void NonGradient::printPatch(const PatchData &pd, MsqError &err)
{
if( mNonGradDebug==0 )
{
return;
}
const size_t numNode = pd.num_nodes(); //27, 27 what?
MSQ_PRINT(3)("Number of Vertices: %d\n",(int)pd.num_nodes());
const size_t numVert = pd.num_free_vertices(); // 1
MSQ_PRINT(3)("Num Free = %d\n",(int)pd.num_free_vertices());
const size_t numSlaveVert = pd.num_slave_vertices(); //0
const size_t numCoin = pd.num_corners(); // 64
const MsqVertex* coord = pd.get_vertex_array(err);
MSQ_PRINT(3)("Number of Vertices: %d\n",(int)pd.num_nodes());
std::cout << "Patch " << numNode << " " << numVert << " " << numSlaveVert << " " << numCoin << std::endl;
MSQ_PRINT(3)("");
std::cout << "Coordinate ";
std::cout << " " << std::endl;
for( size_t index = 0; index < numVert; index++ )
{
std::cout << coord[index][0] << " " << coord[index][1] << " " << coord[index][2] << std::endl;
}
//const size_t numElt = pd.num_elements();
if( mNonGradDebug >= 3 )
{
std::cout << "Number of Elements: " << pd.num_elements() << std::endl;
}
MSQ_PRINT(3)("Number of Elements: %d\n",(int)pd.num_elements());
}
bool
NonGradient::testRowSum( int numRow, int numCol, double* matrix, double* oldRowSum)
{
bool same = true;
std::vector<double> rowSum(numRow,0.);
double maxVal = 0.;
for (int col=0;col<numCol;col++)
{
for (int row=0;row<numRow;row++)
{
rowSum[row] += matrix[row+col*numRow];
if( fabs( matrix[row+col*numRow] ) > maxVal )
{
maxVal = fabs( matrix[row+col*numRow] );
}
}
}
double machEps = 1.e-14 * static_cast<double>(numRow); // better to use system parameters
double upperBound = machEps * maxVal + 1.e-15;
for (int row=0;row<numRow;row++)
{
if( fabs( rowSum[row] - oldRowSum[row]) > upperBound )
{
same = false;
if( mNonGradDebug >= 2 )
{
std::cout << " Warning: NonGradient Row Sum " << row << " Test: value " << rowSum[row] << " Discrepancy " << rowSum[row] - oldRowSum[row] << " maxVal " << maxVal << " numRow " << numRow << " numCol " << numCol <<std::endl;
}
MSQ_PRINT(2)("NonGradient Row Sum [%d] Test failure: value %22.15e difference %22.15e \n", row, rowSum[row], rowSum[row] - oldRowSum[row]);
}
}
return(same);
}
void NonGradient::initialize_mesh_iteration(PatchData &pd, MsqError &err)
{
int elementDimension = getPatchDimension( pd, err ); // to do: react to error
int dimension = elementDimension * pd.num_free_vertices();
//printPatch( pd, err );
setDimension(dimension);
int maxNumEval = 100*dimension; // 1. Make this a user parameter
setMaxNumEval(maxNumEval);
double threshold = 1.e-10; // avoid division by zero
setThreshold(threshold);
double minEdgeLen = 0.0;
double maxEdgeLen = 0.0;
// double ftol = 0.;
if( dimension > 0 )
{
pd.get_minmax_edge_length( minEdgeLen, maxEdgeLen );
//ftol = minEdgeLen * 1.e-4; // Turn off Amoeba convergence criterion
if( mNonGradDebug >= 1 )
{
std::cout << "minimum edge length " << minEdgeLen << " maximum edge length " << maxEdgeLen << std::endl;
}
MSQ_PRINT(3)("minimum edge length %e maximum edge length %e\n", minEdgeLen, maxEdgeLen);
}
// setTolerance(ftol);
int numRow = dimension;
int numCol = numRow+1;
if( numRow*numCol <= simplex.max_size() )
{
simplex.assign(numRow*numCol, 0.); // guard against previous simplex value
double scale = minEdgeLen * mScaleDiameter;;
const MsqVertex* coord = pd.get_vertex_array(err);
if( pd.num_free_vertices() > 1 )
{
MSQ_SETERR(err)("Only one free vertex per patch implemented", MsqError::NOT_IMPLEMENTED);
}
size_t index = 0;
for( int col = 0; col < numCol; col++ )
{
for (int row=0;row<numRow;row++)
{
simplex[ row + col*numRow ] = coord[index][row];
if( row == col-1 )
{
simplex[ row + col*numRow ] += scale/ static_cast<double>(numCol);
}
}
}
}
else
{
MSQ_SETERR(err)("Use patch with fewer free vertices", MsqError::OUT_OF_MEMORY);
if( mNonGradDebug >= 1 )
{
std::cout << "ERROR: Too many free vertices in patch" << std::endl;
}
//MSQ_PRINT(1)("ERROR: Too many free vertices in patch\n");
}
}
// Extrapolate by a factor of fac through the face of the simplex
// opposite the high point to a new point. If the new point is
// better, swap it with the high point.
