Hello everyone, I am facing one problem,

I have 3 different non linear data. Let's say x,y and z.for different values of Z I have different data set of x and y. If I fix the value of Z I am able to find the relation between x and y, but if I change the value of Z that relation won't work, I need to find relation between x,y and z independently. Can anyone please help! Thank you in advance.

for z=500 I have x = 1145 to 1240 with the gap of 1,y = (17.75,16.2,15.1,14.25,13.45.... respectively

for z=400, x values remains the same 1145-1240 y values differs.

I need to find a relation between x,y and z independently. in which y = fun(x,z). thank you.

Answer 1

[Image Analyst]

Try the attached code where I fit an exponential growth curve to each curve, which belongs to each x value. It uses fitnlm() of the Statistics and Machine Learning Toolbox.

[Aakash Nanda]

Is it possible to get only one equation for this? As we are getting different coefficients, there will be different equations.

Answer 2

[Image Analyst]

For each z, get or compute the x and y arrays. Then fit a model for y using the x array, and the scalar value of z for those arrays. In pseudocode:

z = [......] % Some list of z values
for k = 1 : length(z)
        thisZ = z(k);
        xVector = ...% Whatever you need to do to get the x vector for this z
        yVector = ....% Whatever you need to do to get the y vector for this z
        % Now find some model passing in the xVector and yVector and this z value.
        yourModel = FitModel(xVector, yVector, thisZ);
        % Now do something with the model, like apply it, save it, plot it, or whatever.....
end

I have no idea what the model for each pair of x and y vectors might be. Would they all be the same, like fitting a line or parabola? Would they be different, like some might be a line and others might need an exponential decay? Would it be empirical so you don't have model parameters, but just a smoothed/fitted y vector as output, like as if you applied smooth() or sgolayfilt() to the raw data? We have no idea since you didn't share that information with us.

[Aakash Nanda]

Thank you Image Analyst. Here is the data. You might get idea from this, what I wanted to find.

for x = 1145

y = [200 300 400 500]; I have z = [ 3.76 5.27 7.88 17.75]

for x = 1155

y = [200 300 400 500]; I have z = [ 3.4055 5.64 6.43 10.3]

for x = 1165

y = [200 300 400 500 600]; I have z = [3.1 4.115 5.48 7.78 14.6]

for x =1175

y = [300 400 500 600 700]; I have z = [3.71 4.79 6.37 9.45 28]

for x =1185

y = [300 400 500 600 700]; I have z = [3.37 4.26 5.44 7.33 11.8]

for x =1195

y = [300 400 500 600 700 800]; I have z = [3.085 3.833 4.77 6.1 8.42 15.5]

for x =1205

y = [400 500 600 700 800 900]; I have z = [3.485 4.25 5.259 6.77 9.7 11.25]

for x =1215

y = [400 500 600 700 800 900]; I have z = [3.191 3.82 4.638 5.72 7.46 8.2]

for x =1225

y = [500 600 700 800 900]; I have z = [3.4955 4.155 4.99 6.18 8.2]

for x =1235

y = [500 600 700 800 900]; I have z = [3.21 3.761 4.435 5.325 6.63]

This data I have. I need to find now z=function(x,y) so I can directly find the value of z from the values of x and y, because x and y are known values.

[Image Analyst]

Why do the first two have only 4 points, and the others have 5 or 6 points? Why aren't they all the same size?

Attached is what I have so far.

I didn't go further because I don't think you have enough points in there to do meaninful fits. Attach more data.

[Aakash Nanda]

For first two point the value is not possible that's why. Like for the big value of x , z is not possible.