#1




steepest descent
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 = 1e8; end %f(x) < TolFun wanted if nargin < 3, TolX = 1e6; 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,xalpha*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 = 1e4; TolFun = 1e9; 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 
#2




Here is the function that you wanted I wrote it bymyself
%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 
#3




About the subroutine 'grad.m'
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,xI(n,*h))/h2; end Thanks. 
#4




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 : ) Last edited by cloyst3r; 08012008 at 03:52 PM. 
#5




For people trying to read code that was posted without code tags:
Pretend you are going to respond to the post (click the Quote button at the lower right). When the response edit window opens, copy/paste the problematic lines to your text editor. Then, of course, unless you are really going to respond to the post, you click the Cancel button. Here's what was in that post: Code:
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,xI(n,:)*h))/h2; end When posting, If you click the Preview Post button before submitting the reply, you can see if you got it right. Quote:
Regards, Dave Last edited by davekw7x; 08022008 at 12:33 PM. 
#6




Thanks Dave !

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