Курсовая работа: Метод наискорейшего спуска
if(ComboBox1.ItemIndex=2) then
zl:=sin(xl)*cos(yl*yl);
if zl>=zlm then begin
zlm:=zl;
clr:=clr+0.01;
clb:=clb-0.01;
glcolor3f(clr,0.0,clb);
end;
glVertex3f(xl*obl,zl*obl,yl*obl); //+++
i:=i+0.1;
xl:=i;
if(ComboBox1.ItemIndex=0) then
zl:=(exp(xl)+exp(yl))/(exp(xl*xl)+exp(yl*yl));
if(ComboBox1.ItemIndex=1) then
zl:=sin(xl)*sin(xl)/(sin(yl)*sin(yl)+1);
if(ComboBox1.ItemIndex=2) then
zl:=sin(xl)*cos(yl*yl);
glVertex3f(xl*obl,zl*obl,yl*obl); //++++
end;
j:=j+h;
end;
glend;
//----------------------
i:=-wn;
j:=-wn;
clr:=0;
clb:=1.0;
zlm:=StrToFloat(StringGrid1.cells[0,3]);
while j<=wn do begin
i:=-wn;
xl:=j;
glBegin(GL_Lines);
glcolor3f(clr,0.0,clb);
while i<=wn do begin
yl:=i; //f(x) ||
if(ComboBox1.ItemIndex=0) then
zl:=(exp(xl)+exp(yl))/(exp(xl*xl)+exp(yl*yl));
if(ComboBox1.ItemIndex=1) then
zl:=sin(xl)*sin(xl)/(sin(yl)*sin(yl)+1);
if(ComboBox1.ItemIndex=2) then
zl:=sin(xl)*cos(yl*yl);
if zl>=zlm then begin
zlm:=zl;
clr:=clr+0.01;
clb:=clb-0.01;
glcolor3f(clr,0.0,clb);
end;
glVertex3f(xl*obl,zl*obl,yl*obl); //+++
i:=i+0.1;
yl:=i;
if(ComboBox1.ItemIndex=0) then
zl:=(exp(xl)+exp(yl))/(exp(xl*xl)+exp(yl*yl));
if(ComboBox1.ItemIndex=1) then
zl:=sin(xl)*sin(xl)/(sin(yl)*sin(yl)+1);
if(ComboBox1.ItemIndex=2) then
zl:=sin(xl)*cos(yl*yl);
glVertex3f(xl*obl,zl*obl,yl*obl); //+++
end;
j:=j+h;
end;
glend;
//------
it:=0;
glLineWidth(2);
glBegin(GL_Line_strip);
glcolor3f(0.0,1.0,0.0);
while it<StringGrid1.ColCount do begin
xl:=StrToFloat(StringGrid1.cells[it,1]); //+
yl:=StrToFloat(StringGrid1.cells[it,2]); //+
zl:=StrToFloat(StringGrid1.cells[it,3]); //+
glVertex3f(xl*obl,zl*obl,yl*obl);
it:=it+1;
end;
glend;
glLineWidth(1);
//tmax
glPointSize(6);
glBegin(GL_points);
glcolor3f(1.0,0.0,0.0);
glVertex3f(xl*obl,zl*obl,yl*obl);
glcolor3f(0.0,0.0,1.0);
glVertex3f(StrToFloat(StringGrid1.cells[0,1])*obl,StrToFloat(StringGrid1.cells[0,3])*obl,StrToFloat(StringGrid1.cells[0,2])*obl);
glend;
glscalef(1.0/masht,1.0/masht,1.0/masht);
glRotatef(verx,1,0,0);
glRotatef(rt,0,1,0);
SwapBuffers(DC);
Label2.Caption:=FloatToStr(zlm);
end;
procedure TForm1.Panel1MouseDown(Sender: TObject; Button: TMouseButton;
Shift: TShiftState; X, Y: Integer);
begin
if(Button=mbleft) then begin
radiobutton1.Checked:=true;
end;
end;
