SVMLight.cpp

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/***********************************************************************/
/*                                                                     */
/*   SVMLight.cpp                                                      */
/*                                                                     */
/*   Author: Thorsten Joachims                                         */
/*   Date: 19.07.99                                                    */
/*                                                                     */
/*   Copyright (c) 1999  Universitaet Dortmund - All rights reserved   */
/*                                                                     */
/*   This software is available for non-commercial use only. It must   */
/*   not be modified and distributed without prior permission of the   */
/*   author. The author is not responsible for implications from the   */
/*   use of this software.                                             */
/*                                                                     */
/*   THIS INCLUDES THE FOLLOWING ADDITIONS                             */
/*   Generic Kernel Interfacing: Soeren Sonnenburg                     */
/*   Parallizations: Soeren Sonnenburg                                 */
/*   Multiple Kernel Learning: Gunnar Raetsch, Soeren Sonnenburg,      */
/*                          Alexander Zien, Marius Kloft, Chen Guohua  */
/*   Linadd Speedup: Gunnar Raetsch, Soeren Sonnenburg                 */
/*                                                                     */
/***********************************************************************/
#include "lib/config.h"

#ifdef USE_SVMLIGHT

#include "lib/io.h"
#include "lib/Signal.h"
#include "lib/Mathematics.h"
#include "lib/Time.h"
#include "lib/lapack.h"

#include "features/SimpleFeatures.h"
#include "classifier/svm/SVMLight.h"
#include "classifier/svm/pr_loqo.h"

#include "kernel/Kernel.h"
#include "classifier/KernelMachine.h"
#include "kernel/CombinedKernel.h"

#include <unistd.h>

#include "base/Parallel.h"

#ifndef WIN32
#include <pthread.h>
#endif

using namespace shogun;

#ifndef DOXYGEN_SHOULD_SKIP_THIS
struct S_THREAD_PARAM_REACTIVATE_LINADD
{
    CKernel* kernel;
    float64_t* lin;
    float64_t* last_lin;
    int32_t* active;
    int32_t* docs;
    int32_t start;
    int32_t end;
};

struct S_THREAD_PARAM
{
    float64_t * lin ;
    float64_t* W;
    int32_t start, end;
    int32_t * active2dnum ;
    int32_t * docs ;
    CKernel* kernel ;
};

struct S_THREAD_PARAM_REACTIVATE_VANILLA
{
    CKernel* kernel;
    float64_t* lin;
    float64_t* aicache;
    float64_t* a;
    float64_t* a_old;
    int32_t* changed2dnum;
    int32_t* inactive2dnum;
    int32_t* label;
    int32_t start;
    int32_t end;
};

struct S_THREAD_PARAM_KERNEL
{
    float64_t *Kval ;
    int32_t *KI, *KJ ;
    int32_t start, end;
    CSVMLight* svmlight;
};

#endif // DOXYGEN_SHOULD_SKIP_THIS

void* CSVMLight::update_linear_component_linadd_helper(void* p)
{
    S_THREAD_PARAM* params = (S_THREAD_PARAM*) p;

    int32_t jj=0, j=0 ;

    for (jj=params->start;(jj<params->end) && (j=params->active2dnum[jj])>=0;jj++)
        params->lin[j]+=params->kernel->compute_optimized(params->docs[j]);

    return NULL ;
}

void* CSVMLight::compute_kernel_helper(void* p)
{
    S_THREAD_PARAM_KERNEL* params = (S_THREAD_PARAM_KERNEL*) p;

    int32_t jj=0 ;
    for (jj=params->start;jj<params->end;jj++)
        params->Kval[jj]=params->svmlight->compute_kernel(params->KI[jj], params->KJ[jj]) ;

    return NULL ;
}

CSVMLight::CSVMLight()
: CSVM()
{
    init();
    set_kernel(NULL);
}

CSVMLight::CSVMLight(float64_t C, CKernel* k, CLabels* lab)
: CSVM(C, k, lab)
{
    init();
}

void CSVMLight::init()
{
    //optimizer settings
    primal=NULL;
    dual=NULL;
    init_margin=0.15;
    init_iter=500;
    precision_violations=0;
    model_b=0;
    verbosity=1;
    opt_precision=DEF_PRECISION;

    // svm variables
    W=NULL;
    model=new MODEL[1];
    learn_parm=new LEARN_PARM[1];
    model->supvec=NULL;
    model->alpha=NULL;
    model->index=NULL;

    // MKL stuff
    mymaxdiff=1 ;
    mkl_converged=false;
}

CSVMLight::~CSVMLight()
{

  delete[] model->supvec;
  delete[] model->alpha;
  delete[] model->index;
  delete[] model;
  delete[] learn_parm;

  // MKL stuff
  delete[] W ;

  // optimizer variables
  delete[] dual;
  delete[] primal;
}

bool CSVMLight::train(CFeatures* data)
{
    //certain setup params
    mkl_converged=false;
    verbosity=1 ;
    init_margin=0.15;
    init_iter=500;
    precision_violations=0;
    opt_precision=DEF_PRECISION;

    strcpy (learn_parm->predfile, "");
    learn_parm->biased_hyperplane= get_bias_enabled() ? 1 : 0;
    learn_parm->sharedslack=0;
    learn_parm->remove_inconsistent=0;
    learn_parm->skip_final_opt_check=0;
    learn_parm->svm_maxqpsize=get_qpsize();
    learn_parm->svm_newvarsinqp=learn_parm->svm_maxqpsize-1;
    learn_parm->maxiter=100000;
    learn_parm->svm_iter_to_shrink=100;
    learn_parm->svm_c=C1;
    learn_parm->transduction_posratio=0.33;
    learn_parm->svm_costratio=C2/C1;
    learn_parm->svm_costratio_unlab=1.0;
    learn_parm->svm_unlabbound=1E-5;
    learn_parm->epsilon_crit=epsilon; // GU: better decrease it ... ??
    learn_parm->epsilon_a=1E-15;
    learn_parm->compute_loo=0;
    learn_parm->rho=1.0;
    learn_parm->xa_depth=0;

    if (!kernel)
        SG_ERROR( "SVM_light can not proceed without kernel!\n");

    if (data)
    {
        if (labels->get_num_labels() != data->get_num_vectors())
            SG_ERROR("Number of training vectors does not match number of labels\n");
        kernel->init(data, data);
    }

    if (!kernel->has_features())
        SG_ERROR( "SVM_light can not proceed without initialized kernel!\n");

    ASSERT(labels && labels->get_num_labels());
    ASSERT(labels->is_two_class_labeling());
    ASSERT(kernel->get_num_vec_lhs()==labels->get_num_labels());

    // in case of LINADD enabled kernels cleanup!
    if (kernel->has_property(KP_LINADD) && get_linadd_enabled())
        kernel->clear_normal() ;

    // output some info
    SG_DEBUG( "threads = %i\n", parallel->get_num_threads()) ;
    SG_DEBUG( "qpsize = %i\n", learn_parm->svm_maxqpsize) ;
    SG_DEBUG( "epsilon = %1.1e\n", learn_parm->epsilon_crit) ;
    SG_DEBUG( "kernel->has_property(KP_LINADD) = %i\n", kernel->has_property(KP_LINADD)) ;
    SG_DEBUG( "kernel->has_property(KP_KERNCOMBINATION) = %i\n", kernel->has_property(KP_KERNCOMBINATION)) ;
    SG_DEBUG( "kernel->has_property(KP_BATCHEVALUATION) = %i\n", kernel->has_property(KP_BATCHEVALUATION)) ;
    SG_DEBUG( "kernel->get_optimization_type() = %s\n", kernel->get_optimization_type()==FASTBUTMEMHUNGRY ? "FASTBUTMEMHUNGRY" : "SLOWBUTMEMEFFICIENT" ) ;
    SG_DEBUG( "get_solver_type() = %i\n", get_solver_type());
    SG_DEBUG( "get_linadd_enabled() = %i\n", get_linadd_enabled()) ;
    SG_DEBUG( "get_batch_computation_enabled() = %i\n", get_batch_computation_enabled()) ;
    SG_DEBUG( "kernel->get_num_subkernels() = %i\n", kernel->get_num_subkernels()) ;

    use_kernel_cache = !((kernel->get_kernel_type() == K_CUSTOM) ||
                         (get_linadd_enabled() && kernel->has_property(KP_LINADD)));

    SG_DEBUG( "use_kernel_cache = %i\n", use_kernel_cache) ;

    if (kernel->get_kernel_type() == K_COMBINED)
    {
        CKernel* kn = ((CCombinedKernel*)kernel)->get_first_kernel();

        while (kn)
        {
            // allocate kernel cache but clean up beforehand
            kn->resize_kernel_cache(kn->get_cache_size());
            SG_UNREF(kn);
            kn = ((CCombinedKernel*) kernel)->get_next_kernel();
        }
    }

    kernel->resize_kernel_cache(kernel->get_cache_size());

    // train the svm
    svm_learn();

    // brain damaged svm light work around
    create_new_model(model->sv_num-1);
    set_bias(-model->b);
    for (int32_t i=0; i<model->sv_num-1; i++)
    {
        set_alpha(i, model->alpha[i+1]);
        set_support_vector(i, model->supvec[i+1]);
    }

    // in case of LINADD enabled kernels cleanup!
    if (kernel->has_property(KP_LINADD) && get_linadd_enabled())
    {
        kernel->clear_normal() ;
        kernel->delete_optimization() ;
    }

    if (use_kernel_cache)
        kernel->kernel_cache_cleanup();

    return true ;
}

int32_t CSVMLight::get_runtime()
{
  clock_t start;
  start = clock();
  return((int32_t)((float64_t)start*100.0/(float64_t)CLOCKS_PER_SEC));
}


void CSVMLight::svm_learn()
{
    int32_t *inconsistent, i;
    int32_t inconsistentnum;
    int32_t misclassified,upsupvecnum;
    float64_t maxdiff, *lin, *c, *a;
    int32_t runtime_start,runtime_end;
    int32_t iterations;
    int32_t trainpos=0, trainneg=0 ;
    int32_t totdoc=0;
    ASSERT(labels);
    int32_t* label=labels->get_int_labels(totdoc);
    ASSERT(label);
    int32_t* docs=new int32_t[totdoc];
    delete[] W;
    W=NULL;
    count = 0 ;

    if (kernel->has_property(KP_KERNCOMBINATION) && callback)
    {
        W = new float64_t[totdoc*kernel->get_num_subkernels()];
        for (i=0; i<totdoc*kernel->get_num_subkernels(); i++)
            W[i]=0;
    }

    for (i=0; i<totdoc; i++)
        docs[i]=i;

    float64_t *xi_fullset; /* buffer for storing xi on full sample in loo */
    float64_t *a_fullset;  /* buffer for storing alpha on full sample in loo */
    TIMING timing_profile;
    SHRINK_STATE shrink_state;

    runtime_start=get_runtime();
    timing_profile.time_kernel=0;
    timing_profile.time_opti=0;
    timing_profile.time_shrink=0;
    timing_profile.time_update=0;
    timing_profile.time_model=0;
    timing_profile.time_check=0;
    timing_profile.time_select=0;

