Public Member Functions | Private Member Functions | Private Attributes
vandermonde Class Reference

vandermonde system solver for interpolating polynomials from their values More...

#include <mpr_numeric.h>

Public Member Functions

 vandermonde (const long _cn, const long _n, const long _maxdeg, number *_p, const bool _homog=true)
 
 ~vandermonde ()
 
number * interpolateDense (const number *q)
 Solves the Vandermode linear system {i=1}^{n} x_i^k-1 w_i = q_k, k=1,..,n. More...
 
poly numvec2poly (const number *q)
 

Private Member Functions

void init ()
 

Private Attributes

long n
 
long cn
 
long maxdeg
 
long l
 
number * p
 
number * x
 
bool homog
 

Detailed Description

vandermonde system solver for interpolating polynomials from their values

Definition at line 28 of file mpr_numeric.h.

Constructor & Destructor Documentation

vandermonde::vandermonde ( const long  _cn,
const long  _n,
const long  _maxdeg,
number *  _p,
const bool  _homog = true 
)

Definition at line 49 of file mpr_numeric.cc.

51  : n(_n), cn(_cn), maxdeg(_maxdeg), p(_p), homog(_homog)
52 {
53  long j;
54  l= (long)pow((double)maxdeg+1,(int)n);
55  x= (number *)omAlloc( cn * sizeof(number) );
56  for ( j= 0; j < cn; j++ ) x[j]= nInit(1);
57  init();
58 }
void init()
Definition: mpr_numeric.cc:67
#define omAlloc(size)
Definition: omAllocDecl.h:210
number * x
Definition: mpr_numeric.h:55
int j
Definition: myNF.cc:70
number * p
Definition: mpr_numeric.h:54
#define nInit(i)
Definition: numbers.h:24
Rational pow(const Rational &a, int e)
Definition: GMPrat.cc:418
vandermonde::~vandermonde ( )

Definition at line 60 of file mpr_numeric.cc.

61 {
62  int j;
63  for ( j= 0; j < cn; j++ ) nDelete( x+j );
64  omFreeSize( (void *)x, cn * sizeof( number ) );
65 }
#define omFreeSize(addr, size)
Definition: omAllocDecl.h:260
number * x
Definition: mpr_numeric.h:55
int j
Definition: myNF.cc:70
#define nDelete(n)
Definition: numbers.h:16

Member Function Documentation

void vandermonde::init ( )
private

Definition at line 67 of file mpr_numeric.cc.

68 {
69  int j;
70  long i,c,sum;
71  number tmp,tmp1;
72 
73  c=0;
74  sum=0;
75 
76  intvec exp( n );
77  for ( j= 0; j < n; j++ ) exp[j]=0;
78 
79  for ( i= 0; i < l; i++ )
80  {
81  if ( !homog || (sum == maxdeg) )
82  {
83  for ( j= 0; j < n; j++ )
84  {
85  nPower( p[j], exp[j], &tmp );
86  tmp1 = nMult( tmp, x[c] );
87  x[c]= tmp1;
88  nDelete( &tmp );
89  }
90  c++;
91  }
92  exp[0]++;
93  sum=0;
94  for ( j= 0; j < n - 1; j++ )
95  {
96  if ( exp[j] > maxdeg )
97  {
98  exp[j]= 0;
99  exp[j + 1]++;
100  }
101  sum+= exp[j];
102  }
103  sum+= exp[n - 1];
104  }
105 }
#define nPower(a, b, res)
Definition: numbers.h:38
number * x
Definition: mpr_numeric.h:55
Definition: intvec.h:16
int j
Definition: myNF.cc:70
#define nMult(n1, n2)
Definition: numbers.h:17
int i
Definition: cfEzgcd.cc:123
#define nDelete(n)
Definition: numbers.h:16
CFList tmp1
Definition: facFqBivar.cc:70
p exp[i]
Definition: DebugPrint.cc:39
number * p
Definition: mpr_numeric.h:54
number * vandermonde::interpolateDense ( const number *  q)

Solves the Vandermode linear system {i=1}^{n} x_i^k-1 w_i = q_k, k=1,..,n.

