Does lsqlin give different solution if the rows of C matrix and d matrix are changed accordingly?

I have two curves(or datasets) which are to be fitted of the form, C1.x=d1 and C2.x=d2, where x is the solution which should satisfy both equations. Here C1 has several subsets of data, for example C1=[c11; c12; c13...] with an associated fit data d1=[d11; d12; d13;..]. Similarly C2 has several subsets of data, for example C2=[c21; c22; c23...] with an associated fit data d2=[d21; d22; d23;..]. So I had clubbed both C1 and C2 into a single matrix and d1 and d2 into single matrix, so that I have the form C=[C1;C2] =[c11;c12;c13;c21;c22;c23] and d=[d1;d2]=[d11;d12;d13;d21;d22;d23]. Then upon solving using lsqlin, I get a solution 'x'.

Alternatively, upon merging the C1 and C2 in different manner, say C=[c11;c21;c12;c22;c13;c23] and correspondingly reordering d as d=[d11;d21;d12;d22;d13;d23] and then solving using lsqlin, I get a solution 'x'.

The solution 'x' for both the cases seemed to be different for my problem in hand. So I tried it with a small random dataset, but here the solution 'x' was same in both cases.

Now I in confusion, if changing the rows of the C matrix and correspondingly changing the d matrix, yield the same solution or not?

Or, can't lsqlin be used for curve fitting multiple independent datasets?

Thanks in advance.

Answer 1

[Torsten]

I don't understand your notation, but here is an example:

If

C1=[1 6
    4 8];
d1=[4 
    7];
C2=[9 2
    3 6
    8 1]
d2=[1
    0
    6]

you have to define C and d as

C=[1 6
   4 8
   9 2
   3 6
   8 1]
d=[4 
   7
   1
   0
   6]

Best wishes

Torsten.

[Thanigaivel Raja T]

Thank you Torsten.

My question with regard to your example is

Does changing rows in C and correspondingly in d, for instance C=[1 6; 9 2; 4 8; 3 6; 8 1]; with d=[4; 1; 7; 0; 6] yield the same solution?

[Torsten]

It is possible, but unlikely that you get different solutions.

You should check whether norm(C*x-d) changes. If not, everything is fine. If it changes, you've made a mistake in the setup.

Best wishes

Torsten.

[Thanigaivel Raja T]

yup...upon changing rows in C and correspondingly in d, the solution x is the same(whatsoever).. I had made mistake in concatenation of matrices forming 'd', so got messed up.

Thanks for your answer, I needed an assertion from someone before I could over check my tedious code for any errors!