CLogDetEstimator::CLogDetEstimator(SGSparseMatrix<float64_t> sparse_mat)
: CSGObject()
{
init();
m_computation_engine=new CSerialComputationEngine();
SG_REF(m_computation_engine);
CSparseMatrixOperator<float64_t>* op=
new CSparseMatrixOperator<float64_t>(sparse_mat);
float64_t accuracy=1E-5;
CLanczosEigenSolver* eig_solver=new CLanczosEigenSolver(op);
CCGMShiftedFamilySolver* linear_solver=new CCGMShiftedFamilySolver();
m_operator_log=new CLogRationalApproximationCGM(op,m_computation_engine,
eig_solver,linear_solver,accuracy);
SG_REF(m_operator_log);
#ifdef HAVE_COLPACK
m_trace_sampler=new CProbingSampler(op,1,NATURAL,DISTANCE_TWO);
#else
m_trace_sampler=new CNormalSampler(op->get_dimension());
#endif
SG_REF(m_trace_sampler);
SG_INFO("LogDetEstimator:Using %s, %s with 1E-5 accuracy, %s as default\n",
m_computation_engine->get_name(), m_operator_log->get_name(),
m_trace_sampler->get_name());
}
template<class ST> bool CDenseFeatures<ST>::apply_preprocessor(bool force_preprocessing)
{
if (m_subset_stack->has_subsets())
SG_ERROR("A subset is set, cannot call apply_preproc\n");
SG_DEBUG( "force: %d\n", force_preprocessing);
if (feature_matrix.matrix && get_num_preprocessors())
{
for (int32_t i = 0; i < get_num_preprocessors(); i++)
{
if ((!is_preprocessed(i) || force_preprocessing))
{
set_preprocessed(i);
CDensePreprocessor<ST>* p =
(CDensePreprocessor<ST>*) get_preprocessor(i);
SG_INFO( "preprocessing using preproc %s\n", p->get_name());
if (p->apply_to_feature_matrix(this).matrix == NULL)
{
SG_UNREF(p);
return false;
}
SG_UNREF(p);
}
}
return true;
}
else
{
if (!feature_matrix.matrix)
SG_ERROR( "no feature matrix\n");
if (!get_num_preprocessors())
SG_ERROR( "no preprocessors available\n");
return false;
}
}
SGVector<complex128_t> CCGMShiftedFamilySolver::solve_shifted_weighted(
CLinearOperator<SGVector<float64_t>, SGVector<float64_t> >* A, SGVector<float64_t> b,
SGVector<complex128_t> shifts, SGVector<complex128_t> weights)
{
SG_DEBUG("Entering\n");
// sanity check
REQUIRE(A, "Operator is NULL!\n");
REQUIRE(A->get_dimension()==b.vlen, "Dimension mismatch! [%d vs %d]\n",
A->get_dimension(), b.vlen);
REQUIRE(shifts.vector,"Shifts are not initialized!\n");
REQUIRE(weights.vector,"Weights are not initialized!\n");
REQUIRE(shifts.vlen==weights.vlen, "Number of shifts and number of "
"weights are not equal! [%d vs %d]\n", shifts.vlen, weights.vlen);
// the solution matrix, one column per shift, initial guess 0 for all
MatrixXcd x_sh=MatrixXcd::Zero(b.vlen, shifts.vlen);
MatrixXcd p_sh=MatrixXcd::Zero(b.vlen, shifts.vlen);
// non-shifted direction
SGVector<float64_t> p_(b.vlen);
// the rest of the part hinges on eigen3 for computing norms
Map<VectorXd> b_map(b.vector, b.vlen);
Map<VectorXd> p(p_.vector, p_.vlen);
// residual r_i=b-Ax_i, here x_0=[0], so r_0=b
VectorXd r=b_map;
// initial direction is same as residual
p=r;
p_sh=r.replicate(1, shifts.vlen).cast<complex128_t>();
// non shifted initializers
float64_t r_norm2=r.dot(r);
float64_t beta_old=1.0;
float64_t alpha=1.0;
// shifted quantities
SGVector<complex128_t> alpha_sh(shifts.vlen);
SGVector<complex128_t> beta_sh(shifts.vlen);
SGVector<complex128_t> zeta_sh_old(shifts.vlen);
SGVector<complex128_t> zeta_sh_cur(shifts.vlen);
SGVector<complex128_t> zeta_sh_new(shifts.vlen);
// shifted initializers
zeta_sh_old.set_const(1.0);
zeta_sh_cur.set_const(1.0);
// the iterator for this iterative solver
IterativeSolverIterator<float64_t> it(r, m_max_iteration_limit,
m_relative_tolerence, m_absolute_tolerence);
// start the timer
CTime time;
time.start();