    /* make sure -n value is reasonable */
    if((learn_parm->svm_newvarsinqp < 2)
            || (learn_parm->svm_newvarsinqp > learn_parm->svm_maxqpsize)) {
        learn_parm->svm_newvarsinqp=learn_parm->svm_maxqpsize;
    }

    init_shrink_state(&shrink_state,totdoc,(int32_t)MAXSHRINK);

    inconsistent = new int32_t[totdoc];
    c = new float64_t[totdoc];
    a = new float64_t[totdoc];
    a_fullset = new float64_t[totdoc];
    xi_fullset = new float64_t[totdoc];
    lin = new float64_t[totdoc];
    if (m_linear_term_len > 0)
        learn_parm->eps=get_linear_term_array();
    else
    {
        learn_parm->eps=new float64_t[totdoc];      /* equivalent regression epsilon for classification */
        CMath::fill_vector(learn_parm->eps, totdoc, -1.0);
    }

    learn_parm->svm_cost = new float64_t[totdoc];

    delete[] model->supvec;
    delete[] model->alpha;
    delete[] model->index;
    model->supvec = new int32_t[totdoc+2];
    model->alpha = new float64_t[totdoc+2];
    model->index = new int32_t[totdoc+2];

    model->at_upper_bound=0;
    model->b=0;
    model->supvec[0]=0;  /* element 0 reserved and empty for now */
    model->alpha[0]=0;
    model->totdoc=totdoc;

    model->kernel=kernel;

    model->sv_num=1;
    model->loo_error=-1;
    model->loo_recall=-1;
    model->loo_precision=-1;
    model->xa_error=-1;
    model->xa_recall=-1;
    model->xa_precision=-1;
    inconsistentnum=0;


    for (i=0;i<totdoc;i++) {    /* various inits */
        inconsistent[i]=0;
        c[i]=0;
        a[i]=0;
        lin[i]=0;

        if(label[i] > 0) {
            learn_parm->svm_cost[i]=learn_parm->svm_c*learn_parm->svm_costratio*
                fabs((float64_t)label[i]);
            label[i]=1;
            trainpos++;
        }
        else if(label[i] < 0) {
            learn_parm->svm_cost[i]=learn_parm->svm_c*fabs((float64_t)label[i]);
            label[i]=-1;
            trainneg++;
        }
        else {
            learn_parm->svm_cost[i]=0;
        }
    }

  /* compute starting state for initial alpha values */
    SG_DEBUG( "alpha:%d num_sv:%d\n", m_alpha, get_num_support_vectors());

    if(m_alpha && get_num_support_vectors()) {
        if(verbosity>=1) {
            SG_INFO( "Computing starting state...");
        }

    float64_t* alpha = new float64_t[totdoc];

    for (i=0; i<totdoc; i++)
        alpha[i]=0;

    for (i=0; i<get_num_support_vectors(); i++)
        alpha[get_support_vector(i)]=get_alpha(i);

    int32_t* index = new int32_t[totdoc];
    int32_t* index2dnum = new int32_t[totdoc+11];
    float64_t* aicache = new float64_t[totdoc];
    for (i=0;i<totdoc;i++) {    /* create full index and clip alphas */
      index[i]=1;
      alpha[i]=fabs(alpha[i]);
      if(alpha[i]<0) alpha[i]=0;
      if(alpha[i]>learn_parm->svm_cost[i]) alpha[i]=learn_parm->svm_cost[i];
    }

    if (use_kernel_cache)
    {
        if (callback &&
                (!((CCombinedKernel*)kernel)->get_append_subkernel_weights())
           )
        {
            CCombinedKernel* k      = (CCombinedKernel*) kernel;
            CKernel* kn = k->get_first_kernel();

            while (kn)
            {
                for (i=0;i<totdoc;i++)     // fill kernel cache with unbounded SV
                    if((alpha[i]>0) && (alpha[i]<learn_parm->svm_cost[i])
                            && (kn->kernel_cache_space_available()))
                        kn->cache_kernel_row(i);

                for (i=0;i<totdoc;i++)     // fill rest of kernel cache with bounded SV
                    if((alpha[i]==learn_parm->svm_cost[i])
                            && (kn->kernel_cache_space_available()))
                        kn->cache_kernel_row(i);

                SG_UNREF(kn);
                kn = k->get_next_kernel();
            }
        }
        else
        {
            for (i=0;i<totdoc;i++)     /* fill kernel cache with unbounded SV */
                if((alpha[i]>0) && (alpha[i]<learn_parm->svm_cost[i])
                        && (kernel->kernel_cache_space_available()))
                    kernel->cache_kernel_row(i);

            for (i=0;i<totdoc;i++)     /* fill rest of kernel cache with bounded SV */
                if((alpha[i]==learn_parm->svm_cost[i])
                        && (kernel->kernel_cache_space_available()))
                    kernel->cache_kernel_row(i);
        }
    }
    (void)compute_index(index,totdoc,index2dnum);
    update_linear_component(docs,label,index2dnum,alpha,a,index2dnum,totdoc,
                lin,aicache,NULL);
    (void)calculate_svm_model(docs,label,lin,alpha,a,c,
                  index2dnum,index2dnum);
    for (i=0;i<totdoc;i++) {    /* copy initial alphas */
      a[i]=alpha[i];
    }

    delete[] index;
    delete[] index2dnum;
    delete[] aicache;
    delete[] alpha;

    if(verbosity>=1)
        SG_DONE();
  }
        SG_DEBUG( "%d totdoc %d pos %d neg\n", totdoc, trainpos, trainneg);
        SG_DEBUG( "Optimizing...\n");

    /* train the svm */
  iterations=optimize_to_convergence(docs,label,totdoc,
                     &shrink_state,inconsistent,a,lin,
                     c,&timing_profile,
                     &maxdiff,(int32_t)-1,
                     (int32_t)1);


    if(verbosity>=1) {
        if(verbosity==1)
        {
            SG_DONE();
            SG_DEBUG("(%ld iterations)", iterations);
        }

        misclassified=0;
        for (i=0;(i<totdoc);i++) { /* get final statistic */
            if((lin[i]-model->b)*(float64_t)label[i] <= 0.0)
                misclassified++;
        }

        SG_INFO( "Optimization finished (%ld misclassified, maxdiff=%.8f).\n",
                misclassified,maxdiff);

        SG_INFO( "obj = %.16f, rho = %.16f\n",get_objective(),model->b);
        if (maxdiff>epsilon)
            SG_WARNING( "maximum violation (%f) exceeds svm_epsilon (%f) due to numerical difficulties\n", maxdiff, epsilon);

        runtime_end=get_runtime();
        upsupvecnum=0;
        for (i=1;i<model->sv_num;i++)
        {
            if(fabs(model->alpha[i]) >=
                    (learn_parm->svm_cost[model->supvec[i]]-
                     learn_parm->epsilon_a))
                upsupvecnum++;
        }
        SG_INFO( "Number of SV: %ld (including %ld at upper bound)\n",
                model->sv_num-1,upsupvecnum);
    }

    shrink_state_cleanup(&shrink_state);
    delete[] label;
    delete[] inconsistent;
    delete[] c;
    delete[] a;
    delete[] a_fullset;
    delete[] xi_fullset;
    delete[] lin;
    delete[] learn_parm->eps;
    delete[] learn_parm->svm_cost;
    delete[] docs;
}

int32_t CSVMLight::optimize_to_convergence(int32_t* docs, int32_t* label, int32_t totdoc,
                 SHRINK_STATE *shrink_state,
                 int32_t *inconsistent,
                 float64_t *a, float64_t *lin, float64_t *c,
                 TIMING *timing_profile, float64_t *maxdiff,
                 int32_t heldout, int32_t retrain)
     /* docs: Training vectors (x-part) */
     /* label: Training labels/value (y-part, zero if test example for
                  transduction) */
     /* totdoc: Number of examples in docs/label */
     /* laern_parm: Learning paramenters */
     /* kernel_parm: Kernel paramenters */
     /* kernel_cache: Initialized/partly filled Cache, if using a kernel.
                      NULL if linear. */
     /* shrink_state: State of active variables */
     /* inconsistent: examples thrown out as inconstistent */
     /* a: alphas */
     /* lin: linear component of gradient */
     /* c: right hand side of inequalities (margin) */
     /* maxdiff: returns maximum violation of KT-conditions */
     /* heldout: marks held-out example for leave-one-out (or -1) */
     /* retrain: selects training mode (1=regular / 2=holdout) */
{
  int32_t *chosen,*key,i,j,jj,*last_suboptimal_at,noshrink;
  int32_t inconsistentnum,choosenum,already_chosen=0,iteration;
  int32_t misclassified,supvecnum=0,*active2dnum,inactivenum;
  int32_t *working2dnum,*selexam;
  int32_t activenum;
  float64_t criterion, eq;
  float64_t *a_old;
  int32_t t0=0,t1=0,t2=0,t3=0,t4=0,t5=0,t6=0; /* timing */
  int32_t transductcycle;
  int32_t transduction;
  float64_t epsilon_crit_org;
  float64_t bestmaxdiff;
  float64_t worstmaxdiff;
  int32_t   bestmaxdiffiter,terminate;
  bool reactivated=false;

  float64_t *selcrit;  /* buffer for sorting */
  float64_t *aicache;  /* buffer to keep one row of hessian */
  QP qp;            /* buffer for one quadratic program */

  epsilon_crit_org=learn_parm->epsilon_crit; /* save org */
  if(kernel->has_property(KP_LINADD) && get_linadd_enabled()) {
      learn_parm->epsilon_crit=2.0;
      /* caching makes no sense for linear kernel */
  }
  learn_parm->epsilon_shrink=2;
  (*maxdiff)=1;

  SG_DEBUG("totdoc:%d\n",totdoc);
  chosen = new int32_t[totdoc];
  last_suboptimal_at =new int32_t[totdoc];
  key =new int32_t[totdoc+11];
  selcrit =new float64_t[totdoc];
  selexam =new int32_t[totdoc];
  a_old =new float64_t[totdoc];
  aicache =new float64_t[totdoc];
  working2dnum =new int32_t[totdoc+11];
  active2dnum =new int32_t[totdoc+11];
  qp.opt_ce =new float64_t[learn_parm->svm_maxqpsize];
  qp.opt_ce0 =new float64_t[1];
  qp.opt_g =new float64_t[learn_parm->svm_maxqpsize*learn_parm->svm_maxqpsize];
  qp.opt_g0 =new float64_t[learn_parm->svm_maxqpsize];
  qp.opt_xinit =new float64_t[learn_parm->svm_maxqpsize];
  qp.opt_low=new float64_t[learn_parm->svm_maxqpsize];
  qp.opt_up=new float64_t[learn_parm->svm_maxqpsize];

  choosenum=0;
  inconsistentnum=0;
  transductcycle=0;
  transduction=0;
  if(!retrain) retrain=1;
  iteration=1;
  bestmaxdiffiter=1;
  bestmaxdiff=999999999;
  worstmaxdiff=1e-10;
  terminate=0;

  kernel->set_time(iteration);  /* for lru cache */

  for (i=0;i<totdoc;i++) {    /* various inits */
    chosen[i]=0;
    a_old[i]=a[i];
    last_suboptimal_at[i]=1;
    if(inconsistent[i])
      inconsistentnum++;
  }
  activenum=compute_index(shrink_state->active,totdoc,active2dnum);
  inactivenum=totdoc-activenum;
  clear_index(working2dnum);

  /* repeat this loop until we have convergence */
  CTime start_time;
  mkl_converged=false;

