Mathc matrices/c22c
Application 
Installer et compiler ces fichiers dans votre répertoire de travail.
/* ------------------------------------ */
/* Save as : c00b.c */
int main(void)
double ab[R4*C7]={
 1, -5, 3, -8, 2, +2, 0,
 3, -7, 1, -9, 8, 2, 0,
 3, -7, 1, -9, 9, 7, 0, 
 -1, 5, -3, 8, -2, -2, 0, 
double **Ab = ca_A_mR(ab,i_Abr_Ac_bc_mR(R4,C6,C1));
double **A = c_Ab_A_mR(Ab,i_mR(R4,C6));
double **b = c_Ab_b_mR(Ab,i_mR(R4,C1));
double **B = i_mR(R3,C6);
 clrscrn();
 printf(" Basis for a Row Space by Row Reduction :\n\n");
 printf(" A :");
 p_mR(A,S6,P1,C10);
 printf(" b :");
 p_mR(b,S6,P1,C10);
 printf(" Ab :");
 p_mR(Ab,S6,P1,C10);
 stop();
 clrscrn();
 printf(" The nonzero row vectors of R form a basis\n"
 " for the row space of R, and hence form a \n"
 " basis for the row space of A \n\n"
 " Ab :");
 p_mR(Ab,S7,P3,C10);
 printf(" R : gj_PP_mR(Ab,NO) :");
 gj_PP_mR(Ab,NO);
 p_mR(Ab,S7,P3,C10);
 c_r_mR(Ab,R1,B,R1);
 c_r_mR(Ab,R2,B,R2);
 c_r_mR(Ab,R3,B,R3);
 printf(" B : Basis for a Row Space of A by Row Reduction");
 p_mR(B,S7,P3,C10); 
 stop(); 
 f_mR(Ab);
 f_mR(b);
 f_mR(A);
 f_mR(B); 
 return 0;
/* ------------------------------------ */
 Exemple de sortie écran :
 Basis for a Row Space by Row Reduction :
 A :
 +1.0 -5.0 +3.0 -8.0 +2.0 +2.0 
 +3.0 -7.0 +1.0 -9.0 +8.0 +2.0 
 +3.0 -7.0 +1.0 -9.0 +9.0 +7.0 
 -1.0 +5.0 -3.0 +8.0 -2.0 -2.0 
 b :
 +0.0 
 +0.0 
 +0.0 
 +0.0 
 Ab :
 +1.0 -5.0 +3.0 -8.0 +2.0 +2.0 +0.0 
 +3.0 -7.0 +1.0 -9.0 +8.0 +2.0 +0.0 
 +3.0 -7.0 +1.0 -9.0 +9.0 +7.0 +0.0 
 -1.0 +5.0 -3.0 +8.0 -2.0 -2.0 +0.0 
 Press return to continue. 
 The nonzero row vectors of R form a basis
 for the row space of R, and hence form a 
 basis for the row space of A 
 Ab :
 +1.000 -5.000 +3.000 -8.000 +2.000 +2.000 +0.000 
 +3.000 -7.000 +1.000 -9.000 +8.000 +2.000 +0.000 
 +3.000 -7.000 +1.000 -9.000 +9.000 +7.000 +0.000 
 -1.000 +5.000 -3.000 +8.000 -2.000 -2.000 +0.000 
 R : gj_PP_mR(Ab,NO) :
 +1.000 -2.333 +0.333 -3.000 +2.667 +0.667 +0.000 
 -0.000 +1.000 -1.000 +1.875 +0.250 -0.500 -0.000 
 +0.000 +0.000 -0.000 +0.000 +1.000 +5.000 +0.000 
 +0.000 +0.000 +0.000 +0.000 +0.000 +0.000 +0.000 
 B : Basis for a Row Space of A by Row Reduction
 +1.000 -2.333 +0.333 -3.000 +2.667 +0.667 
 -0.000 +1.000 -1.000 +1.875 +0.250 -0.500 
 +0.000 +0.000 -0.000 +0.000 +1.000 +5.000 
 Press return to continue.

Mathc matrices/c22g
Application
Installer et compiler ces fichiers dans votre répertoire de travail.
