#include <stdio.h>
#include <stdlib.h>
#include "linear_assert.h"
#include "boolean.h"
#include "arithmetique.h"
#include "matrix.h"

Include dependency graph for matrix.c:

Functions
Value *	matrix_elem_ref (Pmatrix M, int r, int c)
	package matrix More...

Value	matrix_elem (Pmatrix M, int r, int c)

void	matrix_transpose (const Pmatrix A, Pmatrix At)
	void matrix_transpose(Pmatrix a, Pmatrix a_t): transpose an (nxm) rational matrix a into a (mxn) rational matrix a_t More...

void	matrix_multiply (const Pmatrix a, const Pmatrix b, Pmatrix c)
	void matrix_multiply(Pmatrix a, Pmatrix b, Pmatrix c): multiply rational matrix a by rational matrix b and store result in matrix c More...

void	matrix_normalize (Pmatrix a)
	void matrix_normalize(Pmatrix a) More...

void	matrix_normalizec (Pmatrix MAT)
	void matrix_normalizec(Pmatrix MAT): Normalisation des coefficients de la matrice MAT, i.e. More...

void	matrix_swap_columns (Pmatrix A, int c1, int c2)
	void matrix_swap_columns(Pmatrix a, int c1, int c2): exchange columns c1,c2 of an (nxm) rational matrix More...

void	matrix_swap_rows (Pmatrix A, int r1, int r2)
	void matrix_swap_rows(Pmatrix a, int r1, int r2): exchange rows r1 and r2 of an (nxm) rational matrix a More...

void	matrix_assign (Pmatrix A, Pmatrix B)
	void matrix_assign(Pmatrix A, Pmatrix B) Copie de la matrice A dans la matrice B More...

bool	matrix_equality (Pmatrix A, Pmatrix B)
	bool matrix_equality(Pmatrix A, Pmatrix B) test de l'egalite de deux matrices A et B; elles doivent avoir ete normalisees au prealable pour que le test soit mathematiquement exact More...

void	matrix_nulle (Pmatrix Z)
	void matrix_nulle(Pmatrix Z): Initialisation de la matrice Z a la valeur matrice nulle More...

bool	matrix_nulle_p (Pmatrix Z)
	bool matrix_nulle_p(Pmatrix Z): test de nullite de la matrice Z More...

bool	matrix_diagonal_p (Pmatrix Z)
	bool matrix_diagonal_p(Pmatrix Z): test de nullite de la matrice Z More...

bool	matrix_triangular_p (Pmatrix Z, bool inferieure)
	bool matrix_triangular_p(Pmatrix Z, bool inferieure): test de triangularite de la matrice Z More...

bool	matrix_triangular_unimodular_p (Pmatrix Z, bool inferieure)
	bool matrix_triangular_unimodular_p(Pmatrix Z, bool inferieure) test de la triangulaire et unimodulaire de la matrice Z. More...

void	matrix_substract (Pmatrix a, Pmatrix b, Pmatrix c)
	void matrix_substract(Pmatrix a, Pmatrix b, Pmatrix c): substract rational matrix c from rational matrix b and store result in matrix a More...

void	matrix_add (Pmatrix a, Pmatrix b, Pmatrix c)
	a = b + c More...

void	matrix_subtraction_column (Pmatrix MAT, int c1, int c2, Value x)
	void matrix_subtraction_column(Pmatrix MAT,int c1,int c2,int x): Soustrait x fois la colonne c2 de la colonne c1 Precondition: n > 0; m > 0; 0 < c1, c2 < m; Effet: c1[0..n-1] = c1[0..n-1] - x*c2[0..n-1]. More...

void	matrix_subtraction_line (Pmatrix MAT, int r1, int r2, Value x)
	void matrix_subtraction_line(Pmatrix MAT,int r1,int r2,int x): Soustrait x fois la ligne r2 de la ligne r1 Precondition: n > 0; m > 0; 0 < r1, r2 < n; Effet: r1[0..m-1] = r1[0..m-1] - x*r2[0..m-1] More...

void	matrix_uminus (Pmatrix A, Pmatrix mA)
	void matrix_uminus(A, mA) More...

Function Documentation

◆ matrix_add()

void matrix_add	(	Pmatrix	a,
		Pmatrix	b,
		Pmatrix	c
	)

a = b + c

precondition

Definition at line 471 of file matrix.c.

