wolffd@0: /***********************************************************************/
wolffd@0: /*                                                                     */
wolffd@0: /*   svm_hideo.c                                                       */
wolffd@0: /*                                                                     */
wolffd@0: /*   The Hildreth and D'Espo solver specialized for SVMs.              */
wolffd@0: /*                                                                     */
wolffd@0: /*   Author: Thorsten Joachims                                         */
wolffd@0: /*   Date: 02.07.02                                                    */
wolffd@0: /*                                                                     */
wolffd@0: /*   Copyright (c) 2002  Thorsten Joachims - All rights reserved       */
wolffd@0: /*                                                                     */
wolffd@0: /*   This software is available for non-commercial use only. It must   */
wolffd@0: /*   not be modified and distributed without prior permission of the   */
wolffd@0: /*   author. The author is not responsible for implications from the   */
wolffd@0: /*   use of this software.                                             */
wolffd@0: /*                                                                     */
wolffd@0: /***********************************************************************/
wolffd@0: 
wolffd@0: # include <math.h>
wolffd@0: # include "svm_common.h"
wolffd@0: 
wolffd@0: /* 
wolffd@0:   solve the quadratic programming problem
wolffd@0:  
wolffd@0:   minimize   g0 * x + 1/2 x' * G * x
wolffd@0:   subject to ce*x = ce0
wolffd@0:              l <= x <= u
wolffd@0:  
wolffd@0:   The linear constraint vector ce can only have -1/+1 as entries 
wolffd@0: */
wolffd@0: 
wolffd@0: /* Common Block Declarations */
wolffd@0: 
wolffd@0: long verbosity;
wolffd@0: 
wolffd@0: # define PRIMAL_OPTIMAL      1
wolffd@0: # define DUAL_OPTIMAL        2
wolffd@0: # define MAXITER_EXCEEDED    3
wolffd@0: # define NAN_SOLUTION        4
wolffd@0: # define ONLY_ONE_VARIABLE   5
wolffd@0: 
wolffd@0: # define LARGEROUND          0
wolffd@0: # define SMALLROUND          1
wolffd@0: 
wolffd@0: /* /////////////////////////////////////////////////////////////// */
wolffd@0: 
wolffd@0: # define DEF_PRECISION          1E-5
wolffd@0: # define DEF_MAX_ITERATIONS     200
wolffd@0: # define DEF_LINDEP_SENSITIVITY 1E-8
wolffd@0: # define EPSILON_HIDEO          1E-20
wolffd@0: # define EPSILON_EQ             1E-5
wolffd@0: 
wolffd@0: double *optimize_qp(QP *, double *, long, double *, LEARN_PARM *);
wolffd@0: double *primal=0,*dual=0;
wolffd@0: long   precision_violations=0;
wolffd@0: double opt_precision=DEF_PRECISION;
wolffd@0: long   maxiter=DEF_MAX_ITERATIONS;
wolffd@0: double lindep_sensitivity=DEF_LINDEP_SENSITIVITY;
wolffd@0: double *buffer;
wolffd@0: long   *nonoptimal;
wolffd@0: 
wolffd@0: long  smallroundcount=0;
wolffd@0: long  roundnumber=0;
wolffd@0: 
wolffd@0: /* /////////////////////////////////////////////////////////////// */
wolffd@0: 
wolffd@0: void *my_malloc();
wolffd@0: 
wolffd@0: int optimize_hildreth_despo(long,long,double,double,double,long,long,long,double,double *,
wolffd@0: 			    double *,double *,double *,double *,double *,
wolffd@0: 			    double *,double *,double *,long *,double *,double *);
wolffd@0: int solve_dual(long,long,double,double,long,double *,double *,double *,
wolffd@0: 	       double *,double *,double *,double *,double *,double *,
wolffd@0: 	       double *,double *,double *,double *,long);
wolffd@0: 
wolffd@0: void linvert_matrix(double *, long, double *, double, long *);
wolffd@0: void lprint_matrix(double *, long);
wolffd@0: void ladd_matrix(double *, long, double);
wolffd@0: void lcopy_matrix(double *, long, double *);
wolffd@0: void lswitch_rows_matrix(double *, long, long, long);
wolffd@0: void lswitchrk_matrix(double *, long, long, long);
wolffd@0: 
wolffd@0: double calculate_qp_objective(long, double *, double *, double *);
wolffd@0: 
wolffd@0: 
wolffd@0: 
wolffd@0: double *optimize_qp(qp,epsilon_crit,nx,threshold,learn_parm)
wolffd@0: QP *qp;
wolffd@0: double *epsilon_crit;
wolffd@0: long nx; /* Maximum number of variables in QP */
wolffd@0: double *threshold; 
wolffd@0: LEARN_PARM *learn_parm;
wolffd@0: /* start the optimizer and return the optimal values */
wolffd@0: /* The HIDEO optimizer does not necessarily fully solve the problem. */
wolffd@0: /* Since it requires a strictly positive definite hessian, the solution */
wolffd@0: /* is restricted to a linear independent subset in case the matrix is */
wolffd@0: /* only semi-definite. */
wolffd@0: {
wolffd@0:   long i,j;
wolffd@0:   int result;
wolffd@0:   double eq,progress;
wolffd@0: 
wolffd@0:   roundnumber++;
wolffd@0: 
wolffd@0:   if(!primal) { /* allocate memory at first call */
wolffd@0:     primal=(double *)my_malloc(sizeof(double)*nx);
