virtual Decomposition<Scalar> _getDecomposition() const override {
Decomposition<Scalar> d(this->getFSpace());
Eigen::SelfAdjointEigenSolver<ScalarMatrix> evd(matrix.template selfadjointView<Eigen::Lower>());
ScalarAltMatrix _mX;
kqp::ThinEVD<ScalarMatrix>::run(evd, _mX, d.mD);
d.mX = FMatrixPtr(new Dense<Scalar>(std::move(ScalarMatrix(_mX))));
d.mY = Eigen::Identity<Scalar>(d.mX->size(), d.mX->size());
return d;
}
//! Actually performs the computation
virtual Decomposition<Scalar> _getDecomposition() const override {
const ScalarMatrix& gram = this->getFSpace()->k(fMatrix);
Eigen::SelfAdjointEigenSolver<ScalarMatrix> evd(gram.template selfadjointView<Eigen::Lower>());
ScalarMatrix _mY;
RealVector _mD;
kqp::ThinEVD<ScalarMatrix>::run(evd, _mY, _mD);
ScalarMatrix __mY;
__mY.noalias() = _mY * _mD.cwiseAbs().cwiseSqrt().cwiseInverse().asDiagonal();
return Decomposition<Scalar>(this->getFSpace(), fMatrix, __mY, _mD, true);
}
//! Actually performs the computation
virtual Decomposition<Scalar> _getDecomposition() const override {
Decomposition<Scalar> d(this->getFSpace());
// Compute A^T X^T X A^T
// where A = diag(A_1 ... A_n) and X = (X_1 ... X_n)
Index size = offsets_A.back();
// Nothing to do
if (size == 0) {
d.mX = this->getFSpace()->newMatrix();
d.mY.resize(0,0);
d.mD.resize(0,1);
return d;
}
ScalarMatrix gram_X = this->getFSpace()->k(fMatrix);
ScalarMatrix gram(size, size);
for(size_t i = 0; i < combination_matrices.size(); i++) {
const ScalarAltMatrix &mAi = combination_matrices[i];
for(size_t j = 0; j <= i; j++) {
const ScalarAltMatrix &mAj = combination_matrices[j];
getBlock(gram, offsets_A, i, j)
= (mAi.adjoint() * ((Eigen::internal::conj(alphas[i]) * alphas[j]) * getBlock(gram_X, offsets_X, i, j))) * mAj;
}
}
// Direct EVD
ScalarMatrix _mY;
RealVector _mD;
Eigen::SelfAdjointEigenSolver<ScalarMatrix> evd(gram.template selfadjointView<Eigen::Lower>());
kqp::ThinEVD<ScalarMatrix>::run(evd, _mY, _mD);
d.mD.swap(_mD);
// Y <- A * Y * D^-1/2 (use cwiseAbs to avoid problems with small negative values)
ScalarMatrix _mY2 = _mY * d.mD.cwiseAbs().cwiseSqrt().cwiseInverse().asDiagonal();
_mY = _mY2;
ScalarMatrix __mY(offsets_X.back(), _mY.cols());
for(size_t i = 0; i < combination_matrices.size(); i++) {
const ScalarAltMatrix &mAi = combination_matrices[i];
__mY.block(offsets_X[i], 0, offsets_X[i+1]-offsets_X[i], __mY.cols()) = mAi * (alphas[i] * _mY.block(offsets_A[i], 0, offsets_A[i+1]-offsets_A[i], _mY.cols()));
}
d.mY.swap(__mY);
d.mX = fMatrix;
return d;
}
int main(void) {
gslpp::complex zi = gslpp::complex::i();
std::vector<double> sd = {10., 5., 1.};
std::vector<gslpp::complex> sc = {30. + zi, 2. + 3. * zi, 1. + 4. * zi};
gslpp::matrix<double> md1(2, 2);
md1(0, 0) = 10.;
md1(1, 0) = 20.;
md1(0, 1) = 5.;
md1(1, 1) = 1.;
gslpp::matrix<double> md2(2, 2);
md2(0, 0) = -3.;
md2(1, 0) = 30.;
md2(0, 1) = -5.;
md2(1, 1) = 4.;
gslpp::matrix<gslpp::complex> mc1(2, 2);
mc1.assign(0, 0, 9. + 2 * zi);
mc1.assign(1, 0, 19. - 4 * zi);
mc1.assign(0, 1, 4. - 6 * zi);
mc1.assign(1, 1, 3. + 2 * zi);
gslpp::matrix<gslpp::complex> mc2(2, 2);
mc2.assign(0, 0, -8. + 3 * zi);