 {
   /* precondition */
   int m = MATRIX_NB_LINES(a);
   int n = MATRIX_NB_COLUMNS(a);
   assert(n>0 && m>0);
   assert(value_pos_p(MATRIX_DENOMINATOR(b)));
   assert(value_pos_p(MATRIX_DENOMINATOR(c)));
  
   Value d1 = MATRIX_DENOMINATOR(b);
   Value d2 = MATRIX_DENOMINATOR(c);
   if (value_eq(d1,d2)){
     int i, j;
     for (i=1; i<=m; i++)
             for (j=1; j<=n; j++)
         MATRIX_ELEM(a,i,j) =
           value_plus(MATRIX_ELEM(b,i,j),MATRIX_ELEM(c,i,j));
     MATRIX_DENOMINATOR(a) = d1;
   }
   else{
     Value lcm = ppcm(d1, d2);
     d1 = value_div(lcm,d1);
     d2 = value_div(lcm,d2);
     int i, j;
     for (i=1; i<=m; i++) {
             for (j=1; j<=n; j++) {
         Value t1 = value_mult(MATRIX_ELEM(b,i,j),d1);
         Value t2 = value_mult(MATRIX_ELEM(c,i,j),d2);
         MATRIX_ELEM(a,i,j) = value_plus(t1,t2);
       }
     }
     MATRIX_DENOMINATOR(a) = lcm;
   }
 }

References assert, MATRIX_DENOMINATOR, MATRIX_ELEM, MATRIX_NB_COLUMNS, MATRIX_NB_LINES, ppcm(), value_div, value_eq, value_mult, value_plus, and value_pos_p.

Referenced by make_reindex(), and prepare_reindexing().

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◆ matrix_assign()

void matrix_assign	(	Pmatrix	A,
		Pmatrix	B
	)

void matrix_assign(Pmatrix A, Pmatrix B) Copie de la matrice A dans la matrice B

Les parametres de la fonction :

int A[] : matrice !int B[] : matrice int n : nombre de lignes de la matrice int m : nombre de colonnes de la matrice

Ancien nom: matrix_dup

Definition at line 259 of file matrix.c.

 {
   int m = MATRIX_NB_LINES(A);
   int n = MATRIX_NB_COLUMNS(A);
   int i;
   for (i=0 ; i<m*n; i++)
     B->coefficients[i] = A->coefficients[i];
 }

References B, MATRIX_NB_COLUMNS, and MATRIX_NB_LINES.

Referenced by matrix_hermite(), matrix_smith(), sc_resol_smith(), and smith_int().

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◆ matrix_diagonal_p()

bool matrix_diagonal_p ( Pmatrix Z )

bool matrix_diagonal_p(Pmatrix Z): test de nullite de la matrice Z

QQ i dans [1..n] QQ j dans [1..n] Z(i,j) == 0 && i != j || i == j

Les parametres de la fonction :

int Z[] : matrice int n : nombre de lignes de la matrice int m : nombre de colonnes de la matrice

Definition at line 336 of file matrix.c.

 {
   int i,j;
   int m = MATRIX_NB_LINES(Z);
   int n = MATRIX_NB_COLUMNS(Z);
   for (i=1;i<=m;i++)
     for (j=1;j<=n;j++)
             if(i!=j && MATRIX_ELEM(Z,i,j)!=0)
         return false;
   return true;
 }

References MATRIX_ELEM, MATRIX_NB_COLUMNS, and MATRIX_NB_LINES.

Referenced by extract_lattice(), and matrix_diagonal_inversion().

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◆ matrix_elem()

Value matrix_elem	(	Pmatrix	M,
		int	r,
		int	c
	)

Definition at line 49 of file matrix.c.

 {
   assert(M != NULL && M->coefficients != NULL);
   assert(1 <= r && r <= M->number_of_lines);
   assert(1 <= c && c <= M->number_of_columns);
   // return M->coefficients[(c-1) * M->number_of_lines + r - 1];
   return MATRIX_ELEM(M, r, c);
 }

References assert, Pmatrix::coefficients, and MATRIX_ELEM.

◆ matrix_elem_ref()

Value* matrix_elem_ref	(	Pmatrix	M,
		int	r,
		int	c
	)

package matrix

matrix.c

Definition at line 41 of file matrix.c.

