Help with For loop during least square fit

Hello,

I want to linearize my stress-number of cycles plot.

I have my StressAmp and FatigueLife-vectors. The thing I want help with my for-loop.

I want to calculate BTak which is

The sum of when Xi and Yi goes from 1 to the maximum of X and Y.

 sum of(Xi-XMean)*(Yi-YMean) / (sum of (Xi-XMean)^2)

It looks like my for loop does not sum BTak, it only gives me the value for each i. What can I do to have each calculated BTak in a vector and add each value?

I know that i have more things to do after calculating BTak, but I am stuck at this Point.

StressAmp=[200 200 200 200 175 175 175 175 150 150 150 150];
FatigueLife=[9.8E3 1.2E4 4.1E4 2.4E4 7.7E6 5.6E5 4.0E6 5.2E6 2.5E7 9E7 4.2E7 3E7];
%Log
X=log10(StressAmp);
Y=log10(FatigueLife);
%Sort X and Y
[StressAmpSortX,i]=sort(X)
FatigueLifeSortY=(Y(i))
%Mean value X and Y
XMean=mean(X);
YMean=mean(Y);
figure
semilogx(FatigueLife,StressAmp,'*');
ylim([100 250])
grid on
for j=[FatigueLifeSortY]
  for k=[StressAmpSortX]
    BTak=((k-XMean)*(j-YMean))/((k-XMean)^2)
  end
end

Thank you.

Answer 1

[dpb]

>> S=[200 200 200 200 175 175 175 175 150 150 150 150];
F=[9.8E3 1.2E4 4.1E4 2.4E4 7.7E6 5.6E5 4.0E6 5.2E6 2.5E7 9E7 4.2E7 3E7];
>> S=fliplr(S);F=fliplr(F);  % same result as sort given S is already ordered decreasing
>> s=(1:N)-mean(log10(S));   % standardized values
>> f=(1:N)-mean(log10(F));
>> BTak=dot(s,f)/dot(s,s)
BTak =
  0.4499
>>

To do it with an explicit sum, you need to use a single loop over 1:length(S) and step thru each array and use a subscript in the LHS assignment. But, Matlab's strength is it's builtin functions that do many of these things innately. Of course, remembering the definition of a dot product is a start plus learning that there is a builtin in function for it takes some time or using the help facilities...Matlab has so much available that it can take a while... :)

[Daniel]

I got s and f to be of different number of columns?... I tried this instead

      for i=1:length(StressAmpSortX)
    BTak(i)=((StressAmpSortX(i)-XMean)*(FatigueLifeSortY(i)-YMean))/((StressAmpSortX(i)-XMean)^2)
      end
BTak=sum(Btak)

and it seems to what I want.

I agree, there are many builtin fuctions, I found out that polyfit just did all my work... Thanks

[dpb]

OK, that's a different definition....

NB: that if

SXmean=StressAmpSortX(i)-XMean;
FXmean=FatigueLifeSortY(i)-YMean;

then the summed quantity can be written as

SXmean*FXmean/FXmean^2

which is simply

SXmean/FXmean

Or using shorthand of lowercase s and f to reduce typing at the command line, I get

>> s=StressAmpSortX-XMean;
>> f=FatigueLifeSortY-YMean;
>> dot(1./s,f)
ans =
275.1711
>> sum(BTak)
ans =
275.1711
>>

Again, no loops needed... :)