/* ------------------------------------ */
/* Save as : c00c.c */
int main(void)
double ab[R4*C7]={
 1, -5, 3, -8, 2, +2, 0,
 5, -9, 6, -9, 6, 2, 0,
 5, -9, 6, -9, 6, 7, 0, 
 -1, 5, -3, 8, -2, -2, 0, 
double **Ab = ca_A_mR(ab,i_Abr_Ac_bc_mR(R4,C6,C1));
double **A = c_Ab_A_mR(Ab,i_mR(R4,C6));
double **b = c_Ab_b_mR(Ab,i_mR(R4,C1));
double **B = i_mR(R3,C6);
 clrscrn();
 printf(" Basis for a Row Space by Row Reduction\n\n");
 printf(" A :");
 p_mR(A,S6,P1,C10);
 printf(" b :");
 p_mR(b,S6,P1,C10);
 printf(" Ab :");
 p_mR(Ab,S6,P1,C10);
 stop();
 clrscrn();
 printf(" The nonzero row vectors of R form a basis\n"
 " for the row space of R, and hence form a \n"
 " basis for the row space of A \n\n"
 " Ab :");
 p_mR(Ab,S7,P3,C10);
 printf(" R : gj_PP_mR(Ab,NO) :");
 gj_PP_mR(Ab,NO);
 p_mR(Ab,S7,P3,C10);
 c_r_mR(Ab,R1,B,R1);
 c_r_mR(Ab,R2,B,R2);
 c_r_mR(Ab,R3,B,R3);
 printf(" B : Basis for a Row Space of A by Row Reduction");
 p_mR(B,S7,P3,C10); 
 stop(); 
 f_mR(Ab);
 f_mR(b);
 f_mR(A);
 f_mR(B); 
 return 0;
/* ------------------------------------ */

Exemple de sortie écran :
 Basis for a Row Space by Row Reduction
 A :
 +1.0 -5.0 +3.0 -8.0 +2.0 +2.0 
 +5.0 -9.0 +6.0 -9.0 +6.0 +2.0 
 +5.0 -9.0 +6.0 -9.0 +6.0 +7.0 
 -1.0 +5.0 -3.0 +8.0 -2.0 -2.0 
 b :
 +0.0 
 +0.0 
 +0.0 
 +0.0 
 Ab :
 +1.0 -5.0 +3.0 -8.0 +2.0 +2.0 +0.0 
 +5.0 -9.0 +6.0 -9.0 +6.0 +2.0 +0.0 
 +5.0 -9.0 +6.0 -9.0 +6.0 +7.0 +0.0 
 -1.0 +5.0 -3.0 +8.0 -2.0 -2.0 +0.0 
 Press return to continue. 
 ------------------------------------ 
 The nonzero row vectors of R form a basis
 for the row space of R, and hence form a 
 basis for the row space of A 
 Ab :
 +1.000 -5.000 +3.000 -8.000 +2.000 +2.000 +0.000 
 +5.000 -9.000 +6.000 -9.000 +6.000 +2.000 +0.000 
 +5.000 -9.000 +6.000 -9.000 +6.000 +7.000 +0.000 
 -1.000 +5.000 -3.000 +8.000 -2.000 -2.000 +0.000 
 R : gj_PP_mR(Ab,NO) :
 +1.000 -1.800 +1.200 -1.800 +1.200 +0.400 +0.000 
 -0.000 +1.000 -0.562 +1.938 -0.250 -0.500 -0.000 
 +0.000 +0.000 -0.000 +0.000 -0.000 +1.000 +0.000 
 +0.000 +0.000 +0.000 +0.000 +0.000 +0.000 +0.000 
 B : Basis for a Row Space of A by Row Reduction
 +1.000 -1.800 +1.200 -1.800 +1.200 +0.400 
 -0.000 +1.000 -0.562 +1.938 -0.250 -0.500 
 +0.000 +0.000 -0.000 +0.000 -0.000 +1.000 
 Press return to continue.

Mathc matrices/c22e
Application 
Installer et compiler ces fichiers dans votre répertoire de travail.
