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#ifndef PROBLEM_H
#define PROBLEM_H
#include <array>
#include <vector>
#include <Eigen/Core>
#include "meta.h"
namespace cppoptlib {
template<typename Scalar_, int Dim_ = Eigen::Dynamic>
class Problem {
public:
static const int Dim = Dim_;
typedef Scalar_ Scalar;
using TVector = Eigen::Matrix<Scalar, Dim, 1>;
using THessian = Eigen::Matrix<Scalar, Dim, Dim>;
using TCriteria = Criteria<Scalar>;
using TIndex = typename TVector::Index;
using MatrixType = Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic>;
public:
Problem() {}
virtual ~Problem()= default;
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wunused-parameter"
virtual bool callback(const Criteria<Scalar> &state, const TVector &x) {
return true;
}
virtual bool detailed_callback(const Criteria<Scalar> &state, SimplexOp op, int index, const MatrixType &x, std::vector<Scalar> f) {
return true;
}
#pragma GCC diagnostic pop
/**
* @brief returns objective value in x
* @details [long description]
*
* @param x [description]
* @return [description]
*/
virtual Scalar value(const TVector &x) = 0;
/**
* @brief overload value for nice syntax
* @details [long description]
*
* @param x [description]
* @return [description]
*/
Scalar operator()(const TVector &x) {
return value(x);
}
/**
* @brief returns gradient in x as reference parameter
* @details should be overwritten by symbolic gradient
*
* @param grad [description]
*/
virtual void gradient(const TVector &x, TVector &grad) {
finiteGradient(x, grad);
}
/**
* @brief This computes the hessian
* @details should be overwritten by symbolic hessian, if solver relies on hessian
*/
virtual void hessian(const TVector &x, THessian &hessian) {
finiteHessian(x, hessian);
}
virtual bool checkGradient(const TVector &x, int accuracy = 3) {
// TODO: check if derived class exists:
// int(typeid(&Rosenbrock<double>::gradient) == typeid(&Problem<double>::gradient)) == 1 --> overwritten
const TIndex D = x.rows();
TVector actual_grad(D);
TVector expected_grad(D);
gradient(x, actual_grad);
finiteGradient(x, expected_grad, accuracy);
for (TIndex d = 0; d < D; ++d) {
Scalar scale = std::max(static_cast<Scalar>(std::max(fabs(actual_grad[d]), fabs(expected_grad[d]))), Scalar(1.));
if(fabs(actual_grad[d]-expected_grad[d])>1e-2 * scale)
return false;
}
return true;
}
virtual bool checkHessian(const TVector &x, int accuracy = 3) {
// TODO: check if derived class exists:
// int(typeid(&Rosenbrock<double>::gradient) == typeid(&Problem<double>::gradient)) == 1 --> overwritten
const TIndex D = x.rows();
THessian actual_hessian = THessian::Zero(D, D);
THessian expected_hessian = THessian::Zero(D, D);
hessian(x, actual_hessian);
finiteHessian(x, expected_hessian, accuracy);
for (TIndex d = 0; d < D; ++d) {
for (TIndex e = 0; e < D; ++e) {
Scalar scale = std::max(static_cast<Scalar>(std::max(fabs(actual_hessian(d, e)), fabs(expected_hessian(d, e)))), Scalar(1.));
if(fabs(actual_hessian(d, e)- expected_hessian(d, e))>1e-1 * scale)
return false;
}
}
return true;
}
void finiteGradient(const TVector &x, TVector &grad, int accuracy = 0) {
// accuracy can be 0, 1, 2, 3
const Scalar eps = 2.2204e-6;
static const std::array<std::vector<Scalar>, 4> coeff =
