cgalg.hh

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// cgalg.H
// created by ADP
// last modified 06/17/04

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#ifndef __RVL_CGALG
#define __RVL_CGALG

#include "alg.hh"
#include "terminator.hh"
#include "linop.hh"

namespace RVLUmin {

  using namespace RVL;
  using namespace RVLAlg;

  template<typename Scalar>
  bool realgt(Scalar left, Scalar right) {
    if (left > right) return true;
    return false;
  }

  template<typename Scalar>
  bool realgt(complex<Scalar> left, complex<Scalar> right) {
    if (real(left) > real(right)) return true;
    return false;
  }

  class CGException: public RVLException {
  public:
    CGException(): RVLException() {
      (*this)<<"Error: RVLUmin::CGAlg::run\n";
    }
    CGException(CGException const & s): RVLException(s) {}
    ~CGException() throw() {}
  };

  template<typename Scalar>
  class CGStep: public Algorithm {

    typedef typename ScalarFieldTraits<Scalar>::AbsType atype;
  
  public:

    void run() {

      Scalar alpha, beta; 

      A.applyOp(p,w);
      curv = p.inner(w);

      if (!realgt(curv,ScalarFieldTraits<Scalar>::Zero()) ) {
    CGException e;
    e<<"RVLUmin::CGStep::run: termination\n";
    e<<"  negative curvature (p^TAp) in search direction p = "<<curv<<"\n";
    throw e;
      }

      if (ProtectedDivision<Scalar>(rnormsq,curv,alpha)) {
    CGException e;
    e<<"RVLUmin::CGStep::run: termination\n";
    e<<"  curvature much smaller than mean square residual, yields zerodivide\n";
    e<<"  curvature = "<<curv<<"\n";
    e<<"  mean square residual  = "<<rnormsq<<"\n";
    throw e;
      }

      x.linComb(alpha, p);    
      r.linComb(-alpha, w);
      beta = rnormsq;
      rnormsq = r.normsq();
      
      if (ProtectedDivision<Scalar>(rnormsq,beta,beta)) {
    CGException e;
    e<<"RVLUmin::CGStep::run: termination\n";
    e<<"  previous square residual much smaller than current, yields zerodivide\n";
    e<<"  previous square residual = "<<beta<<"\n";
    e<<"  current square residual  = "<<rnormsq<<"\n";
    throw e;
      }

      p.linComb(ScalarFieldTraits<Scalar>::One(), r, beta);
    }
     
    CGStep( Vector<Scalar> & x0, LinearOp<Scalar> const & inA, 
        Vector<Scalar> const & rhs, atype & _rnormsq)
      : x(x0), A(inA), b(rhs), r(A.getRange()), 
    curv(numeric_limits<Scalar>::max()),
    rnormsq(_rnormsq), 
    p(A.getRange()), 
    w(A.getRange()) {
      CGStep<Scalar>::restart();
    }

 protected:
    
    void restart() {
      A.applyOp(x, w);
      r.copy(b);
      r.linComb(-1.0, w);
      rnormsq = r.normsq();
      p.copy(r);
    }

    Vector<Scalar> & x;         // the current iterate
    const LinearOp<Scalar> & A; // the linear op we want to invert
    Vector<Scalar> const & b;   // the right hand side
    Vector<Scalar> r;           // r = b - A * x
    Scalar curv;                // p' * A * p
    atype & rnormsq;            // a reference to residual norm squared = r' * r
    Vector<Scalar> p;           // the orthogonal part of the residual
    Vector<Scalar> w;           // A * p
  };

  template<typename Scalar>
  class CGAlg: public Algorithm {

    typedef typename ScalarFieldTraits<Scalar>::AbsType atype;

  public:

    CGAlg(RVL::Vector<Scalar> & _x, 
        LinearOp<Scalar> const & _inA, 
        Vector<Scalar> const & _rhs, 
        atype & _rnormsq,
        atype _tol = 100.0*numeric_limits<atype>::epsilon(),
        int _maxcount = 10,
        atype _maxstep = numeric_limits<atype>::max(),
        ostream & _str = cout)
      : x(_x),
    resname("MS residual"), 
    inA(_inA), 
    rhs(_rhs), 
    tol(_tol), 
    maxcount(_maxcount), 
    maxstep(_maxstep), 
    str(_str), 
    rnormsq(_rnormsq),
    step(x,inA,rhs,rnormsq),
    it(0) {}

    int getCount() { return it; }
    void run() { 
      try {
    // terminator for CG iteration
    CountingThresholdIterationTable<Scalar> stop1(maxcount,rnormsq,tol,resname,str);
    // terminator for Trust Region test and projection
    BallProjTerminator<Scalar> stop2(x,maxstep,str);
    // terminate if either
    OrTerminator stop(stop1,stop2);
    // loop
    LoopAlg doit(step,stop);
    doit.run();
    
    // must recompute residual if scaling occured 
    if (stop2.query()) {
      str<<"CGAlg::run: scale step to trust region boundary\n";
      Vector<Scalar> temp(inA.getDomain());
      inA.applyOp(x,temp);
      temp.linComb(-1.0,rhs);
      rnormsq=temp.normsq();
    }

    it=stop1.getCount();
      }
      catch (CGException & e) {
    throw e;
      }
      catch (RVLException & e) {
    e<<"Error: CGAlg::run\n";
    throw e;
      }
    }

  private:

    LinearOp<Scalar> const & inA;  // operator - should be SPD
    Vector<Scalar> & x;            // state - solution vector
    Vector<Scalar> const & rhs;    // reference to rhs
    atype tol;                     // tolerance for norm squared of residual
    atype maxstep;                 // upper bound for net step x-x0
    int maxcount;                  // upper bound for iteration count
    string resname;                // string to print in output table
    ostream & str;                 // stream for report output
    int it;                        // private iteration count
    atype & rnormsq;               // residual norm squared
    CGStep<Scalar> step;           // alg expressing single CG step

  };

}

#endif

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