How to function a sum

2013 2 23
2 个回答
3 次查看（30 天）

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Hello. I need to create a function, say Req, that is made by summing a function defined by:
function R = resist(T)
R = rand_R0(100,1000).*exp((rand_T0(12,17)./T).^(1/4));
and then
Req = 1./(1./resist(T)+1./resist(T)+...)
How can I do this recursively? I need to sum 1000 terms. Actually I need to plot Req versus T.
Thank you in advance.

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Walter Roberson
Walter Roberson 2013-2-23
For sort, let us write resist(T) as x. Then it looks like your Req equation is
1 / (1/x + 1/x + 1/x + ...)
Is that correct? Or did you intend
1 / (1/x1 + 1/x2 + 1/x3 + ... )
or did you intend
1 / (1 / (x + 1 / (x + 1 / (x + 1 / (x + ...
?
Andre Luis
Andre Luis 2013-2-24
The correct expression is the first one.
1 / (1/x + 1/x + 1/x + ...)
Walter Roberson
Walter Roberson 2013-2-24
Why bother doing it recursively? If all of the resist(T) are the same, adding N of 1/resist(T) will give N/resist(T) and then 1 / that will give resist(T) / N, with no calculation needed.
Andre Luis
Andre Luis 2013-2-24
Oh, I'm sorry! I made a mistake. Functions resist(T) are not the same. Functions rand_R0 and rand_T0 make then different. So Req is made by different terms: Req = 1/(1/x1+1/x2+...).
Walter Roberson
Walter Roberson 2013-2-24
Is each of the calls to resist returning one value or a vector or an array?
If it is returning one value, could rand_R0 and rand_T0 be extended to make them vectorized, to return a number of values at once?
Andre Luis
Andre Luis 2013-2-24
Functions rand_R0(a,b) and rand_T0(c,d) return one value between (a,b) and (c,d). Yes, it could be extended to return a number of values. But how could this help me?
Walter Roberson
Walter Roberson 2013-2-24
If you had it return the 1000 then you would just vectorize everything.
I have not figured out yet why you think recursion would be a good idea for this code.
Andre Luis
Andre Luis 2013-2-24
Walter, I really appreciate your help. Like I said in the comment below, I'm trying to write a function Req that is made by summing the function R which is function of T (so Req is also function of T). It is a problem of parallel resistor and they depend on T (temperature). My functions are
function R = resist(T)
R = rand_R0(100,1000).*exp((rand_T0(12,17)./T).^(1/4));
and
function R0 = rand_R0(R01,R02)
RR0 = R01 + (R02-R01).*rand(1);
R0 = ceil(RR0);
(the same for T0)
And then, plot Req(T) versus T. Do you have any idea how vectorize it?

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回答（2 个）

Muthu Annamalai
Muthu Annamalai 2013-2-23
编辑：Muthu Annamalai 2013-2-23

0 个投票

You can try something like,
function val = Req( fhandle, arg, N )
val = 1;
for itr = N:-1:1 %build from smallest value term upwards to term 1.
val = fhandle(arg,itr) + 1/val;
end
end
While a recursive solution would work most of the times, since MATLAB has a limited stack size, and doesn't convert a tail-recursive call to an iterative solution, you want to write out the iteration explicitly.

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Andre Luis
Andre Luis 2013-2-24
Sorry, but what is fhandle? My resist function depends only on T.

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Youssef Khmou
Youssef Khmou 2013-2-24

0 个投票

hi Andre,
are you trying to write a program that sums Parallel resistors , well you did nt define the whole parameters such rand_R0 and rand_T0 ,
You can use one single function with nested Req function in :
try :
%-----------------------------------------------------------
function Req=Sum_resistors(N)
for T=1:N
Req(T) =1./(1./resist(T));
end
T=1:N;
figure, plot(T,Req), title(' Your funcrion : Resistors vs some Physical param')
function R = resist(T)
R = rand(1).*exp((rand(1)./T).^(1/4));
return
%--------------------------------------------------------------------
I adjusted Rand_R0 and Rand_To so as Req returns a scalar .
You said that you want plot Req vs T, summing wil only return a scalar, i suggest to use cumulative summation:
>>R =@(T) rand(1).*exp((rand(1)./T).^(1/4));
>>plot(cumsum(Req(1:1000)))
>>plot(Req(1:1000))

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Andre Luis
Andre Luis 2013-2-24
Hi Youssef, thanks for your help.
Sorry, I forgot to say that rand_R0(a,b) and rand_T0(c,d) are functions that return a number between the arguments (a,b) and (c,d).
I tried to use cumsum but I don't know if it gives the result that I'm looking for.
Youssef Khmou
Youssef Khmou 2013-2-24
Andre, ok, So you want verify if the serie converges when N->Inf ? i think cumsum will not show you the convergence, lets try a simple prototype :
>>R=50; %50Ohm with identical elements then :
>>Req=R./(1:1000);
>>plot(Req) % It plots directly how the total resistance is when we %increment them 1:N : Decreasing function.
>>figure,plot(cumsum(Req)) % Log like function
which one seems logical to your system ?
Andre Luis
Andre Luis 2013-2-24
Actually, what I'm trying to do is write a function Req that is made by summing the function R which is function of T (so Req is also function of T). Then plot Req versus T.

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Andre Luis
Andre Luis
2013-2-23

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