MATLAB: Zero crossing and inflection point

inflection pointzero crossing

can someone please in detail explain to me what this simple line of coding is doing in order to calculate zero crossing. I thought you needed the second derivative of the function to do this. Thank you

zci = @(v) find(v(:).*circshift(v(:), [-1 0]) <= 0);

Best Answer

Why would you possibly need the second derivative to locate a zero crossing?

All this does is look for consecutive elements of a vector that have different signs.

If you really want to see what it does, read the help for circshift. My re-writing existing help will be a waste of time. Given that, what property do two numbers have if they have different signs? Answer: the product will ALWAYS be negative. So all that line does is look for consecutive elements with opposite signs. (Zero will do too.)

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MATLAB: Problem to find inflection point

Note that with your data, in order to calculate the inflection points correctly, you need to reverse ‘x’ and ‘y’ in my code:

x = yNew;
y = xNew;

The index range worked for the original example (How to find inflection point, PLEASE HELP!), however it needs to be modified in the event that it over-writes the end of the vector.

Try this:

dydx = gradient(y) ./ gradient(x);                                      % Derivative Of Unevenly-Sampled Data
zci = @(v) find(v(:).*circshift(v(:), [-1 0]) <= 0);                    % Returns Approximate Zero-Crossing Indices Of Argument Vector
zxidx = zci(dydx);                                                      % Approximate Indices Where ‘dydx=0’
for k1 = 1:numel(zxidx)                                                 % Loop Finds ‘x’ & ‘y’ For ‘dydx=0’
    ixrng = max(zxidx(k1)-2,1):min(zxidx(k1)+2,numel(x));
    inflptx(k1) = interp1(dydx(ixrng), x(ixrng), 0, 'linear');
    inflpty(k1) = interp1(x(ixrng), y(ixrng), inflptx(k1), 'linear');
end
figure(1)
plot(x, y)
hold on
plot(x, dydx*10)
plot(inflptx, inflpty, 'pg', 'MarkerFaceColor','g')
hold off
grid
legend('Data', 'Derivative', 'Inflection Points', 'Location','best')
inflpts = sprintfc('(%5.3f,%5.3f)', [inflptx; inflpty].');
text(inflptx, inflpty, inflpts,'FontSize',8, 'HorizontalAlignment','center', 'VerticalAlignment','bottom')

I edited my original post to include this change (‘ixrng’).

MATLAB: Polyfit question

It means

avg_Y = 0.0042*x+2.5802

see

doc polyfit

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MATLAB: Polyfit question

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