fvar_ma4.cpp

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#include "fvar.hpp"
#include <math.h>
#ifndef OPT_LIB
  #include <cassert>
  #include <climits>
#endif

#ifdef ISZERO
  #undef ISZERO
#endif
#define ISZERO(d) ((d)==0.0)

static double eps0=1.e-50;

void lubksb(dvar_matrix a, const ivector&  indx,dvar_vector b);
void ludcmp(const dvar_matrix& a, const ivector& indx, const prevariable& d);

void ludcmp(const dvar_matrix& _a, const ivector& _indx, const prevariable& _d)
{
  ADUNCONST(dvar_matrix,a)
  ADUNCONST(prevariable,d)
  ivector& indx= (ivector&) _indx;
  int i,j,k;

#if !defined(OPT_LIB) && (__cplusplus >= 201103L)
  int n = [](unsigned int colsize) -> int
  {
    assert(colsize <= INT_MAX);
    return static_cast<int>(colsize);
  } (a.colsize());
#else
  int n = static_cast<int>(a.colsize());
#endif

  int lb=a.colmin();
  int ub=a.colmax();

  dvariable big,dum,sum,temp;

  dvar_vector vv(lb,ub);


  d=1.0;

  for (i=lb;i<=ub;i++)
  {
    big=0.0;
    for (j=lb;j<=ub;j++)
    {
      temp=fabs(a(i,j));
      if (temp > big)
      {
        big=temp;
      }
    }
    if (big == 0.0)
    {
      cerr << "Error in matrix inverse -- matrix singular in inv(dmatrix)\n";
    }
    vv(i)=1.0/big;
  }

  for (j=lb;j<=ub;j++)
  {
    for (i=lb;i<j;i++)
    {
      sum=a(i,j);
      for (k=lb;k<i;k++)
      {
        sum = sum - a(i,k)*a(k,j);
      }
      a(i,j)=sum;
    }
    int imax = j;
    big=0.0;
    for (i=j;i<=ub;i++)
    {
      sum=a(i,j);
      for (k=lb;k<j;k++)
      {
        sum = sum - a(i,k)*a(k,j);
      }
      a(i,j)=sum;
      dum=vv(i)*fabs(sum);
      if ( dum >= big)
      {
        big=dum;
        imax=i;
      }
    }
    if (j != imax)
    {
      for (k=lb;k<=ub;k++)
      {
        dum=a(imax,k);
        a(imax,k)=a(j,k);
        a(j,k)=dum;
      }
      d = -1.*d;
      vv(imax)=vv(j);
    }
    indx(j)=imax;

    if (a(j,j) == 0.0)
    {
      a(j,j)=eps0;
    }

    if (j != n)
    {
      dum=1.0/(a(j,j));
      for (i=j+1;i<=ub;i++)
      {
        a(i,j) = a(i,j) * dum;
      }
    }
  }
}

void lubksb(dvar_matrix a, const ivector& indx,dvar_vector b)
{
  int i,ii=0,ip,j,iiflag=0;
  dvariable sum;
  int lb=a.colmin();
  int ub=a.colmax();
  for (i=lb;i<=ub;i++)
  {
    ip=indx(i);
    sum=b(ip);
    b(ip)=b(i);
    if (iiflag)
    {
      for (j=ii;j<=i-1;j++)
      {
        sum -= a.elem(i,j)*b.elem(j);
      }
    }
    else if (!ISZERO(value(sum)))
    {
      ii=i;
      iiflag=1;
    }
    b(i)=sum;
  }

  for (i=ub;i>=lb;i--)
  {
    sum=b(i);
    for (j=i+1;j<=ub;j++)
    {                        // !!! remove to show bug
      sum -= a.elem(i,j)*b.elem(j);
    }                        // !!! remove to show bug
    b.elem(i)=sum/a.elem(i,i);
  }
}