hypot

Square root of sum of squares (hypotenuse)

Syntax

C = hypot(A,B)

Description

C = hypot(A,B) returns the hypotenuse of a right triangle with side lengths of A and B. This function computes C = sqrt(abs(A).^2 + abs(B).^2) by avoiding underflow and overflow.

Examples

Compute Hypotenuse

Compute the hypotenuse of a right triangle with side lengths of 3 and 4.

C = hypot(3,4)

C = 
5

Overflow and Underflow Behavior

Examine the difference between using hypot and coding the basic hypot equation in M-code.

Create an anonymous function that performs essentially the same basic function as hypot.

myhypot = @(a,b)sqrt(abs(a).^2+abs(b).^2);

myhypot does not have the same consideration for underflow and overflow behavior that hypot offers.

Find the upper limit at which myhypot returns a useful value. You can see that this test function reaches its maximum at about 1e154, returning an infinite result at that point.

myhypot(1e153,1e153)

ans = 
1.4142e+153

myhypot(1e154,1e154)

ans = 
Inf

Do the same using the hypot function, and observe that hypot operates on values up to about 1e308, which is approximately equal to the value for realmax on your computer (the largest representable double-precision floating-point number).

hypot(1e308,1e308)

ans = 
1.4142e+308

hypot(1e309,1e309)

ans = 
Inf

Input Arguments

A,B — Input arrays

scalars | vectors | matrices | multidimensional arrays

Input arrays, specified as scalars, vectors, matrices, or multidimensional arrays. Inputs A and B must either be the same size or have sizes that are compatible (for example, A is an M-by-N matrix and B is a scalar or 1-by-N row vector). For more information, see Compatible Array Sizes for Basic Operations.

If one or both inputs is NaN, then hypot returns NaN.

Data Types: single | double
Complex Number Support: Yes

More About

IEEE Compliance

For real inputs, hypot has a few behaviors that differ from those recommended in the IEEE^®-754 Standard.

	MATLAB®	IEEE
hypot(NaN,Inf)	NaN	Inf
hypot(NaN,-Inf)	NaN	Inf
hypot(Inf,NaN)	NaN	Inf
hypot(-Inf,NaN)	NaN	Inf

Extended Capabilities

Tall Arrays

Calculate with arrays that have more rows than fit in memory.

The hypot function fully supports tall arrays. For more information, see Tall Arrays.

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

• If you use hypot with single type and double type operands, the generated code might not produce the same result as MATLAB. See Binary Element-Wise Operations with Single and Double Operands (MATLAB Coder).

GPU Code Generation
Generate CUDA® code for NVIDIA® GPUs using GPU Coder™.

Thread-Based Environment

Run code in the background using MATLAB® backgroundPool or accelerate code with Parallel Computing Toolbox™ ThreadPool.

This function fully supports thread-based environments. For more information, see Run MATLAB Functions in Thread-Based Environment.

GPU Arrays

Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

The hypot function fully supports GPU arrays. To run the function on a GPU, specify the input data as a gpuArray (Parallel Computing Toolbox). For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).

Distributed Arrays

Partition large arrays across the combined memory of your cluster using Parallel Computing Toolbox™.

This function fully supports distributed arrays. For more information, see Run MATLAB Functions with Distributed Arrays (Parallel Computing Toolbox).

Version History

Introduced before R2006a