// set the residuals to zero
if (m_store_residuals)
m_residuals.set_const(0.0);
// CG iteration begins
for (it.begin(r); !it.end(r); ++it)
{
SG_DEBUG("CG iteration %d, residual norm %f\n",
it.get_iter_info().iteration_count,
it.get_iter_info().residual_norm);
if (m_store_residuals)
{
m_residuals[it.get_iter_info().iteration_count]
=it.get_iter_info().residual_norm;
}
// apply linear operator to the direction vector
SGVector<float64_t> Ap_=A->apply(p_);
Map<VectorXd> Ap(Ap_.vector, Ap_.vlen);
// compute p^{T}Ap, if zero, failure
float64_t p_dot_Ap=p.dot(Ap);
if (p_dot_Ap==0.0)
break;
// compute the beta parameter of CG_M
float64_t beta=-r_norm2/p_dot_Ap;
// compute the zeta-shifted parameter of CG_M
compute_zeta_sh_new(zeta_sh_old, zeta_sh_cur, shifts, beta_old, beta,
alpha, zeta_sh_new);
// compute beta-shifted parameter of CG_M
compute_beta_sh(zeta_sh_new, zeta_sh_cur, beta, beta_sh);
// update the solution vector and residual
for (index_t i=0; i<shifts.vlen; ++i)
x_sh.col(i)-=beta_sh[i]*p_sh.col(i);
// r_{i}=r_{i-1}+\beta_{i}Ap
r+=beta*Ap;
// compute new ||r||_{2}, if zero, converged
float64_t r_norm2_i=r.dot(r);
if (r_norm2_i==0.0)
break;
// compute the alpha parameter of CG_M
alpha=r_norm2_i/r_norm2;
// update ||r||_{2}
r_norm2=r_norm2_i;
// update direction
p=r+alpha*p;
compute_alpha_sh(zeta_sh_new, zeta_sh_cur, beta_sh, beta, alpha, alpha_sh);
for (index_t i=0; i<shifts.vlen; ++i)
{
p_sh.col(i)*=alpha_sh[i];
p_sh.col(i)+=zeta_sh_new[i]*r;
}
// update parameters
for (index_t i=0; i<shifts.vlen; ++i)
{
zeta_sh_old[i]=zeta_sh_cur[i];
zeta_sh_cur[i]=zeta_sh_new[i];
}
beta_old=beta;
}
float64_t elapsed=time.cur_time_diff();
if (!it.succeeded(r))
SG_WARNING("Did not converge!\n");
SG_INFO("Iteration took %d times, residual norm=%.20lf, time elapsed=%f\n",
it.get_iter_info().iteration_count, it.get_iter_info().residual_norm, elapsed);
// compute the final result vector multiplied by weights
SGVector<complex128_t> result(b.vlen);
result.set_const(0.0);
Map<VectorXcd> x(result.vector, result.vlen);
for (index_t i=0; i<x_sh.cols(); ++i)
x+=x_sh.col(i)*weights[i];
SG_DEBUG("Leaving\n");
return result;
}
SGVector<float64_t> CConjugateGradientSolver::solve(
CLinearOperator<float64_t>* A, SGVector<float64_t> b)
{
SG_DEBUG("CConjugateGradientSolve::solve(): Entering..\n");
// sanity check
REQUIRE(A, "Operator is NULL!\n");
REQUIRE(A->get_dimension()==b.vlen, "Dimension mismatch!\n");
// the final solution vector, initial guess is 0
SGVector<float64_t> result(b.vlen);
result.set_const(0.0);
// the rest of the part hinges on eigen3 for computing norms
Map<VectorXd> x(result.vector, result.vlen);
Map<VectorXd> b_map(b.vector, b.vlen);
// direction vector
SGVector<float64_t> p_(result.vlen);
Map<VectorXd> p(p_.vector, p_.vlen);
// residual r_i=b-Ax_i, here x_0=[0], so r_0=b
VectorXd r=b_map;
// initial direction is same as residual
p=r;
// the iterator for this iterative solver
IterativeSolverIterator<float64_t> it(b_map, m_max_iteration_limit,
m_relative_tolerence, m_absolute_tolerence);
// CG iteration begins
float64_t r_norm2=r.dot(r);
// start the timer
CTime time;
time.start();
// set the residuals to zero
if (m_store_residuals)
m_residuals.set_const(0.0);
for (it.begin(r); !it.end(r); ++it)
{
SG_DEBUG("CG iteration %d, residual norm %f\n",
it.get_iter_info().iteration_count,
it.get_iter_info().residual_norm);
if (m_store_residuals)
{
m_residuals[it.get_iter_info().iteration_count]
=it.get_iter_info().residual_norm;
}
// apply linear operator to the direction vector
SGVector<float64_t> Ap_=A->apply(p_);