double
NonGradient::amotry( std::vector<double>& simplex,
std::vector<double>& height,
double psum[], int ihi, double fac, PatchData &pd, MsqError &err)
{
int numRow = getDimension();
int numCol = numRow + 1;
std::vector<double> ptry(numRow); // does this make sense?
double fac1=(1.0-fac)/static_cast<double>(numRow);
double fac2=fac1-fac;
for (int row=0;row<numRow;row++)
{
ptry[row]=psum[row]*fac1-simplex[row+ihi*numRow]*fac2;
}
if( mNonGradDebug >= 3 )
{
std::cout << "Try ";
}
MSQ_PRINT(3)("Try");
double ytry = evaluate(&ptry[0], pd, err); // value at trial point
if( mNonGradDebug >= 3 )
{
std::cout << ytry << std::endl;
}
MSQ_PRINT(3)("yTry");
if (ytry < height[ihi]) // better than highest (worst)
{
height[ihi]=ytry; // swap ihi and ytry
for (int row=0;row<numRow;row++)
{
psum[row] += (ptry[row]-simplex[row+ihi*numRow]);
simplex[row+ihi*numRow]=ptry[row];
}
}
return ytry;
}
double ConjugateGradient::get_step(PatchData &pd,double f0,int &j,
MsqError &err)
{
// get OF evaluator
OFEvaluator& objFunc = get_objective_function_evaluator();
size_t num_vertices=pd.num_free_vertices();
//initial guess for alp
double alp=1.0;
int jmax=100;
double rho=0.5;
//feasible=false implies the mesh is not in the feasible region
bool feasible=false;
int found=0;
//f and fnew hold the objective function value
double f=0;
double fnew=0;
//Counter to avoid infinitly scaling alp
j=0;
//save memento
pd.recreate_vertices_memento(pMemento, err);
//if we must check feasiblility
//while step takes mesh into infeasible region and ...
while (j<jmax && !feasible && alp>MSQ_MIN) {
++j;
pd.set_free_vertices_constrained(pMemento,arrptr(pGrad),num_vertices,alp,err);
feasible=objFunc.evaluate(pd,f,err); MSQ_ERRZERO(err);
//if not feasible, try a smaller alp (take smaller step)
if(!feasible){
alp*=rho;
}
}//end while ...
//if above while ended due to j>=jmax, no valid step was found.
if(j>=jmax){
MSQ_PRINT(2)("\nFeasible Point Not Found");
return 0.0;
}
//Message::print_info("\nOriginal f %f, first new f = %f, alp = %f",f0,f,alp);
//if new f is larger than original, our step was too large
if(f>=f0){
j=0;
while (j<jmax && found == 0){
++j;
alp *= rho;
pd.set_free_vertices_constrained(pMemento,arrptr(pGrad),num_vertices,alp,err);
//Get new obj value
//if patch is now invalid, then the feasible region is convex or
//we have an error. For now, we assume an error.
