My Project  UNKNOWN_GIT_VERSION
Functions
eigenval.h File Reference

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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.

77 {
78  if(MATELEM(M,k,i)==0||MATELEM(M,k,j)==0)
79  return(M);
80 
82  pNormalize(p);
83 
84  for(int l=1;l<=MATROWS(M);l++)
85  {
88  }
89  for(int l=1;l<=MATCOLS(M);l++)
90  {
93  }
94 
95  pDelete(&p);
96 
97  return(M);
98 }
int l
Definition: cfEzgcd.cc:93
int i
Definition: cfEzgcd.cc:125
int k
Definition: cfEzgcd.cc:92
int p
Definition: cfModGcd.cc:4019
int j
Definition: facHensel.cc:105
#define MATELEM(mat, i, j)
Definition: matpol.h:28
#define MATROWS(i)
Definition: matpol.h:26
#define MATCOLS(i)
Definition: matpol.h:27
static number & pGetCoeff(poly p)
return an alias to the leading coefficient of p assumes that p != NULL NOTE: not copy
Definition: monomials.h:45
#define nDiv(a, b)
Definition: numbers.h:33
#define pAdd(p, q)
Definition: polys.h:198
#define pDelete(p_ptr)
Definition: polys.h:181
#define pNSet(n)
Definition: polys.h:307
#define pSub(a, b)
Definition: polys.h:281
#define ppMult_qq(p, q)
Definition: polys.h:203
#define pNormalize(p)
Definition: polys.h:311
#define M
Definition: sirandom.c:24

◆ evHessenberg()

matrix evHessenberg ( matrix  M)

Definition at line 100 of file eigenval.cc.

101 {
102  int n=MATROWS(M);
103  if(n!=MATCOLS(M))
104  return(M);
105 
106  for(int k=1,j=2;k<n-1;k++,j=k+1)
107  {
108  while((j<=n)
109  &&((MATELEM(M,j,k)==NULL)
110  || (p_Totaldegree(MATELEM(M,j,k),currRing)!=0)))
111  j++;
112 
113  if(j<=n)
114  {
115  M=evSwap(M,j,k+1);
116 
117  for(int i=j+1;i<=n;i++)
118  M=evRowElim(M,i,k+1,k);
119  }
120  }
121 
122  return(M);
123 }
matrix evRowElim(matrix M, int i, int j, int k)
Definition: eigenval.cc:47
matrix evSwap(matrix M, int i, int j)
Definition: eigenval.cc:25
#define NULL
Definition: omList.c:10
static long p_Totaldegree(poly p, const ring r)
Definition: p_polys.h:1444
ring currRing
Widely used global variable which specifies the current polynomial ring for Singular interpreter and ...
Definition: polys.cc:13

◆ evRowElim()

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

Definition at line 47 of file eigenval.cc.

48 {
49  if(MATELEM(M,i,k)==NULL||MATELEM(M,j,k)==NULL)
50  return(M);
51  poly p1=pp_Jet(MATELEM(M,i,k),0,currRing);
52  poly p2=pp_Jet(MATELEM(M,j,k),0,currRing);
53  if ((p1==NULL)||(p2==NULL)) return (M);
54 
55  poly p=pNSet(nDiv(pGetCoeff(p1),pGetCoeff(p2)));
56  pNormalize(p);
57 
58  for(int l=1;l<=MATCOLS(M);l++)
59  {
62  }
63  for(int l=1;l<=MATROWS(M);l++)
64  {
67  }
68 
69  pDelete(&p);
70  pDelete(&p1);
71  pDelete(&p2);
72 
73  return(M);
74 }
poly pp_Jet(poly p, int m, const ring R)
Definition: p_polys.cc:4256

◆ evSwap()

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

Definition at line 25 of file eigenval.cc.

26 {
27  if(i==j)
28  return(M);
29 
30  for(int k=1;k<=MATROWS(M);k++)
31  {
32  poly p=MATELEM(M,i,k);
33  MATELEM(M,i,k)=MATELEM(M,j,k);
34  MATELEM(M,j,k)=p;
35  }
36 
37  for(int k=1;k<=MATCOLS(M);k++)
38  {
39  poly p=MATELEM(M,k,i);
40  MATELEM(M,k,i)=MATELEM(M,k,j);
41  MATELEM(M,k,j)=p;
42  }
43 
44  return(M);
45 }