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399 | /* *****************************************************************
MESQUITE -- The Mesh Quality Improvement Toolkit
Copyright 2004 Sandia Corporation and Argonne National
Laboratory. Under the terms of Contract DE-AC04-94AL85000
with Sandia Corporation, the U.S. Government retains certain
rights in this software.
This library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2.1 of the License, or (at your option) any later version.
This library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public License
(lgpl.txt) along with this library; if not, write to the Free Software
Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
[email protected], [email protected], [email protected],
[email protected], [email protected], [email protected]
[email protected]
***************************************************************** */
/*!
\file QualityMetric.cpp
\brief
\author Michael Brewer
\author Thomas Leurent
\date 2002-05-14
\author Jason Kraftcheck
\date 2006-04-20
*/
#include "QualityMetric.hpp"
#include "MsqVertex.hpp"
#include "PatchData.hpp"
namespace MBMesquite
{
void QualityMetric::initialize_queue( MeshDomainAssoc*, const Settings*, MsqError& ) {}
void QualityMetric::get_single_pass( PatchData& pd,
std::vector< size_t >& handles,
bool free_vertices_only,
MsqError& err )
{
get_evaluations( pd, handles, free_vertices_only, err );
}
static inline double get_delta_C( const PatchData& pd, const std::vector< size_t >& indices, MsqError& err )
{
if( indices.empty() )
{
MSQ_SETERR( err )( MsqError::INVALID_ARG );
return 0.0;
}
std::vector< size_t >::const_iterator beg, iter, iter2, end;
std::vector< size_t > tmp_vect;
if( indices.size() == 1u )
{
pd.get_adjacent_vertex_indices( indices.front(), tmp_vect, err );
MSQ_ERRZERO( err );
assert( !tmp_vect.empty() );
tmp_vect.push_back( indices.front() );
beg = tmp_vect.begin();
end = tmp_vect.end();
}
else
{
beg = indices.begin();
end = indices.end();
}
double min_dist_sqr = HUGE_VAL, sum_dist_sqr = 0.0;
for( iter = beg; iter != end; ++iter )
{
for( iter2 = iter + 1; iter2 != end; ++iter2 )
{
Vector3D diff = pd.vertex_by_index( *iter );
diff -= pd.vertex_by_index( *iter2 );
double dist_sqr = diff % diff;
if( dist_sqr < min_dist_sqr ) min_dist_sqr = dist_sqr;
sum_dist_sqr += dist_sqr;
}
}
return 3e-6 * sqrt( min_dist_sqr ) + 5e-7 * sqrt( sum_dist_sqr / ( end - beg ) );
}
bool QualityMetric::evaluate_with_gradient( PatchData& pd,
size_t handle,
double& value,
std::vector< size_t >& indices,
std::vector< Vector3D >& gradient,
MsqError& err )
{
indices.clear();
bool valid = evaluate_with_indices( pd, handle, value, indices, err );
if( MSQ_CHKERR( err ) || !valid ) return false;
if( indices.empty() ) return true;
// get initial pertubation amount
double delta_C = finiteDiffEps;
if( !haveFiniteDiffEps )
{
delta_C = get_delta_C( pd, indices, err );
MSQ_ERRZERO( err );
if( keepFiniteDiffEps )
{
finiteDiffEps = delta_C;
haveFiniteDiffEps = true;
}
}
const double delta_inv_C = 1.0 / delta_C;
const int reduction_limit = 15;
gradient.resize( indices.size() );
for( size_t v = 0; v < indices.size(); ++v )
{
const Vector3D pos = pd.vertex_by_index( indices[v] );
/* gradient in the x, y, z direction */
for( int j = 0; j < 3; ++j )
{
double delta = delta_C;
double delta_inv = delta_inv_C;
double metric_value;
Vector3D delta_v( 0, 0, 0 );
// perturb the node and calculate gradient. The while loop is a
// safety net to make sure the epsilon perturbation does not take
// the element out of the feasible region.