#ifdef CYGWIN
  for (;((iteration<100 || (!mkl_converged && callback) ) || (retrain && (!terminate))); iteration++){
#else
      CSignal::clear_cancel();
      for (;((!CSignal::cancel_computations()) && ((iteration<3 || (!mkl_converged && callback) ) || (retrain && (!terminate)))); iteration++){
#endif

      if(use_kernel_cache)
          kernel->set_time(iteration);  /* for lru cache */

      if(verbosity>=2) t0=get_runtime();
      if(verbosity>=3) {
          SG_DEBUG( "\nSelecting working set... ");
      }

      if(learn_parm->svm_newvarsinqp>learn_parm->svm_maxqpsize)
          learn_parm->svm_newvarsinqp=learn_parm->svm_maxqpsize;

      i=0;
      for (jj=0;(j=working2dnum[jj])>=0;jj++) { /* clear working set */
          if((chosen[j]>=(learn_parm->svm_maxqpsize/
                          CMath::min(learn_parm->svm_maxqpsize,
                                     learn_parm->svm_newvarsinqp)))
             || (inconsistent[j])
             || (j == heldout)) {
              chosen[j]=0;
              choosenum--;
          }
          else {
              chosen[j]++;
              working2dnum[i++]=j;
          }
      }
      working2dnum[i]=-1;

      if(retrain == 2) {
          choosenum=0;
          for (jj=0;(j=working2dnum[jj])>=0;jj++) { /* fully clear working set */
              chosen[j]=0;
          }
          clear_index(working2dnum);
          for (i=0;i<totdoc;i++) { /* set inconsistent examples to zero (-i 1) */
              if((inconsistent[i] || (heldout==i)) && (a[i] != 0.0)) {
                  chosen[i]=99999;
                  choosenum++;
                  a[i]=0;
              }
          }
          if(learn_parm->biased_hyperplane) {
              eq=0;
              for (i=0;i<totdoc;i++) { /* make sure we fulfill equality constraint */
                  eq+=a[i]*label[i];
              }
              for (i=0;(i<totdoc) && (fabs(eq) > learn_parm->epsilon_a);i++) {
                  if((eq*label[i] > 0) && (a[i] > 0)) {
                      chosen[i]=88888;
                      choosenum++;
                      if((eq*label[i]) > a[i]) {
                          eq-=(a[i]*label[i]);
                          a[i]=0;
                      }
                      else {
                          a[i]-=(eq*label[i]);
                          eq=0;
                      }
                  }
              }
          }
          compute_index(chosen,totdoc,working2dnum);
      }
      else
      {   /* select working set according to steepest gradient */
          if(iteration % 101)
          {
              already_chosen=0;
              if(CMath::min(learn_parm->svm_newvarsinqp, learn_parm->svm_maxqpsize-choosenum)>=4 &&
                      (!(kernel->has_property(KP_LINADD) && get_linadd_enabled())))
              {
                  /* select part of the working set from cache */
                  already_chosen=select_next_qp_subproblem_grad(
                      label,a,lin,c,totdoc,
                      (int32_t)(CMath::min(learn_parm->svm_maxqpsize-choosenum,
                                        learn_parm->svm_newvarsinqp)/2),
                      inconsistent,active2dnum,
                      working2dnum,selcrit,selexam,1,
                      key,chosen);
                  choosenum+=already_chosen;
              }
              choosenum+=select_next_qp_subproblem_grad(
                  label,a,lin,c,totdoc,
                  CMath::min(learn_parm->svm_maxqpsize-choosenum,
                             learn_parm->svm_newvarsinqp-already_chosen),
                  inconsistent,active2dnum,
                  working2dnum,selcrit,selexam,0,key,
                  chosen);
          }
          else { /* once in a while, select a somewhat random working set
                    to get unlocked of infinite loops due to numerical
                    inaccuracies in the core qp-solver */
              choosenum+=select_next_qp_subproblem_rand(
                  label,a,lin,c,totdoc,
                  CMath::min(learn_parm->svm_maxqpsize-choosenum,
                             learn_parm->svm_newvarsinqp),
                  inconsistent,active2dnum,
                  working2dnum,selcrit,selexam,key,
                  chosen,iteration);
          }
      }

      if(verbosity>=2) {
          SG_INFO( " %ld vectors chosen\n",choosenum);
      }

      if(verbosity>=2) t1=get_runtime();

      if (use_kernel_cache)
      {
          // in case of MKL w/o linadd cache each kernel independently
          // else if linadd is disabled cache single kernel
          if ( callback &&
                  (!((CCombinedKernel*) kernel)->get_append_subkernel_weights())
             )
          {
              CCombinedKernel* k      = (CCombinedKernel*) kernel;
              CKernel* kn = k->get_first_kernel();

              while (kn)
              {
                  kn->cache_multiple_kernel_rows(working2dnum, choosenum);
                  SG_UNREF(kn);
                  kn = k->get_next_kernel() ;
              }
          }
          else
              kernel->cache_multiple_kernel_rows(working2dnum, choosenum);
      }

      if(verbosity>=2) t2=get_runtime();

      if(retrain != 2) {
          optimize_svm(docs,label,inconsistent,0.0,chosen,active2dnum,
                       totdoc,working2dnum,choosenum,a,lin,c,
                       aicache,&qp,&epsilon_crit_org);
      }

      if(verbosity>=2) t3=get_runtime();
      update_linear_component(docs,label,active2dnum,a,a_old,working2dnum,totdoc,
                              lin,aicache,c);

      if(verbosity>=2) t4=get_runtime();
      supvecnum=calculate_svm_model(docs,label,lin,a,a_old,c,working2dnum,active2dnum);

      if(verbosity>=2) t5=get_runtime();

      for (jj=0;(i=working2dnum[jj])>=0;jj++) {
          a_old[i]=a[i];
      }

      retrain=check_optimality(label,a,lin,c,totdoc,
                               maxdiff,epsilon_crit_org,&misclassified,
                               inconsistent,active2dnum,last_suboptimal_at,
                               iteration);

      if(verbosity>=2) {
          t6=get_runtime();
          timing_profile->time_select+=t1-t0;
          timing_profile->time_kernel+=t2-t1;
          timing_profile->time_opti+=t3-t2;
          timing_profile->time_update+=t4-t3;
          timing_profile->time_model+=t5-t4;
          timing_profile->time_check+=t6-t5;
      }

      /* checking whether optimizer got stuck */
      if((*maxdiff) < bestmaxdiff) {
          bestmaxdiff=(*maxdiff);
          bestmaxdiffiter=iteration;
      }
      if(iteration > (bestmaxdiffiter+learn_parm->maxiter)) {
          /* int32_t time no progress? */
          terminate=1;
          retrain=0;
          SG_WARNING( "Relaxing KT-Conditions due to slow progress! Terminating!\n");
      }

      noshrink= (get_shrinking_enabled()) ? 0 : 1;

      if ((!callback) && (!retrain) && (inactivenum>0) &&
              ((!learn_parm->skip_final_opt_check) || (kernel->has_property(KP_LINADD) && get_linadd_enabled())))
      {
          t1=get_runtime();
          SG_DEBUG( "reactivating inactive examples\n");

          reactivate_inactive_examples(label,a,shrink_state,lin,c,totdoc,
                                       iteration,inconsistent,
                                       docs,aicache,
                                       maxdiff);
          reactivated=true;
          SG_DEBUG("done reactivating inactive examples (maxdiff:%8f eps_crit:%8f orig_eps:%8f)\n", *maxdiff, learn_parm->epsilon_crit, epsilon_crit_org);
          /* Update to new active variables. */
          activenum=compute_index(shrink_state->active,totdoc,active2dnum);
          inactivenum=totdoc-activenum;
          /* reset watchdog */
          bestmaxdiff=(*maxdiff);
          bestmaxdiffiter=iteration;

          /* termination criterion */
          noshrink=1;
          retrain=0;
          if((*maxdiff) > learn_parm->epsilon_crit)
          {
              SG_INFO( "restarting optimization as we are - due to shrinking - deviating too much (maxdiff(%f) > eps(%f))\n", *maxdiff, learn_parm->epsilon_crit);
              retrain=1;
          }
          timing_profile->time_shrink+=get_runtime()-t1;
          if (((verbosity>=1) && (!(kernel->has_property(KP_LINADD) && get_linadd_enabled())))
             || (verbosity>=2)) {
              SG_DONE();
              SG_DEBUG("Number of inactive variables = %ld\n", inactivenum);
          }
      }

      if((!retrain) && (learn_parm->epsilon_crit>(*maxdiff)))
          learn_parm->epsilon_crit=(*maxdiff);
      if((!retrain) && (learn_parm->epsilon_crit>epsilon_crit_org)) {
          learn_parm->epsilon_crit/=4.0;
          retrain=1;
          noshrink=1;
      }
      if(learn_parm->epsilon_crit<epsilon_crit_org)
          learn_parm->epsilon_crit=epsilon_crit_org;

      if(verbosity>=2) {
          SG_INFO( " => (%ld SV (incl. %ld SV at u-bound), max violation=%.5f)\n",
                       supvecnum,model->at_upper_bound,(*maxdiff));

      }
      mymaxdiff=*maxdiff ;

      //don't shrink w/ mkl
      if (((iteration % 10) == 0) && (!noshrink) && !callback)
      {
          activenum=shrink_problem(shrink_state,active2dnum,last_suboptimal_at,iteration,totdoc,
                  CMath::max((int32_t)(activenum/10),
                      CMath::max((int32_t)(totdoc/500),(int32_t) 100)),
                  a,inconsistent, c, lin, label);

          inactivenum=totdoc-activenum;

          if (use_kernel_cache && (supvecnum>kernel->get_max_elems_cache())
                  && ((kernel->get_activenum_cache()-activenum)>CMath::max((int32_t)(activenum/10),(int32_t) 500))) {

              kernel->kernel_cache_shrink(totdoc, CMath::min((int32_t) (kernel->get_activenum_cache()-activenum),
                          (int32_t) (kernel->get_activenum_cache()-supvecnum)),
                      shrink_state->active);
          }
      }

      if (bestmaxdiff>worstmaxdiff)
          worstmaxdiff=bestmaxdiff;

      SG_ABS_PROGRESS(bestmaxdiff, -CMath::log10(bestmaxdiff), -CMath::log10(worstmaxdiff), -CMath::log10(epsilon), 6);

      /* Terminate loop */
      if (max_train_time > 0 && start_time.cur_time_diff() > max_train_time) {
          terminate = 1;
          retrain = 0;
      }
  } /* end of loop */

  SG_DEBUG( "inactive:%d\n", inactivenum);

  if (inactivenum && !reactivated && !callback)
  {
      SG_DEBUG( "reactivating inactive examples\n");
      reactivate_inactive_examples(label,a,shrink_state,lin,c,totdoc,
              iteration,inconsistent,
              docs,aicache,
              maxdiff);
      SG_DEBUG( "done reactivating inactive examples\n");
      /* Update to new active variables. */
      activenum=compute_index(shrink_state->active,totdoc,active2dnum);
      inactivenum=totdoc-activenum;
      /* reset watchdog */
      bestmaxdiff=(*maxdiff);
      bestmaxdiffiter=iteration;
  }

  criterion=compute_objective_function(a,lin,c,learn_parm->eps,label,totdoc);
  CSVM::set_objective(criterion);

  delete[] chosen;
  delete[] last_suboptimal_at;
  delete[] key;
  delete[] selcrit;
  delete[] selexam;
  delete[] a_old;
  delete[] aicache;
  delete[] working2dnum;
  delete[] active2dnum;
  delete[] qp.opt_ce;
  delete[] qp.opt_ce0;
  delete[] qp.opt_g;
  delete[] qp.opt_g0;
  delete[] qp.opt_xinit;
  delete[] qp.opt_low;
  delete[] qp.opt_up;

  learn_parm->epsilon_crit=epsilon_crit_org; /* restore org */

  return(iteration);
}

float64_t CSVMLight::compute_objective_function(
    float64_t *a, float64_t *lin, float64_t *c, float64_t* eps, int32_t *label,
    int32_t totdoc)
     /* Return value of objective function. */
     /* Works only relative to the active variables! */
{
  /* calculate value of objective function */
  float64_t criterion=0;

  for (int32_t i=0;i<totdoc;i++)
      criterion=criterion+(eps[i]-(float64_t)label[i]*c[i])*a[i]+0.5*a[i]*label[i]*lin[i];

  return(criterion);
}


void CSVMLight::clear_index(int32_t *index)
              /* initializes and empties index */
{
  index[0]=-1;
}

void CSVMLight::add_to_index(int32_t *index, int32_t elem)
     /* initializes and empties index */
{
  register int32_t i;
  for (i=0;index[i] != -1;i++);
  index[i]=elem;
  index[i+1]=-1;
}

int32_t CSVMLight::compute_index(
    int32_t *binfeature, int32_t range, int32_t *index)
     /* create an inverted index of binfeature */
{
  register int32_t i,ii;

  ii=0;
  for (i=0;i<range;i++) {
    if(binfeature[i]) {
      index[ii]=i;
      ii++;
    }
  }
  for (i=0;i<4;i++) {
    index[ii+i]=-1;
  }
  return(ii);
}


void CSVMLight::optimize_svm(
    int32_t* docs, int32_t* label, int32_t *exclude_from_eq_const,
    float64_t eq_target, int32_t *chosen, int32_t *active2dnum, int32_t totdoc,
    int32_t *working2dnum, int32_t varnum, float64_t *a, float64_t *lin,
    float64_t *c, float64_t *aicache, QP *qp, float64_t *epsilon_crit_target)
     /* Do optimization on the working set. */
{
    int32_t i;
    float64_t *a_v;

