C++ MsqHessian::zero_out方法代码示例

/*\ For each element, each entry to be accumulated in the Hessian for
    this objective function (\f$ \sum_{e \in E} Q(e)^p \f$ where \f$ E \f$
    is the set of all elements in the patch) has the form:
    \f$ pQ(e)^{p-1} \nabla^2 Q(e) + p(p-1)Q(e)^{p-2} \nabla Q(e) [\nabla Q(e)]^T \f$.

    For \f$ p=2 \f$, this simplifies to
    \f$ 2Q(e) \nabla^2 Q(e) + 2 \nabla Q(e) [\nabla Q(e)]^T \f$.

    For \f$ p=1 \f$, this simplifies to \f$ \nabla^2 Q(e) \f$.

    The \f$ p=1 \f$ simplified version is implemented directly
    to speed up computation. 

    This function does not support vertex-based metrics.
    
    \param pd The PatchData object for which the objective function
           hessian is computed.
    \param hessian this object must have been previously initialized.
*/
bool LPtoPTemplate::evaluate_with_Hessian( EvalType type, 
                                           PatchData& pd,
                                           double& OF_val,
                                           std::vector<Vector3D>& grad,
                                           MsqHessian& hessian,
                                           MsqError& err )
{
  QualityMetric* qm = get_quality_metric();
  qm->get_evaluations( pd, qmHandles, OF_FREE_EVALS_ONLY, err );  MSQ_ERRFALSE(err);
  double negate_flag = qm->get_negate_flag();
  
    // zero gradient and hessian
  grad.clear();
  grad.resize( pd.num_free_vertices(), 0.0 );
  hessian.zero_out();
  
  double QM_val, QM_pow = 1.0;
  double fac1, fac2;
  Matrix3D elem_outer_product;
  bool qm_bool;
  size_t i, j, n;
  short p;
   
  // Loops over all elements in the patch.
  OF_val = 0.0;
  std::vector<size_t>::const_iterator k;
  for (k = qmHandles.begin(); k != qmHandles.end(); ++k)
  {
    // Computes \nabla^2 Q(e). Only the free vertices will have non-zero entries. 
    qm_bool = qm->evaluate_with_Hessian( pd, *k, QM_val, mIndices, mGradient, mHessian, err );
    if (MSQ_CHKERR(err) || !qm_bool) 
      return false;
    QM_val = fabs(QM_val);

    // **** Computes Hessian ****
    const size_t nve = mIndices.size();
    if (pVal == 1) {
      QM_pow = 1.0;
      n=0;
      for (i=0; i<nve; ++i) {
        for (j=i; j<nve; ++j) {
            //negate if necessary
          mHessian[n] *= negate_flag;
          hessian.add( mIndices[i], mIndices[j], mHessian[n], err ); MSQ_ERRFALSE(err);
          ++n;
        }
      }
      fac1 = 1;
    }
    else if (pVal >= 2) {
       // Computes the coefficients:
      QM_pow = 1.0;
      for (p=0; p<pVal-2; ++p)
        QM_pow *= QM_val;
      // 1 - computes p(p-1)Q(e)^{p-2}
      fac2 = pVal* (pVal-1) * QM_pow;
      // 2 - computes  pQ(e)^{p-1}
      QM_pow *= QM_val;
      fac1 = pVal * QM_pow;

        //fac1 *= qm->get_negate_flag();
        //fac2 *= qm->get_negate_flag();

      n=0;
      for (i=0; i<nve; ++i) {
        for (j=i; j<nve; ++j) {
          elem_outer_product.outer_product(mGradient[i], mGradient[j]);
          elem_outer_product *= fac2;
          mHessian[n] *= fac1;
          mHessian[n] += elem_outer_product;
          mHessian[n] *= negate_flag;
          hessian.add( mIndices[i], mIndices[j], mHessian[n], err ); MSQ_ERRFALSE(err);
          ++n;
        }
      }
    } else {
      MSQ_SETERR(err)(" invalid P value.", MsqError::INVALID_STATE);
      return false;
    }


//.........这里部分代码省略.........

bool PMeanPTemplate::evaluate_with_Hessian( EvalType type, 
                                        PatchData& pd,
                                        double& value_out,
                                        std::vector<Vector3D>& grad_out,
                                        MsqHessian& Hessian_out,
                                        MsqError& err )
{
  QualityMetric* qm = get_quality_metric();
  qm->get_evaluations( pd, qmHandles, OF_FREE_EVALS_ONLY, err );  MSQ_ERRFALSE(err);
  
    // zero gradient and hessian
  grad_out.clear();
  grad_out.resize( pd.num_free_vertices(), 0.0 );
  Hessian_out.zero_out();
  
    // calculate OF value and gradient for just the patch
  std::vector<size_t>::const_iterator i;
  size_t j, k, n;
  double value, working_sum = 0.0;
  const double f1 = qm->get_negate_flag() * mPower.value();
  const double f2 = f1 * (mPower.value() - 1);
  Matrix3D m;
  for (i = qmHandles.begin(); i != qmHandles.end(); ++i)
  {
    bool result = qm->evaluate_with_Hessian( pd, *i, value, mIndices, mGradient, mHessian, err );
    if (MSQ_CHKERR(err) || !result)
      return false;
    if (fabs(value) < DBL_EPSILON)
      continue;
    
