inline void check_pos_definite(const char* function, const char* name,
const Eigen::LDLT<Derived>& cholesky) {
if (cholesky.info() != Eigen::Success
|| !cholesky.isPositive()
|| !(cholesky.vectorD().array() > 0.0).all())
domain_error(function, "LDLT decomposition of", " failed", name);
}
Eigen::LDLT<Eigen::MatrixXd> CKLInference::update_init_helper()
{
Map<MatrixXd> eigen_K(m_ktrtr.matrix, m_ktrtr.num_rows, m_ktrtr.num_cols);
eigen_K=eigen_K+m_noise_factor*MatrixXd::Identity(m_ktrtr.num_rows, m_ktrtr.num_cols);
Eigen::LDLT<Eigen::MatrixXd> ldlt;
ldlt.compute(eigen_K*CMath::exp(m_log_scale*2.0));
float64_t attempt_count=0;
MatrixXd Kernel_D=ldlt.vectorD();
float64_t noise_factor=m_noise_factor;
while (Kernel_D.minCoeff()<=m_min_coeff_kernel)
{
if (m_max_attempt>0 && attempt_count>m_max_attempt)
SG_ERROR("The Kernel matrix is highly non-positive definite since the min_coeff_kernel is less than %.20f",
" even when adding %.20f noise to the diagonal elements at max %d attempts\n",
m_min_coeff_kernel, noise_factor, m_max_attempt);
attempt_count++;
float64_t pre_noise_factor=noise_factor;
noise_factor*=m_exp_factor;
//updat the noise eigen_K=eigen_K+noise_factor*(m_exp_factor^attempt_count)*Identity()
eigen_K=eigen_K+(noise_factor-pre_noise_factor)*MatrixXd::Identity(m_ktrtr.num_rows, m_ktrtr.num_cols);
ldlt.compute(eigen_K*CMath::exp(m_log_scale*2.0));
Kernel_D=ldlt.vectorD();
}
return ldlt;
}
inline bool check_pos_definite(const char* function,
const Eigen::Matrix<T_y,Eigen::Dynamic,Eigen::Dynamic>& y,
const char* name,
T_result* result) {
typedef
typename Eigen::Matrix<T_y,Eigen::Dynamic,Eigen::Dynamic>::size_type
size_type;
if (y.rows() == 1 && y(0,0) <= CONSTRAINT_TOLERANCE) {
std::ostringstream message;
message << name << " is not positive definite. "
<< name << "(0,0) is %1%.";
std::string msg(message.str());
return dom_err(function,y(0,0),name,msg.c_str(),"",result);
}
Eigen::LDLT< Eigen::Matrix<T_y,Eigen::Dynamic,Eigen::Dynamic> > cholesky
= y.ldlt();
if(cholesky.info() != Eigen::Success ||
cholesky.isNegative() ||
(cholesky.vectorD().array() <= CONSTRAINT_TOLERANCE).any()) {
std::ostringstream message;
message << name << " is not positive definite. "
<< name << "(0,0) is %1%.";
std::string msg(message.str());
return dom_err(function,y(0,0),name,msg.c_str(),"",result);
}
return true;
}
Eigen::Matrix<double, N, N> cholesky(Eigen::Matrix<double, N, N> x) {
Eigen::LDLT<Eigen::Matrix<double, N, N> > ldlt = x.ldlt();
Eigen::Array<double, N, 1> d(ldlt.vectorD().array());
for(int i = 0; i < N; i++) {
if(d[i] < 0) d[i] = 0;
}
Eigen::Matrix<double, N, 1> sqrtd(d.sqrt());
return ldlt.transpositionsP().transpose() * Eigen::Matrix<double, N, N>(ldlt.matrixL()) * sqrtd.asDiagonal();
}
/**
* Computes the structure and the expected return of the tangency portfolio;
*/
void EfficientPortfolioWithRisklessAsset::_computeTangencyPortfolio()
{
Eigen::LDLT<Eigen::MatrixXd> ldlt;
ldlt.compute(variance);
Eigen::VectorXd one = Eigen::VectorXd::Constant(dim - 1, 1.0);
Eigen::VectorXd excessReturn = mean - _risklessRate * one;
_inverseTimesExcessReturn = ldlt.solve(excessReturn);
_tangencyPortfolio = Eigen::VectorXd::Constant(dim, 0.0);