    //compute_matrices_for_optimization_parallel(docs,label,
    //                                         exclude_from_eq_const,eq_target,chosen,
    //                                         active2dnum,working2dnum,a,lin,c,
    //                                         varnum,totdoc,aicache,qp);

    compute_matrices_for_optimization(docs,label,
                                      exclude_from_eq_const,eq_target,chosen,
                                      active2dnum,working2dnum,a,lin,c,
                                      varnum,totdoc,aicache,qp);

    if(verbosity>=3) {
     SG_DEBUG( "Running optimizer...");
    }
    /* call the qp-subsolver */
    a_v=optimize_qp(qp,epsilon_crit_target,
            learn_parm->svm_maxqpsize,
            &(model->b),                /* in case the optimizer gives us */
            learn_parm->svm_maxqpsize); /* the threshold for free. otherwise */
                                        /* b is calculated in calculate_model. */
    if(verbosity>=3) {
     SG_DONE();
    }

    for (i=0;i<varnum;i++)
      a[working2dnum[i]]=a_v[i];
}

void CSVMLight::compute_matrices_for_optimization_parallel(
    int32_t* docs, int32_t* label, int32_t *exclude_from_eq_const,
    float64_t eq_target, int32_t *chosen, int32_t *active2dnum, int32_t *key,
    float64_t *a, float64_t *lin, float64_t *c, int32_t varnum, int32_t totdoc,
    float64_t *aicache, QP *qp)
{
    if (parallel->get_num_threads()<=1)
    {
        compute_matrices_for_optimization(docs, label, exclude_from_eq_const, eq_target,
                                                   chosen, active2dnum, key, a, lin, c,
                                                   varnum, totdoc, aicache, qp) ;
    }
#ifndef WIN32
    else
    {
        register int32_t ki,kj,i,j;
        register float64_t kernel_temp;

        qp->opt_n=varnum;
        qp->opt_ce0[0]=-eq_target; /* compute the constant for equality constraint */
        for (j=1;j<model->sv_num;j++) { /* start at 1 */
            if((!chosen[model->supvec[j]])
                    && (!exclude_from_eq_const[(model->supvec[j])])) {
                qp->opt_ce0[0]+=model->alpha[j];
            }
        }
        if(learn_parm->biased_hyperplane)
            qp->opt_m=1;
        else
            qp->opt_m=0;  /* eq-constraint will be ignored */

        /* init linear part of objective function */
        for (i=0;i<varnum;i++) {
            qp->opt_g0[i]=lin[key[i]];
        }

        ASSERT(parallel->get_num_threads()>1);
        int32_t *KI=new int32_t[varnum*varnum] ;
        int32_t *KJ=new int32_t[varnum*varnum] ;
        int32_t Knum=0 ;
        float64_t *Kval = new float64_t[varnum*(varnum+1)/2] ;
        for (i=0;i<varnum;i++) {
            ki=key[i];
            KI[Knum]=docs[ki] ;
            KJ[Knum]=docs[ki] ;
            Knum++ ;
            for (j=i+1;j<varnum;j++)
            {
                kj=key[j];
                KI[Knum]=docs[ki] ;
                KJ[Knum]=docs[kj] ;
                Knum++ ;
            }
        }
        ASSERT(Knum<=varnum*(varnum+1)/2);

        pthread_t* threads = new pthread_t[parallel->get_num_threads()-1];
        S_THREAD_PARAM_KERNEL* params = new S_THREAD_PARAM_KERNEL[parallel->get_num_threads()-1];
        int32_t step= Knum/parallel->get_num_threads();
        //SG_DEBUG( "\nkernel-step size: %i\n", step) ;
        for (int32_t t=0; t<parallel->get_num_threads()-1; t++)
        {
            params[t].svmlight = this;
            params[t].start = t*step;
            params[t].end = (t+1)*step;
            params[t].KI=KI ;
            params[t].KJ=KJ ;
            params[t].Kval=Kval ;
            pthread_create(&threads[t], NULL, CSVMLight::compute_kernel_helper, (void*)&params[t]);
        }
        for (i=params[parallel->get_num_threads()-2].end; i<Knum; i++)
            Kval[i]=compute_kernel(KI[i],KJ[i]) ;

        for (int32_t t=0; t<parallel->get_num_threads()-1; t++)
            pthread_join(threads[t], NULL);

        delete[] params;
        delete[] threads;

        Knum=0 ;
        for (i=0;i<varnum;i++) {
            ki=key[i];

            /* Compute the matrix for equality constraints */
            qp->opt_ce[i]=label[ki];
            qp->opt_low[i]=0;
            qp->opt_up[i]=learn_parm->svm_cost[ki];

            kernel_temp=Kval[Knum] ;
            Knum++ ;
            /* compute linear part of objective function */
            qp->opt_g0[i]-=(kernel_temp*a[ki]*(float64_t)label[ki]);
            /* compute quadratic part of objective function */
            qp->opt_g[varnum*i+i]=kernel_temp;

            for (j=i+1;j<varnum;j++) {
                kj=key[j];
                kernel_temp=Kval[Knum] ;
                Knum++ ;
                /* compute linear part of objective function */
                qp->opt_g0[i]-=(kernel_temp*a[kj]*(float64_t)label[kj]);
                qp->opt_g0[j]-=(kernel_temp*a[ki]*(float64_t)label[ki]);
                /* compute quadratic part of objective function */
                qp->opt_g[varnum*i+j]=(float64_t)label[ki]*(float64_t)label[kj]*kernel_temp;
                qp->opt_g[varnum*j+i]=qp->opt_g[varnum*i+j];//(float64_t)label[ki]*(float64_t)label[kj]*kernel_temp;
            }

            if(verbosity>=3) {
                if(i % 20 == 0) {
                    SG_DEBUG( "%ld..",i);
                }
            }
        }

        delete[] KI ;
        delete[] KJ ;
        delete[] Kval ;

        for (i=0;i<varnum;i++) {
            /* assure starting at feasible point */
            qp->opt_xinit[i]=a[key[i]];
            /* set linear part of objective function */
            qp->opt_g0[i]=(learn_parm->eps[key[i]]-(float64_t)label[key[i]]*c[key[i]])+qp->opt_g0[i]*(float64_t)label[key[i]];
        }

        if(verbosity>=3) {
            SG_DONE();
        }
    }
#endif
}

void CSVMLight::compute_matrices_for_optimization(
    int32_t* docs, int32_t* label, int32_t *exclude_from_eq_const,
    float64_t eq_target, int32_t *chosen, int32_t *active2dnum, int32_t *key,
    float64_t *a, float64_t *lin, float64_t *c, int32_t varnum, int32_t totdoc,
    float64_t *aicache, QP *qp)
{
  register int32_t ki,kj,i,j;
  register float64_t kernel_temp;

  qp->opt_n=varnum;
  qp->opt_ce0[0]=-eq_target; /* compute the constant for equality constraint */
  for (j=1;j<model->sv_num;j++) { /* start at 1 */
    if((!chosen[model->supvec[j]])
       && (!exclude_from_eq_const[(model->supvec[j])])) {
      qp->opt_ce0[0]+=model->alpha[j];
    }
  }
  if(learn_parm->biased_hyperplane)
    qp->opt_m=1;
  else
    qp->opt_m=0;  /* eq-constraint will be ignored */

  /* init linear part of objective function */
  for (i=0;i<varnum;i++) {
    qp->opt_g0[i]=lin[key[i]];
  }

  for (i=0;i<varnum;i++) {
      ki=key[i];

      /* Compute the matrix for equality constraints */
      qp->opt_ce[i]=label[ki];
      qp->opt_low[i]=0;
      qp->opt_up[i]=learn_parm->svm_cost[ki];

      kernel_temp=compute_kernel(docs[ki], docs[ki]);
      /* compute linear part of objective function */
      qp->opt_g0[i]-=(kernel_temp*a[ki]*(float64_t)label[ki]);
      /* compute quadratic part of objective function */
      qp->opt_g[varnum*i+i]=kernel_temp;

      for (j=i+1;j<varnum;j++) {
          kj=key[j];
          kernel_temp=compute_kernel(docs[ki], docs[kj]);

          /* compute linear part of objective function */
          qp->opt_g0[i]-=(kernel_temp*a[kj]*(float64_t)label[kj]);
          qp->opt_g0[j]-=(kernel_temp*a[ki]*(float64_t)label[ki]);
          /* compute quadratic part of objective function */
          qp->opt_g[varnum*i+j]=(float64_t)label[ki]*(float64_t)label[kj]*kernel_temp;
          qp->opt_g[varnum*j+i]=qp->opt_g[varnum*i+j];//(float64_t)label[ki]*(float64_t)label[kj]*kernel_temp;
      }

      if(verbosity>=3) {
          if(i % 20 == 0) {
              SG_DEBUG( "%ld..",i);
          }
      }
  }

  for (i=0;i<varnum;i++) {
      /* assure starting at feasible point */
      qp->opt_xinit[i]=a[key[i]];
      /* set linear part of objective function */
      qp->opt_g0[i]=(learn_parm->eps[key[i]]-(float64_t)label[key[i]]*c[key[i]]) + qp->opt_g0[i]*(float64_t)label[key[i]];
  }

  if(verbosity>=3) {
      SG_DONE();
  }
}


int32_t CSVMLight::calculate_svm_model(
    int32_t* docs, int32_t *label, float64_t *lin, float64_t *a,
    float64_t *a_old, float64_t *c, int32_t *working2dnum, int32_t *active2dnum)
     /* Compute decision function based on current values */
     /* of alpha. */
{
  int32_t i,ii,pos,b_calculated=0,first_low,first_high;
  float64_t ex_c,b_temp,b_low,b_high;

  if(verbosity>=3) {
   SG_DEBUG( "Calculating model...");
  }

  if(!learn_parm->biased_hyperplane) {
    model->b=0;
    b_calculated=1;
  }

  for (ii=0;(i=working2dnum[ii])>=0;ii++) {
    if((a_old[i]>0) && (a[i]==0)) { /* remove from model */
      pos=model->index[i];
      model->index[i]=-1;
      (model->sv_num)--;
      model->supvec[pos]=model->supvec[model->sv_num];
      model->alpha[pos]=model->alpha[model->sv_num];
      model->index[model->supvec[pos]]=pos;
    }
    else if((a_old[i]==0) && (a[i]>0)) { /* add to model */
      model->supvec[model->sv_num]=docs[i];
      model->alpha[model->sv_num]=a[i]*(float64_t)label[i];
      model->index[i]=model->sv_num;
      (model->sv_num)++;
    }
    else if(a_old[i]==a[i]) { /* nothing to do */
    }
    else {  /* just update alpha */
      model->alpha[model->index[i]]=a[i]*(float64_t)label[i];
    }

    ex_c=learn_parm->svm_cost[i]-learn_parm->epsilon_a;
    if((a_old[i]>=ex_c) && (a[i]<ex_c)) {
      (model->at_upper_bound)--;
    }
    else if((a_old[i]<ex_c) && (a[i]>=ex_c)) {
      (model->at_upper_bound)++;
    }

    if((!b_calculated)
       && (a[i]>learn_parm->epsilon_a) && (a[i]<ex_c)) {   /* calculate b */
        model->b=((float64_t)label[i]*learn_parm->eps[i]-c[i]+lin[i]);
    b_calculated=1;
    }
  }