int counter = 0;
for( ;; )
{
// perturb the coordinates of the free vertex in the j direction
// by delta
delta_v[j] = delta;
pd.set_vertex_coordinates( pos + delta_v, indices[v], err );
MSQ_ERRZERO( err );
// compute the function at the perturbed point location
valid = evaluate( pd, handle, metric_value, err );
if( !MSQ_CHKERR( err ) && valid ) break;
if( ++counter >= reduction_limit )
{
MSQ_SETERR( err )
( "Perturbing vertex by delta caused an inverted element.", MsqError::INTERNAL_ERROR );
return false;
}
delta *= 0.1;
delta_inv *= 10.;
}
// put the coordinates back where they belong
pd.set_vertex_coordinates( pos, indices[v], err );
// compute the numerical gradient
gradient[v][j] = ( metric_value - value ) * delta_inv;
} // for(j)
} // for(indices)
return true;
}
bool QualityMetric::evaluate_with_Hessian( PatchData& pd,
size_t handle,
double& value,
std::vector< size_t >& indices,
std::vector< Vector3D >& gradient,
std::vector< Matrix3D >& Hessian,
MsqError& err )
{
indices.clear();
gradient.clear();
keepFiniteDiffEps = true;
bool valid = evaluate_with_gradient( pd, handle, value, indices, gradient, err );
keepFiniteDiffEps = false;
if( MSQ_CHKERR( err ) || !valid )
{
haveFiniteDiffEps = false;
return false;
}
if( indices.empty() )
{
haveFiniteDiffEps = false;
return true;
}
// get initial pertubation amount
double delta_C;
if( haveFiniteDiffEps )
{
delta_C = finiteDiffEps;
}
else
{
delta_C = get_delta_C( pd, indices, err );
MSQ_ERRZERO( err );
}
assert( delta_C < 1e30 );
const double delta_inv_C = 1.0 / delta_C;
const int reduction_limit = 15;
std::vector< Vector3D > temp_gradient( indices.size() );
const int num_hess = indices.size() * ( indices.size() + 1 ) / 2;
Hessian.resize( num_hess );
for( unsigned v = 0; v < indices.size(); ++v )
{
const Vector3D pos = pd.vertex_by_index( indices[v] );
for( int j = 0; j < 3; ++j )
{ // x, y, and z
double delta = delta_C;
double delta_inv = delta_inv_C;
double metric_value;
Vector3D delta_v( 0, 0, 0 );
// find finite difference for gradient
int counter = 0;
for( ;; )
{
delta_v[j] = delta;
pd.set_vertex_coordinates( pos + delta_v, indices[v], err );
MSQ_ERRZERO( err );
valid = evaluate_with_gradient( pd, handle, metric_value, indices, temp_gradient, err );
if( !MSQ_CHKERR( err ) && valid ) break;
if( ++counter >= reduction_limit )
{
MSQ_SETERR( err )
( "Algorithm did not successfully compute element's "
"Hessian.\n",
MsqError::INTERNAL_ERROR );
haveFiniteDiffEps = false;
return false;
}
delta *= 0.1;
delta_inv *= 10.0;
}
pd.set_vertex_coordinates( pos, indices[v], err );
MSQ_ERRZERO( err );
// compute the numerical Hessian
for( unsigned w = 0; w <= v; ++w )
{
// finite difference to get some entries of the Hessian
Vector3D fd( temp_gradient[w] );
fd -= gradient[w];
fd *= delta_inv;
// For the block at position w,v in a matrix, we need the corresponding index
// (mat_index) in a 1D array containing only upper triangular blocks.