_tangencyPortfolio.head(dim - 1) = 1.0 / (alpha - gamma * _risklessRate) * _inverseTimesExcessReturn;
_tangencyPortfolioReturn = portfolioReturn(_tangencyPortfolio);
}
inline void check_pos_definite(const char* function, const char* name,
const Eigen::Matrix<T_y, -1, -1>& 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, "is not positive definite.", "");
Eigen::LDLT<Eigen::MatrixXd> cholesky = value_of_rec(y).ldlt();
if (cholesky.info() != Eigen::Success
|| !cholesky.isPositive()
|| (cholesky.vectorD().array() <= 0.0).any())
domain_error(function, name, "is not positive definite.", "");
check_not_nan(function, name, y);
}
void ctms_decompositions()
{
const int maxSize = 16;
const int size = 12;
typedef Eigen::Matrix<Scalar,
Eigen::Dynamic, Eigen::Dynamic,
0,
maxSize, maxSize> Matrix;
typedef Eigen::Matrix<Scalar,
Eigen::Dynamic, 1,
0,
maxSize, 1> Vector;
typedef Eigen::Matrix<std::complex<Scalar>,
Eigen::Dynamic, Eigen::Dynamic,
0,
maxSize, maxSize> ComplexMatrix;
const Matrix A(Matrix::Random(size, size));
const ComplexMatrix complexA(ComplexMatrix::Random(size, size));
const Matrix saA = A.adjoint() * A;
// Cholesky module
Eigen::LLT<Matrix> LLT; LLT.compute(A);
Eigen::LDLT<Matrix> LDLT; LDLT.compute(A);
// Eigenvalues module
Eigen::HessenbergDecomposition<ComplexMatrix> hessDecomp; hessDecomp.compute(complexA);
Eigen::ComplexSchur<ComplexMatrix> cSchur(size); cSchur.compute(complexA);
Eigen::ComplexEigenSolver<ComplexMatrix> cEigSolver; cEigSolver.compute(complexA);
Eigen::EigenSolver<Matrix> eigSolver; eigSolver.compute(A);
Eigen::SelfAdjointEigenSolver<Matrix> saEigSolver(size); saEigSolver.compute(saA);
Eigen::Tridiagonalization<Matrix> tridiag; tridiag.compute(saA);
// LU module
Eigen::PartialPivLU<Matrix> ppLU; ppLU.compute(A);
Eigen::FullPivLU<Matrix> fpLU; fpLU.compute(A);
// QR module
Eigen::HouseholderQR<Matrix> hQR; hQR.compute(A);
Eigen::ColPivHouseholderQR<Matrix> cpQR; cpQR.compute(A);
Eigen::FullPivHouseholderQR<Matrix> fpQR; fpQR.compute(A);
// SVD module
Eigen::JacobiSVD<Matrix> jSVD; jSVD.compute(A, ComputeFullU | ComputeFullV);
}
void LinearRegression::Learn(const std::vector<double>& input, const std::vector<double>& output, int dataSize)
{
Reset();
mInputDim = input.size() / dataSize;
mOutputDim = output.size() / dataSize;
Eigen::MatrixXd matA(dataSize, mInputDim + 1);
Eigen::MatrixXd matB(dataSize, mOutputDim);
for (int dataId = 0; dataId < dataSize; dataId++)
{
int inputBase = dataId * mInputDim;
for (int dimId = 0; dimId < mInputDim; dimId++)
{
matA(dataId, dimId) = input.at(inputBase + dimId);
}
matA(dataId, mInputDim) = 1.0;
int outputBase = dataId * mOutputDim;
for (int dimId = 0; dimId < mOutputDim; dimId++)
{
matB(dataId, dimId) = output.at(outputBase + dimId);
}
}
Eigen::MatrixXd matAT = matA.transpose();
Eigen::MatrixXd matCoefA = matAT * matA;
Eigen::MatrixXd matCoefB = matAT * matB;
Eigen::LDLT<Eigen::MatrixXd> solver;
solver.compute(matCoefA);
Eigen::MatrixXd matRes = solver.solve(matCoefB);
//copy result
mRegMat.resize((mInputDim + 1) * mOutputDim);
for (int colId = 0; colId < mOutputDim; colId++)
{
int baseIndex = colId * (mInputDim + 1);
for (int rowId = 0; rowId <= mInputDim; rowId++)
{
mRegMat.at(baseIndex + rowId) = matRes(rowId, colId);
}
}
}