Hello All,

My name is Kostas and I am new in the forum. I am new in Matlab as well. I am trying to get some advice in executing a code that I found on a book "Numerical Methods using Matlab". The code is as follows:

function [xo,fo] = opt_steep(f,x0,TolX,TolFun,alpha0,MaxIter)
% minimize the function f by the steepest descent method.
%input: f = ftn to be given as a string ’f’
% x0 = the initial guess of the solution
%output: x0 = the minimum point reached
% f0 = f(x(0))
if nargin < 6, MaxIter = 100; end %maximum # of iteration
if nargin < 5, alpha0 = 10; end %initial step size
if nargin < 4, TolFun = 1e-8; end %|f(x)| < TolFun wanted
if nargin < 3, TolX = 1e-6; end %|x(k)- x(k - 1)|<TolX wanted
x = x0; fx0 = feval(f,x0); fx = fx0;
alpha = alpha0; kmax1 = 25;
warning = 0; %the # of vain wanderings to find the optimum step size
for k = 1: MaxIter
g = grad(f,x); g = g/norm(g); %gradient as a row vector
alpha = alpha*2; %for trial move in negative gradient direction
fx1 = feval(f,x - alpha*2*g);
for k1 = 1:kmax1 %find the optimum step size(alpha) by line search
fx2 = fx1; fx1 = feval(f,x-alpha*g);
if fx0 > fx1+TolFun & fx1 < fx2 - TolFun %fx0 > fx1 < fx2
den = 4*fx1 - 2*fx0 - 2*fx2; num = den - fx0 + fx2; %Eq.(7.1.5)
alpha = alpha*num/den;
x = x - alpha*g; fx = feval(f,x); %Eq.(7.1.9)
break;
else alpha = alpha/2;
end
end
if k1 >= kmax1, warning = warning + 1; %failed to find optimum step size
else warning = 0;
end
if warning >= 2|(norm(x - x0) < TolX&abs(fx - fx0) < TolFun), break; end
x0 = x; fx0 = fx;
end
xo = x; fo = fx;
if k == MaxIter, fprintf(’Just best in %d iterations’,MaxIter), end

%nm714
f713 = inline('x(1)*(x(1) - 4 - x(2)) + x(2)*(x(2)- 1)','x');
x0 = [0 0], TolX = 1e-4; TolFun = 1e-9; alpha0 = 1; MaxIter = 100;
[xo,fo] = opt_steep(f713,x0,TolX,TolFun,alpha0,MaxIter)

The problem occurs on line 15 where the grad is not defined as the error message says in matlab. I would appreciate your help, if somebody more familiar can spot out where the problem is.

Many Thanks

BRs

Kostas

%calculate gradient of the function
function gradf=grad(f,x)
lengthx=length(x); % size of input vector
gradf=zeros(size(x)); % intialize the result
for k=1:lengthx % run all over the parameters and calculate the derivative
if x(k)==0 dx=0.001;
else dx=abs(x(k)/100); % take the step size as 1% of the value
end;
diffvect=zeros(size(x)); %zero all the variables in the addition vector except at k
diffvect(k)=dx;
% calculate derivative at k direction
gradf(k)=(feval(f,x+diffvect)-feval(f,x))/dx;
end;
end

As the ist author of 'Applied Numerical Methods Using MATLAB', I apologize for having left out the file 'grad.m'.
It contains the following statements:

function g= grad(f,x,h)
%grad.m to get the gradient of f(x) at x.
if nargin<3, h=.00001; end
h2= 2*h; N= length(x);
I= eye(N);
for n=1:N
g(n)= (feval(f,x+I(n,:)*h)-feval(f,x-I(n,:)*h))/h2;
end

Thanks.

What is behind the smilies in line g(n)= (feval(f,x+I(n............. ???
Can you rewrite this line WITHOUT smilies ???... Cuz it makes no sense replacing the smilies with : )

What is behind the smilies...

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function g= grad(f,x,h)
%grad.m to get the gradient of f(x) at x.
if nargin<3, h=.00001; end
h2= 2*h; N= length(x);
I= eye(N);
for n=1:N
g(n)= (feval(f,x+I(n,:)*h)-feval(f,x-I(n,:)*h))/h2;
end


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Cuz it makes no sense replacing the smilies with : )Actually, it does make sense to Matlab, I'm thinking. I mean, in general, m(n,:) designates the nth row of matrix m, doesn't it?

Regards,

Dave

Thanks Dave ! ;)