Example #1
0
double qFinderDMM::psi(double xx){
    try {
        double psiX = 0.0000;
        
        if(xx < 1.0000){
            
            double t1 = 1.0 / xx;
            psiX = cheb_eval(psi_cs, 22, 2.0*xx-1.0);
            psiX = -t1 + psiX;
            
        }
        else if(xx < 2.0000){
            
            const double v = xx - 1.0;
            psiX = cheb_eval(psi_cs, 22, 2.0*v-1.0);
            
        }
        else{
            const double t = 8.0/(xx*xx)-1.0;
            psiX = cheb_eval(apsi_cs, 15, t);
            psiX += log(xx) - 0.5/xx;
        }
        
        return psiX;
    }
    catch(exception& e){
        m->errorOut(e, "qFinderDMM", "psi");
        exit(1);
    }
}
Example #2
0
// Modified Bessel function of order zero.
nr_double_t fspecial::i0 (nr_double_t x) {
  nr_double_t y = fabs (x);
  nr_double_t val;

  if (y < 2.0 * sqrt (NR_EPSI)) {
    val = 1.0;
  }
  else if (y <= 3.0) {
    val = 2.75 + cheb_eval (&bi0_cs, y * y / 4.5 - 1.0);
  }
  else if (y <= 8.0) {
    val = cheb_eval (&ai0_cs, (48.0 / y - 11.0) / 5.0);
    val = exp (y) * (0.375 + val) / sqrt (y);
  }
  else {
    val = cheb_eval (&ai02_cs, 16.0 / y - 1.0);
    val = exp (y) * (0.375 + val) / sqrt (y);
  }
  return val;
}
Example #3
0
nr_double_t fspecial::erfc (nr_double_t x) {
  const nr_double_t ax = fabs (x);
  nr_double_t val;

  if (ax <= 1.0) {
    nr_double_t t = 2.0 * ax - 1.0;
    val = cheb_eval (&erfc_xlt1_cs, t);
  }
  else if (ax <= 5.0) {
    nr_double_t ex2 = exp (-x * x);
    nr_double_t t = 0.5 * (ax - 3.0);
    val = ex2 * cheb_eval (&erfc_x15_cs, t);
  }
  else if (ax < 10.0) {
    nr_double_t ex = exp(-x * x) / ax;
    nr_double_t t = (2.0 * ax - 15.0) / 5.0;
    val = ex * cheb_eval (&erfc_x510_cs, t);
  }
  else {
    val = erfc8 (ax);
  }
  return (x < 0.0) ? 2.0 - val : val;
}
Example #4
0
int eval_cheb_at_nodes(FMMData *fmm_data, Vec &val_vec){

  FMM_Tree_t* tree=fmm_data->tree;
  const MPI_Comm* comm=tree->Comm();
  int cheb_deg=fmm_data->fmm_mat->ChebDeg();
  PetscInt       m,n, M,N;
  PetscErrorCode ierr;
  // Cheb node points
  size_t n_coeff3=(cheb_deg+1)*(cheb_deg+2)*(cheb_deg+3)/6;
  size_t n_nodes3=(cheb_deg+1)*(cheb_deg+1)*(cheb_deg+1);
  std::vector<double> cheb_node_coord1=pvfmm::cheb_nodes<double>(cheb_deg, 1);

  int omp_p=omp_get_max_threads();
  //int omp_p=1;
#pragma omp parallel for
  for(size_t i=0;i<cheb_node_coord1.size();i++){
    cheb_node_coord1[i]=cheb_node_coord1[i]*2.0-1.0;
  }


  std::vector<FMMNode_t*> nlist;
  { // Get non-ghost, leaf nodes.
    std::vector<FMMNode_t*>& nlist_=tree->GetNodeList();
    for(size_t i=0;i<nlist_.size();i++){
      if(nlist_[i]->IsLeaf() && !nlist_[i]->IsGhost()){
	nlist.push_back(nlist_[i]);
      }
    }
  }

  m=fmm_data->m; // local rows
  n=fmm_data->n; // local columns
  M=fmm_data->M; // global rows
  N=fmm_data->N; // global columns

  //create coeff vec
  Vec coeff_vec;
  VecCreateMPI(*comm,m,PETSC_DETERMINE,&coeff_vec);

  tree2vec(*fmm_data,coeff_vec);