mc2.assign(1, 0, 11. - 5 * zi);
mc2.assign(0, 1, 2. + 5 * zi);
mc2.assign(1, 1, -3. + 4 * zi);
gslpp::vector<double> vd1(2);
gslpp::vector<double> vd2(2);
vd1(0) = 14.;
vd1(1) = -5;
vd2(0) = -9.;
vd2(1) = 3;
gslpp::vector<gslpp::complex> vc1(2);
gslpp::vector<gslpp::complex> vc2(2);
vc1.assign(0, 4. - 2. * zi);
vc1.assign(1, 6. - 8. * zi);
vc2.assign(0, 5. + 3. * zi);
vc2.assign(1, 4. - 12. * zi);
Expanded<double> esd(sd);
Expanded<gslpp::complex> esc(sc);
std::vector<gslpp::matrix<double> > mdv = {md1, md2};
Expanded<gslpp::matrix<double> > emd(mdv);
std::vector<gslpp::matrix<gslpp::complex> > mcv = {mc1, mc2};
Expanded<gslpp::matrix<gslpp::complex> > emc(mcv);
std::vector<gslpp::vector<double> > vdv = {vd1, vd2};
Expanded<gslpp::vector<double> > evd(vdv);
std::vector<gslpp::vector<gslpp::complex> > vcv = {vc1, vc2};
Expanded<gslpp::vector<gslpp::complex> > evc(vcv);
// Print Input
std::cout << std::endl;
std::cout << "esd " << esd << std::endl;
std::cout << "esc " << esc << std::endl;
std::cout << "evd " << evd << std::endl;
std::cout << "evc " << evc << std::endl;
std::cout << "emd " << emd << std::endl;
std::cout << "emc " << emc << std::endl;
std::cout << "-------------" << std::endl;
std::cout << "-sd " << -esd << std::endl;
std::cout << "-sc " << -esc << std::endl;
std::cout << "-vd " << -evd << std::endl;
std::cout << "-vc " << -evc << std::endl;
std::cout << "-md " << -emd << std::endl;
std::cout << "-mc " << -emc << std::endl;
std::cout << "-------------" << std::endl;
// Expanded * Expanded
std::cout << "sd*sd " << esd * esd << std::endl;
std::cout << "sd*sc " << esd * esc << std::endl;
std::cout << "sd*vd " << esd * evd << std::endl;
std::cout << "sd*vc " << esd * evc << std::endl;
std::cout << "sd*md " << esd * emd << std::endl;
std::cout << "sd*mc " << esd * emc << std::endl;
std::cout << "sc*sd " << esc * esd << std::endl;
std::cout << "sc*sc " << esc * esc << std::endl;
std::cout << "sc*vd " << esc * evd << std::endl;
std::cout << "sc*vc " << esc * evc << std::endl;
std::cout << "sc*md " << esc * emd << std::endl;
std::cout << "sc*mc " << esc * emc << std::endl;
std::cout << "vd*sd " << evd * esd << std::endl;
std::cout << "vd*sc " << evd * esc << std::endl;
std::cout << "vd*vd " << evd * evd << std::endl;
std::cout << "vd*vc " << evd * evc << std::endl;
std::cout << "vd*md " << evd * emd << std::endl;
std::cout << "vd*mc " << evd * emc << std::endl;
std::cout << "vc*sd " << evc * esd << std::endl;
std::cout << "vc*sc " << evc * esc << std::endl;
std::cout << "vc*vd " << evc * evd << std::endl;
std::cout << "vc*vc " << evc * evc << std::endl;
std::cout << "vc*md " << evc * emd << std::endl;
std::cout << "vc*mc " << evc * emc << std::endl;
std::cout << "md*sd " << emd * esd << std::endl;
std::cout << "md*sc " << emd * esc << std::endl;
std::cout << "md*vd " << emd * evd << std::endl;
std::cout << "md*vc " << emd * evc << std::endl;
std::cout << "md*md " << emd * emd << std::endl;
std::cout << "md*mc " << emd * emc << std::endl;
std::cout << "mc*sd " << emc * esd << std::endl;
std::cout << "mc*sc " << emc * esc << std::endl;
