solution.cpp

矩阵计算库

//$$ solution.cpp                    // solve routines

// Copyright (C) 1994: R B Davies


#define WANT_STREAM                  // include.h will get stream fns
#define WANT_MATH                    // include.h will get math fns

#include "include.h"
#include "boolean.h"
#include "myexcept.h"

#include "solution.h"

int SolutionException::action = 1;

int iabs(int i) { return (i>=0) ? i : -i; }

SolutionException::SolutionException(char* c) : Exception(iabs(action))
{
   if (action) cout << "Error detected by solution package\n"
      << c << "\n";
   if (action < 0) exit(1);
};

inline Real square(Real x) { return x*x; }

void OneDimSolve::LookAt(int V)
{
   lim--;
   if (!lim) Throw(SolutionException("Does not converge"));
   Last = V;
   Real yy = function(x[V]) - YY;
   Finish = (fabs(yy) < acc);
   y[V] = vpol*yy;
}

void OneDimSolve::HFlip() { hpol=-hpol; State(U,C,L); }

void OneDimSolve::VFlip()
   { vpol = -vpol; y[0] = -y[0]; y[1] = -y[1]; y[2] = -y[2]; }

void OneDimSolve::Flip()
{
   hpol=-hpol; vpol=-vpol; State(U,C,L);
   y[0] = -y[0]; y[1] = -y[1]; y[2] = -y[2];
}

void OneDimSolve::Linear(int I, int J, int K)
{
   x[J] = (x[I]*y[K] - x[K]*y[I])/(y[K] - y[I]);
   // cout << "Linear\n";
}

void OneDimSolve::Quadratic(int I, int J, int K)
{
   // result to overwrite I
   Real YJK, YIK, YIJ, XKI, XKJ;
   YJK = y[J] - y[K]; YIK = y[I] - y[K]; YIJ = y[I] - y[J];
   XKI = (x[K] - x[I]);
   XKJ = (x[K]*y[J] - x[J]*y[K])/YJK;
   if ( square(YJK/YIK)>(x[K] - x[J])/XKI ||
      square(YIJ/YIK)>(x[J] - x[I])/XKI )
   {
      x[I] = XKJ;
      // cout << "Quadratic - exceptional\n";
   }
   else
   {
      XKI = (x[K]*y[I] - x[I]*y[K])/YIK;
      x[I] = (XKJ*y[I] - XKI*y[J])/YIJ;
      // cout << "Quadratic - normal\n";
   }
}

Real OneDimSolve::Solve(Real Y, Real X, Real Dev, int Lim)
{
   Tracer et("OneDimSolve::Solve");
   lim=Lim;
   if (Dev==0.0)Throw(SolutionException("Dev is zero"));
   L=0; C=1; U=2; vpol=1; hpol=1; y[C]=0.0; y[U]=0.0;
   if (Dev<0.0) { hpol=-1; Dev = -Dev; }
   YY=Y;                                // target value
   x[L] = X;                            // initial trial value
   LookAt(L); if (Finish) goto finish;
   if (y[L]>0.0) VFlip();               // so Y[L] < 0
   x[U] = X + Dev * hpol;
   LookAt(U); if (Finish) goto finish;
   if (y[U] > 0.0) goto captured1;
   if (y[U] == y[L])
      Throw(SolutionException("Function is flat"));
   if (y[U] < y[L]) HFlip();             // Change direction
   State(L,U,C);
   for (i=0; i<20; i++)
   {
      // cout << "Searching for crossing point\n";
      // Have L C then crossing point, Y[L]<Y[C]<0
      x[U] = x[C] + Dev*hpol;
      LookAt(U); if (Finish) goto finish;
      if (y[U] > 0) goto captured2;
      if (y[U] < y[C])
         Throw(SolutionException("Function is not monotone"));
      Dev *= 2.0;
      State(C,U,L);
   }
   Throw(SolutionException("Can't locate a crossing point"));

captured1:
   // cout << "Captured - 1\n";
   // We have 2 points L and U with crossing between them
   Linear(L,C,U);                   // linear interpolation - result to C
   LookAt(C); if (Finish) goto finish;
   if (y[C] > 0.0) Flip();            // Want y[C] < 0
   if (y[C] < 0.5*y[L]) { State(C,L,U); goto binary; }

captured2:
   // cout << "Captured - 2\n";
   // We have L,C before crossing, U after crossing
   Quadratic(L,C,U);                // quad interpolation - result to L
   LookAt(L); if (Finish) goto finish;
   if ((x[L] - x[C])*hpol <= 0.0 || (x[L] - x[U])*hpol >= 0.0)
      { State(C,L,U); goto captured1; }
   State(C,L,U);
   // cout << "Through first stage\n";
   if (y[C] > 0.0) Flip();
   if (y[C] > 0.5*y[L]) goto captured2;
   else { State(C,L,U); goto captured1; }

binary:
   // We have L, U around crossing - do binary search
   // cout << "Binary\n";
   for (i=3; i; i--)
   {
      x[C] = 0.5*(x[L]+x[U]);
      LookAt(C); if (Finish) goto finish;
      if (y[C]>0.0) State(L,U,C); else State(C,L,U);
   }
   goto captured1;

finish:
   return x[Last];
}