  PetscInt coeff_vec_size;
  ierr = VecGetLocalSize(coeff_vec, &coeff_vec_size);
  int data_dof=coeff_vec_size/(n_coeff3*nlist.size());
  assert(data_dof*n_coeff3*nlist.size()==coeff_vec_size);

  PetscScalar *coeff_vec_ptr;
  PetscScalar *val_vec_ptr;
  ierr = VecGetArray(coeff_vec, &coeff_vec_ptr);
  ierr = VecGetArray(val_vec, &val_vec_ptr);
#pragma omp parallel for
  for(size_t tid=0;tid<omp_p;tid++){
    size_t i_start=(nlist.size()* tid   )/omp_p;
    size_t i_end  =(nlist.size()*(tid+1))/omp_p;
    pvfmm::Vector<double> single_node_coeff_vec(n_coeff3*data_dof);
    pvfmm::Vector<double> single_node_val_vec(n_nodes3*data_dof);
    for(size_t i=i_start;i<i_end;i++){
      double s=std::pow(2.0,COORD_DIM*nlist[i]->Depth()*0.5*SCAL_EXP);

      { // coeff_vec: Cheb coeff data for this node
	size_t coeff_vec_offset=i*n_coeff3*data_dof;
	for(size_t j=0;j<n_coeff3*data_dof;j++) single_node_coeff_vec[j]=PetscRealPart(coeff_vec_ptr[j+coeff_vec_offset])*s;
      }

      // val_vec: Evaluate coeff_vec at Chebyshev node points
      cheb_eval(single_node_coeff_vec, cheb_deg, cheb_node_coord1, cheb_node_coord1, cheb_node_coord1, single_node_val_vec);
      //std::cout << "here" << std::endl; 
      { // val_vec: places the values into the vector
	size_t val_vec_offset=i*n_nodes3*data_dof;
	for(size_t j=0;j<n_nodes3*data_dof;j++){
	  //std::cout << single_node_val_vec[j] << std::endl;
	  val_vec_ptr[j+val_vec_offset] = single_node_val_vec[j];
	}
      }
      //std::cout << "not here though" << std::endl;
    }
  }
  ierr = VecRestoreArray(coeff_vec, &coeff_vec_ptr);
  ierr = VecRestoreArray(val_vec, &val_vec_ptr);

  return 1;

}
Example #5
0
int mult(Mat M, Vec U, Vec Y){
  PetscErrorCode ierr;
  FMMData* fmm_data=NULL;
  MatShellGetContext(M, &fmm_data);
  FMM_Tree_t* tree=fmm_data->tree;
  const MPI_Comm* comm=tree->Comm();
  int cheb_deg=fmm_data->fmm_mat->ChebDeg();
  std::vector<double>& eta_vec=fmm_data->eta;
  Vec& phi_0_vec=fmm_data->phi_0_vec;
  int omp_p=omp_get_max_threads();
  //int omp_p=1;
  pvfmm::Profile::Tic("FMM_Mul",comm,true);

  std::vector<FMMNode_t*> nlist;
  { // Get non-ghost, leaf nodes.
    std::vector<FMMNode_t*>& nlist_=tree->GetNodeList();
    for(size_t i=0;i<nlist_.size();i++){
      if(nlist_[i]->IsLeaf() && !nlist_[i]->IsGhost()){
	nlist.push_back(nlist_[i]);
      }
    }
  }
  assert(nlist.size()>0);

  // Cheb node points
  size_t n_coeff3=(cheb_deg+1)*(cheb_deg+2)*(cheb_deg+3)/6;
  size_t n_nodes3=(cheb_deg+1)*(cheb_deg+1)*(cheb_deg+1);
  std::vector<double> cheb_node_coord1=pvfmm::cheb_nodes<double>(cheb_deg, 1);
#pragma omp parallel for
  for(size_t i=0;i<cheb_node_coord1.size();i++){
    cheb_node_coord1[i]=cheb_node_coord1[i]*2.0-1.0;
  }

  // Input Vector ( \phi_0_vec * U )
  pvfmm::Profile::Tic("FMM_Input",comm,true);
  {
    PetscInt U_size;
    PetscInt phi_0_size;
    ierr = VecGetLocalSize(U, &U_size);
    ierr = VecGetLocalSize(phi_0_vec, &phi_0_size);
    int data_dof=U_size/(n_coeff3*nlist.size());
    assert(data_dof*n_coeff3*nlist.size()==U_size);

