abs

Symbolic absolute value (complex modulus or magnitude)

Syntax

abs(z)

Description

abs(z) returns the absolute value (or complex modulus) of z. Because symbolic variables are assumed to be complex by default, abs returns the complex modulus (magnitude) by default. If z is an array, abs acts element-wise on each element of z.

Examples

Compute Absolute Values of Symbolic Numbers

[abs(sym(1/2)), abs(sym(0)), abs(sym(pi) - 4)]

ans =
[ 1/2, 0, 4 - pi]

Compute Absolute Value of Complex Numbers

Compute abs(x)^2 and simplify the result. Because symbolic variables are assumed to be complex by default, the result does not simplify to x^2.

syms x
simplify(abs(x)^2)

ans =
abs(x)^2

Assume x is real, and repeat the calculation. Now, the result is simplified to x^2.

assume(x,'real')
simplify(abs(x)^2)

ans =
x^2

Remove assumptions on x for further calculations. For details, see Use Assumptions on Symbolic Variables.

assume(x,'clear')

Absolute Values of Elements of Array

Compute the absolute values of each element of matrix A.

A = sym([1/2+i  -25;
          i     pi/2]);
abs(A)

ans =
[ 5^(1/2)/2,   25]
[         1, pi/2]

Effect of Assumptions on Absolute Value

Compute the absolute value of this expression assuming that the value of x is negative.

syms x
assume(x < 0)
abs(5*x^3)

ans =
-5*x^3

For further computations, clear the assumption on x by recreating it using syms:

syms x

Input Arguments

z — Input

number | vector | matrix | multidimensional array | symbolic number | symbolic array | symbolic function | symbolic expression

Input, specified as a number, vector, matrix, or array, or a symbolic number, vector, matrix, or array, variable, function, or expression.

More About

Complex Modulus

The absolute value of a complex number z = x + y*i is the value $$\left|z\right|=\sqrt{x^2+y^2}$$. Here, x and y are real numbers. The absolute value of a complex number is also called a complex modulus.

Tips

• Calling abs for a number that is not a symbolic object invokes the MATLAB^® abs function.