procedure TForm1.Panel1MouseUp(Sender: TObject; Button: TMouseButton;
Shift: TShiftState; X, Y: Integer);
begin
radiobutton1.Checked:=false;
end;
procedure TForm1.Panel1MouseMove(Sender: TObject; Shift: TShiftState; X, Y: Integer);
begin
rt:=0;
verx:=0;
if radiobutton1.Checked=true then begin
rt:=x- xmaus;
verx:=y-ymaus;
refresh;
end;
xmaus:=x;
ymaus:=y;
end;
procedure TForm1.Button2Click(Sender: TObject);
var
hx,hy,h,x0,y0,f0,gx,gy,g1x,g1y,e,f1: real;
i : integer;
begin
StringGrid1.ColCount:=1;
h :=0.001;
hx:=0.001;
hy:=0.001;
e:=0.002;
x0:=StrToInt(Edit1.Text);
y0:=StrToInt(Edit2.Text);
if(ComboBox1.ItemIndex=0) then begin
f0:=(exp(x0)+exp(y0))/(exp(x0*x0)+exp(y0*y0));
gx:=exp(x0)/(exp(x0*x0)+exp(y0*y0))-exp(x0*x0)*x0*(2*(exp(x0)+exp(y0))/((exp(x0*x0)+exp(y0*y0))*(exp(x0*x0)+exp(y0*y0))));
gy:=exp(y0)/(exp(y0*y0)+exp(x0*x0))-exp(y0*y0)*y0*(2*(exp(y0)+exp(x0))/((exp(y0*y0)+exp(x0*x0))*(exp(y0*y0)+exp(x0*x0))));
end;
if(ComboBox1.ItemIndex=1) then begin
f0:=sin(x0)*sin(x0)/(sin(y0)*sin(y0)+1);
gx:=2*sin(x0)*cos(x0)/(sin(y0)*sin(y0)+1);
gy:=-2*sin(x0)*sin(x0)*cos(y0)*sin(y0)/((sin(y0)*sin(y0)+1)*(sin(y0)*sin(y0)+1));
end;
if(ComboBox1.ItemIndex=2) then begin
f0:=sin(x0)*cos(y0*y0);
gx:= cos(x0)*cos(y0*y0);
gy:=-2*sin(x0)*sin(y0*y0)*y0;
end;
g1x:=gx;
g1y:=gy;
x0:=x0+hx*gx;
y0:=y0+hy*gy;
if(ComboBox1.ItemIndex=0) then
f1:=(exp(x0)+exp(y0))/(exp(x0*x0)+exp(y0*y0));
if(ComboBox1.ItemIndex=1) then
f1:=sin(x0)*sin(x0)/(sin(y0)*sin(y0)+1);
if(ComboBox1.ItemIndex=2) then
f1:=sin(x0)*cos(y0*y0);
StringGrid1.Cells[0,0]:='1';
StringGrid1.Cells[0,1]:=FloatToStr(x0);
StringGrid1.Cells[0,2]:=FloatToStr(y0);
StringGrid1.Cells[0,3]:=FloatToStr(f1);
if f1<f0 then begin
hx:=h;
hy:=h;
end
else begin
hx:=hx*2;
hy:=hy*2;
end;
i:=1;
while not((abs(g1x)<e) and (abs(g1y)<e))do
begin
f0:=f1;
x0:=x0+hx*gx;
y0:=y0+hy*gy;
if(ComboBox1.ItemIndex=0) then begin
g1x:=exp(x0)/(exp(x0*x0)+exp(y0*y0))-exp(x0*x0)*x0*(2*(exp(x0)+exp(y0))/((exp(x0*x0)+exp(y0*y0))*(exp(x0*x0)+exp(y0*y0))));
g1y:=exp(y0)/(exp(y0*y0)+exp(x0*x0))-exp(y0*y0)*y0*(2*(exp(y0)+exp(x0))/((exp(y0*y0)+exp(x0*x0))*(exp(y0*y0)+exp(x0*x0))));
f1:=(exp(x0)+exp(y0))/(exp(x0*x0)+exp(y0*y0));
end;
if(ComboBox1.ItemIndex=1) then begin
g1x:=2*sin(x0)*cos(x0)/(sin(y0)*sin(y0)+1);
g1y:=-2*sin(x0)*sin(x0)*cos(y0)*sin(y0)/((sin(y0)*sin(y0)+1)*(sin(y0)*sin(y0)+1));
