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293 | /* *****************************************************************
MESQUITE -- The Mesh Quality Improvement Toolkit
Copyright 2007 Sandia National Laboratories. Developed at the
University of Wisconsin--Madison under SNL contract number
624796. The U.S. Government and the University of Wisconsin
retain certain rights to 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
(2008) [email protected]
***************************************************************** */
/** \file QuasiNewton.cpp
* \brief Port Todd Munson's quasi-Newton solver to Mesquite
* \author Jason Kraftcheck (Mesquite Port)
*/
#include "Mesquite.hpp"
#include "QuasiNewton.hpp"
#include "MsqDebug.hpp"
#include "MsqError.hpp"
#include "PatchData.hpp"
namespace MBMesquite
{
// Force std::vector to release allocated memory
template < typename T >
static inline void free_vector( std::vector< T >& v )
{
std::vector< T > temp;
temp.swap( v );
}
std::string QuasiNewton::get_name() const
{
return "QuasiNewton";
}
PatchSet* QuasiNewton::get_patch_set()
{
return PatchSetUser::get_patch_set();
}
QuasiNewton::QuasiNewton( ObjectiveFunction* of ) : VertexMover( of ), PatchSetUser( true ), mMemento( 0 ) {}
QuasiNewton::~QuasiNewton()
{
delete mMemento;
mMemento = 0;
}
void QuasiNewton::initialize( PatchData& pd, MsqError& err )
{
if( !mMemento )
{
mMemento = pd.create_vertices_memento( err );MSQ_CHKERR( err );
}
}
void QuasiNewton::initialize_mesh_iteration( PatchData& /*pd*/, MsqError& /*err*/ ) {}
void QuasiNewton::terminate_mesh_iteration( PatchData& /*pd*/, MsqError& /*err*/ ) {}
void QuasiNewton::cleanup()
{
// release memento
delete mMemento;
mMemento = 0;
// release coordinates
for( size_t i = 0; i < ( sizeof( w ) / sizeof( w[0] ) ); ++i )
free_vector( w[i] );
// release gradients
for( size_t i = 0; i < ( sizeof( v ) / sizeof( v[0] ) ); ++i )
free_vector( v[i] );
// release Hessian memory
free_vector( mHess );
// release temporary array memory
free_vector( x );
free_vector( d );
}
// Do v += s * x, where v and x are arrays of length n
static inline void plus_eq_scaled( Vector3D* v, double s, const Vector3D* x, size_t n )
{
Vector3D* end = v + n;
for( ; v != end; ++v, ++x )
*v += s * *x;
}
void QuasiNewton::solve( Vector3D* z_arr, const Vector3D* v_arr ) const
{
SymMatrix3D pd;
const double small = DBL_EPSILON;
const size_t nn = mHess.size();
for( size_t i = 0; i < nn; ++i )
{
// ensure positive definite: perturb a bit if
// diagonal values are zero.
SymMatrix3D dd = mHess[i];
while( fabs( dd[0] ) < small || fabs( dd[3] ) < small || fabs( dd[5] ) < small )
dd += small;
// factor
pd[0] = 1.0 / dd[0];
pd[1] = dd[1] * pd[0];
pd[2] = dd[2] * pd[0];
pd[3] = 1.0 / ( dd[3] - dd[1] * pd[1] );
pd[5] = dd[4] - dd[2] * pd[1];
pd[4] = pd[3] * pd[5];
pd[5] = 1.0 / ( dd[5] - dd[2] * pd[2] - pd[4] * pd[5] );
if( pd[0] <= 0.0 || pd[3] <= 0.0 || pd[5] <= 0.0 )
{
if( dd[0] + dd[3] + dd[5] <= 0 )
{
// switch to diagonal
pd[0] = 1.0 / fabs( dd[0] );
pd[1] = 0.0;
pd[2] = 0.0;
pd[3] = 1.0 / fabs( dd[3] );
pd[4] = 0.0;
pd[5] = 1.0 / fabs( dd[5] );
}
else
{
// diagonal preconditioner
pd[0] = pd[3] = pd[5] = 1.0 / ( dd[0] + dd[3] + dd[5] );
pd[1] = pd[2] = pd[4] = 0.0;
}
}
// solve
const Vector3D& vv = v_arr[i];
Vector3D& z = z_arr[i];
z[0] = vv[0];
z[1] = vv[1] - pd[1] * z[0];
z[2] = vv[2] - pd[2] * z[0] - pd[4] * z[1];
z[0] *= pd[0];
z[1] *= pd[3];
z[2] *= pd[5];
z[1] -= pd[4] * z[2];
z[0] -= pd[1] * z[1] + pd[2] * z[2];
}
}
void QuasiNewton::optimize_vertex_positions( PatchData& pd, MsqError& err )
{
TerminationCriterion& term = *get_inner_termination_criterion();
OFEvaluator& func = get_objective_function_evaluator();
const double sigma = 1e-4;
const double beta0 = 0.25;
const double beta1 = 0.80;
const double tol1 = 1e-8;
const double epsilon = 1e-10;
// double norm_r; //, norm_g;
double alpha, beta;<--- The scope of the variable 'alpha' can be reduced. [+]The scope of the variable 'alpha' can be reduced. Warning: Be careful when fixing this message, especially when there are inner loops. Here is an example where cppcheck will write that the scope for 'i' can be reduced:
void f(int x)
{
int i = 0;
if (x) {
// it's safe to move 'int i = 0;' here
for (int n = 0; n < 10; ++n) {
// it is possible but not safe to move 'int i = 0;' here
do_something(&i);
}
}
}
When you see this message it is always safe to reduce the variable scope 1 level. <--- The scope of the variable 'beta' can be reduced. [+]The scope of the variable 'beta' can be reduced. Warning: Be careful when fixing this message, especially when there are inner loops. Here is an example where cppcheck will write that the scope for 'i' can be reduced:
void f(int x)
{
int i = 0;
if (x) {
// it's safe to move 'int i = 0;' here
for (int n = 0; n < 10; ++n) {
// it is possible but not safe to move 'int i = 0;' here
do_something(&i);
}
}
}
When you see this message it is always safe to reduce the variable scope 1 level.
