How to create a 2x2 matrix out of 4 matrices?

I have 3 matrices, each of size 1x100000 and the fourth element is a single numerical value. I am trying to make a square matrix 'Z' of size 2x2 which shall contain each of these 4 elements and do some operations on its inverse.

Could you please tell how I can do that?

[Sean de Wolski]

How can a matrix with 4*1000000 elements be size 2x2?

Please be clear and provide a small example.

[Jan]

How do you want to reduce the number of elements? Which of the resulting 400.000 elements should be used to create the wanted 4 elements??

[Santosh Kasula]

Ananth, moving your comments here:

Ok, I want the final matrix of size 2x2 to contain 4 elements, each with 1x100000 values. Then, take its inverse. Could I do that by padding the 4th element with zeros to make the dimensions equal to the other 3 sub-matrices? The context is impedance calculations. The 100000 values are those multiplied by frequency points.

[Santosh Kasula]

the cyclist says:

It's still not 100% clear to me what you want. Do you expect, in effect, to be taking the inverse of 100,000 2x2 matrices?

[Santosh Kasula]

Ananth says:

I was trying to comment but instead pressed 'accept'. Cyclist, you are right. I am trying to take the inverse of the 100,000 2x2 matricces. But, the problem is inverses can be taken only on square matrices. I am unsure how to tackle this. Any suggestions?

Answer 1

[the cyclist]

After you create z as above, then a simple loop can calculate the inverse over the third dimension:

>> invz = zeros(2,2,100000);
>> for zi = 1:100000,
>>     invz(:,:,zi)=inv(z(:,:,zi));
>> end

Don't neglect the preallocation of memory in that first line.

I feel like there may be a may to do all the inverse in one fell swoop (with accumarray?), but it's not coming to me. The loop above only takes a couple seconds on my machine.

[Ananth]

That hit the spot. Thank you Cyclist!!

[Michelle Hirsch]

Ananth - could you please mark this answer as accepted, so that other MATLAB Answers readers will know that this is a solved problem? Thanks!

Answer 2

[the cyclist]

It's not entirely clear to me what you want the output matrix to look like, so this is a guess. Using Paulo's notation for your input arrays, then

>> z = reshape([mat1; mat2; mat3; mat4], [2 2 100000]);

will give you a 2x2x100000 array where each "slice" is a 2x2, with one element from each of the input matrices. Is that what you want?

Answer 3

[James Tursa]

You might also look at Bruno Luong's FEX submission for this particular problem:

http://www.mathworks.com/matlabcentral/fileexchange/27762-small-size-linear-solver