/* ------------------------------------ */
/* Save as : c00d.c */
int main(void)
double ab[R4*C7]={
 1, -5, 3, -8, 2, +2, 0,
 5, -9, 6, -9, 6, 2, 0,
 5, -9, 6, -9, 6, 7, 0, 
 -5, 9, -3, 8, -2, -2, 0, 
double **Ab = ca_A_mR(ab,i_Abr_Ac_bc_mR(R4,C6,C1));
double **A = c_Ab_A_mR(Ab,i_mR(R4,C6));
double **b = c_Ab_b_mR(Ab,i_mR(R4,C1));
double **B = i_mR(R4,C6);
 clrscrn();
 printf(" Basis for a Row Space by Row Reduction\n\n");
 printf(" A :");
 p_mR(A,S6,P1,C10);
 printf(" b :");
 p_mR(b,S6,P1,C10);
 printf(" Ab :");
 p_mR(Ab,S6,P1,C10);
 stop();
 clrscrn();
 printf(" The nonzero row vectors of R form a basis\n"
 " for the row space of R, and hence form a \n"
 " basis for the row space of A \n\n"
 " Ab :");
 p_mR(Ab,S7,P3,C10);
 printf(" R : gj_PP_mR(Ab,NO) :");
 gj_PP_mR(Ab,NO);
 p_mR(Ab,S7,P3,C10);
 c_r_mR(Ab,R1,B,R1);
 c_r_mR(Ab,R2,B,R2);
 c_r_mR(Ab,R3,B,R3);
 c_r_mR(Ab,R4,B,R4);
 printf(" B : Basis for a Row Space of A by Row Reduction");
 p_mR(B,S7,P3,C10); 
 stop(); 
 f_mR(Ab);
 f_mR(b);
 f_mR(A);
 f_mR(B); 
 return 0;
/* ------------------------------------ */
 Exemple de sortie écran :
 Basis for a Row Space by Row Reduction
 A :
 +1.0 -5.0 +3.0 -8.0 +2.0 +2.0 
 +5.0 -9.0 +6.0 -9.0 +6.0 +2.0 
 +5.0 -9.0 +6.0 -9.0 +6.0 +7.0 
 -5.0 +9.0 -3.0 +8.0 -2.0 -2.0 
 b :
 +0.0 
 +0.0 
 +0.0 
 +0.0 
 Ab :
 +1.0 -5.0 +3.0 -8.0 +2.0 +2.0 +0.0 
 +5.0 -9.0 +6.0 -9.0 +6.0 +2.0 +0.0 
 +5.0 -9.0 +6.0 -9.0 +6.0 +7.0 +0.0 
 -5.0 +9.0 -3.0 +8.0 -2.0 -2.0 +0.0 
 Press return to continue. 
 The nonzero row vectors of R form a basis
 for the row space of R, and hence form a 
 basis for the row space of A 
 Ab :
 +1.000 -5.000 +3.000 -8.000 +2.000 +2.000 +0.000 
 +5.000 -9.000 +6.000 -9.000 +6.000 +2.000 +0.000 
 +5.000 -9.000 +6.000 -9.000 +6.000 +7.000 +0.000 
 -5.000 +9.000 -3.000 +8.000 -2.000 -2.000 +0.000 
 R : gj_PP_mR(Ab,NO) :
 +1.000 -1.800 +1.200 -1.800 +1.200 +0.400 +0.000 
 -0.000 +1.000 -0.562 +1.938 -0.250 -0.500 -0.000 
 +0.000 +0.000 +1.000 -0.333 +1.333 +0.000 +0.000 
 +0.000 +0.000 +0.000 -0.000 +0.000 +1.000 +0.000 
 B : Basis for a Row Space of A by Row Reduction
 +1.000 -1.800 +1.200 -1.800 +1.200 +0.400 
 -0.000 +1.000 -0.562 +1.938 -0.250 -0.500 
 +0.000 +0.000 +1.000 -0.333 +1.333 +0.000 
 +0.000 +0.000 +0.000 -0.000 +0.000 +1.000 
 Press return to continue.

Mathc matrices/c22k
Application
Résoudre un même problème avec plusieurs algorithmes :
Exemples aléatoires :
Méthode des moindres carrés :
Ajustement d'une courbe linéaire aux données.
Ajustement d'une courbe quadratique aux données.
Ajustement d'une courbe cubique aux données.
Ajustement d'une courbe quartique aux données.
L'équation d'un conique :
L'équation d'un cercle :