
  CPXfreeprob(env, &lp);
  free(rc);
  free(s);
  free(y);
  free(x);
  return ret;

}