How can I do sigma over functions

Hi all,

Suppose if I know y(j) and z(j) (suppose j varies from 1 to 100) and there are two functions : which vary with x,y,z and with the value of j

 f1(x,y,z,y1(j),z1(j)),f2(x,y,z,y1(j),z1(j)). 
And if f3(x,y,z,y1(j),z1(j))=f1*f2.

How can I do do summation of f3 over j?

I should be left with a function of x,y,z after summation over j. Can some one please tell me in a sequential way?

Thank you,

Srinath

Answer 1

[Matt J]

If your functions are vectorized and written to return column vectors, then it should be straightforward. For example,

 yj=rand(100,1); %fake y(j)
 zj=rand(100,1); %fake z(j)

 f1=@(x,y,z) x+y+z+yj+zj;
 f2=@(x,y,z) 2*(x+y+z).^2+yj.^2+zj.^2;

then

 f3=@(x,y,z)  sum(f1(x,y,z).*f2(x,y,z));

and you can then do things like,

     >> f3(1,2,1)

    ans =

       1.6280e+04

[srinath]

Thanks for your reply. It worked for most of my work. But there is some problem. Actually, I have three such f3's and I will have to solve for x,y,z using the three expressions(like f3).

I know that there is 'solve' command. But it is not working here. I used it like this. Please correct me if you can

sum1,sum2,sum3 are three summations.
[x,y,z]=solve(sum1,sum2,sum3,x,y,z);

 I am getting an error like this

Error using internal.matlab.Message In 'symbolic:solve:errmsg1', data type supplied is incorrect for parameter {1}.

Error in message (line 11) msgObj = internal.matlab.Message(msgID,varargin{:});

Error in solve>processString (line 337) error(message('symbolic:solve:errmsg1', v))

Error in solve>getEqns (line 267) eqns = processString(eqns, v, vc);

Error in solve (line 150) [eqns,vars,options] = getEqns(varargin{:});

Error in expression (line 34) [y1 z1 theta]=solve(sum1,sum2,sum3);

[Matt J]

You should probably be using FSOLVE instead

 F=@(p) [sum1(p(1),p(2),p(3));...
         sum2(p(1),p(2),p(3));...
         sum3(p(1),p(2),p(3))];

 fsolve(F,initialpoint);

[srinath]

I didn't get what are those p(1),p(2),p(3). Also,what should I keep for the initial point. Because the solution that I finally get will depend on initial point right? Can you just elaborate that? Thanks again.

[Matt J]

p is a vector whose components p(1),p(2), and p(3) are your 3 unknowns. As you've been saying throughout, the quantities sum1, sum2, and sum3 depend on 3 unknown variables, so sum1(p(1), p(2), p(3)) is a way to express that in terms of a single unknown vector, p.

Yes, the solution could depend on the initial point if you have multiple solutions. In that case, you have to choose the initial guess based on approximate knowledge of where the particular solution you're looking for might lie. But that's always the burden in equation solving, when a symbolic solution of the equations is unavailable.