 {
   assert(M != NULL && M->coefficients != NULL);
   assert(1 <= r && r <= M->number_of_lines);
   assert(1 <= c && c <= M->number_of_columns);
   return &(MATRIX_ELEM(M, r, c));
 }

References assert, Pmatrix::coefficients, and MATRIX_ELEM.

◆ matrix_equality()

bool matrix_equality	(	Pmatrix	A,
		Pmatrix	B
	)

bool matrix_equality(Pmatrix A, Pmatrix B) test de l'egalite de deux matrices A et B; elles doivent avoir ete normalisees au prealable pour que le test soit mathematiquement exact

Definition at line 273 of file matrix.c.

 {
   int m = MATRIX_NB_LINES(A);
   int n = MATRIX_NB_COLUMNS(A);
   int i;
   for (i = 0 ; i < m*n; i++)
     if (B->coefficients[i] != A->coefficients[i])
             return false;
   return true;
 }

References B, MATRIX_NB_COLUMNS, and MATRIX_NB_LINES.

◆ matrix_multiply()

void matrix_multiply	(	const Pmatrix	a,
		const Pmatrix	b,
		Pmatrix	c
	)

void matrix_multiply(Pmatrix a, Pmatrix b, Pmatrix c): multiply rational matrix a by rational matrix b and store result in matrix c

 a is a (pxq) matrix, b a (qxr) and c a (pxr)

 c := a x b ;

Algorithm used is directly from definition, and space has to be provided for output matrix c by caller. Matrix c is not necessarily normalized: its denominator may divide all its elements (see matrix_normalize()).

Precondition: p > 0; q > 0; r > 0; c != a; c != b; – aliasing between c and a or b – is not supported

validate dimensions

simplified aliasing test

set denominator

use ordinary school book algorithm

Definition at line 95 of file matrix.c.

 {
   /* validate dimensions */
   int   p = MATRIX_NB_LINES(a);
   int   q = MATRIX_NB_COLUMNS(a);
   int   r = MATRIX_NB_COLUMNS(b);
   // should check that all dimensions are compatible & well allocated?!
  
   assert(p > 0 && q > 0 && r > 0);
   /* simplified aliasing test */
   assert(c != a && c != b);
  
   /* set denominator */
   MATRIX_DENOMINATOR(c) =
     value_mult(MATRIX_DENOMINATOR(a), MATRIX_DENOMINATOR(b));
  
   /* use ordinary school book algorithm */
   int i, j, k;
   for(i=1; i<=p; i++) {
     for(j=1; j<=r; j++) {
             Value v = VALUE_ZERO;
             for(k=1; k<=q; k++) {
         Value va = MATRIX_ELEM(a, i, k);
         Value vb = MATRIX_ELEM(b, k, j);
         value_addto(v, value_mult(va, vb));
             }
             MATRIX_ELEM(c, i, j) = v;
     }
   }
 }

References assert, MATRIX_DENOMINATOR, MATRIX_ELEM, MATRIX_NB_COLUMNS, MATRIX_NB_LINES, value_addto, value_mult, and VALUE_ZERO.

Referenced by extract_lattice(), fusion_buffer(), make_reindex(), matrices_to_1D_lattice(), matrix_general_inversion(), matrix_unimodular_inversion(), prepare_reindexing(), region_sc_minimal(), sc_resol_smith(), smith_int(), and Tiling_buffer_allocation().

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◆ matrix_normalize()

void matrix_normalize ( Pmatrix a )

void matrix_normalize(Pmatrix a)

 A rational matrix is stored as an integer one with one extra
 integer, the denominator for all the elements. To normalise the
 matrix in this sense means to reduce this denominator to the
 smallest positive number possible. All elements are also reduced
 to their smallest possible value.

Precondition: MATRIX_DENOMINATOR(a)!=0

we must find the GCD of all elements of matrix

factor out

ensure denominator is positive

FI: this code is useless because pgcd()always return a positive integer, even if a is the null matrix; its denominator CANNOT be 0

Definition at line 136 of file matrix.c.