  /* No alpha in the working set not at bounds, so b was not
     calculated in the usual way. The following handles this special
     case. */
  if(learn_parm->biased_hyperplane
     && (!b_calculated)
     && (model->sv_num-1 == model->at_upper_bound)) {
    first_low=1;
    first_high=1;
    b_low=0;
    b_high=0;
    for (ii=0;(i=active2dnum[ii])>=0;ii++) {
      ex_c=learn_parm->svm_cost[i]-learn_parm->epsilon_a;
      if(a[i]<ex_c) {
    if(label[i]>0)  {
      b_temp=-(learn_parm->eps[i]-c[i]+lin[i]);
      if((b_temp>b_low) || (first_low)) {
        b_low=b_temp;
        first_low=0;
      }
    }
    else {
      b_temp=-(-learn_parm->eps[i]-c[i]+lin[i]);
      if((b_temp<b_high) || (first_high)) {
        b_high=b_temp;
        first_high=0;
      }
    }
      }
      else {
    if(label[i]<0)  {
      b_temp=-(-learn_parm->eps[i]-c[i]+lin[i]);
      if((b_temp>b_low) || (first_low)) {
        b_low=b_temp;
        first_low=0;
      }
    }
    else {
      b_temp=-(learn_parm->eps[i]-c[i]+lin[i]);
      if((b_temp<b_high) || (first_high)) {
        b_high=b_temp;
        first_high=0;
      }
    }
      }
    }
    if(first_high) {
      model->b=-b_low;
    }
    else if(first_low) {
      model->b=-b_high;
    }
    else {
      model->b=-(b_high+b_low)/2.0;  /* select b as the middle of range */
    }
  }

  if(verbosity>=3) {
   SG_DONE();
  }

  return(model->sv_num-1); /* have to substract one, since element 0 is empty*/
}

int32_t CSVMLight::check_optimality(
    int32_t* label, float64_t *a, float64_t *lin, float64_t *c, int32_t totdoc,
    float64_t *maxdiff, float64_t epsilon_crit_org, int32_t *misclassified,
    int32_t *inconsistent, int32_t *active2dnum, int32_t *last_suboptimal_at,
    int32_t iteration)
     /* Check KT-conditions */
{
  int32_t i,ii,retrain;
  float64_t dist,ex_c,target;

  if (kernel->has_property(KP_LINADD) && get_linadd_enabled())
      learn_parm->epsilon_shrink=-learn_parm->epsilon_crit+epsilon_crit_org;
  else
      learn_parm->epsilon_shrink=learn_parm->epsilon_shrink*0.7+(*maxdiff)*0.3;
  retrain=0;
  (*maxdiff)=0;
  (*misclassified)=0;
  for (ii=0;(i=active2dnum[ii])>=0;ii++) {
      if((!inconsistent[i]) && label[i]) {
          dist=(lin[i]-model->b)*(float64_t)label[i];/* 'distance' from
                                                     hyperplane*/
          target=-(learn_parm->eps[i]-(float64_t)label[i]*c[i]);
          ex_c=learn_parm->svm_cost[i]-learn_parm->epsilon_a;
          if(dist <= 0) {
              (*misclassified)++;  /* does not work due to deactivation of var */
          }
          if((a[i]>learn_parm->epsilon_a) && (dist > target)) {
              if((dist-target)>(*maxdiff))  /* largest violation */
                  (*maxdiff)=dist-target;
          }
          else if((a[i]<ex_c) && (dist < target)) {
              if((target-dist)>(*maxdiff))  /* largest violation */
                  (*maxdiff)=target-dist;
          }
          /* Count how int32_t a variable was at lower/upper bound (and optimal).*/
          /* Variables, which were at the bound and optimal for a int32_t */
          /* time are unlikely to become support vectors. In case our */
          /* cache is filled up, those variables are excluded to save */
          /* kernel evaluations. (See chapter 'Shrinking').*/
          if((a[i]>(learn_parm->epsilon_a))
             && (a[i]<ex_c)) {
              last_suboptimal_at[i]=iteration;         /* not at bound */
          }
          else if((a[i]<=(learn_parm->epsilon_a))
                  && (dist < (target+learn_parm->epsilon_shrink))) {
              last_suboptimal_at[i]=iteration;         /* not likely optimal */
          }
          else if((a[i]>=ex_c)
                  && (dist > (target-learn_parm->epsilon_shrink)))  {
              last_suboptimal_at[i]=iteration;         /* not likely optimal */
          }
      }
  }

  /* termination criterion */
  if((!retrain) && ((*maxdiff) > learn_parm->epsilon_crit)) {
      retrain=1;
  }
  return(retrain);
}

void CSVMLight::update_linear_component(
    int32_t* docs, int32_t* label, int32_t *active2dnum, float64_t *a,
    float64_t *a_old, int32_t *working2dnum, int32_t totdoc, float64_t *lin,
    float64_t *aicache, float64_t* c)
     /* keep track of the linear component */
     /* lin of the gradient etc. by updating */
     /* based on the change of the variables */
     /* in the current working set */
{
    register int32_t i=0,ii=0,j=0,jj=0;

    if (kernel->has_property(KP_LINADD) && get_linadd_enabled())
    {
        if (callback)
        {
            update_linear_component_mkl_linadd(docs, label, active2dnum, a,
                    a_old, working2dnum, totdoc, lin, aicache);
        }
        else
        {
            kernel->clear_normal();

            int32_t num_working=0;
            for (ii=0;(i=working2dnum[ii])>=0;ii++) {
                if(a[i] != a_old[i]) {
                    kernel->add_to_normal(docs[i], (a[i]-a_old[i])*(float64_t)label[i]);
                    num_working++;
                }
            }

            if (num_working>0)
            {
                if (parallel->get_num_threads() < 2)
                {
                    for (jj=0;(j=active2dnum[jj])>=0;jj++) {
                        lin[j]+=kernel->compute_optimized(docs[j]);
                    }
                }
#ifndef WIN32
                else
                {
                    int32_t num_elem = 0 ;
                    for (jj=0;(j=active2dnum[jj])>=0;jj++) num_elem++ ;

                    pthread_t* threads = new pthread_t[parallel->get_num_threads()-1] ;
                    S_THREAD_PARAM* params = new S_THREAD_PARAM[parallel->get_num_threads()-1] ;
                    int32_t start = 0 ;
                    int32_t step = num_elem/parallel->get_num_threads();
                    int32_t end = step ;

                    for (int32_t t=0; t<parallel->get_num_threads()-1; t++)
                    {
                        params[t].kernel = kernel ;
                        params[t].lin = lin ;
                        params[t].docs = docs ;
                        params[t].active2dnum=active2dnum ;
                        params[t].start = start ;
                        params[t].end = end ;
                        start=end ;
                        end+=step ;
                        pthread_create(&threads[t], NULL, update_linear_component_linadd_helper, (void*)&params[t]) ;
                    }

                    for (jj=params[parallel->get_num_threads()-2].end;(j=active2dnum[jj])>=0;jj++) {
                        lin[j]+=kernel->compute_optimized(docs[j]);
                    }
                    void* ret;
                    for (int32_t t=0; t<parallel->get_num_threads()-1; t++)
                        pthread_join(threads[t], &ret) ;

                    delete[] params;
                    delete[] threads;
                }
#endif
            }
        }
    }
    else
    {
        if (callback)
        {
            update_linear_component_mkl(docs, label, active2dnum,
                    a, a_old, working2dnum, totdoc, lin, aicache);
        }
        else {
            for (jj=0;(i=working2dnum[jj])>=0;jj++) {
                if(a[i] != a_old[i]) {
                    kernel->get_kernel_row(i,active2dnum,aicache);
                    for (ii=0;(j=active2dnum[ii])>=0;ii++)
                        lin[j]+=(a[i]-a_old[i])*aicache[j]*(float64_t)label[i];
                }
            }
        }
    }
}


void CSVMLight::update_linear_component_mkl(
    int32_t* docs, int32_t* label, int32_t *active2dnum, float64_t *a,
    float64_t *a_old, int32_t *working2dnum, int32_t totdoc, float64_t *lin,
    float64_t *aicache)
{
    //int inner_iters=0;
    int32_t num = kernel->get_num_vec_rhs();
    int32_t num_weights = -1;
    int32_t num_kernels = kernel->get_num_subkernels() ;
    const float64_t* old_beta   = kernel->get_subkernel_weights(num_weights);
    ASSERT(num_weights==num_kernels);

    if ((kernel->get_kernel_type()==K_COMBINED) &&
             (!((CCombinedKernel*)kernel)->get_append_subkernel_weights()))// for combined kernel
    {
        CCombinedKernel* k      = (CCombinedKernel*) kernel;
        CKernel* kn = k->get_first_kernel() ;
        int32_t n = 0, i, j ;

        while (kn!=NULL)
        {
            for (i=0;i<num;i++)
            {
                if(a[i] != a_old[i])
                {
                    kn->get_kernel_row(i,NULL,aicache, true);
                    for (j=0;j<num;j++)
                        W[j*num_kernels+n]+=(a[i]-a_old[i])*aicache[j]*(float64_t)label[i];
                }
            }

            SG_UNREF(kn);
            kn = k->get_next_kernel();
            n++ ;
        }
    }
    else // hope the kernel is fast ...
    {
        float64_t* w_backup = new float64_t[num_kernels] ;
        float64_t* w1 = new float64_t[num_kernels] ;

        // backup and set to zero
        for (int32_t i=0; i<num_kernels; i++)
        {
            w_backup[i] = old_beta[i] ;
            w1[i]=0.0 ;
        }
        for (int32_t n=0; n<num_kernels; n++)
        {
            w1[n]=1.0 ;
            kernel->set_subkernel_weights(w1, num_weights) ;

            for (int32_t i=0;i<num;i++)
            {
                if(a[i] != a_old[i])
                {
                    for (int32_t j=0;j<num;j++)
                        W[j*num_kernels+n]+=(a[i]-a_old[i])*compute_kernel(i,j)*(float64_t)label[i];
                }
            }
            w1[n]=0.0 ;
        }

        // restore old weights
        kernel->set_subkernel_weights(w_backup,num_weights) ;

        delete[] w_backup ;
        delete[] w1 ;
    }

    call_mkl_callback(a, label, lin);
}


void CSVMLight::update_linear_component_mkl_linadd(
    int32_t* docs, int32_t* label, int32_t *active2dnum, float64_t *a,
    float64_t *a_old, int32_t *working2dnum, int32_t totdoc, float64_t *lin,
    float64_t *aicache)
{
    //int inner_iters=0;