wolffd@0:     dual=(double *)my_malloc(sizeof(double)*((nx+1)*2));
wolffd@0:     nonoptimal=(long *)my_malloc(sizeof(long)*(nx));
wolffd@0:     buffer=(double *)my_malloc(sizeof(double)*((nx+1)*2*(nx+1)*2+
wolffd@0: 					       nx*nx+2*(nx+1)*2+2*nx+1+2*nx+
wolffd@0: 					       nx+nx+nx*nx));
wolffd@0:     (*threshold)=0;
wolffd@0:     for(i=0;i<nx;i++) {
wolffd@0:       primal[i]=0;
wolffd@0:     }
wolffd@0:   }
wolffd@0: 
wolffd@0:   if(verbosity>=4) { /* really verbose */
wolffd@0:     printf("\n\n");
wolffd@0:     eq=qp->opt_ce0[0];
wolffd@0:     for(i=0;i<qp->opt_n;i++) {
wolffd@0:       eq+=qp->opt_xinit[i]*qp->opt_ce[i];
wolffd@0:       printf("%f: ",qp->opt_g0[i]);
wolffd@0:       for(j=0;j<qp->opt_n;j++) {
wolffd@0: 	printf("%f ",qp->opt_g[i*qp->opt_n+j]);
wolffd@0:       }
wolffd@0:       printf(": a=%.10f < %f",qp->opt_xinit[i],qp->opt_up[i]);
wolffd@0:       printf(": y=%f\n",qp->opt_ce[i]);
wolffd@0:     }
wolffd@0:     if(qp->opt_m) {
wolffd@0:       printf("EQ: %f*x0",qp->opt_ce[0]);
wolffd@0:       for(i=1;i<qp->opt_n;i++) {
wolffd@0: 	printf(" + %f*x%ld",qp->opt_ce[i],i);
wolffd@0:       }
wolffd@0:       printf(" = %f\n\n",-qp->opt_ce0[0]);
wolffd@0:     }
wolffd@0:   }
wolffd@0: 
wolffd@0:   result=optimize_hildreth_despo(qp->opt_n,qp->opt_m,
wolffd@0: 				 opt_precision,(*epsilon_crit),
wolffd@0: 				 learn_parm->epsilon_a,maxiter,
wolffd@0: 				 /* (long)PRIMAL_OPTIMAL, */
wolffd@0: 				 (long)0, (long)0,
wolffd@0: 				 lindep_sensitivity,
wolffd@0: 				 qp->opt_g,qp->opt_g0,qp->opt_ce,qp->opt_ce0,
wolffd@0: 				 qp->opt_low,qp->opt_up,primal,qp->opt_xinit,
wolffd@0: 				 dual,nonoptimal,buffer,&progress);
wolffd@0:   if(verbosity>=3) { 
wolffd@0:     printf("return(%d)...",result);
wolffd@0:   }
wolffd@0: 
wolffd@0:   if(learn_parm->totwords < learn_parm->svm_maxqpsize) { 
wolffd@0:     /* larger working sets will be linear dependent anyway */
wolffd@0:     learn_parm->svm_maxqpsize=maxl(learn_parm->totwords,(long)2);
wolffd@0:   }
wolffd@0: 
wolffd@0:   if(result == NAN_SOLUTION) {
wolffd@0:     lindep_sensitivity*=2;  /* throw out linear dependent examples more */
wolffd@0:                             /* generously */
wolffd@0:     if(learn_parm->svm_maxqpsize>2) {
wolffd@0:       learn_parm->svm_maxqpsize--;  /* decrease size of qp-subproblems */
wolffd@0:     }
wolffd@0:     precision_violations++;
wolffd@0:   }
wolffd@0: 
wolffd@0:   /* take one round of only two variable to get unstuck */
wolffd@0:   if((result != PRIMAL_OPTIMAL) || (!(roundnumber % 31)) || (progress <= 0)) {
wolffd@0: 
wolffd@0:     smallroundcount++;
wolffd@0: 
wolffd@0:     result=optimize_hildreth_despo(qp->opt_n,qp->opt_m,
wolffd@0: 				   opt_precision,(*epsilon_crit),
wolffd@0: 				   learn_parm->epsilon_a,(long)maxiter,
wolffd@0: 				   (long)PRIMAL_OPTIMAL,(long)SMALLROUND,
wolffd@0: 				   lindep_sensitivity,
wolffd@0: 				   qp->opt_g,qp->opt_g0,qp->opt_ce,qp->opt_ce0,
wolffd@0: 				   qp->opt_low,qp->opt_up,primal,qp->opt_xinit,
wolffd@0: 				   dual,nonoptimal,buffer,&progress);
wolffd@0:     if(verbosity>=3) { 
wolffd@0:       printf("return_srd(%d)...",result);
wolffd@0:     }
wolffd@0: 
wolffd@0:     if(result != PRIMAL_OPTIMAL) {
wolffd@0:       if(result != ONLY_ONE_VARIABLE) 
wolffd@0: 	precision_violations++;
wolffd@0:       if(result == MAXITER_EXCEEDED) 
wolffd@0: 	maxiter+=100;
wolffd@0:       if(result == NAN_SOLUTION) {
wolffd@0: 	lindep_sensitivity*=2;  /* throw out linear dependent examples more */
wolffd@0: 	                        /* generously */
wolffd@0: 	/* results not valid, so return inital values */
wolffd@0: 	for(i=0;i<qp->opt_n;i++) {
wolffd@0: 	  primal[i]=qp->opt_xinit[i];
wolffd@0: 	}
wolffd@0:       }
wolffd@0:     }
wolffd@0:   }
wolffd@0: 
wolffd@0: 
wolffd@0:   if(precision_violations > 50) {
wolffd@0:     precision_violations=0;
wolffd@0:     (*epsilon_crit)*=10.0; 
wolffd@0:     if(verbosity>=1) {
wolffd@0:       printf("\nWARNING: Relaxing epsilon on KT-Conditions (%f).\n",
wolffd@0: 	     (*epsilon_crit));
wolffd@0:     }
wolffd@0:   }	  
wolffd@0: 
wolffd@0:   if((qp->opt_m>0) && (result != NAN_SOLUTION) && (!isnan(dual[1]-dual[0])))
wolffd@0:     (*threshold)=dual[1]-dual[0];
wolffd@0:   else
wolffd@0:     (*threshold)=0;
wolffd@0: 
wolffd@0:   if(verbosity>=4) { /* really verbose */
wolffd@0:     printf("\n\n");
wolffd@0:     eq=qp->opt_ce0[0];
wolffd@0:     for(i=0;i<qp->opt_n;i++) {
wolffd@0:       eq+=primal[i]*qp->opt_ce[i];
wolffd@0:       printf("%f: ",qp->opt_g0[i]);
wolffd@0:       for(j=0;j<qp->opt_n;j++) {
wolffd@0: 	printf("%f ",qp->opt_g[i*qp->opt_n+j]);
wolffd@0:       }
wolffd@0:       printf(": a=%.30f",primal[i]);
wolffd@0:       printf(": nonopti=%ld",nonoptimal[i]);
wolffd@0:       printf(": y=%f\n",qp->opt_ce[i]);
wolffd@0:     }
wolffd@0:     printf("eq-constraint=%.30f\n",eq);
wolffd@0:     printf("b=%f\n",(*threshold));