 {
   int m = MATRIX_NB_LINES(a);
   int n = MATRIX_NB_COLUMNS(a);
   assert(MATRIX_DENOMINATOR(a) != 0);
  
   /* we must find the GCD of all elements of matrix */
   Value factor = MATRIX_DENOMINATOR(a);
  
   int i, j;
   for(i=1; i<=m; i++)
     for(j=1; j<=n; j++)
             factor = pgcd(factor, MATRIX_ELEM(a,i,j));
  
   /* factor out */
   if (value_notone_p(factor)) {
     for(i=1; i<=m; i++)
             for(j=1; j<=n; j++)
         value_division(MATRIX_ELEM(a,i,j), factor);
     value_division(MATRIX_DENOMINATOR(a),factor);
   }
  
   /* ensure denominator is positive */
   /* FI: this code is useless because pgcd()always return a positive integer,
      even if a is the null matrix; its denominator CANNOT be 0 */
   assert(value_pos_p(MATRIX_DENOMINATOR(a)));
  
 /*
     if(MATRIX_DENOMINATOR(a) < 0) {
         MATRIX_DENOMINATOR(a) = MATRIX_DENOMINATOR(a)*-1;
         for(loop1=1; loop1<=n; loop1++)
             for(loop2=1; loop2<=m; loop2++)
                 MATRIX_ELEM(a,loop1,loop2) = 
                     -1 * MATRIX_ELEM(a,loop1,loop2);
     }*/
 }

References assert, MATRIX_DENOMINATOR, MATRIX_ELEM, MATRIX_NB_COLUMNS, MATRIX_NB_LINES, pgcd, value_division, value_notone_p, and value_pos_p.

Referenced by make_reindex(), and prepare_reindexing().

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◆ matrix_normalizec()

void matrix_normalizec ( Pmatrix MAT )

void matrix_normalizec(Pmatrix MAT): Normalisation des coefficients de la matrice MAT, i.e.

division des coefficients de la matrice MAT et de son denominateur par leur pgcd

La matrice est modifiee.

Les parametres de la fonction :

!int MAT[] : matrice de dimension (n,m) int n : nombre de lignes de la matrice int m : nombre de colonnes de la matrice

??? matrix is supposed to be positive?

Parameters

MAT AT

Definition at line 187 of file matrix.c.

 {
   int m = MATRIX_NB_LINES(MAT);
   int n = MATRIX_NB_COLUMNS(MAT);
   assert( n>0 && m>0);
  
   Value a = MATRIX_DENOMINATOR(MAT);
   int i;
   for (i = 0; i<m*n  && value_gt(a, VALUE_ONE); i++)
     a = pgcd(a, MAT->coefficients[i]);
  
   if (value_gt(a,VALUE_ONE)) {
     for (i = 0; i<m*n; i++)
             value_division(MAT->coefficients[i],a);
   }
 }

References assert, Pmatrix::coefficients, MATRIX_DENOMINATOR, MATRIX_NB_COLUMNS, MATRIX_NB_LINES, pgcd, value_division, value_gt, and VALUE_ONE.

Referenced by sc_resol_smith(), and smith_int().

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◆ matrix_nulle()

void matrix_nulle ( Pmatrix Z )

void matrix_nulle(Pmatrix Z): Initialisation de la matrice Z a la valeur matrice nulle

Post-condition:

QQ i dans [1..n] QQ j dans [1..n] Z(i,j) == 0

Definition at line 293 of file matrix.c.

 {
   int m = MATRIX_NB_LINES(Z);
   int n = MATRIX_NB_COLUMNS(Z);
   int i,j;
   for (i=1; i<=m; i++)
     for (j=1; j<=n; j++)
             MATRIX_ELEM(Z,i,j) = VALUE_ZERO;
   MATRIX_DENOMINATOR(Z) = VALUE_ONE;
 }

References MATRIX_DENOMINATOR, MATRIX_ELEM, MATRIX_NB_COLUMNS, MATRIX_NB_LINES, VALUE_ONE, and VALUE_ZERO.

Referenced by build_contraction_matrices(), compute_delay_merged_nest(), compute_delay_tiled_nest(), constraints_to_matrices(), constraints_with_sym_cst_to_matrices(), egalites_to_matrice(), matrix_diagonal_inversion(), matrix_hermite(), matrix_perm_col(), matrix_perm_line(), matrix_triangular_inversion(), my_constraints_with_sym_cst_to_matrices(), sc_resol_smith(), smith_int(), and sys_mat_conv().

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◆ matrix_nulle_p()

bool matrix_nulle_p ( Pmatrix Z )

bool matrix_nulle_p(Pmatrix Z): test de nullite de la matrice Z

QQ i dans [1..n] QQ j dans [1..n] Z(i,j) == 0

Definition at line 311 of file matrix.c.