    PetscScalar *U_ptr;
    PetscScalar* phi_0_ptr;
    ierr = VecGetArray(U, &U_ptr);
    ierr = VecGetArray(phi_0_vec, &phi_0_ptr);
#pragma omp parallel for
    for(size_t tid=0;tid<omp_p;tid++){
      size_t i_start=(nlist.size()* tid   )/omp_p;
      size_t i_end  =(nlist.size()*(tid+1))/omp_p;
      pvfmm::Vector<double> coeff_vec(n_coeff3*data_dof);
      pvfmm::Vector<double> val_vec(n_nodes3*data_dof);
      pvfmm::Vector<double> phi_0_part(n_nodes3*data_dof);
      for(size_t i=i_start;i<i_end;i++){
	double s=std::pow(2.0,COORD_DIM*nlist[i]->Depth()*0.5*SCAL_EXP);

	{ // coeff_vec: Cheb coeff data for this node
	  size_t U_offset=i*n_coeff3*data_dof;
	  size_t phi_0_offset = i*n_nodes3*data_dof;
	  for(size_t j=0;j<n_coeff3*data_dof;j++){
	    coeff_vec[j]=PetscRealPart(U_ptr[j+U_offset])*s;
	  }
	  for(size_t j=0;j<n_nodes3*data_dof;j++){
	    phi_0_part[j]=PetscRealPart(phi_0_ptr[j+phi_0_offset]);
	  }
	}
	// val_vec: Evaluate coeff_vec at Chebyshev node points
	cheb_eval(coeff_vec, cheb_deg, cheb_node_coord1, cheb_node_coord1, cheb_node_coord1, val_vec);

	{// phi_0_part*val_vec
	  for(size_t j0=0;j0<data_dof;j0++){
	    double* vec=&val_vec[j0*n_nodes3];
	    double* phi_0=&phi_0_part[j0*n_nodes3];
	    for(size_t j1=0;j1<n_nodes3;j1++) vec[j1]*=phi_0[j1];
	  }
	}

	{ // Compute Chebyshev approx
	  pvfmm::Vector<double>& coeff_vec=nlist[i]->ChebData();
	  if(coeff_vec.Dim()!=(data_dof*(cheb_deg+1)*(cheb_deg+2)*(cheb_deg+3))/6){
	    coeff_vec.ReInit((data_dof*(cheb_deg+1)*(cheb_deg+2)*(cheb_deg+3))/6);
	  }
	  pvfmm::cheb_approx<double,double>(&val_vec[0], cheb_deg, data_dof, &coeff_vec[0]);
	  nlist[i]->DataDOF()=data_dof;
	}
      }
    }
  }
  pvfmm::Profile::Toc();

  // Run FMM ( Compute: G[ \eta * u ] )
  tree->ClearFMMData();
  tree->RunFMM();

  // Copy data from tree to Y
  pvfmm::Profile::Tic("tree2vec",comm,true);
  {
    PetscInt Y_size;
    ierr = VecGetLocalSize(Y, &Y_size);
    int data_dof=Y_size/(n_coeff3*nlist.size());

    PetscScalar *Y_ptr;
    ierr = VecGetArray(Y, &Y_ptr);

#pragma omp parallel for
    for(size_t tid=0;tid<omp_p;tid++){
      size_t i_start=(nlist.size()* tid   )/omp_p;
      size_t i_end  =(nlist.size()*(tid+1))/omp_p;
      for(size_t i=i_start;i<i_end;i++){
	pvfmm::Vector<double>& coeff_vec=((FMM_Mat_t::FMMData*) nlist[i]->FMMData())->cheb_out;
	double s=std::pow(0.5,COORD_DIM*nlist[i]->Depth()*0.5*SCAL_EXP);

	size_t Y_offset=i*n_coeff3*data_dof;
	for(size_t j=0;j<n_coeff3*data_dof;j++) Y_ptr[j+Y_offset]=coeff_vec[j]*s;
      }
    }

    ierr = VecRestoreArray(Y, &Y_ptr);
  }
  pvfmm::Profile::Toc();
  // Regularize

  Vec alpha;
  PetscScalar sca = (PetscScalar).00001;
  VecDuplicate(Y,&alpha);
  VecSet(alpha,sca);
  ierr = VecPointwiseMult(alpha,alpha,U);
  ierr = VecAXPY(Y,1,alpha);
  // Output Vector ( Compute:  U + G[ \eta * U ] )
  pvfmm::Profile::Tic("FMM_Output",comm,true);
  ierr = VecAXPY(Y,1,U);CHKERRQ(ierr);
  pvfmm::Profile::Toc();
  ierr = VecDestroy(&alpha); CHKERRQ(ierr);