if(! objFunc.evaluate(pd,f,err) ){
MSQ_SETERR(err)("Non-convex feasiblility region found.",MsqError::INVALID_MESH);
}
pd.set_to_vertices_memento(pMemento,err);MSQ_ERRZERO(err);
//if our step has now improved the objective function value
if(f<f0){
found=1;
}
}// end while j less than jmax
//Message::print_info("\nj = %d found = %d f = %20.18f f0 = %20.18f\n",j,found,f,f0);
//if above ended because of j>=jmax, take no step
if(found==0){
//Message::print_info("alp = %10.8f, but returning zero\n",alp);
alp=0.0;
return alp;
}
j=0;
//while shrinking the step improves the objFunc value further,
//scale alp down. Return alp, when scaling once more would
//no longer improve the objFunc value.
while(j<jmax){
++j;
alp*=rho;
//step alp in search direction from original positions
pd.set_free_vertices_constrained(pMemento,arrptr(pGrad),num_vertices,alp,err);MSQ_ERRZERO(err);
//get new objective function value
if (! objFunc.evaluate(pd,fnew,err))
MSQ_SETERR(err)("Non-convex feasiblility region found while "
"computing new f.",MsqError::INVALID_MESH);
if(fnew<f){
f=fnew;
}
else{
//Reset the vertices to original position
pd.set_to_vertices_memento(pMemento,err);MSQ_ERRZERO(err);
alp/=rho;
return alp;
}
}
//Reset the vertices to original position and return alp
pd.set_to_vertices_memento(pMemento,err);MSQ_ERRZERO(err);
return alp;
}
//else our new f was already smaller than our original
else{
j=0;
//check to see how large of step we can take
while (j<jmax && found == 0) {
++j;
//scale alp up (rho must be less than 1)
alp /= rho;
//step alp in search direction from original positions
pd.set_free_vertices_constrained(pMemento,arrptr(pGrad),num_vertices,alp,err);MSQ_ERRZERO(err);
feasible = objFunc.evaluate(pd,fnew, err);MSQ_ERRZERO(err);
if ( ! feasible ){
alp *= rho;
//Reset the vertices to original position and return alp
pd.set_to_vertices_memento(pMemento,err);MSQ_ERRZERO(err);
return alp;
}
if (fnew<f) {
f = fnew;
}
else {
found=1;
alp *= rho;
}
}
//Reset the vertices to original position and return alp
pd.set_to_vertices_memento(pMemento,err);MSQ_ERRZERO(err);
return alp;
}
}
/*!Performs Conjugate gradient minimization on the PatchData, pd.*/
void ConjugateGradient::optimize_vertex_positions(PatchData &pd,
MsqError &err){
// pd.reorder();
MSQ_FUNCTION_TIMER( "ConjugateGradient::optimize_vertex_positions" );
Timer c_timer;
size_t num_vert=pd.num_free_vertices();
if(num_vert<1){
MSQ_DBGOUT(1) << "\nEmpty free vertex list in ConjugateGradient\n";
return;
}
/*
//zero out arrays
int zero_loop=0;
while(zero_loop<arraySize){
fGrad[zero_loop].set(0,0,0);
pGrad[zero_loop].set(0,0,0);
fNewGrad[zero_loop].set(0,0,0);
++zero_loop;
}
*/
// get OF evaluator
OFEvaluator& objFunc = get_objective_function_evaluator();
size_t ind;
//Michael cull list: possibly set soft_fixed flags here
//MsqFreeVertexIndexIterator free_iter(pd, err); MSQ_ERRRTN(err);
double f=0;
//Michael, this isn't equivalent to CUBIT because we only want to check
//the objective function value of the 'bad' elements
//if invalid initial patch set an error.
bool temp_bool = objFunc.update(pd, f, fGrad, err);
assert(fGrad.size() == num_vert);
if(MSQ_CHKERR(err))
return;
if( ! temp_bool){
MSQ_SETERR(err)("Conjugate Gradient not able to get valid gradient "
"and function values on intial patch.",
MsqError::INVALID_MESH);
return;
}
double grad_norm=MSQ_MAX_CAP;
if(conjGradDebug>0){
MSQ_PRINT(2)("\nCG's DEGUB LEVEL = %i \n",conjGradDebug);
grad_norm=Linf(arrptr(fGrad),fGrad.size());
MSQ_PRINT(2)("\nCG's FIRST VALUE = %f,grad_norm = %f",f,grad_norm);
MSQ_PRINT(2)("\n TIME %f",c_timer.since_birth());
grad_norm=MSQ_MAX_CAP;
}
//Initializing pGrad (search direction).