 {
   int m = MATRIX_NB_LINES(Z);
   int n = MATRIX_NB_COLUMNS(Z);
   int i, j;
   for (i=1; i<=m; i++)
     for (j=1; j<=n; j++)
             if (MATRIX_ELEM(Z,i,j) != VALUE_ZERO)
         return false;
   return true;
 }

References MATRIX_ELEM, MATRIX_NB_COLUMNS, MATRIX_NB_LINES, and VALUE_ZERO.

◆ matrix_substract()

void matrix_substract	(	Pmatrix	a,
		Pmatrix	b,
		Pmatrix	c
	)

void matrix_substract(Pmatrix a, Pmatrix b, Pmatrix c): substract rational matrix c from rational matrix b and store result in matrix a

 a is a (nxm) matrix, b a (nxm) and c a (nxm)

 a = b - c ;

Algorithm used is directly from definition, and space has to be provided for output matrix a by caller. Matrix a is not necessarily normalized: its denominator may divide all its elements (see matrix_normalize()).

Precondition: n > 0; m > 0; Note: aliasing between a and b or c is supported

denominators of b, c

ppcm of b,c

precondition

Definition at line 435 of file matrix.c.

 {
   Value d1,d2;   /* denominators of b, c */
   Value lcm;     /* ppcm of b,c */
   int i,j;
  
   /* precondition */
   int m = MATRIX_NB_LINES(a);
   int n = MATRIX_NB_COLUMNS(a);
   assert(n>0 && m>0);
   assert(value_pos_p(MATRIX_DENOMINATOR(b)));
   assert(value_pos_p(MATRIX_DENOMINATOR(c)));
  
   d1 = MATRIX_DENOMINATOR(b);
   d2 = MATRIX_DENOMINATOR(c);
   if (value_eq(d1,d2)){
     for (i=1; i<=m; i++)
             for (j=1; j<=n; j++)
         MATRIX_ELEM(a,i,j) =
           value_minus(MATRIX_ELEM(b,i,j),MATRIX_ELEM(c,i,j));
     MATRIX_DENOMINATOR(a) = d1;
   }
   else {
     lcm = ppcm(d1,d2);
     d1 = value_div(lcm,d1);
     d2 = value_div(lcm,d2);
     for (i=1; i<=m; i++)
       for (j=1; j<=n; j++)
         MATRIX_ELEM(a,i,j) =
           value_minus(value_mult(MATRIX_ELEM(b,i,j),d1),
                       value_mult(MATRIX_ELEM(c,i,j),d2));
     MATRIX_DENOMINATOR(a) = lcm;
   }
 }

References assert, MATRIX_DENOMINATOR, MATRIX_ELEM, MATRIX_NB_COLUMNS, MATRIX_NB_LINES, ppcm(), value_div, value_eq, value_minus, value_mult, and value_pos_p.

Referenced by compute_delay_merged_nest(), compute_delay_tiled_nest(), fusion_buffer(), and Tiling_buffer_allocation().

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◆ matrix_subtraction_column()

void matrix_subtraction_column	(	Pmatrix	MAT,
		int	c1,
		int	c2,
		Value	x
	)

void matrix_subtraction_column(Pmatrix MAT,int c1,int c2,int x): Soustrait x fois la colonne c2 de la colonne c1 Precondition: n > 0; m > 0; 0 < c1, c2 < m; Effet: c1[0..n-1] = c1[0..n-1] - x*c2[0..n-1].

Les parametres de la fonction :

int MAT[] : matrice int c1 : numero du colonne int c2 : numero du colonne int x :

Parameters

MAT	AT
c1	1
c2	2

Definition at line 518 of file matrix.c.

 {
   int m = MATRIX_NB_LINES(MAT);
   int i;
   for (i=1; i<=m; i++)
     value_substract(MATRIX_ELEM(MAT,i,c1),
                     value_mult(x, MATRIX_ELEM(MAT,i,c2)));
 }

References MATRIX_ELEM, MATRIX_NB_LINES, value_mult, value_substract, and x.

Referenced by matrix_hermite(), matrix_smith(), and matrix_unimodular_triangular_inversion().