wolffd@0:     printf(" smallroundcount=%ld ",smallroundcount);
wolffd@0:   }
wolffd@0: 
wolffd@0:   return(primal);
wolffd@0: }
wolffd@0: 
wolffd@0: 
wolffd@0: 
wolffd@0: int optimize_hildreth_despo(n,m,precision,epsilon_crit,epsilon_a,maxiter,goal,
wolffd@0: 			    smallround,lindep_sensitivity,g,g0,ce,ce0,low,up,
wolffd@0: 			    primal,init,dual,lin_dependent,buffer,progress)
wolffd@0:      long   n;            /* number of variables */
wolffd@0:      long   m;            /* number of linear equality constraints [0,1] */
wolffd@0:      double precision;    /* solve at least to this dual precision */
wolffd@0:      double epsilon_crit; /* stop, if KT-Conditions approx fulfilled */
wolffd@0:      double epsilon_a;    /* precision of alphas at bounds */
wolffd@0:      long   maxiter;      /* stop after this many iterations */
wolffd@0:      long   goal;         /* keep going until goal fulfilled */
wolffd@0:      long   smallround;   /* use only two variables of steepest descent */
wolffd@0:      double lindep_sensitivity; /* epsilon for detecting linear dependent ex */
wolffd@0:      double *g;           /* hessian of objective */
wolffd@0:      double *g0;          /* linear part of objective */
wolffd@0:      double *ce,*ce0;     /* linear equality constraints */
wolffd@0:      double *low,*up;     /* box constraints */
wolffd@0:      double *primal;      /* primal variables */
wolffd@0:      double *init;        /* initial values of primal */
wolffd@0:      double *dual;        /* dual variables */
wolffd@0:      long   *lin_dependent;
wolffd@0:      double *buffer;
wolffd@0:      double *progress;    /* delta in the objective function between
wolffd@0:                              before and after */
wolffd@0: {
wolffd@0:   long i,j,k,from,to,n_indep,changed;
wolffd@0:   double sum,bmin=0,bmax=0;
wolffd@0:   double *d,*d0,*ig,*dual_old,*temp,*start;       
wolffd@0:   double *g0_new,*g_new,*ce_new,*ce0_new,*low_new,*up_new;
wolffd@0:   double add,t;
wolffd@0:   int result;
wolffd@0:   double obj_before,obj_after; 
wolffd@0:   long b1,b2;
wolffd@0:   double g0_b1,g0_b2,ce0_b;
wolffd@0: 
wolffd@0:   g0_new=&(buffer[0]);    /* claim regions of buffer */
wolffd@0:   d=&(buffer[n]);
wolffd@0:   d0=&(buffer[n+(n+m)*2*(n+m)*2]);
wolffd@0:   ce_new=&(buffer[n+(n+m)*2*(n+m)*2+(n+m)*2]);
wolffd@0:   ce0_new=&(buffer[n+(n+m)*2*(n+m)*2+(n+m)*2+n]);
wolffd@0:   ig=&(buffer[n+(n+m)*2*(n+m)*2+(n+m)*2+n+m]);
wolffd@0:   dual_old=&(buffer[n+(n+m)*2*(n+m)*2+(n+m)*2+n+m+n*n]);
wolffd@0:   low_new=&(buffer[n+(n+m)*2*(n+m)*2+(n+m)*2+n+m+n*n+(n+m)*2]);
wolffd@0:   up_new=&(buffer[n+(n+m)*2*(n+m)*2+(n+m)*2+n+m+n*n+(n+m)*2+n]);
wolffd@0:   start=&(buffer[n+(n+m)*2*(n+m)*2+(n+m)*2+n+m+n*n+(n+m)*2+n+n]);
wolffd@0:   g_new=&(buffer[n+(n+m)*2*(n+m)*2+(n+m)*2+n+m+n*n+(n+m)*2+n+n+n]);
wolffd@0:   temp=&(buffer[n+(n+m)*2*(n+m)*2+(n+m)*2+n+m+n*n+(n+m)*2+n+n+n+n*n]);
wolffd@0: 
wolffd@0:   b1=-1;
wolffd@0:   b2=-1;
wolffd@0:   for(i=0;i<n;i++) {   /* get variables with steepest feasible descent */
wolffd@0:     sum=g0[i];         
wolffd@0:     for(j=0;j<n;j++) 
wolffd@0:       sum+=init[j]*g[i*n+j];
wolffd@0:     sum=sum*ce[i];
wolffd@0:     if(((b1==-1) || (sum<bmin)) 
wolffd@0:        && (!((init[i]<=(low[i]+epsilon_a)) && (ce[i]<0.0)))
wolffd@0:        && (!((init[i]>=( up[i]-epsilon_a)) && (ce[i]>0.0)))
wolffd@0:        ) {
wolffd@0:       bmin=sum;
wolffd@0:       b1=i;
wolffd@0:     }
wolffd@0:     if(((b2==-1) || (sum>=bmax)) 
wolffd@0:        && (!((init[i]<=(low[i]+epsilon_a)) && (ce[i]>0.0)))
wolffd@0:        && (!((init[i]>=( up[i]-epsilon_a)) && (ce[i]<0.0)))
wolffd@0:        ) {
wolffd@0:       bmax=sum;
wolffd@0:       b2=i;
wolffd@0:     }
wolffd@0:   }
wolffd@0:   /* in case of unbiased hyperplane, the previous projection on */
wolffd@0:   /* equality constraint can lead to b1 or b2 being -1. */
wolffd@0:   if((b1 == -1) || (b2 == -1)) {
wolffd@0:     b1=maxl(b1,b2);
wolffd@0:     b2=maxl(b1,b2);
wolffd@0:   }
wolffd@0: 
wolffd@0:   for(i=0;i<n;i++) {
wolffd@0:     start[i]=init[i];
wolffd@0:   }
wolffd@0: 
wolffd@0:   /* in case both example vectors are linearly dependent */
wolffd@0:   /* WARNING: Assumes that ce[] in {-1,1} */
wolffd@0:   add=0;
wolffd@0:   changed=0;
wolffd@0:   if((b1 != b2) && (m==1)) {
wolffd@0:     for(i=0;i<n;i++) {  /* fix other vectors */
wolffd@0:       if(i==b1) 
wolffd@0: 	g0_b1=g0[i];
wolffd@0:       if(i==b2) 
wolffd@0: 	g0_b2=g0[i];
wolffd@0:     }
wolffd@0:     ce0_b=ce0[0];
wolffd@0:     for(i=0;i<n;i++) {  
wolffd@0:       if((i!=b1) && (i!=b2)) {
wolffd@0: 	for(j=0;j<n;j++) {
wolffd@0: 	  if(j==b1) 
wolffd@0: 	    g0_b1+=start[i]*g[i*n+j];
wolffd@0: 	  if(j==b2) 
wolffd@0: 	    g0_b2+=start[i]*g[i*n+j];
wolffd@0: 	}
wolffd@0: 	ce0_b-=(start[i]*ce[i]);
wolffd@0:       }
wolffd@0:     }
wolffd@0:     if((g[b1*n+b2] == g[b1*n+b1]) && (g[b1*n+b2] == g[b2*n+b2])) {
wolffd@0:       /* printf("euqal\n"); */
