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434 | /* *****************************************************************
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]
***************************************************************** */
//
// AUTHOR: Thomas Leurent <[email protected]>
// ORG: Argonne National Laboratory
// E-MAIL: [email protected]
//
// ORIG-DATE: 15-Jan-03 at 08:05:56
// LAST-MOD: 15-Jun-04 at 15:45:00 by Thomas Leurent
//
// DESCRIPTION:
// ============
/*!
\file FeasibleNewton.cpp
\brief
Implements the FeasibleNewton class member functions.
\author Thomas Leurent
\author Todd Munson
\date 2003-01-15
*/
// DESCRIP-END.
//
#include "FeasibleNewton.hpp"
#include "MsqFreeVertexIndexIterator.hpp"
#include "MsqDebug.hpp"
#include "XYPlanarDomain.hpp"
using namespace MBMesquite;
std::string FeasibleNewton::get_name() const
{
return "FeasibleNewton";
}
PatchSet* FeasibleNewton::get_patch_set()
{
return PatchSetUser::get_patch_set();
}
FeasibleNewton::FeasibleNewton( ObjectiveFunction* of )
: VertexMover( of ), PatchSetUser( true ), convTol( 1e-6 ), coordsMem( 0 ), havePrintedDirectionMessage( false )
{
TerminationCriterion* default_crit = get_inner_termination_criterion();
default_crit->add_absolute_gradient_L2_norm( 5e-5 );
}
void FeasibleNewton::initialize( PatchData& pd, MsqError& err )
{
// Cannot do anything. Variable sizes with maximum size dependent
// upon the entire MeshSet.
coordsMem = pd.create_vertices_memento( err );MSQ_CHKERR( err );
havePrintedDirectionMessage = false;
}
void FeasibleNewton::initialize_mesh_iteration( PatchData& pd, MsqError& /*err*/ )
{
pd.reorder();
}
void FeasibleNewton::optimize_vertex_positions( PatchData& pd, MsqError& err )
{
MSQ_FUNCTION_TIMER( "FeasibleNewton::optimize_vertex_positions" );
MSQ_DBGOUT( 2 ) << "\no Performing Feasible Newton optimization.\n";
//
// the only valid 2D meshes that FeasibleNewton works for are truly planar which
// lie in the X-Y coordinate plane.
//
XYPlanarDomain* xyPlanarDomainPtr = dynamic_cast< XYPlanarDomain* >( pd.get_domain() );
// only optimize if input mesh is a volume or an XYPlanarDomain
if( !pd.domain_set() || xyPlanarDomainPtr != NULL )
{
const double sigma = 1e-4;
const double beta0 = 0.25;
const double beta1 = 0.80;
const double tol1 = 1e-8;
const double tol2 = 1e-12;
const double epsilon = 1e-10;
double original_value, new_value;
double beta;<--- 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.
int nv = pd.num_free_vertices();
std::vector< Vector3D > grad( nv ), d( nv );
bool fn_bool = true; // bool used for determining validity of patch<--- The scope of the variable 'fn_bool' can be reduced. [+]The scope of the variable 'fn_bool' 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:<--- Variable 'fn_bool' is assigned a value that is never used.
void f(int x)<--- Variable 'fn_bool' is assigned a value that is never used.
{<--- Variable 'fn_bool' is assigned a value that is never used.
int i = 0;<--- Variable 'fn_bool' is assigned a value that is never used.
if (x) {<--- Variable 'fn_bool' is assigned a value that is never used.
// it's safe to move 'int i = 0;' here<--- Variable 'fn_bool' is assigned a value that is never used.
for (int n = 0; n < 10; ++n) {<--- Variable 'fn_bool' is assigned a value that is never used.
// it is possible but not safe to move 'int i = 0;' here<--- Variable 'fn_bool' is assigned a value that is never used.
do_something(&i);<--- Variable 'fn_bool' is assigned a value that is never used.
}<--- Variable 'fn_bool' is assigned a value that is never used.