unsigned sum_w = w * ( w + 1 ) / 2; // 1+2+3+...+w
unsigned mat_index = w * indices.size() + v - sum_w;
Hessian[mat_index][0][j] = fd[0];
Hessian[mat_index][1][j] = fd[1];
Hessian[mat_index][2][j] = fd[2];
}
} // for(j)
} // for(indices)
haveFiniteDiffEps = false;
return true;
}
bool QualityMetric::evaluate_with_Hessian_diagonal( PatchData& pd,
size_t handle,
double& value,
std::vector< size_t >& indices,
std::vector< Vector3D >& gradient,
std::vector< SymMatrix3D >& Hessian_diagonal,
MsqError& err )
{
bool rval = evaluate_with_Hessian( pd, handle, value, indices, gradient, tmpHess, err );
if( MSQ_CHKERR( err ) || !rval ) return rval;
size_t s = indices.size();
Hessian_diagonal.resize( s );
std::vector< Matrix3D >::const_iterator h = tmpHess.begin();
for( size_t i = 0; i < indices.size(); ++i )
{
Hessian_diagonal[i] = h->upper();
h += s--;
}
return rval;
}
uint32_t QualityMetric::fixed_vertex_bitmap( PatchData& pd, const MsqMeshEntity* elem, std::vector< size_t >& indices )
{
indices.clear();
uint32_t result = ~(uint32_t)0;
unsigned num_vtx = elem->vertex_count();
const size_t* vertices = elem->get_vertex_index_array();
indices.clear();
for( unsigned i = 0; i < num_vtx; ++i )
{
if( vertices[i] < pd.num_free_vertices() )
{
indices.push_back( vertices[i] );
result &= ~(uint32_t)( 1 << i );
}
}
return result;
}
void QualityMetric::remove_fixed_gradients( EntityTopology elem_type, uint32_t fixed, std::vector< Vector3D >& grads )
{
const unsigned num_vertex = TopologyInfo::corners( elem_type );
unsigned r, w;
for( r = 0; r < num_vertex && !( fixed & ( 1 << r ) ); ++r )
;
for( w = r++; r < num_vertex; ++r )
{
if( !( fixed & ( 1 << r ) ) )
{
grads[w] = grads[r];
++w;
}
}
grads.resize( w );
}
void QualityMetric::remove_fixed_diagonals( EntityTopology type,
uint32_t fixed,
std::vector< Vector3D >& grads,
std::vector< SymMatrix3D >& diags )
{
const unsigned num_vertex = TopologyInfo::corners( type );
unsigned r, w;
for( r = 0; r < num_vertex && !( fixed & ( 1 << r ) ); ++r )
;
for( w = r++; r < num_vertex; ++r )
{
if( !( fixed & ( 1 << r ) ) )
{
grads[w] = grads[r];
diags[w] = diags[r];
++w;
}
}
grads.resize( w );
diags.resize( w );
}
void QualityMetric::remove_fixed_hessians( EntityTopology elem_type, uint32_t fixed, std::vector< Matrix3D >& hessians )
{
const unsigned num_vertex = TopologyInfo::corners( elem_type );
unsigned r, c, i = 0, w = 0;
for( r = 0; r < num_vertex; ++r )
{
if( fixed & ( 1 << r ) )
{
i += num_vertex - r;
continue;
}
for( c = r; c < num_vertex; ++c )
{
if( !( fixed & ( 1 << c ) ) )
{
hessians[w] = hessians[i];
++w;
}
++i;
}
}
hessians.resize( w );
}
double QualityMetric::weighted_average_metrics( const double coef[],<--- The function 'weighted_average_metrics' is never used.
const double metric_values[],
const int& num_values,
MsqError& /*err*/ )
{
// MSQ_MAX needs to be made global?
// double MSQ_MAX=1e10;
double total_value = 0.0;
int i = 0;
// if no values, return zero
if( num_values <= 0 )
{
return 0.0;
}
for( i = 0; i < num_values; ++i )
{
total_value += coef[i] * metric_values[i];
}
total_value /= (double)num_values;
return total_value;
}
} // namespace MBMesquite
|