int Solver_Core::Solve(int num_basis, double cvm_eps)
{
timeusedForModelSaving = 0;
modelsWritten = 0;
algorithmStartTime = pnow();
nextSaveTime = param->saveFactor * (modelsWritten+1) + floor (pow (param->saveExponential, 1));
saveExponential = param->saveExponential;
this->maxNumBasis = num_basis;
// The convergence of CVM does not require the exact MEB on the core-set.
// With the recent advance of core-set approximation, the (1+epsilon/2)-MEB approximation on the core-set
// can guarantee the quality and the convergence of the (1+epsilon)-MEB approximation for the whole data set.
// See [Kumar, Mitchell, and Yildirim, 2003]
//
// iterate on epsilons
double epsilonFactor = EPS_SCALING;
for(double currentEpsilon = INITIAL_EPS; currentEpsilon/epsilonFactor > cvm_eps; currentEpsilon *= epsilonFactor)
{
// check epsilon
currentEpsilon = (currentEpsilon < cvm_eps ? cvm_eps : currentEpsilon);
// solve problem with current epsilon (warm start from the previous solution)
double maxDistance2 = 0.0;
int maxDistance2Idx = 0;
double factor = 1.0 + currentEpsilon;
factor *= factor;
// The convergence of CVM does not require the exact most violating point.
// A violating point is enough for the convergence of CVM.
// Probabilistic speedup lead to a good tradeoff between convergence and complexity at each iteration
//
while (maxDistance2Idx != -1)
{
// get a probabilistic sample
maxDistance2 = r2 * factor;
maxDistance2Idx = -1;
for(int sampleIter = 0; (sampleIter < 7) && (maxDistance2Idx == -1); sampleIter++)
maxDistance2 = _maxDistFromSampling(maxDistance2, maxDistance2Idx);
// check maximal distance
if (maxDistance2Idx != -1)
{
_UpdateCoreSet(maxDistance2Idx);
#ifndef RELEASE_VER
printf("#%d eps: %g |c|: %.10f R: %.10f |c-x|: %.10f r: %.10f\n",coreNum, currentEpsilon, coreNorm2, r2, maxDistance2, sqrt(maxDistance2/r2)-1.0);
#endif
solver->Solve(coreIdx,coreNum,tempD);
outAlpha = solver->getAlpha();
ComputeRadius2();
// if (coreNum%20 < 1) info(".");
}
double currentTime = pnow ();
if ((param->saveExponential >= 0.0) && (currentTime - algorithmStartTime >= nextSaveTime + timeusedForModelSaving )) {
modelsWritten++;
printf( "&%d..", modelsWritten);
nextSaveTime = param->saveFactor * (modelsWritten+1) + pow (param->saveExponential, modelsWritten + 1);
// std::cout << "Algorithm time is now " << currentTime - algorithmStartTime - timeusedForModelSaving << "\n";
// std::cout << " Saving model now at " << currentTime - startTime << "\n";
double before = pnow();
svm_model *model = Malloc(svm_model,1);
model->param = *param;
model->free_sv = 0; // XXX
model->nr_class = param->nr_classes;
model->label = Malloc(int,model->nr_class);
for(int i=0;i<model->nr_class;i++)
model->label[i] = param->label[i];
model->rho = Malloc(double,1);
double *alpha = Malloc(double,param->prob->l);
double THRESHOLD = 1e-5/coreNum;
for(int i=0;i<1;i++)
model->rho[i] = -ComputeSolution(alpha, THRESHOLD); //overwrite alphas!
