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# Recursive HYPOT Function for Multiple Inputs

### Drew Compston (view profile)

01 Mar 2012 (Updated )

Extension of the built-in MATLAB function hypot for multiple inputs.

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MATLAB provides a function called hypot to calculate sqrt(abs(A).^2 + abs(B).^2) in a robust way to avoid underflow and overflow (see http://www.mathworks.com/help/techdoc/ref/hypot.html and http://en.wikipedia.org/wiki/Hypot). Frequently, though, I need to make this calculation with more than just two inputs A and B. Say, to compute the magnitude of a vector with three components (x, y, z). So I wrote this function to recursively call MATLAB's hypot function for multiple inputs:

Usage: Y = HYPOTR(X) or Y = HYPOTR(X1, X2, X3, ...)

This function works the same as the built-in MATLAB function hypot but allows for more than two inputs (or a single array) via recursion. The output Y is:

Y = sqrt(sum(X(:).^2)) (for single array X input)
Y = sqrt(X1.^2 + X2.^2 + X3.^2 + ...) (for arrays X1, X2, X3, ... input)

But the computation is done in a more robust way to avoid overflow and underflow (see HYPOT). Note that when multiple arrays are input, they must all be the same size (but any or all of them can also be scalars).

MATLAB release MATLAB 7.5 (R2007b)