pGrad.resize(fGrad.size());
for (ind = 0; ind < num_vert; ++ind)
pGrad[ind]=(-fGrad[ind]);
int j=0; // total nb of step size changes ... not used much
int i=0; // iteration counter
unsigned m=0; //
double alp=MSQ_MAX_CAP; // alp: scale factor of search direction
//we know inner_criterion is false because it was checked in
//loop_over_mesh before being sent here.
TerminationCriterion* term_crit=get_inner_termination_criterion();
//while ((i<maxIteration && alp>stepBound && grad_norm>normGradientBound)
// && !inner_criterion){
while(!term_crit->terminate()){
++i;
//std::cout<<"\Michael delete i = "<<i;
int k=0;
alp=get_step(pd,f,k,err);
j+=k;
if(conjGradDebug>2){
MSQ_PRINT(2)("\n Alp initial, alp = %20.18f",alp);
}
// if alp == 0, revert to steepest descent search direction
if(alp==0){
for (m = 0; m < num_vert; ++m) {
pGrad[m]=(-fGrad[m]);
}
alp=get_step(pd,f,k,err);
j+=k;
if(conjGradDebug>1){
MSQ_PRINT(2)("\n CG's search direction reset.");
if(conjGradDebug>2)
MSQ_PRINT(2)("\n Alp was zero, alp = %20.18f",alp);
}
}
if(alp!=0){
pd.move_free_vertices_constrained( arrptr(pGrad), num_vert, alp, err );
MSQ_ERRRTN(err);
if (! objFunc.update(pd, f, fNewGrad, err)){
MSQ_SETERR(err)("Error inside Conjugate Gradient, vertices moved "
"making function value invalid.",
MsqError::INVALID_MESH);
return;
}
assert(fNewGrad.size() == (unsigned)num_vert);
if(conjGradDebug>0){
grad_norm=Linf(arrptr(fNewGrad),num_vert);
MSQ_PRINT(2)("\nCG's VALUE = %f, iter. = %i, grad_norm = %f, alp = %f",f,i,grad_norm,alp);
MSQ_PRINT(2)("\n TIME %f",c_timer.since_birth());
}
double s11=0;
double s12=0;
double s22=0;
//free_iter.reset();
//while (free_iter.next()) {
// m=free_iter.value();
for (m = 0; m < num_vert; ++m) {
s11+=fGrad[m]%fGrad[m];
s12+=fGrad[m]%fNewGrad[m];
s22+=fNewGrad[m]%fNewGrad[m];
}
// Steepest Descent (takes 2-3 times as long as P-R)
//double bet=0;
// Fletcher-Reeves (takes twice as long as P-R)
//double bet = s22/s11;
// Polack-Ribiere
double bet;
if (!divide( s22-s12, s11, bet ))
return; // gradient is zero
//free_iter.reset();
//while (free_iter.next()) {
// m=free_iter.value();
for (m = 0; m < num_vert; ++m) {
pGrad[m]=(-fNewGrad[m]+(bet*pGrad[m]));
fGrad[m]=fNewGrad[m];
}
if(conjGradDebug>2){
MSQ_PRINT(2)(" \nSEARCH DIRECTION INFINITY NORM = %e",
Linf(arrptr(fNewGrad),num_vert));
}
}//end if on alp == 0
term_crit->accumulate_patch( pd, err ); MSQ_ERRRTN(err);
term_crit->accumulate_inner( pd, f, arrptr(fGrad), err ); MSQ_ERRRTN(err);
}//end while
if(conjGradDebug>0){
MSQ_PRINT(2)("\nConjugate Gradient complete i=%i ",i);
MSQ_PRINT(2)("\n- FINAL value = %f, alp=%4.2e grad_norm=%4.2e",f,alp,grad_norm);
MSQ_PRINT(2)("\n FINAL TIME %f",c_timer.since_birth());
}
}