double obj, objn;
size_t i;
// Initialize stuff
const size_t nn = pd.num_free_vertices();
double a[QNVEC], b[QNVEC], r[QNVEC];
for( i = 0; i < QNVEC; ++i )
r[i] = 0;
for( i = 0; i <= QNVEC; ++i )
{
v[i].clear();
v[i].resize( nn, Vector3D( 0.0 ) );
w[i].clear();
w[i].resize( nn, Vector3D( 0.0 ) );
}
d.resize( nn );
mHess.resize( nn ); // hMesh(mesh);
bool valid = func.update( pd, obj, v[QNVEC], mHess, err );MSQ_ERRRTN( err );
if( !valid )
{
MSQ_SETERR( err )( "Initial objective function is not valid", MsqError::INVALID_MESH );
return;
}
while( !term.terminate() )
{
pd.recreate_vertices_memento( mMemento, err );MSQ_ERRRTN( err );
pd.get_free_vertex_coordinates( w[QNVEC] );
x = v[QNVEC];
for( i = QNVEC; i--; )
{
a[i] = r[i] * inner( &( w[i][0] ), arrptr( x ), nn );
plus_eq_scaled( arrptr( x ), -a[i], &v[i][0], nn );
}
solve( arrptr( d ), arrptr( x ) );
for( i = QNVEC; i--; )
{
b[i] = r[i] * inner( &( v[i][0] ), arrptr( d ), nn );
plus_eq_scaled( arrptr( d ), a[i] - b[i], &( w[i][0] ), nn );
}
alpha = -inner( &( v[QNVEC][0] ), arrptr( d ), nn ); /* direction is negated */
if( alpha > 0.0 )
{
MSQ_SETERR( err )( "No descent.", MsqError::INVALID_MESH );
return;
}
alpha *= sigma;
beta = 1.0;
pd.move_free_vertices_constrained( arrptr( d ), nn, -beta, err );MSQ_ERRRTN( err );
valid = func.evaluate( pd, objn, v[QNVEC], err );
if( err.error_code() == err.BARRIER_VIOLATED )
err.clear(); // barrier violated does not represent an actual error here
MSQ_ERRRTN( err );
if( !valid || ( obj - objn < -alpha * beta - epsilon && length( &( v[QNVEC][0] ), nn ) >= tol1 ) )
{
if( !valid ) // function not defined at trial point
beta *= beta0;
else // unacceptable iterate
beta *= beta1;
for( ;; )
{
if( beta < tol1 )
{
pd.set_to_vertices_memento( mMemento, err );MSQ_ERRRTN( err );
MSQ_SETERR( err )( "Newton step not good", MsqError::INTERNAL_ERROR );
return;
}
pd.set_free_vertices_constrained( mMemento, arrptr( d ), nn, -beta, err );MSQ_ERRRTN( err );
valid = func.evaluate( pd, objn, err );
if( err.error_code() == err.BARRIER_VIOLATED )
err.clear(); // barrier violated does not represent an actual error here
MSQ_ERRRTN( err );
if( !valid ) // function undefined at trial point
beta *= beta0;
else if( obj - objn < -alpha * beta - epsilon ) // unacceptlable iterate
beta *= beta1;
else
break;
}
}
for( i = 0; i < QNVEC - 1; ++i )
{
r[i] = r[i + 1];
w[i].swap( w[i + 1] );
v[i].swap( v[i + 1] );
}
w[QNVEC - 1].swap( w[0] );
v[QNVEC - 1].swap( v[0] );
func.update( pd, obj, v[QNVEC], mHess, err );MSQ_ERRRTN( err );
// norm_r = length_squared( &(v[QNVEC][0]), nn );
// norm_g = sqrt(norm_r);
// checks stopping criterion
term.accumulate_patch( pd, err );MSQ_ERRRTN( err );
term.accumulate_inner( pd, objn, &v[QNVEC][0], err );MSQ_ERRRTN( err );
}
}
} // namespace MBMesquite
|