Shif factors in X and y directions

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]

Any inputs please ?

[Stephen23]

Do you mean "shift factor" as translation or scaling factor ?

[SK]

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.

Answer 1

[Stephen23]

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.

Answer 2

[Raj Raj]

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.

[Raj Raj]

Able to solve the global minimum using

gs = GlobalSearch;
[coeffs,f] = run(gs,problem)

Cheers to all