Octave - Mark zero crossings with an red X mark

Question

Hi have made this code to plot a function.

I need to mark with an red X all the crossings between x = 0 and the blue wave line in the graph.

I have made some tries but with '-xr' in the plot function but it places X marks out of the crossings.

Anyone knows how to do it. Many thanks.

Code:

% entrada
a = input('Introduza o valor de a: ');
% ficheiro fonte para a função
raizes; 
% chamada à função
x = 0:.1:50;
or = x;
or(:) = 0;
h = @(x) cos(x);
g = @(x) exp(a*x)-1;
f = @(x) h(x) - g(x);
zeros = fzero(f,0);
plot(x,f(x));
hold on
plot(zeros,f(zeros),'-xr')
hold off

Graph (it only marks one zero, i need all the zero crossings):

Answer 1

As mentioned in the comments above, you need to look for the zeros of your function before you can plot them. You can do this mathematically (in this case set f(x) = g(x) and solve for x) or you can do this analytically with something like fsolve .

If you read the documentation for fsolve , you will see that it searches for the zero closest to the provided x0 if passed a scalar or the first zero if passed an interval. What we can do for a quick attempt at a solution is to pass our x values into fsolve as initial guesses and filter out the unique values.

% Set up sample data
a = .05;
x = 0:.1:50;

% Set up equations
h = @(x) cos(x);
g = @(x) exp(a*x)-1;
f = @(x) h(x) - g(x);

% Find zeros of f(x)
crossingpoints = zeros(length(x), 1); % Initialize array
for ii = 1:length(x) % Use x data points as guesses for fzero
    try
      crossingpoints(ii) = fzero(f, x(ii)); % Find zero closest to guess
    end
end
crossingpoints(crossingpoints < 0) = []; % Throw out zeros where x < 0

% Find unique zeros
tol = 10^-8;
crossingpoints = sort(crossingpoints(:)); % Sort data for easier diff
temp = false(size(crossingpoints)); % Initialize testing array

% Find where the difference between 'zeros' is less than or equal to the
% tolerance and throw them out
temp(1:end-1) = abs(diff(crossingpoints)) <= tol; 
crossingpoints(temp) = [];

% Sometimes catches beginning of the data set, filter it out if this happens
if abs(f(crossingpoints(1))) >= (0 + tol)
    crossingpoints(1) = [];
end

% Plot data
plot(x, f(x))
hold on
plot(crossingpoints, f(crossingpoints), 'rx')
hold off
grid on
axis([0 20 -2 2]);

Which gives us the following:

Note that due to errors arising from floating point arithmetic we have to utilize a tolerance to filter our zeros rather than utilizing a function like unique .