wolffd@0:       if(ce[b1] == ce[b2]) { 
wolffd@0: 	if(g0_b1 <= g0_b2) { /* set b1 to upper bound */
wolffd@0: 	  /* printf("case +=<\n"); */
wolffd@0: 	  changed=1;
wolffd@0: 	  t=up[b1]-init[b1];
wolffd@0: 	  if((init[b2]-low[b2]) < t) {
wolffd@0: 	    t=init[b2]-low[b2];
wolffd@0: 	  }
wolffd@0: 	  start[b1]=init[b1]+t;
wolffd@0: 	  start[b2]=init[b2]-t;
wolffd@0: 	}
wolffd@0: 	else if(g0_b1 > g0_b2) { /* set b2 to upper bound */
wolffd@0: 	  /* printf("case +=>\n"); */
wolffd@0: 	  changed=1;
wolffd@0: 	  t=up[b2]-init[b2];
wolffd@0: 	  if((init[b1]-low[b1]) < t) {
wolffd@0: 	    t=init[b1]-low[b1];
wolffd@0: 	  }
wolffd@0: 	  start[b1]=init[b1]-t;
wolffd@0: 	  start[b2]=init[b2]+t;
wolffd@0: 	}
wolffd@0:       }
wolffd@0:       else if(((g[b1*n+b1]>0) || (g[b2*n+b2]>0))) { /* (ce[b1] != ce[b2]) */ 
wolffd@0: 	/* printf("case +!\n"); */
wolffd@0: 	t=((ce[b2]/ce[b1])*g0[b1]-g0[b2]+ce0[0]*(g[b1*n+b1]*ce[b2]/ce[b1]-g[b1*n+b2]/ce[b1]))/((ce[b2]*ce[b2]/(ce[b1]*ce[b1]))*g[b1*n+b1]+g[b2*n+b2]-2*(g[b1*n+b2]*ce[b2]/ce[b1]))-init[b2];
wolffd@0: 	changed=1;
wolffd@0: 	if((up[b2]-init[b2]) < t) {
wolffd@0: 	  t=up[b2]-init[b2];
wolffd@0: 	}
wolffd@0: 	if((init[b2]-low[b2]) < -t) {
wolffd@0: 	  t=-(init[b2]-low[b2]);
wolffd@0: 	}
wolffd@0: 	if((up[b1]-init[b1]) < t) {
wolffd@0: 	  t=(up[b1]-init[b1]);
wolffd@0: 	}
wolffd@0: 	if((init[b1]-low[b1]) < -t) {
wolffd@0: 	  t=-(init[b1]-low[b1]);
wolffd@0: 	}
wolffd@0: 	start[b1]=init[b1]+t;
wolffd@0: 	start[b2]=init[b2]+t;
wolffd@0:       }
wolffd@0:     }
wolffd@0:     if((-g[b1*n+b2] == g[b1*n+b1]) && (-g[b1*n+b2] == g[b2*n+b2])) {
wolffd@0:       /* printf("diffeuqal\n"); */
wolffd@0:       if(ce[b1] != ce[b2]) {
wolffd@0: 	if((g0_b1+g0_b2) < 0) { /* set b1 and b2 to upper bound */
wolffd@0: 	  /* printf("case -!<\n"); */
wolffd@0: 	  changed=1;
wolffd@0: 	  t=up[b1]-init[b1];
wolffd@0: 	  if((up[b2]-init[b2]) < t) {
wolffd@0: 	    t=up[b2]-init[b2];
wolffd@0: 	  }
wolffd@0: 	  start[b1]=init[b1]+t;
wolffd@0: 	  start[b2]=init[b2]+t;
wolffd@0: 	}     
wolffd@0: 	else if((g0_b1+g0_b2) >= 0) { /* set b1 and b2 to lower bound */
wolffd@0: 	  /* printf("case -!>\n"); */
wolffd@0: 	  changed=1;
wolffd@0: 	  t=init[b1]-low[b1];
wolffd@0: 	  if((init[b2]-low[b2]) < t) {
wolffd@0: 	    t=init[b2]-low[b2];
wolffd@0: 	  }
wolffd@0: 	  start[b1]=init[b1]-t;
wolffd@0: 	  start[b2]=init[b2]-t;
wolffd@0: 	}
wolffd@0:       }
wolffd@0:       else if(((g[b1*n+b1]>0) || (g[b2*n+b2]>0))) { /* (ce[b1]==ce[b2]) */
wolffd@0: 	/*  printf("case -=\n"); */
wolffd@0: 	t=((ce[b2]/ce[b1])*g0[b1]-g0[b2]+ce0[0]*(g[b1*n+b1]*ce[b2]/ce[b1]-g[b1*n+b2]/ce[b1]))/((ce[b2]*ce[b2]/(ce[b1]*ce[b1]))*g[b1*n+b1]+g[b2*n+b2]-2*(g[b1*n+b2]*ce[b2]/ce[b1]))-init[b2];
wolffd@0: 	changed=1;
wolffd@0: 	if((up[b2]-init[b2]) < t) {
wolffd@0: 	  t=up[b2]-init[b2];
wolffd@0: 	}
wolffd@0: 	if((init[b2]-low[b2]) < -t) {
wolffd@0: 	  t=-(init[b2]-low[b2]);
wolffd@0: 	}
wolffd@0: 	if((up[b1]-init[b1]) < -t) {
wolffd@0: 	  t=-(up[b1]-init[b1]);
wolffd@0: 	}
wolffd@0: 	if((init[b1]-low[b1]) < t) {
wolffd@0: 	  t=init[b1]-low[b1];
wolffd@0: 	}
wolffd@0: 	start[b1]=init[b1]-t;
wolffd@0: 	start[b2]=init[b2]+t;
wolffd@0:       }	
wolffd@0:     }
wolffd@0:   }
wolffd@0:   /* if we have a biased hyperplane, then adding a constant to the */
wolffd@0:   /* hessian does not change the solution. So that is done for examples */
wolffd@0:   /* with zero diagonal entry, since HIDEO cannot handle them. */
wolffd@0:   if((m>0) 
wolffd@0:      && ((fabs(g[b1*n+b1]) < lindep_sensitivity) 
wolffd@0: 	 || (fabs(g[b2*n+b2]) < lindep_sensitivity))) {
wolffd@0:     /* printf("Case 0\n"); */
wolffd@0:     add+=0.093274;
wolffd@0:   }    
wolffd@0:   /* in case both examples are linear dependent */
wolffd@0:   else if((m>0) 
wolffd@0: 	  && (g[b1*n+b2] != 0 && g[b2*n+b2] != 0)
wolffd@0: 	  && (fabs(g[b1*n+b1]/g[b1*n+b2] - g[b1*n+b2]/g[b2*n+b2])
wolffd@0: 	      < lindep_sensitivity)) { 
wolffd@0:     /* printf("Case lindep\n"); */
wolffd@0:     add+=0.078274;
wolffd@0:   }
wolffd@0: 
wolffd@0:   /* special case for zero diagonal entry on unbiased hyperplane */
wolffd@0:   if((m==0) && (b1>=0))  {
wolffd@0:     if(fabs(g[b1*n+b1]) < lindep_sensitivity) { 
wolffd@0:       /* printf("Case 0b1\n"); */
wolffd@0:       for(i=0;i<n;i++) {  /* fix other vectors */
wolffd@0: 	if(i==b1) 
wolffd@0: 	  g0_b1=g0[i];
wolffd@0:       }
wolffd@0:       for(i=0;i<n;i++) {  
wolffd@0: 	if(i!=b1) {
wolffd@0: 	  for(j=0;j<n;j++) {
wolffd@0: 	    if(j==b1) 
wolffd@0: 	      g0_b1+=start[i]*g[i*n+j];
wolffd@0: 	  }
wolffd@0: 	}
wolffd@0:       }
wolffd@0:       if(g0_b1<0)
wolffd@0: 	start[b1]=up[b1];
wolffd@0:       if(g0_b1>=0)
wolffd@0: 	start[b1]=low[b1];
wolffd@0:     }
wolffd@0:   }
wolffd@0:   if((m==0) && (b2>=0))  {
wolffd@0:     if(fabs(g[b2*n+b2]) < lindep_sensitivity) { 
wolffd@0:       /* printf("Case 0b2\n"); */
wolffd@0:       for(i=0;i<n;i++) {  /* fix other vectors */
