Recursive HYPOT Function for Multiple Inputs

Extension of the built-in MATLAB function hypot for multiple inputs.
Updated 25 Apr 2012

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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 and 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).

See also: HYPOT.

Cite As

Drew Compston (2024). Recursive HYPOT Function for Multiple Inputs (, MATLAB Central File Exchange. Retrieved .

MATLAB Release Compatibility
Created with R2007b
Compatible with any release
Platform Compatibility
Windows macOS Linux
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Version Published Release Notes

Greatly simplified the code.

Replaced iscolumn, which was not introduced until R2010b, with size(A, 2) == 1, which should make this compatible with at least R2007b and later.