nicefunction.hh

#ifndef NICE_FUNCTION_HH
#define NICE_FUNCTION_HH

#include <algorithm>
#include <cmath>
#include <limits>

#include <dune/common/exceptions.hh>
#include <dune/common/function.hh>

namespace Dune {
class NiceFunction {
public:
  virtual ~NiceFunction() {}

  double virtual leftDifferential(double s) const = 0;
  double virtual rightDifferential(double s) const = 0;

  double virtual second_deriv(double x) const {
    DUNE_THROW(NotImplemented, "second derivative not implemented");
  }

  double virtual regularity(double s) const {
    DUNE_THROW(NotImplemented, "regularity not implemented");
  }

  // Whether H(|.|) is smooth at zero
  bool virtual smoothesNorm() const { return false; }

  void virtual evaluate(double const &x, double &y) const = 0;
};

class RuinaFunction : public NiceFunction {
public:
  RuinaFunction(double coefficient, double a, double mu, double eta,
                double normalStress, double b, double state, double L, double h)
      : coefficient(coefficient),
        a(a),
        mu(mu),
        eta(eta),
        normalStress(normalStress),
        compound_state(b * (state - std::log(eta * L))),
        h(h),
        rho(exp(-(mu + compound_state) / a)) {}

  // TODO: untested
  void virtual evaluate(double const &x, double &y) const {
    assert(false);
    double const arg = eta * x / h;
    double const expstar = (arg == 0) ? 0 : arg * std::log(arg) - arg;
    double const gamma =
        normalStress * (mu + a * std::log(eta) + compound_state);
    y = a * normalStress * expstar + gamma * arg;
    y *= coefficient * h * normalStress / eta;
  }

  double virtual leftDifferential(double s) const {
    double const arg = eta * s / h;
    if (arg == 0)
      return 0;

    double const gamma =
        normalStress * (mu + a * std::log(eta) + compound_state);
    return coefficient * (a * normalStress * std::log(arg) + gamma);
  }

  /* see above */
  double virtual rightDifferential(double s) const {
    return leftDifferential(s);
  }

  double virtual second_deriv(double s) const {
    return coefficient * a * normalStress / s;
  }

  double virtual regularity(double s) const {
    if (s == 0)
      return std::numeric_limits<double>::infinity();

    return std::abs(second_deriv(s));
  }

private:
  double const coefficient;
  double const a;
  double const mu;
  double const eta;
  double const normalStress;
  double const compound_state;
  double const h;

  double const rho;
};

class LinearFunction : public NiceFunction {
public:
  LinearFunction(double a) : coefficient(a) {}

  void virtual evaluate(double const &x, double &y) const {
    y = coefficient * x;
  }

  double virtual leftDifferential(double s) const { return coefficient; }

  double virtual rightDifferential(double s) const { return coefficient; }

  double virtual second_deriv(double) const { return 0; }

  double virtual regularity(double s) const { return 0; }

private:
  double const coefficient;
};

template <int slope> class SampleFunction : public NiceFunction {
public:
  void virtual evaluate(double const &x, double &y) const {
    y = (x < 1) ? x : (slope * (x - 1) + 1);
  }

  double virtual leftDifferential(double s) const {
    return (s <= 1) ? 1 : slope;
  }

  double virtual rightDifferential(double s) const {
    return (s < 1) ? 1 : slope;
  }
};

class SteepFunction : public NiceFunction {
public:
  void virtual evaluate(double const &x, double &y) const { y = 100 * x; }

  double virtual leftDifferential(double s) const { return 100; }

  double virtual rightDifferential(double s) const { return 100; }
};

class TrivialFunction : public NiceFunction {
public:
  void virtual evaluate(double const &x, double &y) const { y = 0; }

  double virtual leftDifferential(double) const { return 0; }

  double virtual rightDifferential(double) const { return 0; }

  double virtual second_deriv(double) const { return 0; }

  double virtual regularity(double) const { return 0; }

  bool virtual smoothesNorm() const { return true; }
};

// slope in [n-1,n] is n
class HorribleFunction : public NiceFunction {
public:
  void virtual evaluate(double const &x, double &y) const {
    double const fl = floor(x);
    double const sum = fl * (fl + 1) / 2;
    y = sum + (fl + 1) * (x - fl);
  }

  double virtual leftDifferential(double x) const {
    double const fl = floor(x);
    if (x - fl < 1e-14)
      return fl;
    else
      return fl + 1;
  }

  double virtual rightDifferential(double x) const {
    double const c = ceil(x);
    if (c - x < 1e-14)
      return c + 1;
    else
      return c;
  }
};

// slope in [n-1,n] is log(n+1)
class HorribleFunctionLogarithmic : public NiceFunction {
public:
  void virtual evaluate(double const &x, double &y) const {
    y = 0;
    size_t const fl = floor(x);
    for (size_t i = 1; i <= fl;)
      y += std::log(
          ++i); // factorials grow to fast so we compute this incrementally

    y += std::log(fl + 2) * (x - fl);
  }

  double virtual leftDifferential(double x) const {
    double const fl = floor(x);
    if (x - fl < 1e-14)
      return std::log(fl + 1);
    else
      return std::log(fl + 2);
  }

  double virtual rightDifferential(double x) const {
    double const c = ceil(x);
    if (c - x < 1e-14)
      return std::log(c + 2);
    else
      return std::log(c + 1);
  }
};
}
#endif