    // kernel with LP_LINADD property is assumed to have
    // compute_by_subkernel functions
    int32_t num = kernel->get_num_vec_rhs();
    int32_t num_weights = -1;
    int32_t num_kernels = kernel->get_num_subkernels() ;
    const float64_t* old_beta   = kernel->get_subkernel_weights(num_weights);
    ASSERT(num_weights==num_kernels);

    float64_t* w_backup = new float64_t[num_kernels] ;
    float64_t* w1 = new float64_t[num_kernels] ;

    // backup and set to one
    for (int32_t i=0; i<num_kernels; i++)
    {
        w_backup[i] = old_beta[i] ;
        w1[i]=1.0 ;
    }
    // set the kernel weights
    kernel->set_subkernel_weights(w1, num_weights) ;

    // create normal update (with changed alphas only)
    kernel->clear_normal();
    for (int32_t ii=0, i=0;(i=working2dnum[ii])>=0;ii++) {
        if(a[i] != a_old[i]) {
            kernel->add_to_normal(docs[i], (a[i]-a_old[i])*(float64_t)label[i]);
        }
    }

    if (parallel->get_num_threads() < 2)
    {
        // determine contributions of different kernels
        for (int32_t i=0; i<num; i++)
            kernel->compute_by_subkernel(i,&W[i*num_kernels]);
    }
#ifndef WIN32
    else
    {
        pthread_t* threads = new pthread_t[parallel->get_num_threads()-1];
        S_THREAD_PARAM* params = new S_THREAD_PARAM[parallel->get_num_threads()-1];
        int32_t step= num/parallel->get_num_threads();

        for (int32_t t=0; t<parallel->get_num_threads()-1; t++)
        {
            params[t].kernel = kernel;
            params[t].W = W;
            params[t].start = t*step;
            params[t].end = (t+1)*step;
            pthread_create(&threads[t], NULL, CSVMLight::update_linear_component_mkl_linadd_helper, (void*)&params[t]);
        }

        for (int32_t i=params[parallel->get_num_threads()-2].end; i<num; i++)
            kernel->compute_by_subkernel(i,&W[i*num_kernels]);

        for (int32_t t=0; t<parallel->get_num_threads()-1; t++)
            pthread_join(threads[t], NULL);

        delete[] params;
        delete[] threads;
    }
#endif

    // restore old weights
    kernel->set_subkernel_weights(w_backup,num_weights);

    delete[] w_backup;
    delete[] w1;

    call_mkl_callback(a, label, lin);
}

void* CSVMLight::update_linear_component_mkl_linadd_helper(void* p)
{
    S_THREAD_PARAM* params = (S_THREAD_PARAM*) p;

    int32_t num_kernels=params->kernel->get_num_subkernels();

    // determine contributions of different kernels
    for (int32_t i=params->start; i<params->end; i++)
        params->kernel->compute_by_subkernel(i,&(params->W[i*num_kernels]));

    return NULL ;
}

void CSVMLight::call_mkl_callback(float64_t* a, int32_t* label, float64_t* lin)
{
    int32_t num = kernel->get_num_vec_rhs();
    int32_t num_kernels = kernel->get_num_subkernels() ;

    int nk = (int) num_kernels; /* calling external lib */

    float64_t suma=0;
    float64_t* sumw=new float64_t[num_kernels];
#ifdef HAVE_LAPACK
    double* alphay  = new double[num];

    for (int32_t i=0; i<num; i++)
    {
        alphay[i]=a[i]*label[i];
        suma+=a[i];
    }

    for (int32_t i=0; i<num_kernels; i++)
        sumw[i]=0;

    cblas_dgemv(CblasColMajor, CblasNoTrans, num_kernels, (int) num, 0.5, (double*) W,
            num_kernels, alphay, 1, 1.0, (double*) sumw, 1);

    delete[] alphay;
#else
    for (int32_t i=0; i<num; i++)
        suma += a[i];

    for (int32_t d=0; d<num_kernels; d++)
    {
        sumw[d]=0;
        for (int32_t i=0; i<num; i++)
            sumw[d] += a[i]*(0.5*label[i]*W[i*num_kernels+d]);
    }
#endif

    if (callback)
        mkl_converged=callback(mkl, sumw, suma);


    const float64_t* new_beta   = kernel->get_subkernel_weights(num_kernels);

    // update lin
#ifdef HAVE_LAPACK
    cblas_dgemv(CblasColMajor, CblasTrans, nk, (int) num, 1.0, (double*) W,
        nk, (double*) new_beta, 1, 0.0, (double*) lin, 1);
#else
    for (int32_t i=0; i<num; i++)
        lin[i]=0 ;
    for (int32_t d=0; d<num_kernels; d++)
        if (new_beta[d]!=0)
            for (int32_t i=0; i<num; i++)
                lin[i] += new_beta[d]*W[i*num_kernels+d] ;
#endif

    delete[] sumw;
}


/*************************** Working set selection ***************************/

int32_t CSVMLight::select_next_qp_subproblem_grad(
    int32_t* label, float64_t *a, float64_t *lin, float64_t *c, int32_t totdoc,
    int32_t qp_size, int32_t *inconsistent, int32_t *active2dnum,
    int32_t *working2dnum, float64_t *selcrit, int32_t *select,
    int32_t cache_only, int32_t *key, int32_t *chosen)
    /* Use the feasible direction approach to select the next
       qp-subproblem (see chapter 'Selecting a good working set'). If
       'cache_only' is true, then the variables are selected only among
       those for which the kernel evaluations are cached. */
{
    int32_t choosenum,i,j,k,activedoc,inum,valid;
    float64_t s;

    for (inum=0;working2dnum[inum]>=0;inum++); /* find end of index */
    choosenum=0;
    activedoc=0;
    for (i=0;(j=active2dnum[i])>=0;i++) {
        s=-label[j];
        if(cache_only)
        {
            if (use_kernel_cache)
                valid=(kernel->kernel_cache_check(j));
            else
                valid = 1 ;
        }
        else
            valid=1;
        if(valid
           && (!((a[j]<=(0+learn_parm->epsilon_a)) && (s<0)))
           && (!((a[j]>=(learn_parm->svm_cost[j]-learn_parm->epsilon_a))
                 && (s>0)))
           && (!chosen[j])
           && (label[j])
           && (!inconsistent[j]))
        {
            selcrit[activedoc]=(float64_t)label[j]*(learn_parm->eps[j]-(float64_t)label[j]*c[j]+(float64_t)label[j]*lin[j]);
            key[activedoc]=j;
            activedoc++;
        }
    }
    select_top_n(selcrit,activedoc,select,(int32_t)(qp_size/2));
    for (k=0;(choosenum<(qp_size/2)) && (k<(qp_size/2)) && (k<activedoc);k++) {
        i=key[select[k]];
        chosen[i]=1;
        working2dnum[inum+choosenum]=i;
        choosenum+=1;
        if (use_kernel_cache)
            kernel->kernel_cache_touch(i);
        /* make sure it does not get kicked */
        /* out of cache */
    }

    activedoc=0;
    for (i=0;(j=active2dnum[i])>=0;i++) {
        s=label[j];
        if(cache_only)
        {
            if (use_kernel_cache)
                valid=(kernel->kernel_cache_check(j));
            else
                valid = 1 ;
        }
        else
            valid=1;
        if(valid
           && (!((a[j]<=(0+learn_parm->epsilon_a)) && (s<0)))
           && (!((a[j]>=(learn_parm->svm_cost[j]-learn_parm->epsilon_a))
                 && (s>0)))
           && (!chosen[j])
           && (label[j])
           && (!inconsistent[j]))
        {
            selcrit[activedoc]=-(float64_t)label[j]*(learn_parm->eps[j]-(float64_t)label[j]*c[j]+(float64_t)label[j]*lin[j]);
            /*  selcrit[activedoc]=-(float64_t)(label[j]*(-1.0+(float64_t)label[j]*lin[j])); */
            key[activedoc]=j;
            activedoc++;
        }
    }
    select_top_n(selcrit,activedoc,select,(int32_t)(qp_size/2));
    for (k=0;(choosenum<qp_size) && (k<(qp_size/2)) && (k<activedoc);k++) {
        i=key[select[k]];
        chosen[i]=1;
        working2dnum[inum+choosenum]=i;
        choosenum+=1;
        if (use_kernel_cache)
            kernel->kernel_cache_touch(i); /* make sure it does not get kicked */
        /* out of cache */
    }
    working2dnum[inum+choosenum]=-1; /* complete index */
    return(choosenum);
}

int32_t CSVMLight::select_next_qp_subproblem_rand(
    int32_t* label, float64_t *a, float64_t *lin, float64_t *c, int32_t totdoc,
    int32_t qp_size, int32_t *inconsistent, int32_t *active2dnum,
    int32_t *working2dnum, float64_t *selcrit, int32_t *select, int32_t *key,
    int32_t *chosen, int32_t iteration)
/* Use the feasible direction approach to select the next
   qp-subproblem (see section 'Selecting a good working set'). Chooses
   a feasible direction at (pseudo) random to help jump over numerical
   problem. */
{
  int32_t choosenum,i,j,k,activedoc,inum;
  float64_t s;

  for (inum=0;working2dnum[inum]>=0;inum++); /* find end of index */
  choosenum=0;
  activedoc=0;
  for (i=0;(j=active2dnum[i])>=0;i++) {
    s=-label[j];
    if((!((a[j]<=(0+learn_parm->epsilon_a)) && (s<0)))
       && (!((a[j]>=(learn_parm->svm_cost[j]-learn_parm->epsilon_a))
         && (s>0)))
       && (!inconsistent[j])
       && (label[j])
       && (!chosen[j])) {
      selcrit[activedoc]=(j+iteration) % totdoc;
      key[activedoc]=j;
      activedoc++;
    }
  }
  select_top_n(selcrit,activedoc,select,(int32_t)(qp_size/2));
  for (k=0;(choosenum<(qp_size/2)) && (k<(qp_size/2)) && (k<activedoc);k++) {
    i=key[select[k]];
    chosen[i]=1;
    working2dnum[inum+choosenum]=i;
    choosenum+=1;
    if (use_kernel_cache)
        kernel->kernel_cache_touch(i); /* make sure it does not get kicked */
                                        /* out of cache */
  }

  activedoc=0;
  for (i=0;(j=active2dnum[i])>=0;i++) {
    s=label[j];
    if((!((a[j]<=(0+learn_parm->epsilon_a)) && (s<0)))
       && (!((a[j]>=(learn_parm->svm_cost[j]-learn_parm->epsilon_a))
         && (s>0)))
       && (!inconsistent[j])
       && (label[j])
       && (!chosen[j])) {
      selcrit[activedoc]=(j+iteration) % totdoc;
      key[activedoc]=j;
      activedoc++;
    }
  }
  select_top_n(selcrit,activedoc,select,(int32_t)(qp_size/2));
  for (k=0;(choosenum<qp_size) && (k<(qp_size/2)) && (k<activedoc);k++) {
    i=key[select[k]];
    chosen[i]=1;
    working2dnum[inum+choosenum]=i;
    choosenum+=1;
    if (use_kernel_cache)
        kernel->kernel_cache_touch(i); /* make sure it does not get kicked */
                                        /* out of cache */
  }
  working2dnum[inum+choosenum]=-1; /* complete index */
  return(choosenum);
}



void CSVMLight::select_top_n(
    float64_t *selcrit, int32_t range, int32_t* select, int32_t n)
{
  register int32_t i,j;

  for (i=0;(i<n) && (i<range);i++) { /* Initialize with the first n elements */
    for (j=i;j>=0;j--) {
      if((j>0) && (selcrit[select[j-1]]<selcrit[i])){
    select[j]=select[j-1];
      }
      else {
    select[j]=i;
    j=-1;
      }
    }
  }
  if(n>0) {
    for (i=n;i<range;i++) {
      if(selcrit[i]>selcrit[select[n-1]]) {
    for (j=n-1;j>=0;j--) {
      if((j>0) && (selcrit[select[j-1]]<selcrit[i])) {
        select[j]=select[j-1];
      }
      else {
        select[j]=i;
        j=-1;
      }
    }
      }
    }
  }
}


