Nugroho's blog.: "Auto" Gauss Naif in Delphi.

## Thursday, April 27, 2017

### "Auto" Gauss Naif in Delphi.

After do this in Python, now it's time to bring it back to Delphi, where all of this is started, :)

The heart of code lay on this one

```procedure tform1.gauss;
var i,j,k:integer; temp:real;
begin
for i:=1 to 9 do begin
for j:= 1 to i do begin
if t[i,j]<>0 then begin
temp:=t[i,j];
for k:= 1 to 10 do begin
if i=j then
t[j,k]:=t[j,k]/temp
else t[i,k]:=t[i,k]/temp - t[j,k];
end;
end;
end;
end;
//back subtitution
for i:=9 downto 1 do begin
x[i]:=t[i,10];
for j:=9  downto i do begin
if i<>j then
x[i]:=x[i]-x[j]*t[i,j];
end;
end;

```

You could say that it consists of zeroing lower tringle and normalizing the diagonal and then subtituting the value.

There's little failsafe code here, that is if we already have zero cell, don't proceed, or it will gave divided by zero error.

The rest of the code is here.

```unit Unit1;

interface

uses
Windows, Messages, SysUtils, Variants, Classes, Graphics, Controls, Forms,
Dialogs, Grids, StdCtrls;

type
TForm1 = class(TForm)
StringGrid1: TStringGrid;
StringGrid2: TStringGrid;
Button1: TButton;
procedure bacaMatrik;
procedure gauss;
procedure tulisMatrik;
procedure FormCreate(Sender: TObject);
procedure Button1Click(Sender: TObject);
private
{ Private declarations }
public
{ Public declarations }
end;

var
Form1: TForm1;
t:array[1..9,1..10]of real;
x:array[1..9]of real;

implementation

{\$R *.dfm}

procedure TForm1.FormCreate(Sender: TObject);
var i,j:integer;
begin
for i:=1 to 9 do begin
x[i]:=0;
for j:=1 to 9 do begin
t[i,j]:=0;
end;
end;
for i:=1 to 9 do begin
for j:=1 to 9 do begin
if i=j then begin
t[i,j]:=-2;
if j<>1 then t[i,j-1]:=1;
if j<>9 then t[i,j+1]:=1;
end;
end;
t[i,10]:=1;
end;
t[1,10]:=1-100;
t[9,10]:=1-25;

tulisMatrik;
end;
procedure tform1.bacaMatrik;
var i,j:integer;
begin
for i:=1 to 9 do begin
for j:=1 to 10 do begin
t[i,j]:=strToFloat(stringgrid1.Cells[j-1,i-1]);
end;
end;

end;
procedure tform1.tulisMatrik;
var i,j:integer;
begin
for i:=1 to 9 do begin
stringgrid2.Cells[i,0]:=floatToStr(x[i]);
for j:=1 to 10 do begin
stringgrid1.Cells[j-1,i-1]:=floatTostr(t[i,j]);
end;
end;
stringgrid2.Cells[0,0]:='100';
stringgrid2.Cells[10,0]:='25';

end;

procedure tform1.gauss;
var i,j,k:integer; temp:real;
begin
for i:=1 to 9 do begin
for j:= 1 to i do begin
if t[i,j]<>0 then begin
temp:=t[i,j];
for k:= 1 to 10 do begin
if i=j then
t[j,k]:=t[j,k]/temp
else t[i,k]:=t[i,k]/temp - t[j,k];
end;
end;
end;
end;
//subtitusi balik
for i:=9 downto 1 do begin
x[i]:=t[i,10];
for j:=9  downto i do begin
if i<>j then
x[i]:=x[i]-x[j]*t[i,j];
end;
end;

end;
procedure TForm1.Button1Click(Sender: TObject);
begin
bacaMatrik;
Gauss;
tulisMatrik;
end;

end.
```
.