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◆ matrix_subtraction_line()

void matrix_subtraction_line	(	Pmatrix	MAT,
		int	r1,
		int	r2,
		Value	x
	)

void matrix_subtraction_line(Pmatrix MAT,int r1,int r2,int x): Soustrait x fois la ligne r2 de la ligne r1 Precondition: n > 0; m > 0; 0 < r1, r2 < n; Effet: r1[0..m-1] = r1[0..m-1] - x*r2[0..m-1]

Les parametres de la fonction :

int MAT[] : matrice int n : nombre de lignes de la matrice int m : nombre de colonnes de la matrice int r1 : numero du ligne int r2 : numero du ligne int x :

Parameters

MAT	AT
r1	1
r2	2

Definition at line 541 of file matrix.c.

 {
   int n = MATRIX_NB_COLUMNS(MAT);
   int i;
   for (i=1; i<=n; i++)
     value_substract(MATRIX_ELEM(MAT,r1,i),
                     value_mult(x,MATRIX_ELEM(MAT,r2,i)));
 }

References MATRIX_ELEM, MATRIX_NB_COLUMNS, value_mult, value_substract, and x.

Referenced by matrix_smith().

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◆ matrix_swap_columns()

void matrix_swap_columns	(	Pmatrix	A,
		int	c1,
		int	c2
	)

void matrix_swap_columns(Pmatrix a, int c1, int c2): exchange columns c1,c2 of an (nxm) rational matrix

 Precondition:      n > 0; m > 0; 0 < c1 <= m; 0 < c2 <= m;

Parameters

c1	1
c2	2

Definition at line 209 of file matrix.c.

 {
   int m = MATRIX_NB_LINES(A);
   int n = MATRIX_NB_COLUMNS(A);
   assert(n > 0 && m > 0);
   assert(0 < c1 && c1 <= n);
   assert(0 < c2 && c2 <= n);
  
   int i;
   for(i=1; i<=m; i++) {
     Value temp = MATRIX_ELEM(A,i,c1);
     MATRIX_ELEM(A,i,c1) = MATRIX_ELEM(A,i,c2);
     MATRIX_ELEM(A,i,c2) = temp;
   }
 }

References assert, MATRIX_ELEM, MATRIX_NB_COLUMNS, and MATRIX_NB_LINES.

Referenced by matrix_hermite(), and matrix_smith().

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◆ matrix_swap_rows()

void matrix_swap_rows	(	Pmatrix	A,
		int	r1,
		int	r2
	)

void matrix_swap_rows(Pmatrix a, int r1, int r2): exchange rows r1 and r2 of an (nxm) rational matrix a

Precondition: n > 0; m > 0; 1 <= r1 <= n; 1 <= r2 <= n

Parameters

r1	1
r2	2

Definition at line 230 of file matrix.c.

 {
   int m = MATRIX_NB_LINES(A);
   int n = MATRIX_NB_COLUMNS(A);
   assert(n > 0);
   assert(m > 0);
   assert(0 < r1 && r1 <= m);
   assert(0 < r2 && r2 <= m);
  
   int i;
   for(i=1; i<=n; i++) {
     Value temp = MATRIX_ELEM(A,r1,i);
     MATRIX_ELEM(A,r1,i) = MATRIX_ELEM(A,r2,i);
     MATRIX_ELEM(A,r2,i) = temp;
   }
 }

References assert, MATRIX_ELEM, MATRIX_NB_COLUMNS, and MATRIX_NB_LINES.

Referenced by matrix_hermite(), and matrix_smith().

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◆ matrix_transpose()

void matrix_transpose	(	const Pmatrix	A,
		Pmatrix	At
	)

void matrix_transpose(Pmatrix a, Pmatrix a_t): transpose an (nxm) rational matrix a into a (mxn) rational matrix a_t

At := A ;

verification step

copy from a to a_t

Parameters

At t

Definition at line 64 of file matrix.c.

 {
   /* verification step */
   int m = MATRIX_NB_LINES(A);
   int n = MATRIX_NB_COLUMNS(A);
   assert(n >= 0 && m >= 0);
  
   /* copy from a to a_t */
   MATRIX_DENOMINATOR(At) = MATRIX_DENOMINATOR(A);
   int i, j;
   for(i=1; i<=m; i++)
     for(j=1; j<=n; j++)
             MATRIX_ELEM(At,j,i) = MATRIX_ELEM(A,i,j);
 }

References assert, MATRIX_DENOMINATOR, MATRIX_ELEM, MATRIX_NB_COLUMNS, and MATRIX_NB_LINES.

Referenced by region_sc_minimal().

