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| unit Unit1;
interface
uses
Windows, Messages, SysUtils, Variants, Classes, Graphics, Controls, Forms,
Dialogs, Grids, StdCtrls, Spin, CategoryButtons, ExtCtrls;
type
TForm1 = class(TForm)
GroupBox1: TGroupBox;
Label2: TLabel;
Button1: TButton;
GroupBox2: TGroupBox;
GroupBox3: TGroupBox;
Label3: TLabel;
Edit1: TEdit;
Button4: TButton;
Label5: TLabel;
Label6: TLabel;
Label7: TLabel;
Label8: TLabel;
Label4: TLabel;
Button3: TButton;
Timer1: TTimer;
StringGrid1: TStringGrid;
StringGrid2: TStringGrid;
StringGrid5: TStringGrid;
StringGrid3: TStringGrid;
StringGrid4: TStringGrid;
procedure Button4Click(Sender: TObject);
procedure Button1Click(Sender: TObject);
procedure Button3Click(Sender: TObject);
procedure Timer1Timer(Sender: TObject);
private
{ Private declarations }
public
{ Public declarations }
end;
var
Form1: TForm1;
implementation
{$R *.dfm}
procedure TForm1.Button1Click(Sender: TObject);
var
a,b,a2,a3,a4,e,Aret: array [0..3,0..3] of real;
s1,s2,s3,s4,p1,p2,p3,p4:real;
I: Integer;
j: Integer;
///возведение исходной матрицы в квадрат
begin
for I := 0 to 3 do
for j := 0 to 3 do
begin
a[i,j]:=strtofloat(stringgrid1.Cells[i,j]);
b[i,j]:=strtofloat(stringgrid1.Cells[i,j]);
end;
for j := 0 to 3 do
begin
a2[0,j]:=a[0,j]*b[0,0]+a[1,j]*b[0,1]+a[2,j]*b[0,2]+a[3,j]*b[0,3];
stringgrid2.Cells[0,j]:=floattostr(a2[0,j]);
a2[1,j]:=a[0,j]*b[1,0]+a[1,j]*b[1,1]+a[2,j]*b[1,2]+a[3,j]*b[1,3];
stringgrid2.Cells[1,j]:=floattostr(a2[1,j]);
a2[2,j]:=a[0,j]*b[2,0]+a[1,j]*b[2,1]+a[2,j]*b[2,2]+a[3,j]*b[2,3];
stringgrid2.Cells[2,j]:=floattostr(a2[2,j]);
a2[3,j]:=a[0,j]*b[3,0]+a[1,j]*b[3,1]+a[2,j]*b[3,2]+a[3,j]*b[3,3];
stringgrid2.Cells[3,j]:=floattostr(a2[3,j]);
end;
///возведение исходной матрицы в куб
for j := 0 to 3 do
begin
a3[0,j]:=a2[0,j]*b[0,0]+a2[1,j]*b[0,1]+a2[2,j]*b[0,2]+a2[3,j]*b[0,3];
stringgrid3.Cells[0,j]:=floattostr(a3[0,j]);
a3[1,j]:=a2[0,j]*b[1,0]+a2[1,j]*b[1,1]+a2[2,j]*b[1,2]+a2[3,j]*b[1,3];
stringgrid3.Cells[1,j]:=floattostr(a3[1,j]);
a3[2,j]:=a2[0,j]*b[2,0]+a2[1,j]*b[2,1]+a2[2,j]*b[2,2]+a2[3,j]*b[2,3];
stringgrid3.Cells[2,j]:=floattostr(a3[2,j]);
a3[3,j]:=a2[0,j]*b[3,0]+a2[1,j]*b[3,1]+a2[2,j]*b[3,2]+a2[3,j]*b[3,3];
stringgrid3.Cells[3,j]:=floattostr(a3[3,j]);
end;
///возведение исходной матрицы в четвертую степень
