lsqr.hh

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// lsqr.hh
// created by WWS 26.01.14

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#ifndef __RVLALG_UMIN_LSQR__
#define __RVLALG_UMIN_LSQR__

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

using namespace RVLAlg;

namespace RVLUmin {

  using namespace RVL;
  using namespace RVLAlg;    

  template<typename Scalar>
  class LSQRStep : public Algorithm {

    typedef typename ScalarFieldTraits<Scalar>::AbsType atype;

  public:

    LSQRStep(LinearOp<Scalar> const & _A,
         Vector<Scalar> & _x,
         Vector<Scalar> const & _b,
         atype & _rnorm, 
         atype & _nrnorm)
      : A(_A), x(_x), b(_b), rnorm(_rnorm), nrnorm(_nrnorm), v(A.getDomain()), alphav(A.getDomain()),
    u(A.getRange()), betau(A.getRange()), w(A.getDomain()) { 
      // NOTE: initial x assumed to be zero vector
      // method body implements step one in P&S p. 8
      beta=b.norm();
      rnorm=beta;
      atype tmp;
      if (ProtectedDivision<atype>(ScalarFieldTraits<atype>::One(),beta,tmp)) {
    RVLException e;
    e<<"Error: LSQRStep constructor\n";
    e<<"  RHS has vanishing norm\n";
    throw e;
      }
      u.scale(tmp,b);
      A.applyAdjOp(u,v);
      alpha = v.norm();
      nrnorm = alpha*rnorm;
      if (ProtectedDivision<atype>(ScalarFieldTraits<atype>::One(),alpha,tmp)) {
    RVLException e;
    e<<"Error: LSQRStep constructor\n";
    e<<"  Normal residual has vanishing norm\n";
    throw e;
      }
      v.scale(tmp);
      w.copy(v);
      phibar = beta;
      rhobar = alpha;
    }
      
    void run() {
      try {
    // 3a store Av_i over betau
    A.applyOp(v,betau);
    // increment with -alpha_i u_i
    Scalar stmp = -alpha;
    betau.linComb(stmp,u);
    // beta_{i+1} = norm
    beta=betau.norm();
    atype tmp;
    if (ProtectedDivision<atype>(ScalarFieldTraits<atype>::One(),beta,tmp)) {
      RVLException e;
      e<<"Error: LSQRStep::run\n";
      e<<"  beta vanishes\n";
      throw e;
    }
    // u_{i+1} = unit vector
    stmp = tmp;
    u.scale(stmp,betau);    

    // 3b. store A^Tu_{i+1} over alphav
    A.applyAdjOp(u,alphav);
    // increment with -beta_{i+1} v_i
    stmp = -beta;
    alphav.linComb(stmp,v);
    // alpha_{i+1}=norm
    alpha = alphav.norm();
    if (ProtectedDivision<atype>(ScalarFieldTraits<atype>::One(),alpha,tmp)) {
      RVLException e;
      e<<"Error: LSQRStep::run\n";
      e<<"  beta vanishes\n";
      throw e;
    }
    // v_{i+1} = unit vector 
    stmp=tmp;
    v.scale(tmp,alphav);        
    
    // 4 (a)
        atype rho = sqrt(rhobar*rhobar + beta*beta);
    // 4 (b)
    atype c = rhobar/rho;
    // 4 (c)
    atype s = beta/rho;
    // 4 (d) 
    atype theta = s*alpha;
    // 4 (e) 
    rhobar = - c*alpha;
    // 4 (f) 
    atype phi = c*phibar;
    // 4 (g)
    phibar = s*phibar;

    // 5 (a)
    x.linComb(phi/rho,w);
    // 5 (b)
    w.scale(-theta/rho);
    w.linComb(ScalarFieldTraits<Scalar>::One(),v);

    // assign residual, normal residual
    rnorm = phibar;
    nrnorm = phibar*alpha*abs(c);

      }
      catch (RVLException & e) {
    e<<"\ncalled from CGNEStep::run()\n";
    throw e;
      }
     
    }

    ~LSQRStep() {}

  private:

    // references to external objects
    LinearOp<Scalar> const & A;
    Vector<Scalar> & x;
    Vector<Scalar> const & b;
    atype & rnorm;
    atype & nrnorm;

    // need six work vectors and four scalars as persistent object data
    Vector<Scalar> u;
    Vector<Scalar> v;
    Vector<Scalar> betau;
    Vector<Scalar> alphav;
    Vector<Scalar> w;
    atype alpha;
    atype beta;
    atype rhobar;
    atype phibar;
  };
  
  template<typename Scalar>
  class LSQRAlg: public Algorithm, public Terminator {

    typedef typename ScalarFieldTraits<Scalar>::AbsType atype;

  public:

    LSQRAlg(RVL::Vector<Scalar> & _x, 
        LinearOp<Scalar> const & _inA, 
        Vector<Scalar> const & _rhs, 
        atype & _rnorm,
        atype & _nrnorm,
        atype _rtol = 100.0*numeric_limits<atype>::epsilon(),
        atype _nrtol = 100.0*numeric_limits<atype>::epsilon(),
        int _maxcount = 10,
        atype _maxstep = numeric_limits<atype>::max(),
        ostream & _str = cout)
    : inA(_inA), 
      x(_x), 
      rhs(_rhs), 
      rnorm(_rnorm), 
      nrnorm(_nrnorm), 
      rtol(_rtol), 
      nrtol(_nrtol), 
      maxstep(_maxstep), 
      maxcount(_maxcount), 
      count(0), 
      proj(false), 
      str(_str), 
      step(inA,x,rhs,rnorm,nrnorm) 
    { x.zero(); }

