scanning_base.c File Reference

#include <stdlib.h>
#include <stdio.h>
#include "genC.h"
#include "linear.h"
#include "ri.h"
#include "misc.h"
#include "boolean.h"
#include "arithmetique.h"
#include "vecteur.h"
#include "contrainte.h"
#include "sc.h"
#include "matrice.h"
#include "hyperplane.h"

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Functions
void	scanning_base_hyperplane (h, int n, matrice G)
	package hyperplane. More...
void	base_G_h1_unnull (h, int n, matrice G)
	oid base_G_h1_unnull(int h[],int n,matrice G) More...

Function Documentation

base_G_h1_unnull()

void base_G_h1_unnull	(	h	,
		int	n,
		matrice	G
	)

oid base_G_h1_unnull(int h[],int n,matrice G)

determinant of Ui and Ui-1

computation of matrix U

initialisation

computation of Xi,Yi / Xi.det(Ui-1) - Yi.hi = GCD(det(Ui-1),hi)

make Ui - the i-th line: U[i,1]=h[i-1],U[i,2..n-1] =0,U[i,n] = Xi

->i-1

the i-th column:U[1..n-1] = Yi/det(Ui-1) . h

-> ->

divide U1 par GCD(h)

computation of matrix G

Definition at line 94 of file scanning_base.c.

{
    matrice U = matrice_new(n,n);
    matrice G1 = matrice_new(n,n);
    Value det_Ui = VALUE_ONE;
    Value det_Ui1 = VALUE_ZERO; /* determinant of Ui and Ui-1*/
    Value Xi,Yi;
    int i,j;
    Value r;
   
    /* computation of matrix U */
    assert(n>0);
    assert(h[0]!=0);
    /* initialisation */
    matrice_nulle(U,n,n);
    ACCESS(U,n,1,1) = h[0];
    det_Ui1 = h[0];
 
    for(i=2; i<=n; i++){
        /* computation of Xi,Yi / Xi.det(Ui-1) - Yi.hi  = GCD(det(Ui-1),hi) */
        det_Ui = bezout_grl(det_Ui1,h[i-1],&Xi,&Yi);
        if (i ==2 || i%2 != 0)
            value_oppose(Yi);
        /* make  Ui - the i-th line: U[i,1]=h[i-1],U[i,2..n-1] =0,U[i,n] = Xi*/
        ACCESS(U,n,i,1) = h[i-1];
        ACCESS(U,n,i,i) = Xi;
        /*                                            ->i-1 */
        /* the i-th column:U[1..n-1] = Yi/det(Ui-1) . h      */
        for (j=1; j<=i-1; j++){
            r = value_div(h[j-1],det_Ui1);
            ACCESS(U,n,j,i) = value_mult(Yi,r);
        }
        det_Ui1 = det_Ui;
    }
    for (i=1; i<=n; i++)
        /*         ->         ->*/
        /* divide U1 par GCD(h) */
        value_division(ACCESS(U,n,i,1),det_Ui);
 
    /* computation of  matrix G */
    matrice_general_inversion(U,G1,n);
    matrice_transpose(G1,G,n,n);
}

References ACCESS, assert, bezout_grl(), G, matrice_general_inversion(), matrice_new, matrice_nulle(), matrice_transpose(), value_div, value_division, value_mult, VALUE_ONE, value_oppose, and VALUE_ZERO.

Referenced by scanning_base_hyperplane().

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scanning_base_hyperplane()

void scanning_base_hyperplane	(	h	,
		int	n,
		matrice	G
	)

package hyperplane.

Build a change of basis matrix G compatible with a hyperplane direction h include <sys/stdtypes.h> for debug with dbmalloc include "stdlib.h" void scanning_base_hyperplane(int h[],int n,matrice U) compute the matrix U : -> -> -> U1 = h (U1 the first column of U) determinant(U) = +(/-)1.

Let G the scanning basis, the relation between U and T is -1 T
G = (U ) the parameters of the function are:

int h[] : hyperplan direction -— input int n : iteration dimension -— input matrice G : matrix -— output

search the first k / h[k]!=0

permution de h[0] et h[k]

Definition at line 69 of file scanning_base.c.

{
    int k=1;
 
    if (value_zero_p(h[0])){ 
        /* search the first k / h[k]!=0 */
        while(k<n && value_zero_p(h[k]))
            k++;
        if (k==n) user_error("scanning_base_hyperplane", "h is null vector\n");
        else{ /* permution de h[0] et h[k] */
            h[0] = h[k];
            h[k] = VALUE_ZERO;
            base_G_h1_unnull(h,n,G);
            matrice_swap_rows(G,n,n,1,k+1);
        }
    }
    else 
        base_G_h1_unnull(h,n,G);    
}

References base_G_h1_unnull(), G, matrice_swap_rows(), user_error, VALUE_ZERO, and value_zero_p.

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