Plotting a piecewise function

Hey guys. I need a plot of a piecewise function in MATLAB and I don't know how to do it.

f(x) = 
v1(1,1)*exp(1i*alpha*x)+v1(1,1)*exp(-1i*alpha*x), 0<x<1;
v2(1,1)*exp(1i*alpha*(x-1))+v2(2,1)*exp(-1i*alpha*(x-1)), 1<x<2;
v3(1,1)*exp(1i*alpha*(x-2))+v3(1,1)*exp(-1i*alpha*(x-2)), 2<x<3;
and upto (x-10) like this.

here vk(1,1)and vk(2,1) are matrix elements of 2*1 matrix.

How do I plot abs(f(x)) with alpha in MATLAB with alpha = 0:0.1:2?

[Star Strider]

This quickly became so convoluted and ambiguous that I deleted my answer.

Answer 1

[the cyclist]

It is a bit tricky. I think I got this right, but you should definitely check carefully.

x = 0 : 0.001 : 10;

% Define alpha
alpha = 0.3;

% Define some random constants corresponding to your v1...v10.
% Used cell array instead of awkward variables v1, etc.
for n = 1:10
    v{n} = rand();
end

% Define the individual functions. Note that each will be zero over anything but its piecewise domain.
for n=1:10
    f{n} = @(x) (x>(n-1) & x<=n) .* (v{1}*exp(1i*alpha*(x-n+1)) + v{1}*exp(-1i*alpha*(x-n+1)));
end

% Define the combined function
F = @(x) (f{1}(x) + f{2}(x) + f{3}(x) + f{4}(x) + f{5}(x) + f{6}(x) + f{7}(x) + f{8}(x) + f{9}(x) + f{10}(x));

% Plot the real and imaginary parts
figure
subplot(2,1,1), plot(x,real(F(x)))
subplot(2,1,2), plot(x,imag(F(x)))

[the cyclist]

I noticed that I left out

v{1}*

in the second term, so I edited to fix that.