output of function with unknowned size

Question

I want to define a function in matlab that gives a vector as input and gives local minimals as output in the form of a matrix. but i give this error:Too many output arguments. here is my code

    function [index, value] = localminima(x)
    N = length(x);
    a = [];   
     b = [];   
%     at first a & b witch are index and value, respectively are empty
%     then, in the for loop indexes and values of local minimal are added
%     to a & b.
     for k = 2:N-1,
        if((x(k) < x(k+1)) && (x(k) < x(k-1)))
            a = [a; k];
            b = [b; x(k)];
        end
    end
    [index, value] = [a, b]

Answer 1

I think this does what you want, without loops:

d = diff(x);
ind = [false d<0] & [d>0 false];
a = find(ind);
b = x(ind);

Answer 2

When you're trying to assign the values a and b to index and value MATLAB is actually concatenating them into a single vector which it can't assign to two output variables. Instead you could use index = a; value = b or just replace the variable names a and b alltogether with index and value.

Furthermore, performance will probably improve if you don't use a loop but instead use MATLABs built-in functions and logical indexing, so e.g.

function [index, value] = localminima(x)
    dx = diff(x);
    logicalIndex = [ false dx < 0 ] & [ dx > 0 false ];

    index = find(logicalIndex);
    value = x(logicalIndex);
end

Answer 3

[index, value] = [a, b] is incorrect. You should have two separate assignments:

index = a;
value = b;

To get both index and value vectors as outputs from your function, you should call the function in MATLAB command windows as

>> [index, value] = localminima(x)

A bit of an explanation: Both sides of [index, value] = [a, b] look similar, but they mean different things.

• [a, b] is constructing an nx2 matrix by concatenating the nx1 vectors a and b.
• [index, value] is trying to assign the result from the right-hand side of the = symbol to two variables: index and value. Since [a,b] is a single variable, which is a matrix, [index, value] = [a, b] is an invalid operation: there is nothing to assign to the variable value.
• When you call your function [index, value] = localminima(x) and define index=... and value= ... in your function as two separate variables, then your function will return two outputs. Hence [index, value] = localminima(x) will be a valid operation.