/*  tools.cc - miscellaneous useful functions & classes

    Adrian Groves, FMRIB Image Analysis Group

    Copyright (C) 2007 University of Oxford  */

/*  Part of FSL - FMRIB's Software Library
    http://www.fmrib.ox.ac.uk/fsl
    fsl@fmrib.ox.ac.uk
    
    Developed at FMRIB (Oxford Centre for Functional Magnetic Resonance
    Imaging of the Brain), Department of Clinical Neurology, Oxford
    University, Oxford, UK
    
    
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#include "tools.h"
#include "easylog.h"
#include <limits>

double DescendingZeroFinder::FindZero() const
{
    Tracer_Plus tr("DescendingZeroFinder::FindZero");
    
    double lower = searchMin;
    double upper = searchMax;
    double atLower, atUpper;
    
    double atSearchGuess = fcn(searchGuess);

    if (verbosity >= 2)
      LOG_ERR("IG: f(" << (searchGuess) 
	      << ") == " << atSearchGuess << endl);

    if (atSearchGuess < 0) 
    {
        upper = searchGuess;
        atUpper = atSearchGuess;
        atLower = fcn(lower);
	if (verbosity >= 2)
	  LOG_ERR("LG: f(" << (lower) << ") == " << atLower << endl);
        if (atLower <= 0)
            return lower;  // hit the limit
    }
    else
    {
        lower = searchGuess;
        atLower = atSearchGuess;
        atUpper = fcn(upper);
	if (verbosity >= 2)
	  LOG_ERR("UG: f(" << (upper) << ") == " << atUpper << endl);
        if (atUpper >= 0)
            return upper; // hit the limit
    }
    
    int evals = maxEvaluations - 2;
    double maxJump = searchScale;
    double guess, prevGuess = searchGuess;
    //    double nonlinearity = 10; // force a bisection first time
    
    // Interpolation only
    while ( (evals > 0) && 
	    (upper-lower > tolX || 
	     atLower-atUpper > tolY || 
	     upper/lower > ratioTolX ||
	     atUpper/atLower > ratioTolY) )
    {
        guess = guesstimator->GetGuess(lower, upper, atLower, atUpper);
	
	if (lower == guess || guess == upper)
	  {
	    // This should only happen if we're near the limits of
	    // double precision (constant factor probably depends on
	    // the guesstimator)
	    assert(upper-lower <= 2*fabs(lower)*numeric_limits<double>::epsilon());
	    LOG_ERR("DescendingZeroFinder: giving up without reaching tolerances because we're at the limits of double precision!\n");
	    LOG_ERR("Lower: f(" << lower << ") == " << atLower << endl <<
		    "Upper: f(" << upper << ") == " << atUpper << endl);
	    break;
	  }

	assert( lower < guess && guess < upper );
	//cout << lower << "<" << guess << "<" << upper << endl;
	if (!fcn.PickFasterGuess(&guess, lower, upper)) 
	  evals--; // only count the non-cached evaluations.
	//cout << lower << "<" << guess << "<" << upper << endl;
	assert(lower < guess && guess < upper);

        if ( guess-prevGuess > maxJump)
            guess = prevGuess + maxJump;
        else if ( guess-prevGuess < -maxJump )
            guess = prevGuess - maxJump;
            
        maxJump *= searchScaleGrowth;
        prevGuess = guess;
         
        // never mind -- already out of bounds
        // from checking the limits above.

	//        cout << "upper" << "\t" << "guess" << "\t" << "lower" << endl;
	//        cout << upper << "\t" << guess << "\t" << lower << endl;
        assert(guess > lower); assert(guess < upper);
        double atGuess = fcn(guess);
	//        cout << atUpper << "\t" << atGuess << "\t" << atLower << endl << endl;

	if (verbosity >= 2)
	  LOG_ERR("NG: f(" << (guess) << ") == " << atGuess << endl);


	//        double atGuessIfLinear = 
	  //            ( atLower+(atUpper-atLower)*(guess-lower)/(upper-lower) - atGuess );
	//        if (atGuess > atGuessIfLinear)
	  //            nonlinearity = (atGuess-atGuessIfLinear)/(atGuess-atUpper);
	//        else
	  //            nonlinearity = (atGuessIfLinear-atGuess)/(atLower-atGuess);
            
   
	//        cout << "Nonlinearity = " << nonlinearity << endl;
	//        cout << "atGuess = " << atGuess
	//             << "\natGuessIfLinear = " << atGuessIfLinear
	//             << "\natLower = " << atLower
	//             << "\natUpper = " << atUpper << endl;
       
        if (atGuess < 0) 
        {
            upper = guess;
            atUpper = atGuess;
        }
        else
        {
            lower = guess;
            atLower = atGuess;
        }
    } 

    /*    
    // One final interpolation -- not necessary, we could pick anything
    // between lower and upper really.
    guess = guesstimator->GetGuess(lower, upper, atLower, atUpper);
    assert( lower <= guess && guess <= upper );
    fcn.PickFasterGuess(&guess, lower, upper, true);
    assert( lower <= guess && guess <= upper );
    */

    // Pick either lower or upper bound, depending on which is closer to zero
    assert(atLower >= 0 && -atUpper >= 0);
    if (atLower < -atUpper)
      guess = lower;
    else
      guess = upper;

    if (verbosity >= 1)
      LOG_ERR("Final upper/lower ratio: " << (upper/lower) << endl);

    return guess;
}

double RiddlersGuesstimator::GetGuess(double lower, double upper, double atLower, double atUpper)
{
  Tracer_Plus tr("RiddlersGuesstimator::GetGuess");
  // equations below: from NRIC, section 9.2.  Simpler than Brent, slightly less reliable.

  if (halfDone)
    {
      // Phase two: fancy estimation.
      halfDone = false;
      double x3, fx3;

      if (x1 == lower)
	{
	  x3 = upper;
	  fx3 = atUpper;
	}
      else
	{
	  assert(x2 == upper);
	  x3 = lower;
	  fx3 = atLower;
	}
      
      assert(x1 < x3 && x3 < x2);
      assert(fx2 < fx1);

      Warning::IssueOnce("Riddler's Method; No special cases!");

      if (false) //x3 != (x1 + x2)/2)
	{
	  LOG_ERR("x3 == " << x3 << ", x1 == " << x1 << ", x2 = " << x2 << endl);
	  LOG_ERR("x3 - (x1+x2)/2 == " << x3 - (x1+x2)/2 << endl);
	  Warning::IssueAlways("Riddler's Method: x3 != (x1+x2)/2");
	}
      else if (true) //(fx2 < fx3 && fx3 < fx1)
	{
	  double s = (fx1-fx2 > 0) ? +1.0 : -1.0; // s = sign(fx1-fx2)
	  double x4 = x3 + (x3-x1)*s*fx3/sqrt(fx3*fx3-fx1*fx2);
      
	  Warning::IssueAlways("Riddler's Method: phase two");

	  assert(lower < x4 && x4 < upper);

	  return x4;
	}
      else
	{
	  Warning::IssueAlways("Riddler's Method cheat: dropping back to the bisection method!");
	}
    }
  
  halfDone = true;
  // Phase one: just pick the midpoint, but save the values for phase two
  x1 = lower;
  fx1 = atLower;
  x2 = upper;
  fx2 = atUpper;
  
  Warning::IssueAlways("Riddler's Method: phase one");
  
  double x3 = (x1 + x2)/2;
  return x3;

}