std::cout << "mc*vd " << emc * evd << std::endl;
std::cout << "mc*vc " << emc * evc << std::endl;
std::cout << "mc*md " << emc * emd << std::endl;
std::cout << "mc*mc " << emc * emc << std::endl;
std::cout << "-------------" << std::endl;
// Expanded + Expanded
std::cout << "sd + sd " << esd + esd << std::endl;
std::cout << "sd + sc " << esd + esc << std::endl;
std::cout << "sc + sd " << esc + esd << std::endl;
std::cout << "sc + sc " << esc + esc << std::endl;
std::cout << "vd + vd " << evd + evd << std::endl;
std::cout << "vd + vc " << evd + evc << std::endl;
std::cout << "vc + vd " << evc + evd << std::endl;
std::cout << "vc + vc " << evc + evc << std::endl;
std::cout << "md + md " << emd + emd << std::endl;
std::cout << "md + mc " << emd + emc << std::endl;
std::cout << "mc + md " << emc + emd << std::endl;
std::cout << "mc + mc " << emc + emc << std::endl;
//
std::cout << "-------------" << std::endl;
// Expanded - Expanded
std::cout << "sd - sd " << esd - esd << std::endl;
std::cout << "sd - sc " << esd - esc << std::endl;
std::cout << "sc - sd " << esc - esd << std::endl;
std::cout << "sc - sc " << esc - esc << std::endl;
std::cout << "vd - vd " << evd - evd << std::endl;
std::cout << "vd - vc " << evd - evc << std::endl;
std::cout << "vc - vd " << evc - evd << std::endl;
std::cout << "vc - vc " << evc - evc << std::endl;
std::cout << "md - md " << emd - emd << std::endl;
std::cout << "md - mc " << emd - emc << std::endl;
std::cout << "mc - md " << emc - emd << std::endl;
std::cout << "mc - mc " << emc - emc << std::endl;
std::cout << "-------------" << std::endl;
// Expanded * UnExpanded
std::cout << "esd*5 = " << esd * 5. << std::endl;
std::cout << "esd*(4-2I) = " << esd * (4. - 2. * zi) << std::endl;
std::cout << "esd*vd1 = " << esd * vd1 << std::endl;
std::cout << "esd*vc1 = " << esd * vc1 << std::endl;
std::cout << "esd*md1 = " << esd * md1 << std::endl;
std::cout << "esd*mc1 = " << esd * mc1 << std::endl;
//
std::cout << "esc*5 = " << esc * 5. << std::endl;
std::cout << "esc*(4-2I) = " << esc * (4. - 2. * zi) << std::endl;
std::cout << "esc*vd1 = " << esc * vd1 << std::endl;
std::cout << "esc*vc1 = " << esc * vc1 << std::endl;
std::cout << "esc*md1 = " << esc * md1 << std::endl;
std::cout << "esc*mc1 = " << esc * mc1 << std::endl;
//
std::cout << "evd*5 = " << evd * 5. << std::endl;
std::cout << "evd*(4-2I) = " << evd * (4. - 2. * zi) << std::endl;
std::cout << "evd*vd1 = " << evd * vd1 << std::endl;
std::cout << "evd*vc1 = " << evd * vc1 << std::endl;
std::cout << "evd*md1 = " << evd * md1 << std::endl;
std::cout << "evd*mc1 = " << evd * mc1 << std::endl;
//
std::cout << "evc*5 = " << evc * 5. << std::endl;
std::cout << "evc*(4-2I) = " << evc * (4. - 2. * zi) << std::endl;
std::cout << "evc*vd1 = " << evc * vd1 << std::endl;
std::cout << "evc*vc1 = " << evc * vc1 << std::endl;
std::cout << "evc*md1 = " << evc * md1 << std::endl;
std::cout << "evc*mc1 = " << evc * mc1 << std::endl;
//
std::cout << "emd*5 = " << emd * 5. << std::endl;
std::cout << "emd*(4-2I) = " << emd * (4. - 2. * zi) << std::endl;
std::cout << "emd*vd1 = " << emd * vd1 << std::endl;