  pvfmm::Profile::Toc();
  return 0;
}
Example #6
0
int PtWiseTreeMult(FMMData &fmm_data, FMM_Tree_t &tree2){
  FMM_Tree_t* tree1=fmm_data.tree;
  const MPI_Comm* comm=tree1->Comm();
  //int omp_p=omp_get_max_threads();
  int omp_p = 1;
  int cheb_deg=fmm_data.fmm_mat->ChebDeg();

  std::vector<FMMNode_t*> nlist1;
  std::vector<FMMNode_t*> nlist2;
  { // Get non-ghost, leaf nodes for BOTH trees. They must have the same structure.
    std::vector<FMMNode_t*>& nlist1_=tree1->GetNodeList();
    std::vector<FMMNode_t*>& nlist2_=tree2.GetNodeList();
    for(size_t i=0;i<nlist1_.size();i++){
      if(nlist1_[i]->IsLeaf() && !nlist1_[i]->IsGhost()){
	nlist1.push_back(nlist1_[i]);
	nlist2.push_back(nlist2_[i]);
      }
    }
  }
  //assert(nlist1.size()>0);

  // Cheb node points
  size_t n_coeff3=(cheb_deg+1)*(cheb_deg+2)*(cheb_deg+3)/6;
  size_t n_nodes3=(cheb_deg+1)*(cheb_deg+1)*(cheb_deg+1);
  std::cout << "n_nodes3: " << n_nodes3 << std::endl;
  std::vector<double> cheb_node_coord1=pvfmm::cheb_nodes<double>(cheb_deg, 1);
#pragma omp parallel for
  for(size_t i=0;i<cheb_node_coord1.size();i++){
    cheb_node_coord1[i]=cheb_node_coord1[i]*2.0-1.0;
  }

  // PtWise Mult
  pvfmm::Profile::Tic("FMM_PtWise_Mult",comm,true);
  {
    /*
       PetscInt U_size;
       PetscInt phi_0_size;
       ierr = VecGetLocalSize(U, &U_size);
       ierr = VecGetLocalSize(phi_0_vec, &phi_0_size);
       int data_dof=U_size/(n_coeff3*nlist.size());
       assert(data_dof*n_coeff3*nlist.size()==U_size);
       */
    int data_dof = fmm_data.kernel->ker_dim[0];

    std::cout << "data_dof: " << data_dof << std::endl;
    /*
       PetscScalar *U_ptr;
       PetscScalar* phi_0_ptr;
       ierr = VecGetArray(U, &U_ptr);
       ierr = VecGetArray(phi_0_vec, &phi_0_ptr);

*/
#pragma omp parallel for
    for(size_t tid=0;tid<omp_p;tid++){
      size_t i_start=(nlist1.size()* tid   )/omp_p;
      size_t i_end  =(nlist1.size()*(tid+1))/omp_p;
      pvfmm::Vector<double> coeff_vec1(n_coeff3*data_dof);
      pvfmm::Vector<double> coeff_vec2(n_coeff3*data_dof);
      pvfmm::Vector<double> val_vec1(n_nodes3*data_dof);
      pvfmm::Vector<double> val_vec2(n_nodes3*data_dof);
      std::cout << "val_vec2.Dim() " << val_vec2.Dim() << std::endl;
      for(size_t i=i_start;i<i_end;i++){
	double s=std::pow(2.0,COORD_DIM*nlist1[i]->Depth()*0.5*SCAL_EXP);
	/*
	   { // coeff_vec: Cheb coeff data for this node
	   size_t U_offset=i*n_coeff3*data_dof;
	   size_t phi_0_offset = i*n_nodes3*data_dof;
	   for(size_t j=0;j<n_coeff3*data_dof;j++){
	   coeff_vec[j]=PetscRealPart(U_ptr[j+U_offset])*s;
	   }
	   for(size_t j=0;j<n_nodes3*data_dof;j++){
	   phi_0_part[j]=PetscRealPart(phi_0_ptr[j+phi_0_offset]);
	   }
	   }
	   */
	{ // coeff_vecs: Cheb coeffs for this node for each tree!
	  coeff_vec1 = nlist1[i]->ChebData();
	  coeff_vec2 = nlist2[i]->ChebData();
	}
	// val_vec: Evaluate coeff_vec at Chebyshev node points
	cheb_eval(coeff_vec1, cheb_deg, cheb_node_coord1, cheb_node_coord1, cheb_node_coord1, val_vec1);
	cheb_eval(coeff_vec2, cheb_deg, cheb_node_coord1, cheb_node_coord1, cheb_node_coord1, val_vec2);
	std::cout << "dim :" << val_vec2.Dim() << std::endl;
	std::cout << "dim :" << val_vec1.Dim() << std::endl;

