optimization for minimum difference between 2 graphs

I have two graphs: graph 1 and grph 2

I want to find a,b such that: normalized graph1=graph 1 * a+b.

a and b should be chosen to give the minimum difference between normalized graph 1 and graph 2.

Thank you in advance for your help.

Answer 1

[ag]

Hi Kinda,

To find the optimal values of ( a ) and ( b ) such that the normalized version of graph 1 (i.e., graph1 * a + b) minimizes the difference with graph 2, you can use a least squares approach. This is essentially a linear regression problem where you aim to fit graph1 to graph2.

Below is a basic illustration of how you can achieve it:

graph1 = [1 2 0; 0 4 3]; % Your graph 1 data
graph2 = [8;18]; % Your graph 2 data

% Set up the design matrix for linear regression
X = [graph1, ones(size(graph1))];

% Solve the linear regression problem using the backslash operator
coefficients = X \ graph2;

% Extract the coefficients a and b
a = coefficients(1);
b = coefficients(2);

% Calculate the normalized graph1
normalized_graph1 = graph1 * a + b;

Please ensure to modify the code as per your requirements.

For more details, please refer to the following MathWorks documentation:

• mldivide - https://www.mathworks.com/help/matlab/ref/double.mldivide.html#:~:text=computed%20result%20unreliable.-,Least%2DSquares%20Solution%20of%20Underdetermined%20System,-Linear%20System%20with

Hope this helps!