Решение систем, линейных уравнений Опции

[Altair]

Решение систем линейных уравнений методом Гаусса

uses crt;

const
  nn = 10;
type
  Matrix = array[1..NN,1..NN+1] of real;

(* построчный ввод матрицы *)
Procedure ReadMatr(var A:Matrix; var n:word );
var
  i, j, m: word;
begin
  repeat
    write('Введите количество линейных уравн. в системе: '); readln(N)
  until (N>0) and (N<=NN);

  m:=n+1;
  For i:=1 to n do begin
    For j:=1 to m do begin
      write('A[',i,j,']= '); readln(A[i,j])
    end 
  end
end;

(* построчный вывод матрицы *)
Procedure PrintMatr(A:Matrix; n:word);
Var
  i, j, m: word;
begin
  m:=n+1;
  For i:=1 to n do begin
    For j:=1 to m do write(A[i,j],' ');
    writeln
  end
end;

procedure GaussM(a:matrix;n:word; var s:byte; var x:array of real);
var
  i, k, j: byte;
  m, t: real;
begin
  i:=1;
  s:=1;
  repeat
    j:=i+1;
    k:=i;
    m:=abs(a[i,i]);
    repeat
      if m<abs(a[j,i]) then begin
        m:=abs(a[j,i]);
        k:=j;
      end;
      j:=j+1
    until not(j<=n);

    if m<>0 then begin
      j:=i;
      repeat
        t:=a[i,j];
        a[i,j]:=a[k,j];
        a[k,j]:=t;
        j:=j+1
      until not(j<=n+1);
      k:=i+1;
      repeat
        t:=a[k,i]/a[i,i];
        a[k,i]:=0;
        j:=i+1;
        repeat
          a[k,j]:=a[k,j]-t*a[i,j];
          j:=j+1
        until not(j<=n+1);
        k:=k+1
      until not(k<=n);
    end
    else begin
      s:=0;
    end;
    i:=i+1
  until not((i<=n)and(s=1));

  if s=1 then begin
    i:=n;
    repeat
      x[i]:=a[i,n+1];
      j:=i+1;
      while j<=n do begin
        x[i]:=x[i]-a[i,j]*x[j];
        j:=j+1;
      end;
      x[i]:=x[i]/a[i,i];
      i:=i-1
    until not(i>=1);
  end;
end;

var
  b: array[0..nn] of real;
  a: Matrix;
  n, j: word;
  s: byte;
Begin
  readmatr(a,n);
  printmatr(a,n);
  writeln('press any key'); readkey;
  GaussM(a,n,s,b);
  for j:=1 to n do write (b[j],' ');
  writeln('press any key for exit ...'); readkey
end.