Programmation

PROGRAM Pan_Reiff;

USES Crt;

TYPE Matrice=ARRAY[1..10,1..10] OF REAL;

VAR MatA,MatB,MatC:Matrice;
    N:BYTE;
    OK:BOOLEAN;

PROCEDURE Intro(VAR N:BYTE;VAR Mat:Matrice);
VAR i,j:BYTE;
BEGIN
CLRSCR;
TEXTCOLOR(YELLOW);
WRITE('Nombre de lignes:');READLN(N);
FOR i:=1 TO N DO
  FOR j:=1 TO N DO
    BEGIN
    {GOTOXY(3,4);CLREOL;
    WRITE('Introduisez A(',i,',',j,'): ');
    READLN(Mat[i,j]);}
    Mat[i,j]:=RANDOM(100);{Pour tester}
    END;
END;

PROCEDURE Attente;
VAR St:STRING;
BEGIN
TEXTCOLOR(LIGHTRED);
St:='Une touche pour continuer.';
GOTOXY(40-LENGTH(St) DIV 2,25);WRITE(St);READKEY;
END;

PROCEDURE Affiche(S:STRING;N:BYTE;Mat:Matrice);
VAR i,j:BYTE;
BEGIN
CLRSCR;
TEXTCOLOR(LIGHTGREEN);
WRITELN(S);
FOR i:=1 TO N DO
  BEGIN
  FOR j:=1 TO N DO
      WRITE(Mat[i,j]:9:4);
  WRITELN;
  END;
END;

PROCEDURE Somme(N:BYTE;MatA,MatB:Matrice;VAR MatC:Matrice);
VAR i,j:BYTE;
BEGIN
FOR i:=1 TO N DO
  FOR j:=1 TO N DO
     MatC[i,j]:=MatA[i,j]+MatB[i,j];
END;

PROCEDURE Difference(N:BYTE;MatA,MatB:Matrice;VAR MatC:Matrice);
VAR i,j:BYTE;
BEGIN
FOR i:=1 TO N DO
  FOR j:=1 TO N DO
     MatC[i,j]:=MatA[i,j]-MatB[i,j];
END;

PROCEDURE Produit(N:BYTE;MatA,MatB:Matrice;VAR MatC:Matrice);
VAR i,j,k:BYTE;
BEGIN
FOR i:=1 TO N DO
  FOR j:=1 TO N DO
    BEGIN
    MatC[i,j]:=0;
    FOR k:=1 TO N DO
      MatC[i,j]:=MatC[i,j]+MatA[i,k]*MatB[k,j];
    END;
END;

PROCEDURE Inverse(N:BYTE;A:Matrice;VAR X:Matrice;VAR OK:BOOLEAN);
VAR Id,E,B:Matrice;
    Old,New:REAL;
    Cpt:BYTE;

  FUNCTION Norme_Ligne(N:BYTE;B:Matrice):REAL;
  VAR Tmp,Tmp2:REAL;
      i,j:BYTE;
  BEGIN
  Tmp:=0;
  FOR i:=1 TO N DO
    BEGIN
    Tmp2:=0;
    FOR j:=1 TO N DO
      Tmp2:=Tmp2+ABS(B[i,j]);
    IF Tmp2>Tmp THEN Tmp:=Tmp2;
    END;
  Norme_Ligne:=Tmp
  END;

  FUNCTION Norme_Colonne(N:BYTE;B:Matrice):REAL;
  VAR Tmp,Tmp2:REAL;
      i,j:BYTE;
  BEGIN
  Tmp:=0;
  FOR i:=1 TO N DO
    BEGIN
    Tmp2:=0;
    FOR j:=1 TO N DO
      Tmp2:=Tmp2+ABS(B[j,i]);
    IF Tmp2>Tmp THEN Tmp:=Tmp2;
    END;
  Norme_Colonne:=Tmp
  END;

  PROCEDURE Init(N:BYTE;A:Matrice;VAR B:Matrice;VAR OK:BOOLEAN);
  VAR i,j:BYTE;
      T:REAL;
  BEGIN
  FILLCHAR(Id,SizeOf(Id),0);
  T:=Norme_Ligne(N,A)*Norme_Colonne(N,A);
  IF ABS(T)>1E-10 THEN BEGIN
                       OK:=TRUE;
                       FOR i:=1 TO N DO
                         BEGIN
                         Id[i,i]:=1;
                         B[i,i]:=A[i,i]/T;
                         FOR j:=i+1 TO N DO
                           BEGIN
                           B[i,j]:=A[j,i]/T;
                           B[j,i]:=A[i,j]/T;
                           END;
                         END;
                       END
  ELSE OK:=FALSE;
  END;

  PROCEDURE Calcule_E;
  VAR C:Matrice;
  BEGIN
  Produit(N,B,A,C);
  Difference(N,Id,C,E);
  END;

  PROCEDURE Calcule_B;
  VAR C,D:Matrice;
  BEGIN
  Somme(N,Id,E,D);
  Produit(N,D,B,C);
  B:=C
  END;

BEGIN
Init(N,A,B,OK);
IF NOT OK THEN WRITELN('Matrice nulle!')
ELSE BEGIN
     Calcule_E;
     Old:=Norme_Ligne(N,E);
     New:=Old;
     Cpt:=0;
     WHILE NOT ((New<1E-6) OR ((New>Old) AND (Cpt>5))) DO
       BEGIN
       Old:=New;
       Calcule_B;
       Calcule_E;
       New:=Norme_Ligne(N,E);
       INC(Cpt);
       END;
    OK:=TRUE;
    IF New<1E-6 THEN X:=B
    ELSE OK:=FALSE
    END;
END;

BEGIN
Intro(N,MatA);
Affiche('A=',N,MatA);
Attente;
Inverse(N,MatA,MatB,OK);
IF OK THEN BEGIN
           Affiche('Inverse de A=',N,MatB);
           Attente;
           Produit(N,MatA,MatB,MatC);
           Affiche('Produit des matrices inverses=',N,MatC);
           Attente;
           END
ELSE BEGIN
     CLRSCR;
     WRITELN('Pas d''inverse!');
     END;
END.