Any computations are done using type number to get high pecision results.

Parameters
qn-tuple of results (right hand of equations)
Returns
w n-tuple of coefficients of resulting polynomial, lowest deg first

Definition at line 160 of file mpr_numeric.cc.

161 {
162  int i,j,k;
163  number newnum,tmp1;
164  number b,t,xx,s;
165  number *c;
166  number *w;
167 
168  b=t=xx=s=tmp1=NULL;
169 
170  w= (number *)omAlloc( cn * sizeof(number) );
171  c= (number *)omAlloc( cn * sizeof(number) );
172  for ( j= 0; j < cn; j++ )
173  {
174  w[j]= nInit(0);
175  c[j]= nInit(0);
176  }
177 
178  if ( cn == 1 )
179  {
180  nDelete( &w[0] );
181  w[0]= nCopy(q[0]);
182  }
183  else
184  {
185  nDelete( &c[cn-1] );
186  c[cn-1]= nCopy(x[0]);
187  c[cn-1]= nInpNeg(c[cn-1]); // c[cn]= -x[1]
188 
189  for ( i= 1; i < cn; i++ ) { // i=2; i <= cn
190  nDelete( &xx );
191  xx= nCopy(x[i]);
192  xx= nInpNeg(xx); // xx= -x[i]
193 
194  for ( j= (cn-i-1); j <= (cn-2); j++) { // j=(cn+1-i); j <= (cn-1)
195  nDelete( &tmp1 );
196  tmp1= nMult( xx, c[j+1] ); // c[j]= c[j] + (xx * c[j+1])
197  newnum= nAdd( c[j], tmp1 );
198  nDelete( &c[j] );
199  c[j]= newnum;
200  }
201 
202  newnum= nAdd( xx, c[cn-1] ); // c[cn-1]= c[cn-1] + xx
203  nDelete( &c[cn-1] );
204  c[cn-1]= newnum;
205  }
206 
207  for ( i= 0; i < cn; i++ ) { // i=1; i <= cn
208  nDelete( &xx );
209  xx= nCopy(x[i]); // xx= x[i]
210 
211  nDelete( &t );
212  t= nInit( 1 ); // t= b= 1
213  nDelete( &b );
214  b= nInit( 1 );
215  nDelete( &s ); // s= q[cn-1]
216  s= nCopy( q[cn-1] );
217 
218  for ( k= cn-1; k >= 1; k-- ) { // k=cn; k >= 2
219  nDelete( &tmp1 );
220  tmp1= nMult( xx, b ); // b= c[k] + (xx * b)
221  nDelete( &b );
222  b= nAdd( c[k], tmp1 );
223 
224  nDelete( &tmp1 );
225  tmp1= nMult( q[k-1], b ); // s= s + (q[k-1] * b)
226  newnum= nAdd( s, tmp1 );
227  nDelete( &s );
228  s= newnum;
229 
230  nDelete( &tmp1 );
231  tmp1= nMult( xx, t ); // t= (t * xx) + b
232  newnum= nAdd( tmp1, b );
233  nDelete( &t );
234  t= newnum;
235  }
236 
237  if (!nIsZero(t))
238  {
239  nDelete( &w[i] ); // w[i]= s/t
240  w[i]= nDiv( s, t );
241  nNormalize( w[i] );
242  }
243 
245  }
246  }
247  mprSTICKYPROT("\n");
248 
249  // free mem
250  for ( j= 0; j < cn; j++ ) nDelete( c+j );
251  omFreeSize( (void *)c, cn * sizeof( number ) );
252 
253  nDelete( &tmp1 );
254  nDelete( &s );
255  nDelete( &t );
256  nDelete( &b );
257  nDelete( &xx );
258 
259  // makes quotiens smaller
260  for ( j= 0; j < cn; j++ ) nNormalize( w[j] );
261 
262  return w;
263 }
#define mprSTICKYPROT(msg)
Definition: mpr_global.h:54
const CanonicalForm int s
Definition: facAbsFact.cc:55
#define ST_VANDER_STEP
Definition: mpr_global.h:84
#define nNormalize(n)
Definition: numbers.h:30
#define omFreeSize(addr, size)
Definition: omAllocDecl.h:260
int k
Definition: cfEzgcd.cc:93
#define omAlloc(size)
Definition: omAllocDecl.h:210
number * x
Definition: mpr_numeric.h:55
int j
Definition: myNF.cc:70
#define nInpNeg(n)
Definition: numbers.h:21
#define nMult(n1, n2)
Definition: numbers.h:17
int i
Definition: cfEzgcd.cc:123
#define nDelete(n)
Definition: numbers.h:16
#define nDiv(a, b)
Definition: numbers.h:32
#define nIsZero(n)
Definition: numbers.h:19
#define NULL
Definition: omList.c:10
CFList tmp1
Definition: facFqBivar.cc:70
const CanonicalForm & w
Definition: facAbsFact.cc:55
#define nCopy(n)
Definition: numbers.h:15
#define nInit(i)
Definition: numbers.h:24
const poly b
Definition: syzextra.cc:213
#define nAdd(n1, n2)
Definition: numbers.h:18
poly vandermonde::numvec2poly ( const number *  q)

