# Shif factors in X and y directions

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Raj Raj on 29 Sep 2014
Commented: Raj Raj on 1 Oct 2014
Hi all, I have to find the x and y shift factor of the curves. I started as follows however coudnt know how to proceed further. Here is the code objective. Let me have two data sets {t1, E1} and {t2, E2} and so on. Lets consider only two data sets for time being.
where
E1'
ans =
-1.6817 -1.6806 -1.6796 -1.6788 -1.6775 -1.6766 -1.6758 -1.6751 -1.6748 -1.6737 -1.6731
>> t1'
ans =
-0.7782 -0.9823 -1.1761 -1.3802 -1.5775 -1.7782 -1.9823 -2.1761 -2.2553 -2.5775 -2.7782
>> E2'
ans =
-1.6820 -1.6811 -1.6803 -1.6795 -1.6785 -1.6777 -1.6769 -1.6762 -1.6759 -1.6749 -1.6742
>> t2'
ans =
-0.7782 -0.9823 -1.1761 -1.3802 -1.5775 -1.7782 -1.9823 -2.1761 -2.2553 -2.5775 -2.7782
polynomials were fitted as
p1 =polyfit(t1, E1 , 2); p2 =polyfit(t2, E2 , 2)
I plotted the data as follows for graphical visualization:
plot(t1,E1,'o', t2,E2,'+')
hold on
plot(t1, polyval(p1, t1), t2, polyval(p2, t2) )
Aim is to shift the E2-t2 data in x and y directions to minimize the error such that I can find the shifts in x and y directions. (I have found a similar procedure in this paper, Figure 4: http://www.eng.uc.edu/~beaucag/Classes/Characterization/DMA%20Lab/IF1.1%20Fukushima.pdf)
Please let me know suitable commands to do this. Appreciate your time. Thanks!

Raj Raj on 30 Sep 2014
Stephen Cobeldick on 30 Sep 2014
Do you mean "shift factor" as translation or scaling factor ?
SK on 30 Sep 2014
What is your meaning of "error". Is it sum of squares of differences in the y values?
I notice that t1 and t2 have the same starting and ending point. So if we use the above definition, no x-shift can be done, only y shift.
Also do you want to just shift or rescale each graph non-linearly along the x-axis? Need more details.

Stephen Cobeldick on 30 Sep 2014
Edited: Stephen Cobeldick on 30 Sep 2014
Sounds like homework.
Assuming that the curves are not rotated, repeated, mirrored, dilated, nor sheared, and match for some unique combination of x and y offsets, then this should be do-able.
Some hints:
• define functions that calculate the residual distance between two vectors, with x and y shift factors as variables.
• create vectors for both the x and y shift, containing the range that you would like to consider.
• apply the functions to each combination of x and y offsets...
• find the minimum.
You could also use an optimization function , such as fminbnd.

Raj Raj on 1 Oct 2014
Edited: Raj Raj on 1 Oct 2014
Hi Stephen and SK,
First of all thanks for your attention.
Actually its not a homework. Its a program to process my experimental data. Though its not a major part of my work, I just stuck up at this stage for more than a week. Here is my approach.
y2sampledInx1 = @(c) interp1(c(1)+x2,y2,x1,'cubic', 'extrap');
err = @(c) sum((c(2)+y2sampledInx1(c)-y1).^2);
x0=[10; 10];
%Here I tried three solvers. But all the three solutions are depending highly on the initial guess values i.e. x0. This is the big issue. a
coeffs = fminunc(err,x0)
coeffs = lsqnonlin(err,x0)
coeffs = fminsearch(err,x0)
Hope to hear your inputs. Thanks!
p.s. Is there any way to avoid the sensitivity of the x0 on the final solution.

#### 1 Comment

Raj Raj on 1 Oct 2014
Able to solve the global minimum using
gs = GlobalSearch;
[coeffs,f] = run(gs,problem)
Cheers to all