for j := 0 to 3 do
begin
a4[0,j]:=a3[0,j]*b[0,0]+a3[1,j]*b[0,1]+a3[2,j]*b[0,2]+a3[3,j]*b[0,3];
stringgrid4.Cells[0,j]:=floattostr(a4[0,j]);
a4[1,j]:=a3[0,j]*b[1,0]+a3[1,j]*b[1,1]+a3[2,j]*b[1,2]+a3[3,j]*b[1,3];
stringgrid4.Cells[1,j]:=floattostr(a4[1,j]);
a4[2,j]:=a3[0,j]*b[2,0]+a3[1,j]*b[2,1]+a3[2,j]*b[2,2]+a3[3,j]*b[2,3];
stringgrid4.Cells[2,j]:=floattostr(a4[2,j]);
a4[3,j]:=a3[0,j]*b[3,0]+a3[1,j]*b[3,1]+a3[2,j]*b[3,2]+a3[3,j]*b[3,3];
stringgrid4.Cells[3,j]:=floattostr(a4[3,j]);
end;
///нахождение коэффициентов характеристического многочлена
s1:=a[0,0]+a[1,1]+a[2,2]+a[3,3];
s2:=a2[0,0]+a2[1,1]+a2[2,2]+a2[3,3];
s3:=a3[0,0]+a3[1,1]+a3[2,2]+a3[3,3];
s4:=a4[0,0]+a4[1,1]+a4[2,2]+a4[3,3];
p1:=-s1;
p2:=-1/2*(s2+p1*s1);
p3:=-1/3*(s3+p1*s2+p2*s1);
p4:=-1/4*(s4+p1*s3+p2*s2+p3*s1);
edit1.Text:='L^4 '+floattostr(p1)+'L^3 '+floattostr(p2)+'L^2 '+floattostr(p3)+'L '+floattostr(p4);
///нахождение обратной матрицы
if p4<>0 then
for I := 0 to 3 do
for j := 0 to 3 do
begin
e[i,j]:=0;
e[i,i]:=1;
Aret[i,j]:=-1/p4*(a3[i,j]+p1*a2[i,j]+p2*a[i,j]+p3*e[i,j]);
stringgrid5.Cells[i,j]:=floattostrf(Aret[i,j],ffFixed,10,4);
end
else
if p3<>0 then
for I := 0 to 3 do
for j := 0 to 3 do
begin
Aret[i,j]:=-1/p3*(a2[i,j]+p1*a[i,j]+p2*e[i,j]);
stringgrid5.Cells[i,j]:=floattostrf(Aret[i,j],ffFixed,10,4);
end
else
if p2<>0 then
for I := 0 to 3 do
for j := 0 to 3 do
begin
Aret[i,j]:=-1/p2*(a[i,j]+p1*e[i,j]);
stringgrid5.Cells[i,j]:=floattostrf(Aret[i,j],ffFixed,10,4);
end
else
if p1<>0 then
for I := 0 to 3 do
for j := 0 to 3 do
begin
Aret[i,j]:=-1/p1*(e[i,j]);
stringgrid5.Cells[i,j]:=floattostrf(Aret[i,j],ffFixed,10,4);
end;
end;
procedure TForm1.Button3Click(Sender: TObject);
begin
close;
end;
///процедура очистки
procedure TForm1.Button4Click(Sender: TObject);
var
z,j: Integer;
begin
edit1.Text:='';
for j := 0 to 3 do
for z := 0 to 3 do
begin
stringGrid1.Cells[j,z]:='';
stringGrid2.Cells[j,z]:='';
stringGrid3.Cells[j,z]:='';
stringGrid4.Cells[j,z]:='';
stringGrid5.Cells[j,z]:='';
end;
end;
///управление активностью кнопок
procedure TForm1.Timer1Timer(Sender: TObject);
var
I,j: Integer;
begin
for I := 0 to 3 do
for j := 0 to 3 do
if stringgrid1.Cells[i,j]='' then
begin
button1.Enabled:=false;
end
else
begin
button1.Enabled:=true;
end;
end;
end. |
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