Map<VectorXd> Ap(Ap_.vector, Ap_.vlen);
// compute p^{T}Ap, if zero, failure
float64_t p_dot_Ap=p.dot(Ap);
if (p_dot_Ap==0.0)
break;
// compute the alpha parameter of CG
float64_t alpha=r_norm2/p_dot_Ap;
// update the solution vector and residual
// x_{i}=x_{i-1}+\alpha_{i}p
x+=alpha*p;
// r_{i}=r_{i-1}-\alpha_{i}p
r-=alpha*Ap;
// compute new ||r||_{2}, if zero, converged
float64_t r_norm2_i=r.dot(r);
if (r_norm2_i==0.0)
break;
// compute the beta parameter of CG
float64_t beta=r_norm2_i/r_norm2;
// update direction, and ||r||_{2}
r_norm2=r_norm2_i;
p=r+beta*p;
}
float64_t elapsed=time.cur_time_diff();
if (!it.succeeded(r))
SG_WARNING("Did not converge!\n");
SG_INFO("Iteration took %ld times, residual norm=%.20lf, time elapsed=%lf\n",
it.get_iter_info().iteration_count, it.get_iter_info().residual_norm, elapsed);
SG_DEBUG("CConjugateGradientSolve::solve(): Leaving..\n");
return result;
}
SGVector<float64_t> CLogDetEstimator::sample(index_t num_estimates)
{
SG_DEBUG("Entering\n");
SG_INFO("Computing %d log-det estimates\n", num_estimates);
REQUIRE(m_operator_log, "Operator function is NULL\n");
// call the precompute of operator function to compute the prerequisites
m_operator_log->precompute();
REQUIRE(m_trace_sampler, "Trace sampler is NULL\n");
// call the precompute of the sampler
m_trace_sampler->precompute();
REQUIRE(m_operator_log->get_operator()->get_dimension()\
==m_trace_sampler->get_dimension(),
"Mismatch in dimensions of the operator and trace-sampler, %d vs %d!\n",
m_operator_log->get_operator()->get_dimension(),
m_trace_sampler->get_dimension());
// for storing the aggregators that submit_jobs return
CDynamicObjectArray* aggregators=new CDynamicObjectArray();
index_t num_trace_samples=m_trace_sampler->get_num_samples();
for (index_t i=0; i<num_estimates; ++i)
{
for (index_t j=0; j<num_trace_samples; ++j)
{
SG_INFO("Computing log-determinant trace sample %d/%d\n", j,
num_trace_samples);
SG_DEBUG("Creating job for estimate %d, trace sample %d/%d\n", i, j,
num_trace_samples);
// get the trace sampler vector
SGVector<float64_t> s=m_trace_sampler->sample(j);
// create jobs with the sample vector and store the aggregator
CJobResultAggregator* agg=m_operator_log->submit_jobs(s);
aggregators->append_element(agg);
SG_UNREF(agg);
}
}
REQUIRE(m_computation_engine, "Computation engine is NULL\n");
// wait for all the jobs to be completed
SG_INFO("Waiting for jobs to finish\n");
m_computation_engine->wait_for_all();
SG_INFO("All jobs finished, aggregating results\n");
// the samples vector which stores the estimates with averaging
SGVector<float64_t> samples(num_estimates);
samples.zero();
// use the aggregators to find the final result
// use the same order as job submission to combine results
int32_t num_aggregates=aggregators->get_num_elements();
index_t idx_row=0;
index_t idx_col=0;
for (int32_t i=0; i<num_aggregates; ++i)
{
// this cast is safe due to above way of building the array
CJobResultAggregator* agg=dynamic_cast<CJobResultAggregator*>
(aggregators->get_element(i));
ASSERT(agg);
// call finalize on all the aggregators, cast is safe again
agg->finalize();
CScalarResult<float64_t>* r=dynamic_cast<CScalarResult<float64_t>*>
(agg->get_final_result());
ASSERT(r);
// iterate through indices, group results in the same way as jobs
samples[idx_col]+=r->get_result();
idx_row++;
if (idx_row>=num_trace_samples)
{
idx_row=0;
idx_col++;
}
SG_UNREF(agg);
}
// clear all aggregators
SG_UNREF(aggregators)
SG_INFO("Finished computing %d log-det estimates\n", num_estimates);
SG_DEBUG("Leaving\n");
return samples;
}