/*
	{// phi_0_part*val_vec
	  for(size_t j0=0;j0<data_dof;j0++){
	    double* vec1=&val_vec1[j0*n_nodes3];
	    std::cout << val_vec2.Dim() << " " << j0*n_nodes3 << std::endl;
	    double* vec2=&val_vec2[j0*n_nodes3];
	    for(size_t j1=0;j1<n_nodes3;j1++){
	      vec1[j1]*=vec2[j1];
	    }
	    std::cout << "after " << j0 << std::endl;
	  }
	}
*/
	{
	  for(size_t j0=0;j0<n_nodes3;j0++){
	    for(size_t j1=0;j1<data_dof;j1++){
	      val_vec1[j1*n_nodes3+j0]*=val_vec2[j0];
	    }
	  }
	}

	std::cout << "test1" << std::endl;
	{ // Compute Chebyshev approx
	  pvfmm::Vector<double>& coeff_vec=nlist1[i]->ChebData();
	  if(coeff_vec.Dim()!=(data_dof*(cheb_deg+1)*(cheb_deg+2)*(cheb_deg+3))/6){
	    coeff_vec.ReInit((data_dof*(cheb_deg+1)*(cheb_deg+2)*(cheb_deg+3))/6);
	  }
	  pvfmm::cheb_approx<double,double>(&val_vec1[0], cheb_deg, data_dof, &coeff_vec[0]);
	  nlist1[i]->DataDOF()=data_dof;
	}
      }
    }
  }
  pvfmm::Profile::Toc();

  return 0;
}
Example #7
0
void degree_of_Ptilde(int * _degree, double ** coefs,
		      const double EVMin, const double EVMax,
		      const int sloppy_degree, const double acc, 
		      matrix_mult_nd Qsq, const int repro) {
  int i, j;
  double temp, temp2;
  int degree;
  double sum=0.0;

  spinor *ss=NULL, *ss_=NULL, *sc=NULL, *sc_=NULL;
  spinor *auxs=NULL, *auxs_=NULL, *auxc=NULL, *auxc_=NULL;
  spinor *aux2s=NULL, *aux2s_=NULL, *aux2c=NULL, *aux2c_=NULL;

  *coefs = calloc(phmc_max_ptilde_degree, sizeof(double)); 

  ss_   = calloc(VOLUMEPLUSRAND/2+1, sizeof(spinor));
  auxs_ = calloc(VOLUMEPLUSRAND/2+1, sizeof(spinor));
  aux2s_= calloc(VOLUMEPLUSRAND/2+1, sizeof(spinor));
  sc_   = calloc(VOLUMEPLUSRAND/2+1, sizeof(spinor));
  auxc_ = calloc(VOLUMEPLUSRAND/2+1, sizeof(spinor));
  aux2c_= calloc(VOLUMEPLUSRAND/2+1, sizeof(spinor));

  ss    = (spinor *)(((unsigned long int)(ss_)+ALIGN_BASE)&~ALIGN_BASE);
  auxs  = (spinor *)(((unsigned long int)(auxs_)+ALIGN_BASE)&~ALIGN_BASE);
  aux2s = (spinor *)(((unsigned long int)(aux2s_)+ALIGN_BASE)&~ALIGN_BASE);
  sc    = (spinor *)(((unsigned long int)(sc_)+ALIGN_BASE)&~ALIGN_BASE);
  auxc  = (spinor *)(((unsigned long int)(auxc_)+ALIGN_BASE)&~ALIGN_BASE);
  aux2c = (spinor *)(((unsigned long int)(aux2c_)+ALIGN_BASE)&~ALIGN_BASE);