}<--- Variable 'fn_bool' is assigned a value that is never used.
}<--- Variable 'fn_bool' is assigned a value that is never used.
When you see this message it is always safe to reduce the variable scope 1 level. <--- Variable 'fn_bool' is assigned a value that is never used.
OFEvaluator& objFunc = get_objective_function_evaluator();
int i;
// TODD -- Don't blame the code for bad things happening when using a
// bad termination test or requesting more accuracy than is
// possible.
//
// Also,
// 1. Allocate a hessian and calculate the sparsity pattern.
mHessian.initialize( pd, err );MSQ_ERRRTN( err );
// does the Feasible Newton iteration until stopping is required.
// Terminate when inner termination criterion signals.
/* Computes the value of the stopping criterion*/
TerminationCriterion* term_crit = get_inner_termination_criterion();
while( !term_crit->terminate() )
{
fn_bool = objFunc.update( pd, original_value, grad, mHessian, err );MSQ_ERRRTN( err );
if( !fn_bool )
{
MSQ_SETERR( err )
( "invalid patch for hessian calculation", MsqError::INTERNAL_ERROR );
return;
}
if( MSQ_DBG( 3 ) )
{ // avoid expensive norm calculations if debug flag is off
MSQ_DBGOUT( 3 ) << " o objective function: " << original_value << std::endl;
MSQ_DBGOUT( 3 ) << " o gradient norm: " << length( grad ) << std::endl;
MSQ_DBGOUT( 3 ) << " o Hessian norm: " << mHessian.norm() << std::endl;
}
// Prints out free vertices coordinates.
//
// Comment out the following because it is way to verbose for larger
// problems. Consider doing:
// inner_term_crit->write_mesh_steps( "filename.vtk" );
// instead.
// - j.kraftcheck 2010-11-17
// if (MSQ_DBG(3)) {
// MSQ_DBGOUT(3) << "\n o Free vertices ("<< pd.num_free_vertices()
// <<")original coordinates:\n ";
// MSQ_ERRRTN(err);
// const MsqVertex* toto1 = pd.get_vertex_array(err); MSQ_ERRRTN(err);
// MsqFreeVertexIndexIterator ind1(pd, err); MSQ_ERRRTN(err);
// ind1.reset();
// while (ind1.next()) {
// MSQ_DBGOUT(3) << "\t\t\t" << toto1[ind1.value()];
// }
// }
// 4. Calculate a direction using preconditionned conjugate gradients
// to find a zero of the Newton system of equations (H*d = -g)
// (a) stop if conjugate iteration limit reached
// (b) stop if relative residual is small
// (c) stop if direction of negative curvature is obtained
mHessian.cg_solver( arrptr( d ), arrptr( grad ), err );MSQ_ERRRTN( err );
// 5. Check for descent direction (inner produce of gradient and
// direction is negative.
double alpha = inner( grad, d );
// TODD -- Add back in if you encounter problems -- do a gradient
// step if the direction from the conjugate gradient solver
// is not a descent direction for the objective function. We
// SHOULD always get a descent direction from the conjugate
// method though, unless the preconditioner is not positive
// definite.
// If direction is positive, does a gradient (steepest descent) step.
if( alpha > -epsilon )
{
MSQ_DBGOUT( 3 ) << " o alpha = " << alpha << " (rejected)" << std::endl;
if( !havePrintedDirectionMessage )
{
MSQ_PRINT( 1 )
( "Newton direction not guaranteed descent. Ensure preconditioner is positive "
"definite.\n" );
havePrintedDirectionMessage = true;
}
// TODD: removed performing gradient step here since we will use
// gradient if step does not produce descent. Instead we set
// alpha to a small negative value.