/******************************** Shrinking  *********************************/

void CSVMLight::init_shrink_state(
    SHRINK_STATE *shrink_state, int32_t totdoc, int32_t maxhistory)
{
  int32_t i;

  shrink_state->deactnum=0;
  shrink_state->active = new int32_t[totdoc];
  shrink_state->inactive_since = new int32_t[totdoc];
  shrink_state->a_history = new float64_t*[maxhistory];
  shrink_state->maxhistory=maxhistory;
  shrink_state->last_lin = new float64_t[totdoc];
  shrink_state->last_a = new float64_t[totdoc];

  for (i=0;i<totdoc;i++) {
    shrink_state->active[i]=1;
    shrink_state->inactive_since[i]=0;
    shrink_state->last_a[i]=0;
    shrink_state->last_lin[i]=0;
  }
}

void CSVMLight::shrink_state_cleanup(SHRINK_STATE *shrink_state)
{
  delete[] shrink_state->active;
  delete[] shrink_state->inactive_since;
  if(shrink_state->deactnum > 0)
    delete[] (shrink_state->a_history[shrink_state->deactnum-1]);
  delete[] (shrink_state->a_history);
  delete[] (shrink_state->last_a);
  delete[] (shrink_state->last_lin);
}

int32_t CSVMLight::shrink_problem(
    SHRINK_STATE *shrink_state, int32_t *active2dnum,
    int32_t *last_suboptimal_at, int32_t iteration, int32_t totdoc,
    int32_t minshrink, float64_t *a, int32_t *inconsistent, float64_t* c,
    float64_t* lin, int* label)
     /* Shrink some variables away.  Do the shrinking only if at least
        minshrink variables can be removed. */
{
  int32_t i,ii,change,activenum,lastiter;
  float64_t *a_old=NULL;

  activenum=0;
  change=0;
  for (ii=0;active2dnum[ii]>=0;ii++) {
      i=active2dnum[ii];
      activenum++;
      lastiter=last_suboptimal_at[i];

      if(((iteration-lastiter) > learn_parm->svm_iter_to_shrink)
         || (inconsistent[i])) {
          change++;
      }
  }
  if((change>=minshrink) /* shrink only if sufficiently many candidates */
     && (shrink_state->deactnum<shrink_state->maxhistory)) { /* and enough memory */
      /* Shrink problem by removing those variables which are */
      /* optimal at a bound for a minimum number of iterations */
      if(verbosity>=2) {
          SG_INFO( " Shrinking...");
      }

      if (!(kernel->has_property(KP_LINADD) && get_linadd_enabled())) { /*  non-linear case save alphas */

          a_old=new float64_t[totdoc];
          shrink_state->a_history[shrink_state->deactnum]=a_old;
          for (i=0;i<totdoc;i++) {
              a_old[i]=a[i];
          }
      }
      for (ii=0;active2dnum[ii]>=0;ii++) {
          i=active2dnum[ii];
          lastiter=last_suboptimal_at[i];
          if(((iteration-lastiter) > learn_parm->svm_iter_to_shrink)
             || (inconsistent[i])) {
              shrink_state->active[i]=0;
              shrink_state->inactive_since[i]=shrink_state->deactnum;
          }
      }
      activenum=compute_index(shrink_state->active,totdoc,active2dnum);
      shrink_state->deactnum++;
      if(kernel->has_property(KP_LINADD) && get_linadd_enabled())
          shrink_state->deactnum=0;

      if(verbosity>=2) {
          SG_DONE();
          SG_DEBUG("Number of inactive variables = %ld\n", totdoc-activenum);
      }
  }
  return(activenum);
}

void* CSVMLight::reactivate_inactive_examples_linadd_helper(void* p)
{
    S_THREAD_PARAM_REACTIVATE_LINADD* params = (S_THREAD_PARAM_REACTIVATE_LINADD*) p;

    CKernel* k = params->kernel;
    float64_t* lin = params->lin;
    float64_t* last_lin = params->last_lin;
    int32_t* active = params->active;
    int32_t* docs = params->docs;
    int32_t start = params->start;
    int32_t end = params->end;

    for (int32_t i=start;i<end;i++)
    {
        if (!active[i])
            lin[i] = last_lin[i]+k->compute_optimized(docs[i]);

        last_lin[i]=lin[i];
    }

    return NULL;
}

void* CSVMLight::reactivate_inactive_examples_vanilla_helper(void* p)
{
    S_THREAD_PARAM_REACTIVATE_VANILLA* params = (S_THREAD_PARAM_REACTIVATE_VANILLA*) p;
    ASSERT(params);
    ASSERT(params->kernel);
    ASSERT(params->lin);
    ASSERT(params->aicache);
    ASSERT(params->a);
    ASSERT(params->a_old);
    ASSERT(params->changed2dnum);
    ASSERT(params->inactive2dnum);
    ASSERT(params->label);

    CKernel* k = params->kernel;
    float64_t* lin = params->lin;
    float64_t* aicache = params->aicache;
    float64_t* a= params->a;
    float64_t* a_old = params->a_old;
    int32_t* changed2dnum = params->changed2dnum;
    int32_t* inactive2dnum = params->inactive2dnum;
    int32_t* label = params->label;
    int32_t start = params->start;
    int32_t end = params->end;

    for (int32_t ii=start;ii<end;ii++)
    {
        int32_t i=changed2dnum[ii];
        int32_t j=0;
        ASSERT(i>=0);

        k->get_kernel_row(i,inactive2dnum,aicache);
        for (int32_t jj=0;(j=inactive2dnum[jj])>=0;jj++)
            lin[j]+=(a[i]-a_old[i])*aicache[j]*(float64_t)label[i];
    }
    return NULL;
}

void CSVMLight::reactivate_inactive_examples(
    int32_t* label, float64_t *a, SHRINK_STATE *shrink_state, float64_t *lin,
    float64_t *c, int32_t totdoc, int32_t iteration, int32_t *inconsistent,
    int32_t* docs, float64_t *aicache, float64_t *maxdiff)
     /* Make all variables active again which had been removed by
        shrinking. */
     /* Computes lin for those variables from scratch. */
{
  register int32_t i,j,ii,jj,t,*changed2dnum,*inactive2dnum;
  int32_t *changed,*inactive;
  register float64_t *a_old,dist;
  float64_t ex_c,target;

  if (kernel->has_property(KP_LINADD) && get_linadd_enabled()) { /* special linear case */
      a_old=shrink_state->last_a;

      if (!use_batch_computation || !kernel->has_property(KP_BATCHEVALUATION))
      {
          SG_DEBUG( " clear normal - linadd\n");
          kernel->clear_normal();

          int32_t num_modified=0;
          for (i=0;i<totdoc;i++) {
              if(a[i] != a_old[i]) {
                  kernel->add_to_normal(docs[i], ((a[i]-a_old[i])*(float64_t)label[i]));
                  a_old[i]=a[i];
                  num_modified++;
              }
          }

          if (num_modified>0)
          {
              int32_t num_threads=parallel->get_num_threads();
              ASSERT(num_threads>0);
              if (num_threads < 2)
              {
                  S_THREAD_PARAM_REACTIVATE_LINADD params;
                  params.kernel=kernel;
                  params.lin=lin;
                  params.last_lin=shrink_state->last_lin;
                  params.docs=docs;
                  params.active=shrink_state->active;
                  params.start=0;
                  params.end=totdoc;
                  reactivate_inactive_examples_linadd_helper((void*) &params);
              }
#ifndef WIN32
              else
              {
                  pthread_t* threads = new pthread_t[num_threads-1];
                  S_THREAD_PARAM_REACTIVATE_LINADD* params = new S_THREAD_PARAM_REACTIVATE_LINADD[num_threads];
                  int32_t step= totdoc/num_threads;

                  for (t=0; t<num_threads-1; t++)
                  {
                      params[t].kernel=kernel;
                      params[t].lin=lin;
                      params[t].last_lin=shrink_state->last_lin;
                      params[t].docs=docs;
                      params[t].active=shrink_state->active;
                      params[t].start = t*step;
                      params[t].end = (t+1)*step;
                      pthread_create(&threads[t], NULL, CSVMLight::reactivate_inactive_examples_linadd_helper, (void*)&params[t]);
                  }

                  params[t].kernel=kernel;
                  params[t].lin=lin;
                  params[t].last_lin=shrink_state->last_lin;
                  params[t].docs=docs;
                  params[t].active=shrink_state->active;
                  params[t].start = t*step;
                  params[t].end = totdoc;
                  reactivate_inactive_examples_linadd_helper((void*) &params[t]);

                  for (t=0; t<num_threads-1; t++)
                      pthread_join(threads[t], NULL);

                  delete[] threads;
                  delete[] params;
              }
#endif

          }
      }
      else
      {
          float64_t *alphas = new float64_t[totdoc] ;
          int32_t *idx = new int32_t[totdoc] ;
          int32_t num_suppvec=0 ;

          for (i=0; i<totdoc; i++)
          {
              if(a[i] != a_old[i])
              {
                  alphas[num_suppvec] = (a[i]-a_old[i])*(float64_t)label[i];
                  idx[num_suppvec] = i ;
                  a_old[i] = a[i] ;
                  num_suppvec++ ;
              }
          }

          if (num_suppvec>0)
          {
              int32_t num_inactive=0;
              int32_t* inactive_idx=new int32_t[totdoc]; // infact we only need a subset

              j=0;
              for (i=0;i<totdoc;i++)
              {
                  if(!shrink_state->active[i])
                  {
                      inactive_idx[j++] = i;
                      num_inactive++;
                  }
              }

              if (num_inactive>0)
              {
                  float64_t* dest = new float64_t[num_inactive];
                  memset(dest, 0, sizeof(float64_t)*num_inactive);

                  kernel->compute_batch(num_inactive, inactive_idx, dest, num_suppvec, idx, alphas);

                  j=0;
                  for (i=0;i<totdoc;i++) {
                      if(!shrink_state->active[i]) {
                          lin[i] = shrink_state->last_lin[i] + dest[j++] ;
                      }
                      shrink_state->last_lin[i]=lin[i];
                  }

                  delete[] dest;
              }
              else
              {
                  for (i=0;i<totdoc;i++)
                      shrink_state->last_lin[i]=lin[i];
              }
              delete[] inactive_idx;
          }
          delete[] alphas;
          delete[] idx;
      }

      kernel->delete_optimization();
  }
  else
  {
      changed=new int32_t[totdoc];
      changed2dnum=new int32_t[totdoc+11];
      inactive=new int32_t[totdoc];
      inactive2dnum=new int32_t[totdoc+11];
      for (t=shrink_state->deactnum-1;(t>=0) && shrink_state->a_history[t];t--)
      {
          if(verbosity>=2) {
              SG_INFO( "%ld..",t);
          }
          a_old=shrink_state->a_history[t];
          for (i=0;i<totdoc;i++) {
              inactive[i]=((!shrink_state->active[i])
                           && (shrink_state->inactive_since[i] == t));
              changed[i]= (a[i] != a_old[i]);
          }
          compute_index(inactive,totdoc,inactive2dnum);
          compute_index(changed,totdoc,changed2dnum);


          int32_t num_threads=parallel->get_num_threads();
          ASSERT(num_threads>0);

          if (num_threads < 2)
          {
              for (ii=0;(i=changed2dnum[ii])>=0;ii++) {
                  kernel->get_kernel_row(i,inactive2dnum,aicache);
                  for (jj=0;(j=inactive2dnum[jj])>=0;jj++)
                      lin[j]+=(a[i]-a_old[i])*aicache[j]*(float64_t)label[i];
              }
          }
#ifndef WIN32
          else
          {
              //find number of the changed ones
              int32_t num_changed=0;
              for (ii=0;changed2dnum[ii]>=0;ii++)
                  num_changed++;

              if (num_changed>0)
              {
                  pthread_t* threads= new pthread_t[num_threads-1];
                  S_THREAD_PARAM_REACTIVATE_VANILLA* params = new S_THREAD_PARAM_REACTIVATE_VANILLA[num_threads];
                  int32_t step= num_changed/num_threads;