  Ptilde_cheb_coefs(EVMin, EVMax, *coefs, phmc_max_ptilde_degree, -1.0); 

  if(g_proc_id == g_stdio_proc && g_debug_level > 0){
    printf("# NDPOLY Acceptance Polynomial: EVmin = %f  EVmax = %f\n", EVMin, EVMax);
    printf("# NDPOLY ACceptance Polynomial: desired accuracy is %e \n", acc);
    fflush(stdout);
  }

  degree = 2*sloppy_degree;

  for(i = 0; i < 100 ; i++) {
    if (degree > phmc_max_ptilde_degree) {
      fprintf(stderr, "Error: n_cheby=%d > phmc_max_ptilde_degree=%d in ptilde\n",
              degree, phmc_max_ptilde_degree);
      fprintf(stderr, "Increase n_chebymax\n");
#ifdef MPI
      MPI_Finalize();
#endif
      exit(-5);
    }

    sum=0;
    for(j=degree; j<phmc_max_ptilde_degree; j++){ 
      sum += fabs(coefs[0][j]);
    }

    if((g_proc_id == g_stdio_proc) && (g_debug_level > 0)) {
      printf("# NDPOLY Acceptance Polynomial: Sum remaining | d_n | = %e for degree=%d\n", sum, degree);
      printf("# NDPOLY Acceptance Polynomial: coef[degree] = %e\n", (*coefs)[degree]);
    }
    if(sum < acc) { 
      break;
    }
    degree= (int)(degree*1.2);
  }

  if(g_debug_level > 2) {
    /* Ptilde P S P  Ptilde X - X */
    /* for random spinor X        */
    random_spinor_field_eo(ss, repro, RN_GAUSS);
    random_spinor_field_eo(sc, repro, RN_GAUSS);

    Ptilde_ndpsi(&auxs[0], &auxc[0], *coefs, degree, &ss[0], &sc[0], Qsq);
    Ptilde_ndpsi(&aux2s[0], &aux2c[0], phmc_dop_cheby_coef, phmc_dop_n_cheby, &auxs[0], &auxc[0], Qsq);
    Qsq(&auxs[0], &auxc[0], &aux2s[0], &aux2c[0]);
    Ptilde_ndpsi(&aux2s[0], &aux2c[0], phmc_dop_cheby_coef, phmc_dop_n_cheby, &auxs[0], &auxc[0], Qsq);
    Ptilde_ndpsi(&auxs[0], &auxc[0], *coefs, degree, &aux2s[0], &aux2c[0], Qsq);

    diff(&aux2s[0],&auxs[0], &ss[0], VOLUME/2);
    temp = square_norm(&aux2s[0], VOLUME/2, 1) / square_norm(&ss[0], VOLUME/2, 1) / 4.0;

    diff(&aux2c[0],&auxc[0], &sc[0], VOLUME/2);
    temp2 = square_norm(&aux2c[0], VOLUME/2, 1)/square_norm(&sc[0], VOLUME/2, 1) / 4.0;

    if(g_epsbar == 0){
      temp2 = 0.0;
    }
    /* || (Ptilde P S P Ptilde - 1)X ||^2 / || 2X ||^2 */
    if(g_proc_id == g_stdio_proc) {
      printf("# NDPOLY Acceptance Polynomial: relative squared accuracy in components:\n# UP=%e  DN=%e \n", temp, temp2);
    }

    temp = chebtilde_eval(degree, *coefs, EVMin);
    temp *= cheb_eval(phmc_dop_n_cheby, phmc_dop_cheby_coef, EVMin);
    temp *= EVMin;
    temp *= cheb_eval(phmc_dop_n_cheby, phmc_dop_cheby_coef, EVMin);
    temp *= chebtilde_eval(degree, *coefs, EVMin);
    temp = 0.5*fabs(temp - 1);
    if(g_proc_id == g_stdio_proc) {
      printf("# NDPOLY Acceptance Polynomial: Delta_IR at s=%f: | Ptilde P s_low P Ptilde - 1 |/2 = %e \n", EVMin, temp);
    }
  }
  if(g_proc_id == g_stdio_proc) {
    printf("# NDPOLY Acceptance Polynomial degree set to %d\n\n", degree);
  }

  *_degree = degree;
  free(ss_);
  free(auxs_);
  free(aux2s_);
  free(sc_);
  free(auxc_);
  free(aux2c_);
  return;
}