Fraser Suzuki Function written in MATLAB

I am trying to write a piece of code which will simulate a Fraser Suzuki function, which is an asymmetrically skewed Gaussian. There are a multitude of papers citing the equation, but I cannot seem to get it working in MATLAB.

I've attached an image of the function above. In the paper they also perform a parameter test on the function to make sure they get the desired peak shape. An example I've attached below.

When I write this function myself the

T-p/w

section of the code goes negative, causing the log function to give imaginary values. As this function has been cited multiple times in literature it seems that it's not the function itself that's wrong but my interpenetration in the code. I've attached the code I've been using the simulate the function.

%%FSuzuki
T = linspace(450,700,1000);
h = 0.005;
p = 600;
w = 40;
s = -0.3;
arg1 = log(2*s*T-p/w+1).^2;
y = h*exp(-log(2)/(s^2)*arg1);

Any help would be greatly appreciated.

[Joseph Cheng]

well first of all your matrix operation for arg1 is off. it should be 2*s*(T-p)/w+1. which doesn't solve the issue but should be corrected.

Answer 1

[Joseph Cheng]

Alright, found the paper you mentioned and plotted it in different programs. So... What is happening is that the authors of the paper are ignoring the complex solutions for their Fraser Susuki equation. such that if i re-write your code to be

T = linspace(450,700,1000);
h = [0.005 0.0075 0.01 0.0125 0.015]';
figure(1),hold on
for ind = 1:numel(h)
    p = 600;
    w = 40;
    s = -.3;
    lntpw = log(1+2*s*(T-p)/w).^2;
    FS = h(ind)*exp(-log(2)/s^2*lntpw);
    FS(FS~=real(FS))=0;
    plot(T,FS)
end

you get the same curves that they have in the paper.

[Walter Roberson]

Slightly more favoured would be the test

FS(imag(FS)~=0) = 0;

[Joseph Cheng]

is there much difference? I like your suggestion better but is it due to computation or possible cases where it would fail?

[Christian Reece]

Thank you very much, this works perfectly. So it was simply just ignoring the complex solutions for the equation?

[Joseph Cheng]

that and correcting your order of operations to actually match the equation in the paper.

[Blanca Castells]

Hello,

I found this quite interesting, so I've tryied do deconvolute my curve using FS. However, when using curve fitting tool box (using custom equation of FS with 3 terms), I couldn't avoid the complex numbers. Any idea how to proceed?

Thanks

[Blanca Castells]

My code right now is:

ft=fittype('h1*exp((-log(2)*(log(1 + (2*s1*(x - p1)/w1)))/s1)^2) + h2*exp((-log(2)*(log(1 + (2*s2*(x - p2)/w2)))/s2)^2) + h3*exp((-log(2)*(log(1 + (2*s3*(x - p3)/w3)))/s3)^2);');
opts = fitoptions( 'Method', 'NonlinearLeastSquares' );
opts.Algorithm = 'Levenberg-Marquardt';
opts.Display = 'Off';
opts.Lower = [0 0 0 100 100 100 0 0 0 0 0 0];
opts.Robust = 'Bisquare';
opts.StartPoint = [0.038 252 0.2 43 0.031 340 0.55 103 0.023 360 0.36 89];
opts.Upper = [0.15 0.15 0.15 700 700 700 1 1 1 700 700 700];

[gfit,gof]=fit(T,alpha,ft,opts);

[Rocio Bayon Cabeza]

Hi Blanca!

are you still working on this subject?

I think I can help you with the problem of complex numbers

please let me know

Rocio Bayon

[Chuan Ma]

Hello,

Racio，

Can you tell me how to avoid the complex numbers?

Thank you.

Chuan

[Junmeng Cai]

Dear Joseph Cheng, thank you very much!

Great!