Getting x value for a given y value from a fitted model

Here is my codes:

c=3*10^8; % speed of light
h=6.62606957*10.^-34; %  Planck constant 
k=1.3806488*10.^-23; %   Boltzmann constant
T=(400:1:1000); % Temperatures in Kelvin
Wavelength=(0.925:0.001:0.975).*1e-6; %Wavelength from 0.925 to 0.975um

for i=1:601

I1(i,:)=(2*h*c*c)./((Wavelength.^5).*((exp((h.*c)./(k.*T(i).*Wavelength))-1)));
z(i) = trapz(Wavelength, I1(i,:));
end

Then the T and z are used to get a fitted curve

I know it is easy to get z with z=fever(fittedmodel,T)

Is there any easy way to get T value from z value?

I tried to use z as xData and T as yData, but the fitting results are terrible. And I know I can use vpasolve to calculate z, but the errors in results is large because the coefficients is a range.

So, what can I do?

Answer 1

[Star Strider]

I am not certain that the curve fit is at all relevant to your finding a ‘T’ for a specific ‘z’.

Try this:

c=3*10^8; % speed of light
h=6.62606957*10.^-34; %  Planck constant
k=1.3806488*10.^-23; %   Boltzmann constant
T=(400:1:1000); % Temperatures in Kelvin
Wavelength=(0.925:0.001:0.975).*1e-6; %Wavelength from 0.925 to 0.975um
for i=1:601
    I1(i,:)=(2*h*c*c)./((Wavelength.^5).*((exp((h.*c)./(k.*T(i).*Wavelength))-1)));
    z(i) = trapz(Wavelength, I1(i,:));
end

zv = 2/3;                                           % Desired ‘z’ Value
Tv = interp1(z, T, zv, 'linear');                   % Associated ‘T’ Value

figure
plot(T, z)
hold on
plot(Tv, zv, '+r')
hold off
grid
xlabel('T')
ylabel('z')

Note that because ‘z’ is monotonically increasing with linearly increasing ‘T’, this approach is possible here. That is not allways the situation, so this approach would not be universally appropriate (for example if ‘z’ was periodic, parabolic, or something similar).

Experiment to get the result you want.

[Wei Han]

Thank you vey much!

[Star Strider]

As always, my pleasure!