speeding up a gaussian fitting....

This is a function that will output the full width half max of a Gaussian or SuperGaussian. This function works slowly. I was wondering if I can speed it up. This takes 0.3-0.5 seconds to run an individual Gaussian and 294 second to complete the full data set (or about 49 min). This is a little long for what I need to do. Any time cut from this would be amazing! I have a lot of Gaussian that are being looked through to extract the data in the end. PLEASE help out if you know of some solution. Thank you!

Here is the example code of what I have working and the output in the end:

function testing()

 YProjY = [7.3800   19.7800   20.4200   20.8800   20.7400   21.2000   23.1000   21.8600   21.2600   20.1800   20.8000   21.4800   21.8200   21.6000   21.6000   20.5800   20.5200   20.7400   21.3800   21.6000   21.2000 21.4000   21.5400   21.8200   21.9600   22.5600   25.3000   25.9200   25.5000   23.4600   23.2800   23.2600   23.9800   24.3600   23.8600   23.3000   23.0200   24.2200   25.1600   24.1600   25.0800   23.9600 24.3400   23.1800   23.3400   24.3200   25.0000   25.2800   26.4400   26.5600   27.8400   27.0000   27.2200   27.4000   26.6200   26.6200   26.7000   27.6800   27.3600   26.9000   26.9400   26.2200   25.9000  26.4800   27.1600   26.2600   27.1200   28.3600   30.0600   29.1800   28.4800   28.7800   29.5400   29.4400   29.4600   29.9600   31.1600   30.0400   29.3600   28.7800   29.4800   30.3800   31.1000   31.3600  33.1800   34.8400   35.7200   34.7200   32.9600   33.1800   34.3400   35.4600   35.8400   35.0600   35.3600   34.5000   35.4400   34.7200   35.4800   35.4400   37.0600   37.1600   38.5600   39.3800   40.4200  38.4800   38.5400   38.2200   39.0000   38.7800   38.8600   39.0800   40.7600   40.4400   41.2600   39.6600   40.5800   42.2800   44.2400   45.5600   46.3600   44.8400   45.0200   45.0200   45.7000   45.1000   45.7400   45.7800   46.6400   47.0800   47.3400   46.8600   48.9400   48.8200   49.6200   50.1800   52.0000   52.6200   53.5000   51.9200   53.7000   54.5800   56.8400   58.0800   57.9200   57.0000   57.4200   59.6800   59.6600   61.5600   61.9600   63.8600   62.8600   61.2400   62.4200   63.6600   64.2800   64.5600   65.2400   67.6400   66.8400   67.8000   67.6400   68.3200   68.8200   68.4800   68.9200   69.6200   71.4400   72.2800   73.4600   75.1200   76.6800   76.9000   76.4200   77.6400   79.4400   80.3400   80.6200   80.9200   83.1600   84.7200   87.2000   88.3000   89.4600   88.9000   90.3400   91.5600   95.4200  96.7200   97.3200   97.5200   99.4800  101.1400  102.8200  104.4600  106.3400  107.0800  109.0800  110.9600  112.6800  114.1200  116.3400  118.0800  120.5200  120.7400  121.9200  124.4200  128.9200  131.7600  133.8400  134.6400  135.4600  137.1800  139.1600  141.8600  144.6000  147.5800  149.0200  150.6600  151.6800  153.2800  155.2800  157.9000  161.9800  162.7000  163.5400  163.2600  166.2600  168.1200  168.2800  169.4200  171.0200  172.3600  174.0600  175.1200  176.9200  177.6000  178.2200  177.3800  176.4800  176.2400  176.0600  174.8400  175.7000  175.1000  173.2800  170.7800  168.6600  170.3400  170.7600  171.2600  169.7800  168.4200  166.7200  165.3200  163.1400  161.9400  160.9400  157.4200  154.6600  152.8600  150.6800  149.3400  146.0800  143.6200  140.2200  136.1200  132.1600  129.8200  127.8000  125.3600  122.4600 119.8000  117.2400  116.2000  114.3000  111.4400  110.5800  108.0600  105.7800  100.3400   97.0200   95.1600   94.6800   94.5000   92.6400   91.0200   89.2400   87.6400   86.6000   84.1800   81.0400   79.8200   79.3600   78.2800   76.4200   76.2400   76.9200   76.4400   73.4800   72.3400   71.5000   70.7200   68.9000   66.9000   65.3800   65.2600   65.5200   64.9000   64.1600   62.3200   60.4400   58.4200   58.4600  59.2800   60.7800   60.7000   58.6400   59.6200   61.0600   61.7000   58.7000   55.8400   54.7200   53.4600   54.5600   55.1400   55.0200   52.9800   51.3800   49.7800   49.8600   50.9600   51.0200   52.2000   52.6600   51.6800   51.7200   51.1000   52.4400   52.3800   50.8800   50.9600   49.4800   48.1200   47.4200   48.0600   48.8200   47.8400   46.2200   44.9600   44.1800   45.2600   44.8200   44.5200   44.1000  45.1000   45.5600   44.3000   42.7000   42.5200   43.1000   44.4800   44.9200   43.4400   41.6800   41.5800   40.0200   39.0200   37.9600   38.3400   38.2400   37.4400   36.8800   37.4000   39.1200   39.1200   39.2200   38.1200   38.4400   37.8800   36.9000   35.8200   36.1400   36.5800   36.7000   36.2800   35.7600   34.1000   33.5800   32.9800   33.8800   33.7600   34.5800   34.0600   35.1800   34.7600   36.2400   35.4600   35.0800   33.0800   32.6600   33.8200   33.0000   33.0200   31.0800   29.6600   29.0600   29.4600   29.7800   30.1400   31.5800   31.4400   30.4000   29.3400   29.5800   28.9400   29.0800   28.7000  28.5600   30.5600   30.3600   30.0000   29.1600   29.2400   28.4600   28.3800   28.0200   27.3000   29.2800   29.6400   30.5000   30.9200   31.3000   30.6000   28.3200   28.2200   27.0600   26.4400   25.6600   25.4600   24.9600   23.8800   24.0400   24.8200   26.1000   28.1200   29.5800   30.1000   28.3200   26.0800   25.4800   24.5600   25.7400   27.1000   26.5000   25.5400   26.0800   27.8000   28.3600   29.1000  28.7400   29.2800   28.2800   28.8400   27.2800   26.4600   25.7600   25.6200   26.0200   25.3000   25.9000   26.3000   25.0000   24.7800   25.5000   27.4400   29.5600   27.8600   25.3400   23.5600   22.7800   23.6000   24.7000   26.3000   27.4400   27.0200   25.6000   24.4600   23.8800   23.9200   23.5800   22.5800   22.5200   21.6200   20.8000   19.5600   19.3800   19.5400   21.0600   22.5000   21.6600   21.5600  21.0600   22.1200   21.7800   22.1800   21.8400   22.5800   21.6000   22.3400   22.6400   22.8600   21.7800   20.5800   21.1200   20.0200   19.0400   19.2400   20.0400   20.1400   20.0800   20.5000   19.2800  18.5400   18.1200   20.3600   19.8600   18.8000   17.4400   18.4600   18.6800   18.7600   16.8400   18.1200   17.8400   18.9000   19.0200   19.3200   18.8000   19.1400   19.8800   20.8600   19.5600   19.3000  19.0600   19.0000   19.3000   19.2000   19.5000   18.6400   19.0800   19.3600   20.3400   20.2400   18.6000   17.4200   16.9400   17.0600   19.1600   21.0000   21.5400   18.2600   16.4200   16.9200   16.7000 17.7000   17.1800   17.2200   16.0800   16.8400   16.0600   15.5200   14.7000    3.5400];