wolffd@0: 	if(i==b2) 
wolffd@0: 	  g0_b2=g0[i];
wolffd@0:       }
wolffd@0:       for(i=0;i<n;i++) {  
wolffd@0: 	if(i!=b2) {
wolffd@0: 	  for(j=0;j<n;j++) {
wolffd@0: 	    if(j==b2) 
wolffd@0: 	      g0_b2+=start[i]*g[i*n+j];
wolffd@0: 	  }
wolffd@0: 	}
wolffd@0:       }
wolffd@0:       if(g0_b2<0)
wolffd@0: 	start[b2]=up[b2];
wolffd@0:       if(g0_b2>=0)
wolffd@0: 	start[b2]=low[b2];
wolffd@0:     }
wolffd@0:   }
wolffd@0: 
wolffd@0:   /* printf("b1=%ld,b2=%ld\n",b1,b2); */
wolffd@0: 
wolffd@0:   lcopy_matrix(g,n,d);
wolffd@0:   if((m==1) && (add>0.0)) {
wolffd@0:     for(j=0;j<n;j++) {
wolffd@0:       for(k=0;k<n;k++) {
wolffd@0: 	d[j*n+k]+=add*ce[j]*ce[k];
wolffd@0:       }
wolffd@0:     }
wolffd@0:   }
wolffd@0:   else {
wolffd@0:     add=0.0;
wolffd@0:   }
wolffd@0: 
wolffd@0:   if(n>2) {                    /* switch, so that variables are better mixed */
wolffd@0:     lswitchrk_matrix(d,n,b1,(long)0); 
wolffd@0:     if(b2 == 0) 
wolffd@0:       lswitchrk_matrix(d,n,b1,(long)1); 
wolffd@0:     else
wolffd@0:       lswitchrk_matrix(d,n,b2,(long)1); 
wolffd@0:   }
wolffd@0:   if(smallround == SMALLROUND) {
wolffd@0:     for(i=2;i<n;i++) {
wolffd@0:       lin_dependent[i]=1;
wolffd@0:     }
wolffd@0:     if(m>0) { /* for biased hyperplane, pick two variables */
wolffd@0:       lin_dependent[0]=0;
wolffd@0:       lin_dependent[1]=0;
wolffd@0:     }
wolffd@0:     else {    /* for unbiased hyperplane, pick only one variable */
wolffd@0:       lin_dependent[0]=smallroundcount % 2;
wolffd@0:       lin_dependent[1]=(smallroundcount+1) % 2;
wolffd@0:     }
wolffd@0:   }
wolffd@0:   else {
wolffd@0:     for(i=0;i<n;i++) {
wolffd@0:       lin_dependent[i]=0;
wolffd@0:     }
wolffd@0:   }
wolffd@0:   linvert_matrix(d,n,ig,lindep_sensitivity,lin_dependent);
wolffd@0:   if(n>2) {                    /* now switch back */
wolffd@0:     if(b2 == 0) {
wolffd@0:       lswitchrk_matrix(ig,n,b1,(long)1); 
wolffd@0:       i=lin_dependent[1];  
wolffd@0:       lin_dependent[1]=lin_dependent[b1];
wolffd@0:       lin_dependent[b1]=i;
wolffd@0:     }
wolffd@0:     else {
wolffd@0:       lswitchrk_matrix(ig,n,b2,(long)1); 
wolffd@0:       i=lin_dependent[1];  
wolffd@0:       lin_dependent[1]=lin_dependent[b2];
wolffd@0:       lin_dependent[b2]=i;
wolffd@0:     }
wolffd@0:     lswitchrk_matrix(ig,n,b1,(long)0); 
wolffd@0:     i=lin_dependent[0];  
wolffd@0:     lin_dependent[0]=lin_dependent[b1];
wolffd@0:     lin_dependent[b1]=i;
wolffd@0:   }
wolffd@0:   /* lprint_matrix(d,n); */
wolffd@0:   /* lprint_matrix(ig,n); */
wolffd@0: 
wolffd@0:   lcopy_matrix(g,n,g_new);   /* restore g_new matrix */
wolffd@0:   if(add>0)
wolffd@0:     for(j=0;j<n;j++) {
wolffd@0:       for(k=0;k<n;k++) {
wolffd@0: 	g_new[j*n+k]+=add*ce[j]*ce[k];
wolffd@0:       }
wolffd@0:     }
wolffd@0: 
wolffd@0:   for(i=0;i<n;i++) {  /* fix linear dependent vectors */
wolffd@0:     g0_new[i]=g0[i]+add*ce0[0]*ce[i];
wolffd@0:   }
wolffd@0:   if(m>0) ce0_new[0]=-ce0[0];
wolffd@0:   for(i=0;i<n;i++) {  /* fix linear dependent vectors */
wolffd@0:     if(lin_dependent[i]) {
wolffd@0:       for(j=0;j<n;j++) {
wolffd@0: 	if(!lin_dependent[j]) {
wolffd@0: 	  g0_new[j]+=start[i]*g_new[i*n+j];
wolffd@0: 	}
wolffd@0:       }
wolffd@0:       if(m>0) ce0_new[0]-=(start[i]*ce[i]);
wolffd@0:     }
wolffd@0:   }
wolffd@0:   from=0;   /* remove linear dependent vectors */
wolffd@0:   to=0;
wolffd@0:   n_indep=0;
wolffd@0:   for(i=0;i<n;i++) {
wolffd@0:     if(!lin_dependent[i]) {
wolffd@0:       g0_new[n_indep]=g0_new[i];
wolffd@0:       ce_new[n_indep]=ce[i]; 
wolffd@0:       low_new[n_indep]=low[i];
wolffd@0:       up_new[n_indep]=up[i];
wolffd@0:       primal[n_indep]=start[i];
wolffd@0:       n_indep++;
wolffd@0:     }
wolffd@0:     for(j=0;j<n;j++) {
wolffd@0:       if((!lin_dependent[i]) && (!lin_dependent[j])) {
wolffd@0:         ig[to]=ig[from];
wolffd@0:         g_new[to]=g_new[from];
wolffd@0: 	to++;
wolffd@0:       }
wolffd@0:       from++;
wolffd@0:     }
wolffd@0:   }
wolffd@0: 
wolffd@0:   if(verbosity>=3) {
wolffd@0:     printf("real_qp_size(%ld)...",n_indep);
wolffd@0:   }
wolffd@0:   
wolffd@0:   /* cannot optimize with only one variable */
wolffd@0:   if((n_indep<=1) && (m>0) && (!changed)) { 
wolffd@0:     for(i=n-1;i>=0;i--) {
wolffd@0:       primal[i]=init[i];
wolffd@0:     }
wolffd@0:     return((int)ONLY_ONE_VARIABLE);
wolffd@0:   }
wolffd@0: 
wolffd@0:   if((!changed) || (n_indep>1)) { 
wolffd@0:     result=solve_dual(n_indep,m,precision,epsilon_crit,maxiter,g_new,g0_new,
wolffd@0: 		      ce_new,ce0_new,low_new,up_new,primal,d,d0,ig,
wolffd@0: 		      dual,dual_old,temp,goal);
wolffd@0:   }
wolffd@0:   else {
wolffd@0:     result=PRIMAL_OPTIMAL;
wolffd@0:   }
wolffd@0:   
wolffd@0:   j=n_indep;
wolffd@0:   for(i=n-1;i>=0;i--) {
wolffd@0:     if(!lin_dependent[i]) {
wolffd@0:       j--;
wolffd@0:       primal[i]=primal[j];
wolffd@0:     }
