Multiple histograms and how to measure fwhm?

I have 1 to 144 columns.

I want to draw 144 gaussian histograms fitting according to the column and find the positions of 144 FWHM and Peak.

Each column has a different row size.

What should I do?

Answer 1

[Star Strider]

Try this —

M1 = readmatrix('https://www.mathworks.com/matlabcentral/answers/uploaded_files/833435/1to10_30s_15mm_diff_pivoted.txt')

M1 = 502×144

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 -59 26 -17 -20 15 -56 59 39 93 93 53 12 -180 -3 -101 -56 -69 -38 21 11 -4 95 69 38 -44 -40 -29 -113 15 30 87 -4 47 -17 -23 -44 148 -65 -91 83 -34 10 -150 7 -4 -68 -47 74 121 -29 179 -37 85 85 61 79 4 177 51 -65 153 -21 -29 -95 -124 18 80 119 -130 58 59 11 55 -17 101 107 -175 -33 -298 -19 48 24 93 71 129 34 75 -23 107 126 -53 -92 61 72 66 -70 -70 84 55 178 -30 -7 44 139 -9 -71 156 158 -28 122 -201 -70 -10 262 124 61 -10 -89 -175 -31 -38 -3 -53 -19 -27 -88 145 27 39 76 338 159 110 -47 46 2 47 -94 -47 -224 -113 -93 15 -18 36 -26 -30 -86 21 -90 89 172 -104 -96 8 -26 -8 68 144 65 -14 11 -51 -50 -11 35 -25 110 -69 -109 -72 27 -29 -58 59 13 62 143 113 16 133 19 -133 -45 43 81 55 64 128 136 -43 204 -27 -52 46 -36 -79 72 33 43 46 -27 37 18 254 -35 17 67 -51 -18 -59 -77 33 54 16 82 -168 -85 -11 38 -56 82 109 -4 251 -89 -186 30 -47 261 -93 -139 93 -75 -25 -76 -162 54 158 130 -121 41 -86 -3 -128 -55 -155 -56 105 134 -112 47 58 72 163 -152 -1 29 55 43 -42 -40 -1 -229 120 -89 48 23 43 -34

% figure
% hold on
% for k = 1:size(M1,2)
%     subplot(12,12,k)
%     hf{k} = histfit(M1(:,k));                                                               % Distribution Plot
%     [pks{k},locs{k},fwhm{k},prm{k}] = findpeaks(hf{k}(2).YData, hf{k}(2).XData);
%     pd{k} = fitdist(M1(:,k), 'Normal');                                                     % Parameters
%     grid
%     title(sprintf('Column #%3d (\\mu = %5.2f, \\sigma = %5.2f  FWHM = %7.2f)',k, pd{k}.mu, pd{k}.sigma,fwhm{k}))
% end

figure
hold on
for k = 1:size(M1,2)
    subplot(122,2,k)
    hf{k} = histfit(M1(:,k));                                                               % Distribution Plot
    [pks{k},locs{k},fwhm{k},prm{k}] = findpeaks(hf{k}(2).YData, hf{k}(2).XData);
    pd{k} = fitdist(M1(:,k), 'Normal');                                                     % Parameters
    grid
    title(sprintf('Column #%3d (\\mu = %5.2f, \\sigma = %5.2f  FWHM = %7.2f)',k, pd{k}.mu, pd{k}.sigma,fwhm{k}))
end
hold off

figure
hold on
for k = 1:24:size(M1,2)
    subplot(3,2,ceil(k/24))
    hf{k} = histfit(M1(:,k));                                                               % Distribution Plot
    [pks{k},locs{k},fwhm{k},prm{k}] = findpeaks(hf{k}(2).YData, hf{k}(2).XData);
    pd{k} = fitdist(M1(:,k), 'Normal');                                                     % Parameters
    grid
    title(sprintf('Column #%3d (\\mu = %5.2f, \\sigma = %5.2f  FWHM = %7.2f)',k, pd{k}.mu, pd{k}.sigma,fwhm{k}))
end
hold off

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[수환 김]

Thank you very much for your help.

I have one more question.

How to extract only numerical values of 144 Gaussian fitted FWHM and MEAN according to bin size?

I would like to designate 144 FWHM and MEAN as variables, respectively.

[Star Strider]

As always, my pleasure!

The means are: ‘pd{k}.mu’ and the FWHM are: ‘fwhm{k}’ for each of the 144 distributions subscripted by ‘k’.

Note that they are already in cell arrays, so it is only necessary to use the cell2mat function to create them as double precision numeric vectors in a numeric array.

The displayed (3x2) subplot array is simply a sample to demonstrate what the rest of them would look like if expanded so that they could be easily visualised. (The online Run feature ‘squashes’ them into a format that will fit here, however a figure with all 144 plots have considerable overlap and are not readable here. They would likely be readable with a large format monitor with the figure window expanded to full-screen.)

.

[수환 김]

I understand what you are saying. thank you.

However, what I want is that when drawing a histogram, the Gaussian fitted graph will be different depending on the bin size.

Therefore, the FWHM and Peak (mean) of the fitting graph will also differ depending on the bin size.I want to know how much the numerical values change according to the bin size.

[Star Strider]

‘However, what I want is that when drawing a histogram, the Gaussian fitted graph will be different depending on the bin size.’

The Gaussian (or any other) fit actually had nothing to do with the histogram or bin size. It is entirely independent of it. From the histfit documentation Algorithms section:

• histfit uses fitdist to fit a distribution to data. Use fitdist to obtain parameters used in fitting.

‘Therefore, the FWHM and Peak (mean) of the fitting graph will also differ depending on the bin size.I want to know how much the numerical values change according to the bin size.’

Again, the bin size of the histogram has nothing to do with the distribution fit. It is only there for convenience, so that the fitted curve can be visually compared to the histogram. It is possible to use the histogram frequencies, bin locations, and nonlinear optimisation functions to fit a Gaussian (or any other distribution) curve to the histogram (this has been a topic of several previous Answers posts, some of which I responded to), however that is not accurate (does not produce the same results as directly calculating the mean and std and using them to draw the curve) and does not produce the same results as directly estimating the parameters using fitdist.

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