model->nSV = Malloc(int, model->nr_class);
// assume all the nonzeros are false at the beginning,
// we have binary classification, they will not change in the
// outer loop in svm.cpp
int total_sv = 0;
for(int i=0;i<model->nr_class;i++)
{
int nSV = 0;
for(int j=0;j<param->count[i];j++) {
if(fabs(alpha[param->start[i]+j])) {
++nSV;
++total_sv;
}
}
model->nSV[i] = nSV;
}
model->l = total_sv; //anzahl der sv im model
// ASSUME PERMUTATION IS IDENTITY
svm_node **x = Malloc(svm_node *,param->prob->l);
int i;
for(int i=0;i<param->prob->l;i++)
x[i] = param->prob->x[i]; // x[i] = param->prob->x[perm[i]];
model->SV = Malloc(svm_node *,total_sv);
int p = 0;
for(int i=0;i<param->prob->l;i++) {
if(fabs(alpha[i]) > 0.0) {
model->SV[p++] = x[i];
}
}
model->sv_coef = Malloc(double *,model->nr_class-1);
for(int i=0;i<model->nr_class-1;i++) {
model->sv_coef[i] = Malloc(double,total_sv);
}
// printf ("%d SV class 0, %d SV class 1\n", model->nSV[0], model->nSV[1]);
int q = 0;
for(int i=0;i<model->nr_class;i++)
{
for(int j=0;j < param->count[i];j++) {
if(fabs(alpha[param->start[i]+j]) > 0.0) {
model->sv_coef[0][q++] = alpha[param->start[i]+j];// * param->prob->y[param->start[i]+j];
// printf ("%d -- %f\n", q, alpha[param->start[i]+j]);
}
}
}
p = 0;
char tmp[1000];
if (strlen(param->modelPath) < 2) {
sprintf(tmp,"%s_%d",param->modelFile, (int)floor( before - algorithmStartTime - timeusedForModelSaving) );
} else {
sprintf(tmp,"%s/%d.cvm.model",param->modelPath, (int)floor( before - algorithmStartTime - timeusedForModelSaving) ) ;
}
model->probB = NULL;
model->probA = NULL;
svm_save_model(tmp, model);
// just to keep compability
FILE* fModel = fopen(tmp, "a+t"); // append mode
fprintf(fModel, "CPU Time = %f second\n", before - algorithmStartTime - timeusedForModelSaving);
fclose(fModel);
// svm_destroy_model(model);
//free(x);
double after = pnow();
timeusedForModelSaving += after - before;
}
// check if we are over the walltime
if (pnow() - param->startTime > param->wallTime + timeusedForModelSaving) {
printf ("Hit the walltime, exiting now..\n");
return coreNum;
}
if (IsExitOnMaxIter())
{
return coreNum;
break;
}
}
}
/*
Run with -build_twosided allreduce -pc_type bjacobi -sub_pc_type lu -q 16 -ksp_rtol 1.e-34 (or 1.e-14 for double precision)
-q <q> number of spectral elements to use
-N <N> maximum number of GLL points per element
*/
int main(int argc,char **args)
{
PetscErrorCode ierr;
PetscGLL gll;
PetscInt N = 80,n,q = 8,xs,xn,j,l;
PetscReal **A;
Mat K;
KSP ksp;
PC pc;
Vec x,b;
PetscInt *rows;
PetscReal norm,xc,yc,h;
PetscScalar *f;
PetscDraw draw;
PetscDrawLG lg;
PetscDrawAxis axis;
DM da;
PetscMPIInt rank,size;
ierr = PetscInitialize(&argc,&args,NULL,NULL);if (ierr) return ierr;
ierr = MPI_Comm_rank(PETSC_COMM_WORLD,&rank);CHKERRQ(ierr);
ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,NULL,"-N",&N,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,NULL,"-q",&q,NULL);CHKERRQ(ierr);
ierr = PetscDrawCreate(PETSC_COMM_WORLD,NULL,"Log(Error norm) vs Number of GLL points",0,0,500,500,&draw);CHKERRQ(ierr);
ierr = PetscDrawSetFromOptions(draw);CHKERRQ(ierr);
ierr = PetscDrawLGCreate(draw,1,&lg);CHKERRQ(ierr);
ierr = PetscDrawLGSetUseMarkers(lg,PETSC_TRUE);CHKERRQ(ierr);
ierr = PetscDrawLGGetAxis(lg,&axis);CHKERRQ(ierr);
ierr = PetscDrawAxisSetLabels(axis,NULL,"Number of GLL points","Log(Error Norm)");CHKERRQ(ierr);
