eigenval.h File Reference

Go to the source code of this file.

Functions
matrix	evSwap (matrix M, int i, int j)
matrix	evRowElim (matrix M, int i, int j, int k)
matrix	evColElim (matrix M, int i, int j, int k)
matrix	evHessenberg (matrix M)

Function Documentation

evColElim()

matrix evColElim	(	matrix	M,
		int	i,
		int	j,
		int	k
	)

Definition at line 76 of file eigenval.cc.

{
  if(MATELEM(M,k,i)==0||MATELEM(M,k,j)==0)
    return(M);
 
  poly p=pNSet(nDiv(pGetCoeff(MATELEM(M,k,i)),pGetCoeff(MATELEM(M,k,j))));
  pNormalize(p);
 
  for(int l=1;l<=MATROWS(M);l++)
  {
    MATELEM(M,l,i)=pSub(MATELEM(M,l,i),ppMult_qq(p,MATELEM(M,l,j)));
    pNormalize(MATELEM(M,l,i));
  }
  for(int l=1;l<=MATCOLS(M);l++)
  {
    MATELEM(M,j,l)=pAdd(MATELEM(M,j,l),ppMult_qq(p,MATELEM(M,i,l)));
    pNormalize(MATELEM(M,j,l));
  }
 
  pDelete(&p);
 
  return(M);
}

evHessenberg()

matrix evHessenberg

(

matrix

M

)

Definition at line 100 of file eigenval.cc.

{
  int n=MATROWS(M);
  if(n!=MATCOLS(M))
    return(M);
 
  for(int k=1,j=2;k<n-1;k++,j=k+1)
  {
    while((j<=n)
    &&((MATELEM(M,j,k)==NULL)
      || (p_Totaldegree(MATELEM(M,j,k),currRing)!=0)))
      j++;
 
    if(j<=n)
    {
      M=evSwap(M,j,k+1);
 
      for(int i=j+1;i<=n;i++)
        M=evRowElim(M,i,k+1,k);
    }
  }
 
  return(M);
}

evRowElim()

matrix evRowElim	(	matrix	M,
		int	i,
		int	j,
		int	k
	)

Definition at line 47 of file eigenval.cc.

{
  if(MATELEM(M,i,k)==NULL||MATELEM(M,j,k)==NULL)
    return(M);
  poly p1=pp_Jet(MATELEM(M,i,k),0,currRing);
  poly p2=pp_Jet(MATELEM(M,j,k),0,currRing);
  if ((p1==NULL)||(p2==NULL)) return (M);
 
  poly p=pNSet(nDiv(pGetCoeff(p1),pGetCoeff(p2)));
  pNormalize(p);
 
  for(int l=1;l<=MATCOLS(M);l++)
  {
    MATELEM(M,i,l)=pSub(MATELEM(M,i,l),ppMult_qq(p,MATELEM(M,j,l)));
    pNormalize(MATELEM(M,i,l));
  }
  for(int l=1;l<=MATROWS(M);l++)
  {
    MATELEM(M,l,j)=pAdd(MATELEM(M,l,j),ppMult_qq(p,MATELEM(M,l,i)));
    pNormalize(MATELEM(M,l,j));
  }
 
  pDelete(&p);
  pDelete(&p1);
  pDelete(&p2);
 
  return(M);
}

evSwap()

matrix evSwap	(	matrix	M,
		int	i,
		int	j
	)

Definition at line 25 of file eigenval.cc.

{
  if(i==j)
    return(M);
 
  for(int k=1;k<=MATROWS(M);k++)
  {
    poly p=MATELEM(M,i,k);
    MATELEM(M,i,k)=MATELEM(M,j,k);
    MATELEM(M,j,k)=p;
  }
 
  for(int k=1;k<=MATCOLS(M);k++)
  {
    poly p=MATELEM(M,k,i);
    MATELEM(M,k,i)=MATELEM(M,k,j);
    MATELEM(M,k,j)=p;
  }
 
  return(M);
}