how to determine each local min point?

Hi everyone, I have a urgent question to seek for help...

I have a sine wave however, angle in the sine wave is not a constant variation of x as shown below...

x = 0: 0.00001: 4;

v = x.*exp(x/2);
t = sin(v);

plot(x,t);

My trouble is how to display each of the local xmin point?

From the plot itself i wanted to display xmin1 = 1.859, xmin2 = 2.73, and xmin3 = 3.307.

Hope to hear from anyone soon... been cracking my head for the past weeks... )':

Best Regards

Will*

Answer 1

[Image Analyst]

If you have the Image Processing Toolbox, you can use imregionalmin(), like this:

% Original code
x = 0: 0.00001: 4;
v = x.*exp(x/2);
t = sin(v);
plot(x,t);

% Image Analyst's code:
minsIndexes = imregionalmin(t); % Logical array of where mins are.
% Extract the t values at those min locations;
minValues = t(minsIndexes) 
% Get the x values at those mins.
minX = x(minsIndexes) 
% Plot star over the mins.
hold on;
plot(minX, minValues, 'r*', 'MarkerSize', 10);

In the command window:

minValues =
             0         -1.00         -1.00         -1.00         -1.00         -0.96
minX =
             0          1.86          2.76          3.31          3.70          4.00

[William]

Thanks a lot and it did solve my troubles!!! :)

Answer 2

[Matt J]

 k=3; %Do this for all desired k>=0

 xmin=fzero(@(x) x.*exp(x/2) - 2*pi*k,0)

[Matt J]

There is also a minimum at x=-2, as elementary calculus can tell you.