    ~LSQRAlg() {}

    bool query() { return proj; }

    void run() { 
      // terminator for LSQR iteration
      vector<string> names(2);
      vector<atype *> nums(2);
      vector<atype> tols(2);
      names[0]="Residual Norm"; nums[0]=&rnorm; tols[0]=rtol;
      names[1]="Gradient Norm"; nums[1]=&nrnorm; tols[1]=nrtol;
      str<<"========================== BEGIN LSQR =========================\n";
      VectorCountingThresholdIterationTable<atype> stop1(maxcount,names,nums,tols,str);
      stop1.init();
      // terminator for Trust Region test and projection
      //      BallProjTerminator<Scalar> stop2(x,maxstep,str);
      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 
      proj = stop2.query();
      if (proj) {
    Vector<Scalar> temp(inA.getRange());
    inA.applyOp(x,temp);
    temp.linComb(-1.0,rhs);
    rnorm=temp.norm();
    Vector<Scalar> temp1(inA.getDomain());
    inA.applyAdjOp(temp,temp1);
    nrnorm=temp1.norm();
      }
      count = stop1.getCount();
      str<<"=========================== END LSQR ==========================\n";
    }

    int getCount() const { return count; }

  private:

    LinearOp<Scalar> const & inA;  // operator
    Vector<Scalar> & x;            // state - solution vector
    Vector<Scalar> const & rhs;    // reference to rhs
    atype & rnorm;                 // residual norm
    atype & nrnorm;                // gradient norm
    atype rtol;                    // tolerance residual norm
    atype nrtol;                   // tolerance gradient norm 
    atype maxstep;                 // upper bound for net step x-x0
    int maxcount;                  // upper bound for iteration count
    int count;                     // actual iteration count
    mutable bool proj;             // whether step is projected onto TR boundary
    ostream & str;                 // stream for report output
    LSQRStep<Scalar> step;         // single step of LSQR

    // disable default, copy constructors
    LSQRAlg();
    LSQRAlg(LSQRAlg<Scalar> const &);

  };

  template<typename Scalar>
  class LSQRPolicyData {

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

    atype rtol;
    atype nrtol;
    atype Delta;
    int maxcount;
    bool verbose;

    LSQRPolicyData(atype _rtol = numeric_limits<atype>::max(),
           atype _nrtol = numeric_limits<atype>::max(),
           atype _Delta = numeric_limits<atype>::max(),
           int _maxcount = 0,
           bool _verbose = false)
      : rtol(_rtol), nrtol(_nrtol), Delta(_Delta), maxcount(_maxcount), verbose(_verbose) {}
      
    LSQRPolicyData(LSQRPolicyData<Scalar> const & a) 
      : rtol(a.rtol), nrtol(a.nrtol), Delta(a.Delta), maxcount(a.maxcount), verbose(a.verbose) {}

    ostream & write(ostream & str) const {
      str<<"\n";
      str<<"==============================================\n";
      str<<"LSQRPolicyData: \n";
      str<<"rtol      = "<<rtol<<"\n";
      str<<"nrtol     = "<<nrtol<<"\n";
      str<<"Delta     = "<<Delta<<"\n";
      str<<"maxcount  = "<<maxcount<<"\n";
      str<<"verbose   = "<<verbose<<"\n";
      str<<"==============================================\n";
      return str;
    }
  };

  template<typename Scalar> 
  class LSQRPolicy {

    typedef typename ScalarFieldTraits<Scalar>::AbsType atype;

  public:
    LSQRAlg<Scalar> * build(Vector<Scalar> & x, 
                LinearOp<Scalar> const & A,
                Vector<Scalar> const & d,
                atype & rnorm,
                atype & nrnorm,
                ostream & str) const {
      if (verbose) 
    return new LSQRAlg<Scalar>(x,A,d,rnorm,nrnorm,rtol,nrtol,maxcount,Delta,str);
      else
    return new LSQRAlg<Scalar>(x,A,d,rnorm,nrnorm,rtol,nrtol,maxcount,Delta,nullstr);
    }

    void assign(atype _rtol, atype _nrtol, atype _Delta, int _maxcount, bool _verbose) {
      rtol=_rtol; nrtol=_nrtol; Delta=_Delta; maxcount=_maxcount; verbose=_verbose;
    }

    void assign(Table const & t) {
      rtol=getValueFromTable<atype>(t,"LSQR_ResTol");
      nrtol=getValueFromTable<atype>(t,"LSQR_GradTol"); 
      Delta=getValueFromTable<atype>(t,"TR_Delta");
      maxcount=getValueFromTable<int>(t,"LSQR_MaxItn"); 
      verbose=getValueFromTable<bool>(t,"LSQR_Verbose");
    }

    void assign(LSQRPolicyData<Scalar> const & s) {
      rtol=s.rtol;
      nrtol=s.nrtol;
      Delta=s.Delta;
      maxcount=s.maxcount;
      verbose=s.verbose;
    }

    mutable atype Delta;

    LSQRPolicy(atype _rtol = numeric_limits<atype>::max(),
           atype _nrtol = numeric_limits<atype>::max(),
           atype _Delta = numeric_limits<atype>::max(),
           int _maxcount = 0,
           bool _verbose = true)
      : Delta(_Delta), rtol(_rtol), nrtol(_nrtol), maxcount(_maxcount), verbose(_verbose), nullstr(0) {}

    LSQRPolicy(LSQRPolicy<Scalar> const & p)
      :     Delta(p.Delta), 
        rtol(p.rtol), 
        nrtol(p.nrtol), 
        maxcount(p.maxcount), 
        verbose(p.verbose), 
        nullstr(0) {}
      
  private:
    mutable atype rtol;
    mutable atype nrtol;
    mutable int maxcount;
    mutable bool verbose;
    mutable std::ostream nullstr;
  };
}

#endif

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