bool pdsolve(const SQMATTP& M,const VCTTP& b,VCTTP& res,double* logDet)
{
/* static */ LDLT<SQMATTP> MSr;
MSr = M.ldlt(); // Maybe replace this by a better rank-reaveling criteron
if (MSr.info()!=Success) return false;
res = MSr.solve(b);
if (logDet) {
Diagonal<const SQMATTP> MSrdiag(MSr.vectorD());
*logDet = log(MSrdiag(0));
for (int i=1;i<M.rows();i++) *logDet += log(MSrdiag(i));
}
return true;
}
bool pdsolve(const SQMATTP& M,SQMATTP& MInv,double* logDet)
{
/* static */ LDLT<SQMATTP> MSr;
/* static */ SQMATTP Ip;
/* static */ int Ipdim(0);
int p(M.rows());
if (Ipdim!=p) SetIdentity(Ip,p,&Ipdim);
MSr = M.ldlt(); // Maybe replace this by a better rank-reaveling criteron
if (MSr.info()!=Success) return false;
MInv = MSr.solve(Ip);
if (logDet) {
Diagonal<const SQMATTP> MSrdiag(MSr.vectorD());
*logDet = log(MSrdiag(0));
for (int i=1;i<M.rows();i++) *logDet += log(MSrdiag(i));
}
return true;
}
inline bool
check_pos_definite(const char* function,
const char* name,
const Eigen::Matrix<T_y, Dynamic, Dynamic>& y) {
check_symmetric(function, name, y);
check_positive_size(function, name, "rows", y.rows());
if (y.rows() == 1 && !(y(0, 0) > CONSTRAINT_TOLERANCE))
domain_error(function, name, y, "is not positive definite: ");
using Eigen::LDLT;
using Eigen::Matrix;
using Eigen::Dynamic;
LDLT< Matrix<double, Dynamic, Dynamic> > cholesky
= value_of_rec(y).ldlt();
if (cholesky.info() != Eigen::Success
|| !cholesky.isPositive()
|| (cholesky.vectorD().array() <= CONSTRAINT_TOLERANCE).any())
domain_error(function, name, y, "is not positive definite:\n");
check_not_nan(function, name, y);
return true;
}
int run(const log4cxx::LoggerPtr &logger, KernelEVD<Scalar> &builder) const {
KQP_SCALAR_TYPEDEFS(Scalar);
KQP_LOG_INFO_F(logger, "Kernel EVD with dense vectors and builder \"%s\" (pre-images = %d, linear combination = %d)", %KQP_DEMANGLE(builder) %max_preimages %max_lc);
ScalarMatrix matrix(n,n);
matrix.setConstant(0);
// Construction
for(int i = 0; i < nb_add; i++) {
Scalar alpha = Eigen::internal::abs(Eigen::internal::random_impl<Scalar>::run()) + 1e-3;
int k = (int)std::abs(Eigen::internal::random_impl<double>::run() * (double)(max_preimages-min_preimages)) + min_preimages;
int p = (int)std::abs(Eigen::internal::random_impl<double>::run() * (double)(max_lc-min_lc)) + min_lc;
KQP_LOG_INFO(logger, boost::format("Pre-images (%dx%d) and linear combination (%dx%d)") % n % k % k % p);
// Generate a number of pre-images
ScalarMatrix m = ScalarMatrix::Random(n, k);
// Generate the linear combination matrix
ScalarMatrix mA = ScalarMatrix::Random(k, p);
matrix.template selfadjointView<Eigen::Lower>().rankUpdate(m * mA, alpha);
builder.add(alpha, FMatrixPtr(new Dense<Scalar>(m)), mA);
}
// Computing via EVD
KQP_LOG_INFO(logger, "Computing an LDLT decomposition");
typedef Eigen::LDLT<ScalarMatrix> LDLT;
LDLT ldlt = matrix.template selfadjointView<Eigen::Lower>().ldlt();
ScalarMatrix mL = ldlt.matrixL();
mL = ldlt.transpositionsP().transpose() * mL;
FMatrixPtr mU(Dense<Scalar>::create(mL));
Eigen::Matrix<Scalar,Dynamic,1> mU_d = ldlt.vectorD();
// Comparing the results
KQP_LOG_INFO(logger, "Retrieving the decomposition");
auto kevd = builder.getDecomposition();
ScalarAltMatrix mUY = Eigen::Identity<Scalar>(mL.rows(), mL.rows());
KQP_LOG_DEBUG(logger, "=== Decomposition ===");
// KQP_LOG_DEBUG(logger, "X = " << kevd.mX);
KQP_LOG_DEBUG(logger, "Y = " << kevd.mY);
KQP_LOG_DEBUG(logger, "D = " << kevd.mD);
// Computing the difference between operators || U1 - U2 ||^2
KQP_LOG_INFO(logger, "Comparing the decompositions");
double error = KernelOperators<Scalar>::difference(kevd.fs, kevd.mX, kevd.mY, kevd.mD, mU, mUY, mU_d);
KQP_LOG_INFO_F(logger, "Squared error is %e", %error);
return error < tolerance ? 0 : 1;
}