alpha = -epsilon;
// alpha = inner(grad, grad, nv); // compute norm squared of gradient
// if (alpha < 1) alpha = 1; // take max with constant
// for (i = 0; i < nv; ++i) {
// d[i] = -grad[i] / alpha; // compute scaled gradient
// }
// alpha = inner(grad, d, nv); // recompute alpha
// // equal to one for large gradient
}
else
{
MSQ_DBGOUT( 3 ) << " o alpha = " << alpha << std::endl;
}
alpha *= sigma;
beta = 1.0;
pd.recreate_vertices_memento( coordsMem, err );MSQ_ERRRTN( err );
// TODD: Unrolling the linesearch loop. We do a function and
// gradient evaluation when beta = 1. Otherwise, we end up
// in the linesearch regime. We expect that several
// evaluations will be made, so we only do a function evaluation
// and finish with a gradient evaluation. When beta = 1, we also
// check the gradient for stability.
// TODD -- the Armijo linesearch is based on the objective function,
// so theoretically we only need to evaluate the objective
// function. However, near a very accurate solution, say with
// the two norm of the gradient of the objective function less
// than 1e-5, the numerical error in the objective function
// calculation is enough that the Armijo linesearch will
// fail. To correct this situation, the iterate is accepted
// when the norm of the gradient is also small. If you need
// high accuracy and have a large mesh, talk with Todd about
// the numerical issues so that we can fix it.
// TODD -- the Armijo linesearch here is only good for differentiable
// functions. When projections are involved, you should change
// to a form of the linesearch meant for nondifferentiable
// functions.
pd.move_free_vertices_constrained( arrptr( d ), nv, beta, err );MSQ_ERRRTN( err );
fn_bool = objFunc.evaluate( pd, new_value, grad, err );
if( err.error_code() == err.BARRIER_VIOLATED )
err.clear(); // barrier violated does not represent an actual error here
MSQ_ERRRTN( err );
if( ( fn_bool && ( original_value - new_value >= -alpha * beta - epsilon ) ) ||
( fn_bool && ( length( arrptr( grad ), nv ) < 100 * convTol ) ) )
{
// Armijo linesearch rules passed.
MSQ_DBGOUT( 3 ) << " o beta = " << beta << " (accepted without line search)" << std::endl;
}
else
{
if( !fn_bool )
{
// Function undefined. Use the higher decrease rate.
beta *= beta0;
MSQ_DBGOUT( 3 ) << " o beta = " << beta << " (invalid step)" << std::endl;
}
else
{
// Function defined, but not sufficient decrease
// Use the lower decrease rate.
beta *= beta1;
MSQ_DBGOUT( 3 ) << " o beta = " << beta << " (insufficient decrease)" << std::endl;
}
pd.set_to_vertices_memento( coordsMem, err );MSQ_ERRRTN( err );
// Standard Armijo linesearch rules
MSQ_DBGOUT( 3 ) << " o Doing line search" << std::endl;
while( beta >= tol1 )
{
// 6. Search along the direction
// (a) trial = x + beta*d
pd.move_free_vertices_constrained( arrptr( d ), nv, beta, err );MSQ_ERRRTN( err );
// (b) function evaluation
fn_bool = objFunc.evaluate( pd, new_value, err );
if( err.error_code() == err.BARRIER_VIOLATED )
err.clear(); // barrier violated does not represent an actual error here
MSQ_ERRRTN( err );
// (c) check for sufficient decrease and stop
if( !fn_bool )
{
// function not defined at trial point
beta *= beta0;
}
else if( original_value - new_value >= -alpha * beta - epsilon )
{
// iterate is acceptable.
break;
}
else
{
// iterate is not acceptable -- shrink beta
beta *= beta1;
}
pd.set_to_vertices_memento( coordsMem, err );MSQ_ERRRTN( err );
}
if( beta < tol1 )
{
// assert(pd.set_to_vertices_memento called last)
// TODD -- Lower limit on steplength reached. Direction does not
// appear to make sufficient progress decreasing the
// objective function. This can happen when you are
// very near a solution due to numerical errors in
// computing the objective function. It can also happen
// when the direction is not a descent direction and when
// you are projecting the iterates onto a surface.