wolffd@0:     else {
wolffd@0:       primal[i]=start[i];  /* leave as is */
wolffd@0:     }
wolffd@0:     temp[i]=primal[i];
wolffd@0:   }
wolffd@0:    
wolffd@0:   obj_before=calculate_qp_objective(n,g,g0,init);
wolffd@0:   obj_after=calculate_qp_objective(n,g,g0,primal);
wolffd@0:   (*progress)=obj_before-obj_after;
wolffd@0:   if(verbosity>=3) {
wolffd@0:     printf("before(%.30f)...after(%.30f)...result_sd(%d)...",
wolffd@0: 	   obj_before,obj_after,result); 
wolffd@0:   }
wolffd@0: 
wolffd@0:   return((int)result);
wolffd@0: }
wolffd@0: 
wolffd@0: 
wolffd@0: int solve_dual(n,m,precision,epsilon_crit,maxiter,g,g0,ce,ce0,low,up,primal,
wolffd@0: 	       d,d0,ig,dual,dual_old,temp,goal)
wolffd@0:      /* Solves the dual using the method of Hildreth and D'Espo. */
wolffd@0:      /* Can only handle problems with zero or exactly one */
wolffd@0:      /* equality constraints. */
wolffd@0: 
wolffd@0:      long   n;            /* number of variables */
wolffd@0:      long   m;            /* number of linear equality constraints */
wolffd@0:      double precision;    /* solve at least to this dual precision */
wolffd@0:      double epsilon_crit; /* stop, if KT-Conditions approx fulfilled */
wolffd@0:      long   maxiter;      /* stop after that many iterations */
wolffd@0:      double *g;
wolffd@0:      double *g0;          /* linear part of objective */
wolffd@0:      double *ce,*ce0;     /* linear equality constraints */
wolffd@0:      double *low,*up;     /* box constraints */
wolffd@0:      double *primal;      /* variables (with initial values) */
wolffd@0:      double *d,*d0,*ig,*dual,*dual_old,*temp;       /* buffer  */
wolffd@0:      long goal;
wolffd@0: {
wolffd@0:   long i,j,k,iter;
wolffd@0:   double sum,w,maxviol,viol,temp1,temp2,isnantest;
wolffd@0:   double model_b,dist;
wolffd@0:   long retrain,maxfaktor,primal_optimal=0,at_bound,scalemaxiter;
wolffd@0:   double epsilon_a=1E-15,epsilon_hideo;
wolffd@0:   double eq; 
wolffd@0: 
wolffd@0:   if((m<0) || (m>1)) 
wolffd@0:     perror("SOLVE DUAL: inappropriate number of eq-constrains!");
wolffd@0: 
wolffd@0:   /*  
wolffd@0:   printf("\n");
wolffd@0:   for(i=0;i<n;i++) {
wolffd@0:     printf("%f: ",g0[i]);
wolffd@0:     for(j=0;j<n;j++) {
wolffd@0:       printf("%f ",g[i*n+j]);
wolffd@0:     }
wolffd@0:     printf(": a=%.30f",primal[i]);
wolffd@0:     printf(": y=%f\n",ce[i]);
wolffd@0:   }
wolffd@0:   */
wolffd@0: 
wolffd@0:   for(i=0;i<2*(n+m);i++) {
wolffd@0:     dual[i]=0;
wolffd@0:     dual_old[i]=0;
wolffd@0:   }
wolffd@0:   for(i=0;i<n;i++) {   
wolffd@0:     for(j=0;j<n;j++) {   /* dual hessian for box constraints */
wolffd@0:       d[i*2*(n+m)+j]=ig[i*n+j];
wolffd@0:       d[(i+n)*2*(n+m)+j]=-ig[i*n+j];
wolffd@0:       d[i*2*(n+m)+j+n]=-ig[i*n+j];
wolffd@0:       d[(i+n)*2*(n+m)+j+n]=ig[i*n+j];
wolffd@0:     }
wolffd@0:     if(m>0) {
wolffd@0:       sum=0;              /* dual hessian for eq constraints */
wolffd@0:       for(j=0;j<n;j++) {
wolffd@0: 	sum+=(ce[j]*ig[i*n+j]);
wolffd@0:       }
wolffd@0:       d[i*2*(n+m)+2*n]=sum;
wolffd@0:       d[i*2*(n+m)+2*n+1]=-sum;
wolffd@0:       d[(n+i)*2*(n+m)+2*n]=-sum;
wolffd@0:       d[(n+i)*2*(n+m)+2*n+1]=sum;
wolffd@0:       d[(n+n)*2*(n+m)+i]=sum;
wolffd@0:       d[(n+n+1)*2*(n+m)+i]=-sum;
wolffd@0:       d[(n+n)*2*(n+m)+(n+i)]=-sum;
wolffd@0:       d[(n+n+1)*2*(n+m)+(n+i)]=sum;
wolffd@0:       
wolffd@0:       sum=0;
wolffd@0:       for(j=0;j<n;j++) {
wolffd@0: 	for(k=0;k<n;k++) {
wolffd@0: 	  sum+=(ce[k]*ce[j]*ig[j*n+k]);
wolffd@0: 	}
wolffd@0:       }
wolffd@0:       d[(n+n)*2*(n+m)+2*n]=sum;
wolffd@0:       d[(n+n)*2*(n+m)+2*n+1]=-sum;
wolffd@0:       d[(n+n+1)*2*(n+m)+2*n]=-sum;
wolffd@0:       d[(n+n+1)*2*(n+m)+2*n+1]=sum;
wolffd@0:     } 
wolffd@0:   }
wolffd@0: 
wolffd@0:   for(i=0;i<n;i++) {   /* dual linear component for the box constraints */
wolffd@0:     w=0;
wolffd@0:     for(j=0;j<n;j++) {
wolffd@0:       w+=(ig[i*n+j]*g0[j]); 
wolffd@0:     }
wolffd@0:     d0[i]=up[i]+w;
wolffd@0:     d0[i+n]=-low[i]-w;
wolffd@0:   }
wolffd@0: 
wolffd@0:   if(m>0) {  
wolffd@0:     sum=0;             /* dual linear component for eq constraints */
wolffd@0:     for(j=0;j<n;j++) {
wolffd@0:       for(k=0;k<n;k++) {
wolffd@0: 	sum+=(ce[k]*ig[k*n+j]*g0[j]); 
wolffd@0:       }
wolffd@0:     }
wolffd@0:     d0[2*n]=ce0[0]+sum;
wolffd@0:     d0[2*n+1]=-ce0[0]-sum;
wolffd@0:   }
wolffd@0: 
wolffd@0:   maxviol=999999;
wolffd@0:   iter=0;
wolffd@0:   retrain=1;
wolffd@0:   maxfaktor=1;
wolffd@0:   scalemaxiter=maxiter/5;
wolffd@0:   while((retrain) && (maxviol > 0) && (iter < (scalemaxiter*maxfaktor))) {
wolffd@0:     iter++;
wolffd@0:     
wolffd@0:     while((maxviol > precision) && (iter < (scalemaxiter*maxfaktor))) {
wolffd@0:       iter++;
wolffd@0:       maxviol=0;
wolffd@0:       for(i=0;i<2*(n+m);i++) {
wolffd@0: 	sum=d0[i];
wolffd@0: 	for(j=0;j<2*(n+m);j++) {
wolffd@0: 	  sum+=d[i*2*(n+m)+j]*dual_old[j];
