ROL_ExpectationQuad.hpp

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#ifndef ROL_EXPECTATIONQUAD_HPP
#define ROL_EXPECTATIONQUAD_HPP

#include "ROL_Types.hpp"

namespace ROL {

template<class Real>
class ExpectationQuad {
public:
  virtual ~ExpectationQuad(void) {}
  ExpectationQuad(void) {}

  virtual Real regret(Real x, int deriv = 0) = 0;

  virtual Real error(Real x, int deriv = 0) {
    const Real one(1), zero(0);
    Real X = (deriv==0 ? x : (deriv==1 ? one : zero));
    return regret(x,deriv) - X;
  }

  virtual void check(void) {
    Real zero(0), half(0.5), two(2), one(1), oem3(1.e-3), fem4(5.e-4), p1(0.1);
    // Check v(0) = 0
    Real x = zero;
    Real vx = regret(x,0);
    std::cout << std::right << std::setw(20) << "CHECK REGRET: v(0) = 0? \n";
    std::cout << std::right << std::setw(20) << "v(0)" << "\n";
    std::cout << std::scientific << std::setprecision(11) << std::right 
              << std::setw(20) << std::abs(vx) 
              << "\n";
    std::cout << "\n";
    // Check v(x) > x
    Real scale = two;
    std::cout << std::right << std::setw(20) << "CHECK REGRET: x < v(x) for |x| > 0? \n";
    std::cout << std::right << std::setw(20) << "x"
              << std::right << std::setw(20) << "v(x)"
              << "\n";
    for (int i = 0; i < 10; i++) {
      x = scale*(Real)rand()/(Real)RAND_MAX - scale*half;
      vx = regret(x,0);
      std::cout << std::scientific << std::setprecision(11) << std::right
                << std::setw(20) << x 
                << std::setw(20) << vx 
                << "\n";
      scale *= two;
    }
    std::cout << "\n";
    // Check v(x) is convex
    Real y = zero;
    Real vy = zero;
    Real z = zero;
    Real vz = zero;
    Real l = zero; 
    scale = two;
    std::cout << std::right << std::setw(20) << "CHECK REGRET: v(x) is convex? \n";
    std::cout << std::right << std::setw(20) << "v(l*x+(1-l)*y)" 
                            << std::setw(20) << "l*v(x)+(1-l)*v(y)" 
                            << "\n";
    for (int i = 0; i < 10; i++) {
      x = scale*(Real)rand()/(Real)RAND_MAX - scale*half;
      vx = regret(x,0);
      y = scale*(Real)rand()/(Real)RAND_MAX - scale*half;
      vy = regret(y,0);
      l = (Real)rand()/(Real)RAND_MAX;
      z = l*x + (one-l)*y;
      vz = regret(z,0);
      std::cout << std::scientific << std::setprecision(11) << std::right
                << std::setw(20) << vz 
                << std::setw(20) << l*vx + (one-l)*vy 
                << "\n";
      scale *= two;
    }
    std::cout << "\n";
    // Check v'(x)
    x = oem3*(Real)rand()/(Real)RAND_MAX - fem4;
    vx = regret(x,0);
    Real dv = regret(x,1);
    Real t = one;
    Real diff = zero;
    Real err = zero;
    std::cout << std::right << std::setw(20) << "CHECK REGRET: v'(x) is correct? \n";
    std::cout << std::right << std::setw(20) << "t"
                            << std::setw(20) << "v'(x)"
                            << std::setw(20) << "(v(x+t)-v(x))/t"
                            << std::setw(20) << "Error"
                            << "\n";
    for (int i = 0; i < 13; i++) {
      y = x + t;
      vy = regret(y,0);
      diff = (vy-vx)/t;
      err = std::abs(diff-dv);
      std::cout << std::scientific << std::setprecision(11) << std::right 
                << std::setw(20) << t
                << std::setw(20) << dv 
                << std::setw(20) << diff 
                << std::setw(20) << err 
                << "\n";
      t *= p1;
    }
    std::cout << "\n";
    // Check v''(x)
    x = oem3*(Real)rand()/(Real)RAND_MAX - fem4;
    vx = regret(x,1);
    dv = regret(x,2);
    t = one;
    diff = zero;
    err = zero;
    std::cout << std::right << std::setw(20) << "CHECK REGRET: v''(x) is correct? \n";
    std::cout << std::right << std::setw(20) << "t"
                            << std::setw(20) << "v''(x)"
                            << std::setw(20) << "(v'(x+t)-v'(x))/t"
                            << std::setw(20) << "Error"
                            << "\n";
    for (int i = 0; i < 13; i++) {
      y = x + t;
      vy = regret(y,1);
      diff = (vy-vx)/t;
      err = std::abs(diff-dv);
      std::cout << std::scientific << std::setprecision(11) << std::right 
                << std::setw(20) << t
                << std::setw(20) << dv 
                << std::setw(20) << diff 
                << std::setw(20) << err 
                << "\n";
      t *= p1;
    }
    std::cout << "\n";
  }
};

}

#endif