f1:=sin(x0)*sin(x0)/(sin(y0)*sin(y0)+1);
end;
if(ComboBox1.ItemIndex=2) then begin
f1:=sin(x0)*cos(y0*y0);
g1x:= cos(x0)*cos(y0*y0);
g1y:=-2*sin(x0)*sin(y0*y0)*y0;
end;
StringGrid1.Cells[i,0]:=IntToStr(i+1);
StringGrid1.Cells[i,1]:=FloatToStr(x0);
StringGrid1.Cells[i,2]:=FloatToStr(y0);
StringGrid1.Cells[i,3]:=FloatToStr(f1);
i:=i+1;
StringGrid1.ColCount:=i;
if f1<f0 then begin
if(ComboBox1.ItemIndex=0) then begin
gx:=exp(x0)/(exp(x0*x0)+exp(y0*y0))-exp(x0*x0)*x0*(2*(exp(x0)+exp(y0))/((exp(x0*x0)+exp(y0*y0))*(exp(x0*x0)+exp(y0*y0))));
gy:=exp(y0)/(exp(y0*y0)+exp(x0*x0))-exp(y0*y0)*y0*(2*(exp(y0)+exp(x0))/((exp(y0*y0)+exp(x0*x0))*(exp(y0*y0)+exp(x0*x0))));
end;
if(ComboBox1.ItemIndex=1) then begin
gx:=2*sin(x0)*cos(x0)/(sin(y0)*sin(y0)+1);
gy:=-2*sin(x0)*sin(x0)*cos(y0)*sin(y0)/((sin(y0)*sin(y0)+1)*(sin(y0)*sin(y0)+1));
end;
if(ComboBox1.ItemIndex=2) then begin
gx:= cos(x0)*cos(y0*y0);
gy:=-2*sin(x0)*sin(y0*y0)*y0;
end;
hx:=h;
hy:=h;
end
else begin
hx:=hx*2;
hy:=hy*2;
end;
end;
Label1.Caption:=FloatToStr(f1);
refresh;
end;
procedure TForm1.Edit3Change(Sender: TObject);
var
c : real;
begin
try
c:=StrToFloat(Edit3.text);
except
Edit3.text:='0,05';
end;
end;
procedure TForm1.Edit1Change(Sender: TObject);
var
c : integer;
begin
try
c:=StrToInt(Edit1.text);
except
Edit1.text:='-1';
end;
end;
procedure TForm1.Edit2Change(Sender: TObject);
var
c : integer;
begin
try
c:=StrToInt(Edit2.text);
except
Edit2.text:='-1';
end;
end;
procedure TForm1.Edit4Change(Sender: TObject);
begin
masht:=StrToFloat(Edit4.text)/10;
refresh;
end;
procedure TForm1.Edit5Change(Sender: TObject);
var
c : integer;
begin
try
c:=StrToInt(Edit5.text);
except
Edit5.text:='1';
end;
end;
procedure TForm1.Edit6Change(Sender: TObject);
var
c : real;
begin
try
c:=StrToFloat(Edit6.text);
except
Edit6.text:='1,0';
end;
end;
end.
Приложение Б
Тест 1:
Найдём максимум функции f(x,y)=(exp(x)+exp(y))/(exp(x^2)+exp(y^2))
Простой градиентный метод
программный изделие технический средство
Метод наискорейшего спуска
Тест 2:
Найдём максимум функции f(x,y)=sin(x0)*sin(x0)/(sin(y0)*sin(y0)+1)
Простой градиентный метод
Метод наискорейшего спуска
Тест 3:
Найдём максимум функции f(x,y)= sin(x0)*cos(y0*y0)
Простой градиентный метод
Метод наискорейшего спуска
При изменении начальных точек, может меняться и положение максимума