std::cout << "emd*vc1 = " << emd * vc1 << std::endl;
std::cout << "emd*md1 = " << emd * md1 << std::endl;
std::cout << "emd*mc1 = " << emd * mc1 << std::endl;
//
std::cout << "emc*5 = " << emc * 5. << std::endl;
std::cout << "emc*(4-2I) = " << emc * (4. - 2. * zi) << std::endl;
std::cout << "emc*vd1 = " << emc * vd1 << std::endl;
std::cout << "emc*vc1 = " << emc * vc1 << std::endl;
std::cout << "emc*md1 = " << emc * md1 << std::endl;
std::cout << "emc*mc1 = " << emc * mc1 << std::endl;
std::cout << "-------------" << std::endl;
// // Expanded / UnExpanded-Scalar
std::cout << "esd/5 = " << esd / 5. << std::endl;
std::cout << "esd/(4-2I) = " << esd / (4. - 2. * zi) << std::endl;
std::cout << "esc/5 = " << esc / 5. << std::endl;
std::cout << "esc/(4-2I) = " << esc / (4. - 2. * zi) << std::endl;
std::cout << "evd/5 = " << evd / 5. << std::endl;
std::cout << "evd/(4-2I) = " << evd / (4. - 2. * zi) << std::endl;
std::cout << "evc/5 = " << evc / 5. << std::endl;
std::cout << "evc/(4-2I) = " << evc / (4. - 2. * zi) << std::endl;
std::cout << "emd/5 = " << emd / 5. << std::endl;
std::cout << "emd/(4-2I) = " << emd / (4. - 2. * zi) << std::endl;
std::cout << "emc/5 = " << emc / 5. << std::endl;
std::cout << "emc/(4-2I) = " << emc / (4. - 2. * zi) << std::endl;
std::cout << "-------------" << std::endl;
// UnExpanded * Expanded easy-check (must be 0)
std::cout << "zero1 = " << 5. * esd - esd * 5. << std::endl;
std::cout << "zero1 = " << 5. * esc - esc * 5. << std::endl;
std::cout << "zero1 = " << 5. * evd - evd * 5. << std::endl;
std::cout << "zero1 = " << 5. * evc - evc * 5. << std::endl;
std::cout << "zero1 = " << 5. * emd - emd * 5. << std::endl;
std::cout << "zero1 =" << 5. * emc - emc * 5. << std::endl;
//
std::cout << "zero2 = " << (4 - 2 * zi) * esd - esd * (4 - 2 * zi) << std::endl;
std::cout << "zero2 = " << (4 - 2 * zi) * esc - esc * (4 - 2 * zi) << std::endl;
std::cout << "zero2 = " << (4 - 2 * zi) * evd - evd * (4 - 2 * zi) << std::endl;
std::cout << "zero2 = " << (4 - 2 * zi) * evc - evc * (4 - 2 * zi) << std::endl;
std::cout << "zero2 = " << (4 - 2 * zi) * emd - emd * (4 - 2 * zi) << std::endl;
std::cout << "zero2 = " << (4 - 2 * zi) * emc - emc * (4 - 2 * zi) << std::endl;
std::cout << "zero3 = " << vd1 * esd - esd * vd1 << std::endl;
std::cout << "zero3 = " << vd1 * esc - esc * vd1 << std::endl;
std::cout << "zero3 = " << vd1 * evd - evd * vd1 << std::endl;
std::cout << "zero3 = " << vd1 * evc - evc * vd1 << std::endl;
std::cout << "zero3 = " << vd1 * emd - emd.transpose() * vd1 << std::endl;
std::cout << "zero3 = " << vd1 * emc - emc.transpose() * vd1 << std::endl;
//
std::cout << "zero4 = " << vc1 * esd - esd * vc1 << std::endl;
std::cout << "zero4 = " << vc1 * esc - esc * vc1 << std::endl;
std::cout << "zero4 = " << vc1 * evd - evd * vc1 << std::endl;
std::cout << "zero4 = " << vc1 * evc - evc * vc1 << std::endl;
std::cout << "zero4 = " << vc1 * emd - emd.transpose() * vc1 << std::endl;
std::cout << "zero4 = " << vc1 * emc - emc.transpose() * vc1 << std::endl;
//
std::cout << "zero5 = " << md1 * esd - esd * md1 << std::endl;
