Functions
eigenval.cc File Reference
#include "kernel/mod2.h"
#include "kernel/structs.h"
#include "misc/intvec.h"
#include "coeffs/numbers.h"
#include "kernel/polys.h"
#include "kernel/ideals.h"
#include "polys/matpol.h"
#include "polys/clapsing.h"
#include "kernel/linear_algebra/eigenval.h"

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.

77 {
78  if(MATELEM(M,k,i)==0||MATELEM(M,k,j)==0)
79  return(M);
80 
81  poly p=pNSet(nDiv(pGetCoeff(MATELEM(M,k,i)),pGetCoeff(MATELEM(M,k,j))));
82  pNormalize(p);
83 
84  for(int l=1;l<=MATROWS(M);l++)
85  {
86  MATELEM(M,l,i)=pSub(MATELEM(M,l,i),ppMult_qq(p,MATELEM(M,l,j)));
87  pNormalize(MATELEM(M,l,i));
88  }
89  for(int l=1;l<=MATCOLS(M);l++)
90  {
91  MATELEM(M,j,l)=pAdd(MATELEM(M,j,l),ppMult_qq(p,MATELEM(M,i,l)));
92  pNormalize(MATELEM(M,j,l));
93  }
94 
95  pDelete(&p);
96 
97  return(M);
98 }
#define ppMult_qq(p, q)
Definition: polys.h:203
int j
Definition: facHensel.cc:105
#define pAdd(p, q)
Definition: polys.h:198
#define pNSet(n)
Definition: polys.h:308
int k
Definition: cfEzgcd.cc:92
static number & pGetCoeff(poly p)
return an alias to the leading coefficient of p assumes that p != NULL NOTE: not copy ...
Definition: monomials.h:44
#define pSub(a, b)
Definition: polys.h:282
int i
Definition: cfEzgcd.cc:125
#define nDiv(a, b)
Definition: numbers.h:32
#define MATCOLS(i)
Definition: matpol.h:27
#define pDelete(p_ptr)
Definition: polys.h:181
#define MATROWS(i)
Definition: matpol.h:26
int p
Definition: cfModGcd.cc:4019
int l
Definition: cfEzgcd.cc:93
#define MATELEM(mat, i, j)
1-based access to matrix
Definition: matpol.h:29
#define pNormalize(p)
Definition: polys.h:312

◆ 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 }
int j
Definition: facHensel.cc:105
matrix evRowElim(matrix M, int i, int j, int k)
Definition: eigenval.cc:47
static long p_Totaldegree(poly p, const ring r)
Definition: p_polys.h:1442
int k
Definition: cfEzgcd.cc:92
matrix evSwap(matrix M, int i, int j)
Definition: eigenval.cc:25
int i
Definition: cfEzgcd.cc:125
#define MATCOLS(i)
Definition: matpol.h:27
#define NULL
Definition: omList.c:12
ring currRing
Widely used global variable which specifies the current polynomial ring for Singular interpreter and ...
Definition: polys.cc:12
#define MATROWS(i)
Definition: matpol.h:26
#define MATELEM(mat, i, j)
1-based access to matrix
Definition: matpol.h:29

◆ 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  {
60  MATELEM(M,i,l)=pSub(MATELEM(M,i,l),ppMult_qq(p,MATELEM(M,j,l)));
61  pNormalize(MATELEM(M,i,l));
62  }
63  for(int l=1;l<=MATROWS(M);l++)
64  {
65  MATELEM(M,l,j)=pAdd(MATELEM(M,l,j),ppMult_qq(p,MATELEM(M,l,i)));
66  pNormalize(MATELEM(M,l,j));
67  }
68 
69  pDelete(&p);
70  pDelete(&p1);
71  pDelete(&p2);
72 
73  return(M);
74 }
#define ppMult_qq(p, q)
Definition: polys.h:203
int j
Definition: facHensel.cc:105
#define pAdd(p, q)
Definition: polys.h:198
#define pNSet(n)
Definition: polys.h:308
int k
Definition: cfEzgcd.cc:92
static number & pGetCoeff(poly p)
return an alias to the leading coefficient of p assumes that p != NULL NOTE: not copy ...
Definition: monomials.h:44
#define pSub(a, b)
Definition: polys.h:282
int i
Definition: cfEzgcd.cc:125
#define nDiv(a, b)
Definition: numbers.h:32
#define MATCOLS(i)
Definition: matpol.h:27
#define NULL
Definition: omList.c:12
#define pDelete(p_ptr)
Definition: polys.h:181
ring currRing
Widely used global variable which specifies the current polynomial ring for Singular interpreter and ...
Definition: polys.cc:12
poly pp_Jet(poly p, int m, const ring R)
Definition: p_polys.cc:4264
#define MATROWS(i)
Definition: matpol.h:26
int p
Definition: cfModGcd.cc:4019
int l
Definition: cfEzgcd.cc:93
#define MATELEM(mat, i, j)
1-based access to matrix
Definition: matpol.h:29
#define pNormalize(p)
Definition: polys.h:312

◆ 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 }
int j
Definition: facHensel.cc:105
int k
Definition: cfEzgcd.cc:92
int i
Definition: cfEzgcd.cc:125
#define MATCOLS(i)
Definition: matpol.h:27
#define MATROWS(i)
Definition: matpol.h:26
int p
Definition: cfModGcd.cc:4019
#define MATELEM(mat, i, j)
1-based access to matrix
Definition: matpol.h:29