{ { {1, -1}, {1, -8, 8, -1}, {-1, 9, -45, 45, -9, 1}, {3, -32, 168, -672, 672, -168, 32, -3} } };
static const std::array<std::vector<Scalar>, 4> coeff2 =
{ { {1, -1}, {-2, -1, 1, 2}, {-3, -2, -1, 1, 2, 3}, {-4, -3, -2, -1, 1, 2, 3, 4} } };
static const std::array<Scalar, 4> dd = {2, 12, 60, 840};
grad.resize(x.rows());
TVector& xx = const_cast<TVector&>(x);
const int innerSteps = 2*(accuracy+1);
const Scalar ddVal = dd[accuracy]*eps;
for (TIndex d = 0; d < x.rows(); d++) {
grad[d] = 0;
for (int s = 0; s < innerSteps; ++s)
{
Scalar tmp = xx[d];
xx[d] += coeff2[accuracy][s]*eps;
grad[d] += coeff[accuracy][s]*value(xx);
xx[d] = tmp;
}
grad[d] /= ddVal;
}
}
void finiteHessian(const TVector &x, THessian &hessian, int accuracy = 0) {
const Scalar eps = std::numeric_limits<Scalar>::epsilon()*10e7;
hessian.resize(x.rows(), x.rows());
TVector& xx = const_cast<TVector&>(x);
if(accuracy == 0) {
for (TIndex i = 0; i < x.rows(); i++) {
for (TIndex j = 0; j < x.rows(); j++) {
Scalar tmpi = xx[i];
Scalar tmpj = xx[j];
Scalar f4 = value(xx);
xx[i] += eps;
xx[j] += eps;
Scalar f1 = value(xx);
xx[j] -= eps;
Scalar f2 = value(xx);
xx[j] += eps;
xx[i] -= eps;
Scalar f3 = value(xx);
hessian(i, j) = (f1 - f2 - f3 + f4) / (eps * eps);
xx[i] = tmpi;
xx[j] = tmpj;
}
}
} else {
/*
\displaystyle{{\frac{\partial^2{f}}{\partial{x}\partial{y}}}\approx
\frac{1}{600\,h^2} \left[\begin{matrix}
-63(f_{1,-2}+f_{2,-1}+f_{-2,1}+f_{-1,2})+\\
63(f_{-1,-2}+f_{-2,-1}+f_{1,2}+f_{2,1})+\\
44(f_{2,-2}+f_{-2,2}-f_{-2,-2}-f_{2,2})+\\
74(f_{-1,-1}+f_{1,1}-f_{1,-1}-f_{-1,1})
\end{matrix}\right] }
*/
for (TIndex i = 0; i < x.rows(); i++) {
for (TIndex j = 0; j < x.rows(); j++) {
Scalar tmpi = xx[i];
Scalar tmpj = xx[j];
Scalar term_1 = 0;
xx[i] = tmpi; xx[j] = tmpj; xx[i] += 1*eps; xx[j] += -2*eps; term_1 += value(xx);
xx[i] = tmpi; xx[j] = tmpj; xx[i] += 2*eps; xx[j] += -1*eps; term_1 += value(xx);
xx[i] = tmpi; xx[j] = tmpj; xx[i] += -2*eps; xx[j] += 1*eps; term_1 += value(xx);
xx[i] = tmpi; xx[j] = tmpj; xx[i] += -1*eps; xx[j] += 2*eps; term_1 += value(xx);
Scalar term_2 = 0;
xx[i] = tmpi; xx[j] = tmpj; xx[i] += -1*eps; xx[j] += -2*eps; term_2 += value(xx);
xx[i] = tmpi; xx[j] = tmpj; xx[i] += -2*eps; xx[j] += -1*eps; term_2 += value(xx);
xx[i] = tmpi; xx[j] = tmpj; xx[i] += 1*eps; xx[j] += 2*eps; term_2 += value(xx);
xx[i] = tmpi; xx[j] = tmpj; xx[i] += 2*eps; xx[j] += 1*eps; term_2 += value(xx);
Scalar term_3 = 0;
xx[i] = tmpi; xx[j] = tmpj; xx[i] += 2*eps; xx[j] += -2*eps; term_3 += value(xx);
xx[i] = tmpi; xx[j] = tmpj; xx[i] += -2*eps; xx[j] += 2*eps; term_3 += value(xx);
xx[i] = tmpi; xx[j] = tmpj; xx[i] += -2*eps; xx[j] += -2*eps; term_3 -= value(xx);
xx[i] = tmpi; xx[j] = tmpj; xx[i] += 2*eps; xx[j] += 2*eps; term_3 -= value(xx);
Scalar term_4 = 0;
xx[i] = tmpi; xx[j] = tmpj; xx[i] += -1*eps; xx[j] += -1*eps; term_4 += value(xx);
xx[i] = tmpi; xx[j] = tmpj; xx[i] += 1*eps; xx[j] += 1*eps; term_4 += value(xx);
xx[i] = tmpi; xx[j] = tmpj; xx[i] += 1*eps; xx[j] += -1*eps; term_4 -= value(xx);
xx[i] = tmpi; xx[j] = tmpj; xx[i] += -1*eps; xx[j] += 1*eps; term_4 -= value(xx);
xx[i] = tmpi;
xx[j] = tmpj;
hessian(i, j) = (-63 * term_1+63 * term_2+44 * term_3+74 * term_4)/(600.0 * eps * eps);
}
}
}
}
};
}
#endif /* PROBLEM_H */
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