wolffd@0: 	}
wolffd@0: 	sum-=d[i*2*(n+m)+i]*dual_old[i];
wolffd@0: 	dual[i]=-sum/d[i*2*(n+m)+i];
wolffd@0: 	if(dual[i]<0) dual[i]=0;
wolffd@0: 	
wolffd@0: 	viol=fabs(dual[i]-dual_old[i]);
wolffd@0: 	if(viol>maxviol) 
wolffd@0: 	  maxviol=viol;
wolffd@0: 	dual_old[i]=dual[i];
wolffd@0:       }
wolffd@0:       /*
wolffd@0:       printf("%d) maxviol=%20f precision=%f\n",iter,maxviol,precision); 
wolffd@0:       */
wolffd@0:     }
wolffd@0:   
wolffd@0:     if(m>0) {
wolffd@0:       for(i=0;i<n;i++) {
wolffd@0: 	temp[i]=dual[i]-dual[i+n]+ce[i]*(dual[n+n]-dual[n+n+1])+g0[i];
wolffd@0:       }
wolffd@0:     } 
wolffd@0:     else {
wolffd@0:       for(i=0;i<n;i++) {
wolffd@0: 	temp[i]=dual[i]-dual[i+n]+g0[i];
wolffd@0:       }
wolffd@0:     }
wolffd@0:     for(i=0;i<n;i++) {
wolffd@0:       primal[i]=0;             /* calc value of primal variables */
wolffd@0:       for(j=0;j<n;j++) {
wolffd@0: 	primal[i]+=ig[i*n+j]*temp[j];
wolffd@0:       }
wolffd@0:       primal[i]*=-1.0;
wolffd@0:       if(primal[i]<=(low[i])) {  /* clip conservatively */
wolffd@0: 	primal[i]=low[i];
wolffd@0:       }
wolffd@0:       else if(primal[i]>=(up[i])) {
wolffd@0: 	primal[i]=up[i];
wolffd@0:       }
wolffd@0:     }
wolffd@0: 
wolffd@0:     if(m>0) 
wolffd@0:       model_b=dual[n+n+1]-dual[n+n];
wolffd@0:     else
wolffd@0:       model_b=0;
wolffd@0: 
wolffd@0:     epsilon_hideo=EPSILON_HIDEO;
wolffd@0:     for(i=0;i<n;i++) {           /* check precision of alphas */
wolffd@0:       dist=-model_b*ce[i]; 
wolffd@0:       dist+=(g0[i]+1.0);
wolffd@0:       for(j=0;j<i;j++) {
wolffd@0: 	dist+=(primal[j]*g[j*n+i]);
wolffd@0:       }
wolffd@0:       for(j=i;j<n;j++) {
wolffd@0: 	dist+=(primal[j]*g[i*n+j]);
wolffd@0:       }
wolffd@0:       if((primal[i]<(up[i]-epsilon_hideo)) && (dist < (1.0-epsilon_crit))) {
wolffd@0: 	epsilon_hideo=(up[i]-primal[i])*2.0;
wolffd@0:       }
wolffd@0:       else if((primal[i]>(low[i]+epsilon_hideo)) &&(dist>(1.0+epsilon_crit))) {
wolffd@0: 	epsilon_hideo=(primal[i]-low[i])*2.0;
wolffd@0:       }
wolffd@0:     }
wolffd@0:     /* printf("\nEPSILON_HIDEO=%.30f\n",epsilon_hideo); */
wolffd@0: 
wolffd@0:     for(i=0;i<n;i++) {           /* clip alphas to bounds */
wolffd@0:       if(primal[i]<=(low[i]+epsilon_hideo)) {
wolffd@0: 	primal[i]=low[i];
wolffd@0:       }
wolffd@0:       else if(primal[i]>=(up[i]-epsilon_hideo)) {
wolffd@0: 	primal[i]=up[i];
wolffd@0:       }
wolffd@0:     }
wolffd@0: 
wolffd@0:     retrain=0;
wolffd@0:     primal_optimal=1;
wolffd@0:     at_bound=0;
wolffd@0:     for(i=0;(i<n);i++) {  /* check primal KT-Conditions */
wolffd@0:       dist=-model_b*ce[i]; 
wolffd@0:       dist+=(g0[i]+1.0);
wolffd@0:       for(j=0;j<i;j++) {
wolffd@0: 	dist+=(primal[j]*g[j*n+i]);
wolffd@0:       }
wolffd@0:       for(j=i;j<n;j++) {
wolffd@0: 	dist+=(primal[j]*g[i*n+j]);
wolffd@0:       }
wolffd@0:       if((primal[i]<(up[i]-epsilon_a)) && (dist < (1.0-epsilon_crit))) {
wolffd@0: 	retrain=1;
wolffd@0: 	primal_optimal=0;
wolffd@0:       }
wolffd@0:       else if((primal[i]>(low[i]+epsilon_a)) && (dist > (1.0+epsilon_crit))) {
wolffd@0: 	retrain=1;
wolffd@0: 	primal_optimal=0;
wolffd@0:       }
wolffd@0:       if((primal[i]<=(low[i]+epsilon_a)) || (primal[i]>=(up[i]-epsilon_a))) {
wolffd@0: 	at_bound++;
wolffd@0:       }
wolffd@0:       /*    printf("HIDEOtemp: a[%ld]=%.30f, dist=%.6f, b=%f, at_bound=%ld\n",i,primal[i],dist,model_b,at_bound);  */
wolffd@0:     }
wolffd@0:     if(m>0) {
wolffd@0:       eq=-ce0[0];               /* check precision of eq-constraint */
wolffd@0:       for(i=0;i<n;i++) { 
wolffd@0: 	eq+=(ce[i]*primal[i]);
wolffd@0:       }
wolffd@0:       if((EPSILON_EQ < fabs(eq)) 
wolffd@0: 	 /*
wolffd@0: 	 && !((goal==PRIMAL_OPTIMAL) 
wolffd@0: 	       && (at_bound==n)) */
wolffd@0: 	 ) {
wolffd@0: 	retrain=1;
wolffd@0: 	primal_optimal=0;
wolffd@0:       }
wolffd@0:       /* printf("\n eq=%.30f ce0=%f at-bound=%ld\n",eq,ce0[0],at_bound);  */
wolffd@0:     }
wolffd@0: 
wolffd@0:     if(retrain) {
wolffd@0:       precision/=10;
wolffd@0:       if(((goal == PRIMAL_OPTIMAL) && (maxfaktor < 50000))
wolffd@0: 	 || (maxfaktor < 5)) {
wolffd@0: 	maxfaktor++;
wolffd@0:       }
wolffd@0:     }
wolffd@0:   }
wolffd@0: 
wolffd@0:   if(!primal_optimal) {
wolffd@0:     for(i=0;i<n;i++) {
wolffd@0:       primal[i]=0;             /* calc value of primal variables */
wolffd@0:       for(j=0;j<n;j++) {
wolffd@0: 	primal[i]+=ig[i*n+j]*temp[j];
wolffd@0:       }
wolffd@0:       primal[i]*=-1.0;
wolffd@0:       if(primal[i]<=(low[i]+epsilon_a)) {  /* clip conservatively */
wolffd@0: 	primal[i]=low[i];
wolffd@0:       }
wolffd@0:       else if(primal[i]>=(up[i]-epsilon_a)) {
wolffd@0: 	primal[i]=up[i];
wolffd@0:       }
wolffd@0:     }
wolffd@0:   }
wolffd@0: 
wolffd@0:   isnantest=0;
wolffd@0:   for(i=0;i<n;i++) {           /* check for isnan */
wolffd@0:     isnantest+=primal[i];
wolffd@0:   }
wolffd@0: 