Definition at line 107 of file mpr_numeric.cc.

108 {
109  int j;
110  long i,/*c,*/sum;
111 
112  poly pnew,pit=NULL;
113 
114  // c=0;
115  sum=0;
116 
117  int *exp= (int *) omAlloc( (n+1) * sizeof(int) );
118 
119  for ( j= 0; j < n+1; j++ ) exp[j]=0;
120 
121  for ( i= 0; i < l; i++ )
122  {
123  if ( (!homog || (sum == maxdeg)) && q[i] && !nIsZero(q[i]) )
124  {
125  pnew= pOne();
126  pSetCoeff(pnew,q[i]);
127  pSetExpV(pnew,exp);
128  if ( pit )
129  {
130  pNext(pnew)= pit;
131  pit= pnew;
132  }
133  else
134  {
135  pit= pnew;
136  pNext(pnew)= NULL;
137  }
138  pSetm(pit);
139  }
140  exp[1]++;
141  sum=0;
142  for ( j= 1; j < n; j++ )
143  {
144  if ( exp[j] > maxdeg )
145  {
146  exp[j]= 0;
147  exp[j + 1]++;
148  }
149  sum+= exp[j];
150  }
151  sum+= exp[n];
152  }
153 
154  omFreeSize( (void *) exp, (n+1) * sizeof(int) );
155 
156  pSortAdd(pit);
157  return pit;
158 }
#define pSetm(p)
Definition: polys.h:241
#define omFreeSize(addr, size)
Definition: omAllocDecl.h:260
#define omAlloc(size)
Definition: omAllocDecl.h:210
int j
Definition: myNF.cc:70
#define pSetExpV(p, e)
Definition: polys.h:97
int i
Definition: cfEzgcd.cc:123
#define pOne()
Definition: polys.h:286
#define pSortAdd(p)
sorts p, p may have equal monomials
Definition: polys.h:192
#define nIsZero(n)
Definition: numbers.h:19
#define NULL
Definition: omList.c:10
#define pNext(p)
Definition: monomials.h:43
p exp[i]
Definition: DebugPrint.cc:39
polyrec * poly
Definition: hilb.h:10
#define pSetCoeff(p, n)
deletes old coeff before setting the new one
Definition: polys.h:31

Field Documentation

long vandermonde::cn
private

Definition at line 50 of file mpr_numeric.h.

bool vandermonde::homog
private

Definition at line 57 of file mpr_numeric.h.

long vandermonde::l
private

Definition at line 52 of file mpr_numeric.h.

long vandermonde::maxdeg
private

Definition at line 51 of file mpr_numeric.h.

long vandermonde::n
private

Definition at line 49 of file mpr_numeric.h.

number* vandermonde::p
private

Definition at line 54 of file mpr_numeric.h.

number* vandermonde::x
private

Definition at line 55 of file mpr_numeric.h.


The documentation for this class was generated from the following files: