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

Definition at line 35 of file mpr_numeric.cc.

37  : n(_n), cn(_cn), maxdeg(_maxdeg), p(_p), homog(_homog)
38 {
39  long j;
40  l= (long)pow((double)maxdeg+1,(int)n);
41  x= (number *)omAlloc( cn * sizeof(number) );
42  for ( j= 0; j < cn; j++ ) x[j]= nInit(1);
43  init();
44 }
int j
Definition: facHensel.cc:105
void init()
Definition: mpr_numeric.cc:53
#define omAlloc(size)
Definition: omAllocDecl.h:210
number * x
Definition: mpr_numeric.h:55
number * p
Definition: mpr_numeric.h:54
#define nInit(i)
Definition: numbers.h:24
Rational pow(const Rational &a, int e)
Definition: GMPrat.cc:411

◆ ~vandermonde()

vandermonde::~vandermonde ( )

Definition at line 46 of file mpr_numeric.cc.

47 {
48  int j;
49  for ( j= 0; j < cn; j++ ) nDelete( x+j );
50  omFreeSize( (void *)x, cn * sizeof( number ) );
51 }
int j
Definition: facHensel.cc:105
#define omFreeSize(addr, size)
Definition: omAllocDecl.h:260
number * x
Definition: mpr_numeric.h:55
#define nDelete(n)
Definition: numbers.h:16

Member Function Documentation

◆ init()

void vandermonde::init ( )
private

Definition at line 53 of file mpr_numeric.cc.

54 {
55  int j;
56  long i,c,sum;
57  number tmp,tmp1;
58 
59  c=0;
60  sum=0;
61 
62  intvec exp( n );
63  for ( j= 0; j < n; j++ ) exp[j]=0;
64 
65  for ( i= 0; i < l; i++ )
66  {
67  if ( !homog || (sum == maxdeg) )
68  {
69  for ( j= 0; j < n; j++ )
70  {
71  nPower( p[j], exp[j], &tmp );
72  tmp1 = nMult( tmp, x[c] );
73  x[c]= tmp1;
74  nDelete( &tmp );
75  }
76  c++;
77  }
78  exp[0]++;
79  sum=0;
80  for ( j= 0; j < n - 1; j++ )
81  {
82  if ( exp[j] > maxdeg )
83  {
84  exp[j]= 0;
85  exp[j + 1]++;
86  }
87  sum+= exp[j];
88  }
89  sum+= exp[n - 1];
90  }
91 }
int j
Definition: facHensel.cc:105
gmp_float exp(const gmp_float &a)
Definition: mpr_complex.cc:357
#define nPower(a, b, res)
Definition: numbers.h:38
number * x
Definition: mpr_numeric.h:55
Definition: intvec.h:19
#define nMult(n1, n2)
Definition: numbers.h:17
int i
Definition: cfEzgcd.cc:125
#define nDelete(n)
Definition: numbers.h:16
CFList tmp1
Definition: facFqBivar.cc:70
number * p
Definition: mpr_numeric.h:54

◆ interpolateDense()

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 146 of file mpr_numeric.cc.

147 {
148  int i,j,k;
149  number newnum,tmp1;
150  number b,t,xx,s;
151  number *c;
152  number *w;
153 
154  b=t=xx=s=tmp1=NULL;
155 
156  w= (number *)omAlloc( cn * sizeof(number) );
157  c= (number *)omAlloc( cn * sizeof(number) );
158  for ( j= 0; j < cn; j++ )
159  {
160  w[j]= nInit(0);
161  c[j]= nInit(0);
162  }
163 
164  if ( cn == 1 )
165  {
166  nDelete( &w[0] );
167  w[0]= nCopy(q[0]);
168  }
169  else
170  {
171  nDelete( &c[cn-1] );
172  c[cn-1]= nCopy(x[0]);
173  c[cn-1]= nInpNeg(c[cn-1]); // c[cn]= -x[1]
174 
175  for ( i= 1; i < cn; i++ ) { // i=2; i <= cn
176  nDelete( &xx );
177  xx= nCopy(x[i]);
178  xx= nInpNeg(xx); // xx= -x[i]
179 
180  for ( j= (cn-i-1); j <= (cn-2); j++) { // j=(cn+1-i); j <= (cn-1)
181  nDelete( &tmp1 );
182  tmp1= nMult( xx, c[j+1] ); // c[j]= c[j] + (xx * c[j+1])
183  newnum= nAdd( c[j], tmp1 );
184  nDelete( &c[j] );
185  c[j]= newnum;
186  }
187 
188  newnum= nAdd( xx, c[cn-1] ); // c[cn-1]= c[cn-1] + xx
189  nDelete( &c[cn-1] );
190  c[cn-1]= newnum;
191  }
192 
193  for ( i= 0; i < cn; i++ ) { // i=1; i <= cn
194  nDelete( &xx );
195  xx= nCopy(x[i]); // xx= x[i]
196 
197  nDelete( &t );
198  t= nInit( 1 ); // t= b= 1
199  nDelete( &b );
200  b= nInit( 1 );
201  nDelete( &s ); // s= q[cn-1]
202  s= nCopy( q[cn-1] );
203 
204  for ( k= cn-1; k >= 1; k-- ) { // k=cn; k >= 2
205  nDelete( &tmp1 );
206  tmp1= nMult( xx, b ); // b= c[k] + (xx * b)
207  nDelete( &b );
208  b= nAdd( c[k], tmp1 );
209 
210  nDelete( &tmp1 );
211  tmp1= nMult( q[k-1], b ); // s= s + (q[k-1] * b)
212  newnum= nAdd( s, tmp1 );
213  nDelete( &s );
214  s= newnum;
215 
216  nDelete( &tmp1 );
217  tmp1= nMult( xx, t ); // t= (t * xx) + b
218  newnum= nAdd( tmp1, b );
219  nDelete( &t );
220  t= newnum;
221  }
222 
223  if (!nIsZero(t))
224  {
225  nDelete( &w[i] ); // w[i]= s/t
226  w[i]= nDiv( s, t );
227  nNormalize( w[i] );
228  }
229 
231  }
232  }
233  mprSTICKYPROT("\n");
234 
235  // free mem
236  for ( j= 0; j < cn; j++ ) nDelete( c+j );
237  omFreeSize( (void *)c, cn * sizeof( number ) );
238 
239  nDelete( &tmp1 );
240  nDelete( &s );
241  nDelete( &t );
242  nDelete( &b );
243  nDelete( &xx );
244 
245  // makes quotiens smaller
246  for ( j= 0; j < cn; j++ ) nNormalize( w[j] );
247 
248  return w;
249 }
#define mprSTICKYPROT(msg)
Definition: mpr_global.h:54
const CanonicalForm int s
Definition: facAbsFact.cc:55
int j
Definition: facHensel.cc:105
#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:92
#define omAlloc(size)
Definition: omAllocDecl.h:210
number * x
Definition: mpr_numeric.h:55
CanonicalForm b
Definition: cfModGcd.cc:4044
#define nInpNeg(n)
Definition: numbers.h:21
#define nMult(n1, n2)
Definition: numbers.h:17
int i
Definition: cfEzgcd.cc:125
#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:12
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
#define nAdd(n1, n2)
Definition: numbers.h:18

◆ numvec2poly()

poly vandermonde::numvec2poly ( const number *  q)

Definition at line 93 of file mpr_numeric.cc.

94 {
95  int j;
96  long i,/*c,*/sum;
97 
98  poly pnew,pit=NULL;
99 
100  // c=0;
101  sum=0;
102 
103  int *exp= (int *) omAlloc( (n+1) * sizeof(int) );
104 
105  for ( j= 0; j < n+1; j++ ) exp[j]=0;
106 
107  for ( i= 0; i < l; i++ )
108  {
109  if ( (!homog || (sum == maxdeg)) && q[i] && !nIsZero(q[i]) )
110  {
111  pnew= pOne();
112  pSetCoeff(pnew,q[i]);
113  pSetExpV(pnew,exp);
114  if ( pit )
115  {
116  pNext(pnew)= pit;
117  pit= pnew;
118  }
119  else
120  {
121  pit= pnew;
122  pNext(pnew)= NULL;
123  }
124  pSetm(pit);
125  }
126  exp[1]++;
127  sum=0;
128  for ( j= 1; j < n; j++ )
129  {
130  if ( exp[j] > maxdeg )
131  {
132  exp[j]= 0;
133  exp[j + 1]++;
134  }
135  sum+= exp[j];
136  }
137  sum+= exp[n];
138  }
139 
140  omFreeSize( (void *) exp, (n+1) * sizeof(int) );
141 
142  pSortAdd(pit);
143  return pit;
144 }
int j
Definition: facHensel.cc:105
#define pSetm(p)
Definition: polys.h:266
gmp_float exp(const gmp_float &a)
Definition: mpr_complex.cc:357
#define omFreeSize(addr, size)
Definition: omAllocDecl.h:260
#define omAlloc(size)
Definition: omAllocDecl.h:210
#define pSetExpV(p, e)
Definition: polys.h:97
int i
Definition: cfEzgcd.cc:125
#define pOne()
Definition: polys.h:310
#define pSortAdd(p)
sorts p, p may have equal monomials
Definition: polys.h:216
#define nIsZero(n)
Definition: numbers.h:19
#define NULL
Definition: omList.c:12
#define pNext(p)
Definition: monomials.h:36
#define pSetCoeff(p, n)
deletes old coeff before setting the new one
Definition: polys.h:31

Field Documentation

◆ cn

long vandermonde::cn
private

Definition at line 50 of file mpr_numeric.h.

◆ homog

bool vandermonde::homog
private

Definition at line 57 of file mpr_numeric.h.

◆ l

long vandermonde::l
private

Definition at line 52 of file mpr_numeric.h.

◆ maxdeg

long vandermonde::maxdeg
private

Definition at line 51 of file mpr_numeric.h.

◆ n

long vandermonde::n
private

Definition at line 49 of file mpr_numeric.h.

◆ p

number* vandermonde::p
private

Definition at line 54 of file mpr_numeric.h.

◆ x

number* vandermonde::x
private

Definition at line 55 of file mpr_numeric.h.


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