hypot

Square root of sum of squares (hypotenuse)

Syntax

C = hypot(A,B)

Description

example

C = hypot(A,B) returns the result of the following equation, computed to avoid underflow and overflow:

C = sqrt(abs(A).^2 + abs(B).^2)

Examples

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

C = hypot(3,4)
C = 5

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

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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 neither A nor B is Inf, but one or both inputs is NaN, then hypot returns NaN.

Data Types: single | double
Complex Number Support: Yes

More About

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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

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

See Also

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Introduced before R2006a