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clc 
clear all 
warning off 
prompt = {'Coeficients if X1=','Coefficients of X2=','Coefficeint of X1X2=','Initial Point='}; 
def    = {'[2 1 0]','[1 -1 0]','2','[0 0]'}; 
a=inputdlg(prompt,'Data',1,def); 
a=char(a); 
[m,n]=size(a); 
x1 = eval(a(1,1:n));x2=eval(a(2,1:n));x1x2=eval(a(3,1:n));X1=eval(a(4,1:n)); 
delf1(1) = polyval(polyder(x1),X1(1)); 
delf1(1) = (delf1(1))+(x1x2*X1(2)); 
delf1(2) = polyval(polyder(x2),X1(1)); 
delf1(2) = (delf1(2))+(x1x2*X1(1)); 
s=-delf1; 
srep(1,1:2)=s; 
   x1new(1)=s(1)^2;x1new(2)=2*X1(1)*s(1);x1new(3) = X1(1)^2; 
   x1new=x1new*x1(1); 
   x1new_(2)=x1(2)*s(1);x1new_(3)=x1(2)*X1(1); 
   x1new = x1new+x1new_; 
   
   x2new(1)=s(2)^2;x2new(2)=2*X1(2)*s(2);x2new(3) = X1(2)^2; 
   x2new=x2new*x2(1); 
   x2new_(2)=x2(2)*s(2);x2new_(3)=x2(2)*X1(2); 
   x2new = x2new+x2new_; 
   x1x2new(1)=s(1)*s(2);x1x2new(2)=X1(1)*s(2)+X1(2)*s(1);x1x2new(3)=X1(1)*X1(2); 
   x1x2new=x1x2*x1x2new; 
df = polyder(x1new+x2new+x1x2new); 
lambda(1) = roots(df); 
X1=X1+lambda(1)*s; 
Xrep(1,1:2)=X1; 
delf1(1) = polyval(polyder(x1),X1(1)); 
delf1(1) = (delf1(1))+(x1x2*X1(2)); 
delf1(2) = polyval(polyder(x2),X1(2)); 
delf1(2) = (delf1(2))+(x1x2*X1(1)); 
if all(X1)== 0 
   fprintf('%d %d is the optimum point',X1(1),X1(2)); 
end 
itrep(1)=1; 
it=2; 
while all(delf1)==1 
   s=-delf1; 
   x1new(1)=s(1)^2;x1new(2)=2*X1(1)*s(1);x1new(3) = X1(1)^2; 
   x1new=x1new*x1(1); 
   x1new_(2)=x1(2)*s(1);x1new_(3)=x1(2)*X1(1); 
   x1new = x1new+x1new_; 
   
   x2new(1)=s(2)^2;x2new(2)=2*X1(2)*s(2);x2new(3) = X1(2)^2; 
   x2new=x2new*x2(1); 
   x2new_(2)=x2(2)*s(2);x2new_(3)=x2(2)*X1(2); 
   x2new = x2new+x2new_; 
   x1x2new(1)=s(1)*s(2);x1x2new(2)=X1(1)*s(2)+X1(2)*s(1);x1x2new(3)=X1(1)*X1(2); 
   x1x2new=x1x2*x1x2new; 
   df = polyder(x1new+x2new+x1x2new); 
   lambda(it) = roots(df); 
   X1=X1+lambda(it)*s; 
   delf1(1) = polyval(polyder(x1),X1(1)); 
delf1(1) = (delf1(1))+(x1x2*X1(2)); 
delf1(2) = polyval(polyder(x2),X1(2)); 
   delf1(2) = (delf1(2))+(x1x2*X1(1)); 
   itrep(it)=it; 
   srep(it,1:2)=s; 
   Xrep(it,1:2)=X1; 
   it=it+1; 
end 
[m,n]=size(itrep); 
matrix=[itrep' srep(1:n,1) srep(1:n,2) Xrep(1:n,1) Xrep(1:n,2)]; 
answer = char(num2str(X1)); 
answer = ['The optimal point is [' answer ']']; 
msgbox(answer,'Solution'); 
disp('    Press Any key to View Detailed Report............'); 
pause 
echo off 
report steep; 
clc