Matrix compare and unkonw relationships to find

I have 2 Matrix, for example

Matrix A ={a1 b1 c1; a2 b2 c2; a3 b3 c3}

Matrix B={x1 y1 z1 m1 n1; x2 y2 z2 m2 n2; x3 y3 z3 m3 n3 }

a1 b1 c1 is the result from FEM-Simulation-1, and x1 y1 z1 m1 n1 is the Geometrie-parameter from Simulation-Objekt-1

a2 b2 c2; x2 y2 z2 m2 n2 and the other number in Matrix means the same thing from Simulation-2 and -3.

there must some relationships zwischen Matrix A and B, linear or unlinear, but i don't yet.

How kann i use Matlab this unkonw relationships to find?

Or is it possible to use Matlab this unkonw relationships to find?

which function should i use?

Thankyou very very much for your time!

Answer 1

[Sourabh Kondapaka]

Hi,

You can use “corr()” function to find the relationship between columns of 2 matrices. Here, as you want to find the correlation between rows, you can transpose both the matrices.

Consider two random matrices of sizes 3x3 and 3x5 respectively

matrix_A = rand(3,3);
matrix_B = rand(3,5);

correlationMatrix = corr(matrix_A', matrix_B' );

[Zuyu An]

first of all, thankyou very much for your time.

and the function corr() show me possibility if the correlation between each columns exist, but how kann i konw what is this correlation ?

[Sourabh Kondapaka]

Hi,

corr(matrix_A, matrix_B) function returns a matrix of the pairwise linear or rank correlation coefficient between each pair of columns in the input matrices matrix_A and matrix_B.

You can check for different types of correlation functions for the "corr()" function here.

[Zuyu An]

thankyou very much, it is helpful!

Answer 2

[Bruno Luong]

Use regression methods. If you have a linear/affine model, then use linear algebra. If you have "kind" non-linear, use polynomial, spline, fraction, nurbs regressions, if you have no clue on non-linearity but know the relationship is continuous/C1 relationship use learning technique, neuronal netwroks, deeplearning etc... If you have discontinuous non-linearity (hash code, encryption), you might be in big trouble or wait until a real quatum computer available...

[Zuyu An]

first of all, thankyou very much for your time.

i think it is non-linearity but continuous, how kann i use learning technique, neuronal netwroks, deeplearning ? how does it work on Matlab?