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;
}
