sparse_costs.h

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#ifndef EXOTICA_CORE_TOOLS_SPARSE_COSTS_H_
#define EXOTICA_CORE_TOOLS_SPARSE_COSTS_H_

#include <exotica_core/tools/exception.h>
#include <Eigen/Dense>
#include <vector>

namespace exotica
{
inline double huber_cost(double x, double beta)
{
    if (std::abs(x) < beta)
        return 0.5 * x * x;
    else
        return beta * (std::abs(x) - 0.5 * beta);
}

inline double huber_jacobian(double x, double beta)
{
    if (std::abs(x) < beta)
        return x;
    if (x < 0)
        return -beta;
    return beta;
}

inline double huber_hessian(double x, double beta)
{
    if (std::abs(x) < beta)
        return 1;
    return 0;
}

inline double smooth_l1_cost(double x, double beta)
{
    if (std::abs(x) < beta)
        return 0.5 * x * x / beta;
    return std::abs(x) - 0.5 * beta;
}

inline double smooth_l1_jacobian(double x, double beta)
{
    if (std::abs(x) < beta)
        return x / beta;
    if (x < -beta)
        return -1.0;
    return 1.0;
}

inline double smooth_l1_hessian(double x, double beta)
{
    if (std::abs(x) < beta)
        return 1.0 / beta;
    return 0.0;
}

inline double pseudo_huber_cost(double x, double beta)
{
    return beta * beta * (std::sqrt(1 + std::pow(x / beta, 2)) - 1.0);
}

inline double pseudo_huber_jacobian(double x, double beta)
{
    return x / (std::sqrt(1.0 + x * x / (beta * beta)));
}

inline double pseudo_huber_hessian(double x, double beta)
{
    return std::pow(beta, 4) * std::sqrt(1.0 + x * x / (beta * beta)) / (std::pow(beta * beta + x * x, 2));
}

}  // namespace exotica

#endif  // EXOTICA_CORE_TOOLS_SPARSE_COSTS_H_