std::cout << "zero5 = " << md1 * esc - esc * md1 << std::endl;
std::cout << "zero5 = " << md1 * evd - evd * md1.transpose() << std::endl;
std::cout << "zero5 = " << md1 * evc - evc * md1.transpose() << std::endl;
std::cout << "zero5 = " << md1 * emd - (emd.transpose() * md1.transpose()).transpose() << std::endl;
std::cout << "zero5 = " << md1 * emc - (emc.transpose() * md1.transpose()).transpose() << std::endl;
//
std::cout << "zero6 = " << mc1 * esd - esd * mc1 << std::endl;
std::cout << "zero6 = " << mc1 * esc - esc * mc1 << std::endl;
std::cout << "zero6 = " << mc1 * evd - evd * mc1.transpose() << std::endl;
std::cout << "zero6 = " << mc1 * evc - evc * mc1.transpose() << std::endl;
std::cout << "zero6 = " << mc1 * emd - (emd.transpose() * mc1.transpose()).transpose() << std::endl;
std::cout << "zero6 = " << mc1 * emc - (emc.transpose() * mc1.transpose()).transpose() << std::endl;
std::cout << "true = " << (esd == esd) << std::endl;
std::cout << "true = " << (esc == esc) << std::endl;
std::cout << "true = " << (evd == evd) << std::endl;
std::cout << "true = " << (evc == evc) << std::endl;
std::cout << "true = " << (emd == emd) << std::endl;
std::cout << "true = " << (emc == emc) << std::endl;
std::cout << "false = " << (esd == esd * esd) << std::endl;
std::cout << "false = " << (esc == esc * esc) << std::endl;
std::cout << "false = " << (evd == 5 * evd) << std::endl;
std::cout << "false = " << (evc == 7 * evc) << std::endl;
std::cout << "false = " << (emd == emd * emd) << std::endl;
std::cout << "false = " << (emc == emc * emc) << std::endl;
Expanded<double> esd1(sd, 2);
std::vector<double> sdx = {10., 5., 1.,-7};
Expanded<double> esd2(sdx, 1);
std::cout << "esd1 * esd2 = " << esd1*esd2 << std::endl;
std::cout << "esd1 + esd2 = " << esd1+esd2 << std::endl;
std::cout << "esd1 - esd2 = " << esd1-esd2 << std::endl;
std::vector<double> q1={1.,0.};
std::vector<double> q2={5.,7.};
std::vector<std::vector<double> > v1 = {q1,q2};
std::vector<double> w1={3.,4.};
std::vector<double> w2={8.};
std::vector<std::vector<double> > v2 = {w1,w2};
Expanded<double> ev1(v1, 1, 0);
Expanded<double> ev2(v2);
std::cout << "ev1 = " << ev1 << std::endl;
std::cout << "ev2 = " << ev2 << std::endl;
std::cout << "ev1 * ev2 = " << ev1*ev2 << std::endl;
std::cout << "ev1 + ev2 = " << ev1+ev2 << std::endl;
std::cout << "1/ev1 = " << ev1.inverse() << std::endl;
std::cout << "1/ev2 = " << ev2.inverse() << std::endl;
complex ii(0, 1);
std::vector<complex> r1={1.+2.*ii, 3.+4.*ii};
std::vector<complex> r2={5. + 6.*ii, 7.+8.*ii, 9.+10.*ii};
std::vector<std::vector<complex> > vv1 = {r1,r2};
Expanded<complex> evv1(vv1, 1, 1);
std::cout << "evv1 = " << evv1 << std::endl;
std::cout << "1/evv1 = " << evv1.inverse() << std::endl;
std::cout << "ev1/evv1 = " << ev1/evv1 << std::endl;
std::cout << "evv1/ev1 = " << evv1/ev1 << std::endl;
Expanded<complex> tmp(evv1.truncate(std::vector<int>(2,2),2));
std::cout << "evv1 trunc at (std::vector<int>(2,2),2)" << tmp << std::endl;
std::cout << "evv1 series = " << evv1.Series(std::vector<int>(2,2),2) << std::endl;
Expanded<double> pp;
return (0);
}