    const size_t nfree = mIndices.size();
    n = 0;
    if (mPower.value() == 1.0) {
      working_sum += mPower.raise( value );
      for (j = 0; j < nfree; ++j) {
        mGradient[j] *= f1;
        grad_out[mIndices[j]] += mGradient[j];
        for (k = j; k < nfree; ++k) {
          mHessian[n] *= f1;
          Hessian_out.add( mIndices[j], mIndices[k], mHessian[n], err );  MSQ_ERRFALSE(err);
          ++n;
        }
     }
    }
    else {
      const double r2 = mPowerMinus2.raise( value );
      const double r1 = r2 * value;
      working_sum += r1 * value;
      const double hf = f2 * r2;
      const double gf = f1 * r1;
      for (j = 0; j < nfree; ++j) {
        for (k = j; k < nfree; ++k) {
          m.outer_product( mGradient[j], mGradient[k] );
          m *= hf;
          mHessian[n] *= gf;
          m += mHessian[n];
          Hessian_out.add( mIndices[j], mIndices[k], m, err );  MSQ_ERRFALSE(err);
          ++n;
        }
      }
      for (j = 0; j < nfree; ++j) {
        mGradient[j] *= gf;
        grad_out[mIndices[j]] += mGradient[j];
      }
    }
  }
  
    // get overall OF value, update member data, etc.
  size_t global_count;
  value_out = qm->get_negate_flag() 
            * get_value( working_sum, qmHandles.size(), type, global_count );
  const double inv_n = 1.0 / global_count;
  std::vector<Vector3D>::iterator g;
  for (g = grad_out.begin(); g != grad_out.end(); ++g)
    *g *= inv_n;
  Hessian_out.scale( inv_n );
  return true;
}

/*! \fn LPtoPTemplate::compute_analytical_hessian(PatchData &pd, MsqHessian &hessian, MsqError &err)

    For each element, each entry to be accumulated in the Hessian for
    this objective function (\f$ \sum_{e \in E} Q(e)^p \f$ where \f$ E \f$
    is the set of all elements in the patch) has the form:
    \f$ pQ(e)^{p-1} \nabla^2 Q(e) + p(p-1)Q(e)^{p-2} \nabla Q(e) [\nabla Q(e)]^T \f$.

    For \f$ p=2 \f$, this simplifies to
    \f$ 2Q(e) \nabla^2 Q(e) + 2 \nabla Q(e) [\nabla Q(e)]^T \f$.

    For \f$ p=1 \f$, this simplifies to \f$ \nabla^2 Q(e) \f$.

    The \f$ p=1 \f$ simplified version is implemented directly
    to speed up computation. 

    This function does not support vertex-based metrics.
    
    \param pd The PatchData object for which the objective function
           hessian is computed.
    \param hessian: this object must have been previously initialized.
*/
bool LPtoPTemplate::compute_analytical_hessian(PatchData &pd,
                                               MsqHessian &hessian,
                                               Vector3D *const &grad,
                                               double &OF_val,
                                               MsqError &err)
{
  double scaling_value=1.0;
  
  MSQ_FUNCTION_TIMER( "LPtoPTemplate::compute_analytical_hessian" );

  MsqMeshEntity* elements = pd.get_element_array(err); MSQ_ERRZERO(err);
  MsqVertex* vertices = pd.get_vertex_array(err); MSQ_ERRZERO(err);
  size_t num_elems = pd.num_elements();
    //if scaling divide by the number of elements.
  if(dividingByN){
    if(num_elems<=0) {
      MSQ_SETERR(err)("LPtoP is attempting to divide by zero in analytical Hessian.",
                      MsqError::INVALID_MESH);
      return false;
    }
    scaling_value/=num_elems;
  }
  
  size_t num_vertices = pd.num_vertices();
  Matrix3D elem_hessian[MSQ_MAX_NUM_VERT_PER_ENT*(MSQ_MAX_NUM_VERT_PER_ENT+1)/2];
  Matrix3D elem_outer_product;
  Vector3D grad_vec[MSQ_MAX_NUM_VERT_PER_ENT];
  double QM_val;
  double fac1, fac2;
  Matrix3D grad_outprod;
  bool qm_bool;
  QualityMetric* currentQM = get_quality_metric();
  
  MsqVertex* ele_free_vtces[MSQ_MAX_NUM_VERT_PER_ENT];
  short i;
  for (i=0; i<MSQ_MAX_NUM_VERT_PER_ENT; ++i) ele_free_vtces[i]=NULL;
  
  const size_t* vtx_indices;
    
  size_t e, v;
  size_t nfve; // number of free vertices in element
  short j,n;

  hessian.zero_out();
  for (v=0; v<num_vertices; ++v) grad[v] = 0.;
  OF_val = 0.;
  
  // Loops over all elements in the patch.
  for (e=0; e<num_elems; ++e) {
    short nve = elements[e].vertex_count();
    
    // Gets a list of free vertices in the element.
    vtx_indices = elements[e].get_vertex_index_array();
    nfve=0;
    for (i=0; i<nve; ++i) {
      if ( vertices[vtx_indices[i]].is_free_vertex() ) {
        ele_free_vtces[nfve] = vertices + vtx_indices[i];
        ++nfve;
      }
    }
    
    // Computes \nabla^2 Q(e). Only the free vertices will have non-zero entries. 
    qm_bool = currentQM->compute_element_hessian(pd,
                                    elements+e, ele_free_vtces,
                                    grad_vec, elem_hessian,
                                    nfve, QM_val, err);
    if (MSQ_CHKERR(err) || !qm_bool) return false;


    // **** Computes Hessian ****
    double QM_pow=1.;
    if (pVal == 1) {
      n=0;
      for (i=0; i<nve; ++i) {
        for (j=i; j<nve; ++j) {
            //negate if necessary
          elem_hessian[n] *= (scaling_value * get_negate_flag());
          ++n;
        }
//.........这里部分代码省略.........