wolffd@0:   if(m>0) {
wolffd@0:     temp1=dual[n+n+1];   /* copy the dual variables for the eq */
wolffd@0:     temp2=dual[n+n];     /* constraints to a handier location */
wolffd@0:     for(i=n+n+1;i>=2;i--) {
wolffd@0:       dual[i]=dual[i-2];
wolffd@0:     }
wolffd@0:     dual[0]=temp2;
wolffd@0:     dual[1]=temp1;
wolffd@0:     isnantest+=temp1+temp2;
wolffd@0:   }
wolffd@0: 
wolffd@0:   if(isnan(isnantest)) {
wolffd@0:     return((int)NAN_SOLUTION);
wolffd@0:   }
wolffd@0:   else if(primal_optimal) {
wolffd@0:     return((int)PRIMAL_OPTIMAL);
wolffd@0:   }
wolffd@0:   else if(maxviol == 0.0) {
wolffd@0:     return((int)DUAL_OPTIMAL);
wolffd@0:   }
wolffd@0:   else {
wolffd@0:     return((int)MAXITER_EXCEEDED);
wolffd@0:   }
wolffd@0: }
wolffd@0: 
wolffd@0: 
wolffd@0: void linvert_matrix(matrix,depth,inverse,lindep_sensitivity,lin_dependent)
wolffd@0: double *matrix;
wolffd@0: long depth;
wolffd@0: double *inverse,lindep_sensitivity;
wolffd@0: long *lin_dependent;  /* indicates the active parts of matrix on 
wolffd@0: 			 input and output*/
wolffd@0: {
wolffd@0:   long i,j,k;
wolffd@0:   double factor;
wolffd@0: 
wolffd@0:   for(i=0;i<depth;i++) {
wolffd@0:     /*    lin_dependent[i]=0; */
wolffd@0:     for(j=0;j<depth;j++) {
wolffd@0:       inverse[i*depth+j]=0.0;
wolffd@0:     }
wolffd@0:     inverse[i*depth+i]=1.0;
wolffd@0:   }
wolffd@0:   for(i=0;i<depth;i++) {
wolffd@0:     if(lin_dependent[i] || (fabs(matrix[i*depth+i])<lindep_sensitivity)) {
wolffd@0:       lin_dependent[i]=1;
wolffd@0:     }
wolffd@0:     else {
wolffd@0:       for(j=i+1;j<depth;j++) {
wolffd@0: 	factor=matrix[j*depth+i]/matrix[i*depth+i];
wolffd@0: 	for(k=i;k<depth;k++) {
wolffd@0: 	  matrix[j*depth+k]-=(factor*matrix[i*depth+k]);
wolffd@0: 	}
wolffd@0: 	for(k=0;k<depth;k++) {
wolffd@0: 	  inverse[j*depth+k]-=(factor*inverse[i*depth+k]);
wolffd@0: 	}
wolffd@0:       }
wolffd@0:     }
wolffd@0:   }
wolffd@0:   for(i=depth-1;i>=0;i--) {
wolffd@0:     if(!lin_dependent[i]) {
wolffd@0:       factor=1/matrix[i*depth+i];
wolffd@0:       for(k=0;k<depth;k++) {
wolffd@0: 	inverse[i*depth+k]*=factor;
wolffd@0:       }
wolffd@0:       matrix[i*depth+i]=1;
wolffd@0:       for(j=i-1;j>=0;j--) {
wolffd@0: 	factor=matrix[j*depth+i];
wolffd@0: 	matrix[j*depth+i]=0;
wolffd@0: 	for(k=0;k<depth;k++) {
wolffd@0: 	  inverse[j*depth+k]-=(factor*inverse[i*depth+k]);
wolffd@0: 	}
wolffd@0:       }
wolffd@0:     }
wolffd@0:   }
wolffd@0: }
wolffd@0: 
wolffd@0: void lprint_matrix(matrix,depth)
wolffd@0: double *matrix;
wolffd@0: long depth;
wolffd@0: {
wolffd@0:   long i,j;
wolffd@0:   for(i=0;i<depth;i++) {
wolffd@0:     for(j=0;j<depth;j++) {
wolffd@0:       printf("%5.2f ",(double)(matrix[i*depth+j]));
wolffd@0:     }
wolffd@0:     printf("\n");
wolffd@0:   }
wolffd@0:   printf("\n");
wolffd@0: }
wolffd@0: 
wolffd@0: void ladd_matrix(matrix,depth,scalar)
wolffd@0: double *matrix;
wolffd@0: long depth;
wolffd@0: double scalar;
wolffd@0: {
wolffd@0:   long i,j;
wolffd@0:   for(i=0;i<depth;i++) {
wolffd@0:     for(j=0;j<depth;j++) {
wolffd@0:       matrix[i*depth+j]+=scalar;
wolffd@0:     }
wolffd@0:   }
wolffd@0: }
wolffd@0: 
wolffd@0: void lcopy_matrix(matrix,depth,matrix2) 
wolffd@0: double *matrix;
wolffd@0: long depth;
wolffd@0: double *matrix2;
wolffd@0: {
wolffd@0:   long i;
wolffd@0:   
wolffd@0:   for(i=0;i<(depth)*(depth);i++) {
wolffd@0:     matrix2[i]=matrix[i];
wolffd@0:   }
wolffd@0: }
wolffd@0: 
wolffd@0: void lswitch_rows_matrix(matrix,depth,r1,r2) 
wolffd@0: double *matrix;
wolffd@0: long depth,r1,r2;
wolffd@0: {
wolffd@0:   long i;
wolffd@0:   double temp;
wolffd@0: 
wolffd@0:   for(i=0;i<depth;i++) {
wolffd@0:     temp=matrix[r1*depth+i];
wolffd@0:     matrix[r1*depth+i]=matrix[r2*depth+i];
wolffd@0:     matrix[r2*depth+i]=temp;
wolffd@0:   }
wolffd@0: }
wolffd@0: 
wolffd@0: void lswitchrk_matrix(matrix,depth,rk1,rk2) 
wolffd@0: double *matrix;
wolffd@0: long depth,rk1,rk2;
wolffd@0: {
wolffd@0:   long i;
wolffd@0:   double temp;
wolffd@0: 
wolffd@0:   for(i=0;i<depth;i++) {
wolffd@0:     temp=matrix[rk1*depth+i];
wolffd@0:     matrix[rk1*depth+i]=matrix[rk2*depth+i];
wolffd@0:     matrix[rk2*depth+i]=temp;
wolffd@0:   }
wolffd@0:   for(i=0;i<depth;i++) {
wolffd@0:     temp=matrix[i*depth+rk1];
wolffd@0:     matrix[i*depth+rk1]=matrix[i*depth+rk2];
wolffd@0:     matrix[i*depth+rk2]=temp;
wolffd@0:   }
wolffd@0: }
wolffd@0: 
wolffd@0: double calculate_qp_objective(opt_n,opt_g,opt_g0,alpha)
wolffd@0: long opt_n;
wolffd@0: double *opt_g,*opt_g0,*alpha;
wolffd@0: {
wolffd@0:   double obj;
wolffd@0:   long i,j;
wolffd@0:   obj=0;  /* calculate objective  */
wolffd@0:   for(i=0;i<opt_n;i++) {
wolffd@0:     obj+=(opt_g0[i]*alpha[i]);
wolffd@0:     obj+=(0.5*alpha[i]*alpha[i]*opt_g[i*opt_n+i]);
wolffd@0:     for(j=0;j<i;j++) {
wolffd@0:       obj+=(alpha[j]*alpha[i]*opt_g[j*opt_n+i]);
wolffd@0:     }
wolffd@0:   }
wolffd@0:   return(obj);
wolffd@0: }