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◆ matrix_triangular_p()

bool matrix_triangular_p	(	Pmatrix	Z,
		bool	inferieure
	)

bool matrix_triangular_p(Pmatrix Z, bool inferieure): test de triangularite de la matrice Z

si inferieure == true QQ i dans [1..n] QQ j dans [i+1..m] Z(i,j) == 0

si inferieure == false (triangulaire superieure) QQ i dans [1..n] QQ j dans [1..i-1] Z(i,j) == 0

Les parametres de la fonction :

int Z[] : matrice int n : nombre de lignes de la matrice int m : nombre de colonnes de la matrice

Parameters

inferieure nferieure

Definition at line 367 of file matrix.c.

 {
   int m = MATRIX_NB_LINES(Z);
   int n = MATRIX_NB_COLUMNS(Z);
   int i,j;
   for (i=1; i<=m; i++)
     if(inferieure) {
             for (j=i+1; j<=n; j++)
         if(MATRIX_ELEM(Z,i,j)!=0)
           return false;
     }
     else
             for (j=1; j<=i-1; j++)
         if(MATRIX_ELEM(Z,i,j)!=0)
           return false;
   return true;
 }

References MATRIX_ELEM, MATRIX_NB_COLUMNS, and MATRIX_NB_LINES.

Referenced by matrix_triangular_inversion(), and matrix_triangular_unimodular_p().

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◆ matrix_triangular_unimodular_p()

bool matrix_triangular_unimodular_p	(	Pmatrix	Z,
		bool	inferieure
	)

bool matrix_triangular_unimodular_p(Pmatrix Z, bool inferieure) test de la triangulaire et unimodulaire de la matrice Z.

si inferieure == true QQ i dans [1..n] QQ j dans [i+1..n] Z(i,j) == 0 i dans [1..n] Z(i,i) == 1

si inferieure == false (triangulaire superieure) QQ i dans [1..n] QQ j dans [1..i-1] Z(i,j) == 0 i dans [1..n] Z(i,i) == 1 les parametres de la fonction : matrice Z : la matrice entre

Parameters

inferieure nferieure

Definition at line 403 of file matrix.c.

 {
   int m = MATRIX_NB_LINES(Z);
   assert(MATRIX_NB_COLUMNS(Z) == m);
   bool triangulaire = matrix_triangular_p(Z,inferieure);
   if (triangulaire) {
     int i;
     for(i=1; i<=m; i++)
             if (value_notone_p(MATRIX_ELEM(Z,i,i)))
         return false;
     return true;
   }
   else
     return false;
 }

References assert, MATRIX_ELEM, MATRIX_NB_COLUMNS, MATRIX_NB_LINES, matrix_triangular_p(), and value_notone_p.

Referenced by extract_lattice(), matrix_unimodular_inversion(), and matrix_unimodular_triangular_inversion().

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◆ matrix_uminus()

void matrix_uminus	(	Pmatrix	A,
		Pmatrix	mA
	)

void matrix_uminus(A, mA)

computes mA = - A

input: A, larger allocated mA output: none modifies: mA

Parameters

mA A

Definition at line 558 of file matrix.c.

 {
   assert(MATRIX_NB_LINES(mA)>=MATRIX_NB_LINES(A) &&
          MATRIX_NB_COLUMNS(mA)>=MATRIX_NB_COLUMNS(A));
  
   int i,j;
   for (i=1; i<=MATRIX_NB_LINES(A); i++)
     for (j=1; j<=MATRIX_NB_COLUMNS(A); j++)
             MATRIX_ELEM(mA, i, j) = value_uminus(MATRIX_ELEM(A, i, j));
 }

References assert, MATRIX_ELEM, MATRIX_NB_COLUMNS, MATRIX_NB_LINES, and value_uminus.

Referenced by extract_lattice().

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Functions

Function Documentation

◆ matrix_add()

◆ matrix_assign()

◆ matrix_diagonal_p()

◆ matrix_elem()

◆ matrix_elem_ref()

◆ matrix_equality()

◆ matrix_multiply()

◆ matrix_normalize()

◆ matrix_normalizec()

◆ matrix_nulle()

◆ matrix_nulle_p()

◆ matrix_substract()

◆ matrix_subtraction_column()

◆ matrix_subtraction_line()

◆ matrix_swap_columns()

◆ matrix_swap_rows()

◆ matrix_transpose()

◆ matrix_triangular_p()

◆ matrix_triangular_unimodular_p()

◆ matrix_uminus()