//
// The latter cases require the use of a linesearch on
// a gradient step. If this linesearch terminate with
// insufficient decrease, then you are at a critical
// point and should stop!
//
// The numerical errors with the objective function cannot
// be overcome. Eventually, the gradient step will
// fail to compute a new direction and you will stop.
MSQ_PRINT( 1 )
( "Sufficient decrease not obtained in linesearch; switching to gradient.\n" );
alpha = inner( arrptr( grad ), arrptr( grad ),
nv ); // compute norm squared of gradient
if( alpha < 1 ) alpha = 1; // take max with constant
for( i = 0; i < nv; ++i )
{
d[i] = -grad[i] / alpha; // compute scaled gradient
}
alpha = inner( arrptr( grad ), arrptr( d ), nv ); // recompute alpha
alpha *= sigma; // equal to one for large gradient
beta = 1.0;
// Standard Armijo linesearch rules
while( beta >= tol2 )
{
// 6. Search along the direction
// (a) trial = x + beta*d
pd.move_free_vertices_constrained( arrptr( d ), nv, beta, err );MSQ_ERRRTN( err );
// (b) function evaluation
fn_bool = objFunc.evaluate( pd, new_value, err );
if( err.error_code() == err.BARRIER_VIOLATED )
err.clear(); // barrier violated does not represent an actual error
// here
MSQ_ERRRTN( err );
// (c) check for sufficient decrease and stop
if( !fn_bool )
{
// function not defined at trial point
beta *= beta0;
}
else if( original_value - new_value >= -alpha * beta - epsilon )
{
// iterate is acceptable.
break;
}
else
{
// iterate is not acceptable -- shrink beta
beta *= beta1;
}
pd.set_to_vertices_memento( coordsMem, err );MSQ_ERRRTN( err );
}
if( beta < tol2 )
{
// assert(pd.set_to_vertices_memento called last)
// TODD -- Lower limit on steplength reached. Gradient does not
// appear to make sufficient progress decreasing the
// objective function. This can happen when you are
// very near a solution due to numerical errors in
// computing the objective function. Most likely you
// are at a critical point for the problem.
MSQ_PRINT( 1 )
( "Sufficient decrease not obtained with gradient; critical point likely "
"found.\n" );
break;
}
}
// Compute the gradient at the new point -- needed by termination check
fn_bool = objFunc.update( pd, new_value, grad, err );MSQ_ERRRTN( err );<--- Variable 'fn_bool' is assigned a value that is never used.
}
// Prints out free vertices coordinates.
// if (MSQ_DBG(3)) {
// MSQ_DBGOUT(3) << " o Free vertices new coordinates: \n";
// const MsqVertex* toto1 = pd.get_vertex_array(err); MSQ_ERRRTN(err);
// MsqFreeVertexIndexIterator ind(pd, err); MSQ_ERRRTN(err);
// ind.reset();
// while (ind.next()) {
// MSQ_DBGOUT(3) << "\t\t\t" << toto1[ind.value()];
// }
// }
// checks stopping criterion
term_crit->accumulate_patch( pd, err );MSQ_ERRRTN( err );
term_crit->accumulate_inner( pd, new_value, arrptr( grad ), err );MSQ_ERRRTN( err );
}
MSQ_PRINT( 2 )( "FINISHED\n" );
}
else
{
std::cout << "WARNING: Feasible Newton optimization only supported for volume meshes" << std::endl
<< " and XYPlanarDomain surface meshes." << std::endl
<< std::endl
<< "Try a different solver such as Steepest Descent." << std::endl;
}
}
void FeasibleNewton::terminate_mesh_iteration( PatchData& /*pd*/, MsqError& /*err*/ )
{
// Michael:: Should the vertices memento be delete here???
// cout << "- Executing FeasibleNewton::iteration_complete()\n";
}
void FeasibleNewton::cleanup()
{
delete coordsMem;
coordsMem = NULL;
}
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