                  // alloc num_threads many tmp buffers
                  float64_t* tmp_lin=new float64_t[totdoc*num_threads];
                  memset(tmp_lin, 0, sizeof(float64_t)*((size_t) totdoc)*num_threads);
                  float64_t* tmp_aicache=new float64_t[totdoc*num_threads];
                  memset(tmp_aicache, 0, sizeof(float64_t)*((size_t) totdoc)*num_threads);

                  int32_t thr;
                  for (thr=0; thr<num_threads-1; thr++)
                  {
                      params[thr].kernel=kernel;
                      params[thr].lin=&tmp_lin[thr*totdoc];
                      params[thr].aicache=&tmp_aicache[thr*totdoc];
                      params[thr].a=a;
                      params[thr].a_old=a_old;
                      params[thr].changed2dnum=changed2dnum;
                      params[thr].inactive2dnum=inactive2dnum;
                      params[thr].label=label;
                      params[thr].start = thr*step;
                      params[thr].end = (thr+1)*step;
                      pthread_create(&threads[thr], NULL, CSVMLight::reactivate_inactive_examples_vanilla_helper, (void*)&params[thr]);
                  }

                  params[thr].kernel=kernel;
                  params[thr].lin=&tmp_lin[thr*totdoc];
                  params[thr].aicache=&tmp_aicache[thr*totdoc];
                  params[thr].a=a;
                  params[thr].a_old=a_old;
                  params[thr].changed2dnum=changed2dnum;
                  params[thr].inactive2dnum=inactive2dnum;
                  params[thr].label=label;
                  params[thr].start = thr*step;
                  params[thr].end = num_changed;
                  reactivate_inactive_examples_vanilla_helper((void*) &params[thr]);

                  for (jj=0;(j=inactive2dnum[jj])>=0;jj++)
                      lin[j]+=tmp_lin[totdoc*thr+j];

                  for (thr=0; thr<num_threads-1; thr++)
                  {
                      pthread_join(threads[thr], NULL);

                      //add up results
                      for (jj=0;(j=inactive2dnum[jj])>=0;jj++)
                          lin[j]+=tmp_lin[totdoc*thr+j];
                  }

                  delete[] tmp_lin;
                  delete[] tmp_aicache;
                  delete[] threads;
                  delete[] params;
              }
          }
#endif
      }
      delete[] changed;
      delete[] changed2dnum;
      delete[] inactive;
      delete[] inactive2dnum;
  }

  (*maxdiff)=0;
  for (i=0;i<totdoc;i++) {
    shrink_state->inactive_since[i]=shrink_state->deactnum-1;
    if(!inconsistent[i]) {
      dist=(lin[i]-model->b)*(float64_t)label[i];
      target=-(learn_parm->eps[i]-(float64_t)label[i]*c[i]);
      ex_c=learn_parm->svm_cost[i]-learn_parm->epsilon_a;
      if((a[i]>learn_parm->epsilon_a) && (dist > target)) {
    if((dist-target)>(*maxdiff))  /* largest violation */
      (*maxdiff)=dist-target;
      }
      else if((a[i]<ex_c) && (dist < target)) {
    if((target-dist)>(*maxdiff))  /* largest violation */
      (*maxdiff)=target-dist;
      }
      if((a[i]>(0+learn_parm->epsilon_a))
     && (a[i]<ex_c)) {
    shrink_state->active[i]=1;                         /* not at bound */
      }
      else if((a[i]<=(0+learn_parm->epsilon_a)) && (dist < (target+learn_parm->epsilon_shrink))) {
    shrink_state->active[i]=1;
      }
      else if((a[i]>=ex_c)
          && (dist > (target-learn_parm->epsilon_shrink))) {
    shrink_state->active[i]=1;
      }
      else if(learn_parm->sharedslack) { /* make all active when sharedslack */
    shrink_state->active[i]=1;
      }
    }
  }

  if (!(kernel->has_property(KP_LINADD) && get_linadd_enabled())) { /* update history for non-linear */
      for (i=0;i<totdoc;i++) {
          (shrink_state->a_history[shrink_state->deactnum-1])[i]=a[i];
      }
      for (t=shrink_state->deactnum-2;(t>=0) && shrink_state->a_history[t];t--) {
          delete[] shrink_state->a_history[t];
          shrink_state->a_history[t]=0;
      }
  }
}



/* start the optimizer and return the optimal values */
float64_t* CSVMLight::optimize_qp(
        QP *qp, float64_t *epsilon_crit, int32_t nx, float64_t *threshold,
        int32_t& svm_maxqpsize)
{
    register int32_t i, j, result;
    float64_t margin, obj_before, obj_after;
    float64_t sigdig, dist, epsilon_loqo;
    int32_t iter;

    if(!primal) { /* allocate memory at first call */
        primal=new float64_t[nx*3];
        dual=new float64_t[nx*2+1];
    }

    obj_before=0; /* calculate objective before optimization */
    for(i=0;i<qp->opt_n;i++) {
        obj_before+=(qp->opt_g0[i]*qp->opt_xinit[i]);
        obj_before+=(0.5*qp->opt_xinit[i]*qp->opt_xinit[i]*qp->opt_g[i*qp->opt_n+i]);
        for(j=0;j<i;j++) {
            obj_before+=(qp->opt_xinit[j]*qp->opt_xinit[i]*qp->opt_g[j*qp->opt_n+i]);
        }
    }

    result=STILL_RUNNING;
    qp->opt_ce0[0]*=(-1.0);
    /* Run pr_loqo. If a run fails, try again with parameters which lead */
    /* to a slower, but more robust setting. */
    for(margin=init_margin,iter=init_iter;
        (margin<=0.9999999) && (result!=OPTIMAL_SOLUTION);) {

        opt_precision=CMath::max(opt_precision, DEF_PRECISION);
        sigdig=-log10(opt_precision);

        result=pr_loqo((int32_t)qp->opt_n,(int32_t)qp->opt_m,
                (float64_t *)qp->opt_g0,(float64_t *)qp->opt_g,
                (float64_t *)qp->opt_ce,(float64_t *)qp->opt_ce0,
                (float64_t *)qp->opt_low,(float64_t *)qp->opt_up,
                (float64_t *)primal,(float64_t *)dual,
                (int32_t)(verbosity-2),
                (float64_t)sigdig,(int32_t)iter,
                (float64_t)margin,(float64_t)(qp->opt_up[0])/4.0,(int32_t)0);

        if(CMath::is_nan(dual[0])) {     /* check for choldc problem */
            if(verbosity>=2) {
                SG_SDEBUG("Restarting PR_LOQO with more conservative parameters.\n");
            }
            if(init_margin<0.80) { /* become more conservative in general */
                init_margin=(4.0*margin+1.0)/5.0;
            }
            margin=(margin+1.0)/2.0;
            (opt_precision)*=10.0;   /* reduce precision */
            if(verbosity>=2) {
                SG_SDEBUG("Reducing precision of PR_LOQO.\n");
            }
        }
        else if(result!=OPTIMAL_SOLUTION) {
            iter+=2000;
            init_iter+=10;
            (opt_precision)*=10.0;   /* reduce precision */
            if(verbosity>=2) {
                SG_SDEBUG("Reducing precision of PR_LOQO due to (%ld).\n",result);
            }
        }
    }

    if(qp->opt_m)         /* Thanks to Alex Smola for this hint */
        model_b=dual[0];
    else
        model_b=0;

    /* Check the precision of the alphas. If results of current optimization */
    /* violate KT-Conditions, relax the epsilon on the bounds on alphas. */
    epsilon_loqo=1E-10;
    for(i=0;i<qp->opt_n;i++) {
        dist=-model_b*qp->opt_ce[i];
        dist+=(qp->opt_g0[i]+1.0);
        for(j=0;j<i;j++) {
            dist+=(primal[j]*qp->opt_g[j*qp->opt_n+i]);
        }
        for(j=i;j<qp->opt_n;j++) {
            dist+=(primal[j]*qp->opt_g[i*qp->opt_n+j]);
        }
        /*  SG_SDEBUG("LOQO: a[%d]=%f, dist=%f, b=%f\n",i,primal[i],dist,dual[0]); */
        if((primal[i]<(qp->opt_up[i]-epsilon_loqo)) && (dist < (1.0-(*epsilon_crit)))) {
            epsilon_loqo=(qp->opt_up[i]-primal[i])*2.0;
        }
        else if((primal[i]>(0+epsilon_loqo)) && (dist > (1.0+(*epsilon_crit)))) {
            epsilon_loqo=primal[i]*2.0;
        }
    }

    for(i=0;i<qp->opt_n;i++) {  /* clip alphas to bounds */
        if(primal[i]<=(0+epsilon_loqo)) {
            primal[i]=0;
        }
        else if(primal[i]>=(qp->opt_up[i]-epsilon_loqo)) {
            primal[i]=qp->opt_up[i];
        }
    }

    obj_after=0;  /* calculate objective after optimization */
    for(i=0;i<qp->opt_n;i++) {
        obj_after+=(qp->opt_g0[i]*primal[i]);
        obj_after+=(0.5*primal[i]*primal[i]*qp->opt_g[i*qp->opt_n+i]);
        for(j=0;j<i;j++) {
            obj_after+=(primal[j]*primal[i]*qp->opt_g[j*qp->opt_n+i]);
        }
    }

    /* if optimizer returned NAN values, reset and retry with smaller */
    /* working set. */
    if(CMath::is_nan(obj_after) || CMath::is_nan(model_b)) {
        for(i=0;i<qp->opt_n;i++) {
            primal[i]=qp->opt_xinit[i];
        }
        model_b=0;
        if(svm_maxqpsize>2) {
            svm_maxqpsize--;  /* decrease size of qp-subproblems */
        }
    }

    if(obj_after >= obj_before) { /* check whether there was progress */
        (opt_precision)/=100.0;
        precision_violations++;
        if(verbosity>=2) {
            SG_SDEBUG("Increasing Precision of PR_LOQO.\n");
        }
    }

    if(precision_violations > 500) {
        (*epsilon_crit)*=10.0;
        precision_violations=0;
        SG_SINFO("Relaxing epsilon on KT-Conditions.\n");
    }

    (*threshold)=model_b;

    if(result!=OPTIMAL_SOLUTION) {
        SG_SERROR("PR_LOQO did not converge.\n");
        return(qp->opt_xinit);
    }
    else {
        return(primal);
    }
}


#endif //USE_SVMLIGHT