XProjY = 1:576;

%---Y Projection starts here---

% a(1) = base

% a(2) = A; amplitude

% a(3) = x0; center

% a(4) = D; sigma_0

% a(5) = N;

a1Y = 100;

a2Y = 200;

a3Y = 280;

a4Y = 50;

a5Y = 1.5;

a0Y = [a1Y,a2Y,a3Y,a4Y,a5Y];

optsY = optimset('TolX',1e-4,'MaxFunEvals',10000,'MaxIter',10000,'Display','on'); [fitpara] = fminsearch(@SuperGaussianY,a0Y,optsY,XProjY,YProjY);

function chisq = SuperGaussianY(a,X,Y)

SupGau = a(1)+a(2)*exp( -0.5*(abs(X-a(3))/(a(4))).^a(5) );

csq = (Y - SupGau).^2;

chisq = sum(csq);

return

The output returns:

fitpara =

 21.2322  168.4825  239.5092   31.9488    1.0939

[Jan]

Please learn how to format code in this forum. It is really easy, but increases the readability substantially. Thanks.

[Emma]

Hi, I was actually looking for ideas for a code to do exactly this! I realise you posted this quite a while ago, but was just wondering if you could give me any pointers on what you've done? (Sorry, your formatting is a bit confusing and I'm also quite rusty with MATLAB at the moment, so more commenting of the code would help me).

Answer 1

[Eric]

I don't have time to work this in detail now, but here are my thoughts:

1. One way to speed the optimization would be to calculate the gradients of your error metric with respect to the fit parameters. Then you could use another optimization routine that uses gradient information (e.g., fminunc if you have the Optimization Toolbox).

2. You might look for ways to algorithmically determine the initial parameter values. If you can find better initial values the optimization will be faster. One way to do this may be to break the operation up into a couple steps. You may have better success first performing an optimization to a Gaussian and then fitting to a super-Gaussian. Alternatively, if you know your data sets are similar you might use an average of previous fit parameters as your initial guess.

Of these two approaches I would start with the first. The difficulty here will be in analytically calculating derivatives of your error metric. If you can do this, supplying gradient information to a good optimization routine should significantly speed convergence.

Good luck,

Eric

[Chris E.]

Thanks Eric! At least it gives me a direction to go to. I will try to see what I can do.

[Eric]

If you don't have the Optimization Toolbox, you might check out the software at:

https://software.sandia.gov/trac/poblano

described in the report at

http://www.sandia.gov/~dmdunla/publications/SAND2010-1422.pdf

Good luck,

Eric