for (n=4; n<N; n+=2) {
/*
da contains the information about the parallel layout of the elements
*/
ierr = DMDACreate1d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,q*(n-1)+1,1,1,NULL,&da);CHKERRQ(ierr);
ierr = DMSetFromOptions(da);CHKERRQ(ierr);
ierr = DMSetUp(da);CHKERRQ(ierr);
ierr = DMDAGetInfo(da,NULL,&q,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL);CHKERRQ(ierr);
q = (q-1)/(n-1); /* number of spectral elements */
/*
gll simply contains the GLL node and weight values
*/
ierr = PetscGLLCreate(n,PETSCGLL_VIA_LINEARALGEBRA,&gll);CHKERRQ(ierr);
ierr = DMDASetGLLCoordinates(da,&gll);CHKERRQ(ierr);
/*
Creates the element stiffness matrix for the given gll
*/
ierr = PetscGLLElementLaplacianCreate(&gll,&A);CHKERRQ(ierr);
/*
Scale the element stiffness and weights by the size of the element
*/
h = 2.0/q;
for (j=0; j<n; j++) {
gll.weights[j] *= .5*h;
for (l=0; l<n; l++) {
A[j][l] = 2.*A[j][l]/h;
}
}
/*
Create the global stiffness matrix and add the element stiffness for each local element
*/
ierr = DMCreateMatrix(da,&K);CHKERRQ(ierr);
ierr = MatSetOption(K,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_FALSE);CHKERRQ(ierr);
ierr = DMDAGetCorners(da,&xs,NULL,NULL,&xn,NULL,NULL);CHKERRQ(ierr);
xs = xs/(n-1);
xn = xn/(n-1);
ierr = PetscMalloc1(n,&rows);CHKERRQ(ierr);
/*
loop over local elements
*/
for (j=xs; j<xs+xn; j++) {
for (l=0; l<n; l++) rows[l] = j*(n-1)+l;
ierr = MatSetValues(K,n,rows,n,rows,&A[0][0],ADD_VALUES);CHKERRQ(ierr);
}
ierr = MatAssemblyBegin(K,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(K,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatCreateVecs(K,&x,&b);CHKERRQ(ierr);
ierr = ComputeRhs(da,&gll,b);CHKERRQ(ierr);
/*
Replace the first and last rows/columns of the matrix with the identity to obtain the zero Dirichlet boundary conditions
*/
rows[0] = 0;
rows[1] = q*(n-1);
ierr = MatZeroRowsColumns(K,2,rows,1.0,x,b);CHKERRQ(ierr);
ierr = PetscFree(rows);CHKERRQ(ierr);
ierr = KSPCreate(PETSC_COMM_WORLD,&ksp);CHKERRQ(ierr);
ierr = KSPSetOperators(ksp,K,K);CHKERRQ(ierr);
ierr = KSPGetPC(ksp,&pc);CHKERRQ(ierr);
ierr = PCSetType(pc,PCLU);CHKERRQ(ierr);
ierr = KSPSetFromOptions(ksp);CHKERRQ(ierr);
ierr = KSPSolve(ksp,b,x);CHKERRQ(ierr);
/* compute the error to the continium problem */
ierr = ComputeSolution(da,&gll,b);CHKERRQ(ierr);
ierr = VecAXPY(x,-1.0,b);CHKERRQ(ierr);
/* compute the L^2 norm of the error */
ierr = VecGetArray(x,&f);CHKERRQ(ierr);
ierr = PetscGLLIntegrate(&gll,f,&norm);CHKERRQ(ierr);
ierr = VecRestoreArray(x,&f);CHKERRQ(ierr);
norm = PetscSqrtReal(norm);
ierr = PetscViewerASCIIPrintf(PETSC_VIEWER_STDOUT_WORLD,"L^2 norm of the error %D %g\n",n,(double)norm);CHKERRQ(ierr);
if (n > 10 && norm > 1.e-8) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_PLIB,"Slower convergence than expected");
xc = (PetscReal)n;
yc = PetscLog10Real(norm);
ierr = PetscDrawLGAddPoint(lg,&xc,&yc);CHKERRQ(ierr);
ierr = PetscDrawLGDraw(lg);CHKERRQ(ierr);
ierr = VecDestroy(&b);CHKERRQ(ierr);
ierr = VecDestroy(&x);CHKERRQ(ierr);
ierr = KSPDestroy(&ksp);CHKERRQ(ierr);
ierr = MatDestroy(&K);CHKERRQ(ierr);
ierr = PetscGLLElementLaplacianDestroy(&gll,&A);CHKERRQ(ierr);
ierr = PetscGLLDestroy(&gll);CHKERRQ(ierr);
ierr = DMDestroy(&da);CHKERRQ(ierr);
}
ierr = PetscDrawLGDestroy(&lg);CHKERRQ(ierr);
ierr = PetscDrawDestroy(&draw);CHKERRQ(ierr);
ierr = PetscFinalize();
return ierr;
}
