abs

abs(x: array, /) → array

Calculates the absolute value for each element x_i of the input array x.

For real-valued input arrays, the element-wise result has the same magnitude as the respective element in x but has positive sign.

Note

For signed integer data types, the absolute value of the minimum representable integer is implementation-dependent.

Note

For complex floating-point operands, the complex absolute value is known as the norm, modulus, or magnitude and, for a complex number \(z = a + bj\) is computed as

\[\operatorname{abs}(z) = \sqrt{a^2 + b^2}\]

Note

For complex floating-point operands, conforming implementations should take care to avoid undue overflow or underflow during intermediate stages of computation.

Parameters:

x (array) – input array. Should have a numeric data type.

Returns:

out (array) – an array containing the absolute value of each element in x. If x has a real-valued data type, the returned array must have the same data type as x. If x has a complex floating-point data type, the returned array must have a real-valued floating-point data type whose precision matches the precision of x (e.g., if x is complex128, then the returned array must have a float64 data type).

Notes

Special Cases

For real-valued floating-point operands,

  • If x_i is NaN, the result is NaN.

  • If x_i is -0, the result is +0.

  • If x_i is -infinity, the result is +infinity.

For complex floating-point operands, let a = real(x_i), b = imag(x_i), and

  • If a is either +infinity or -infinity and b is any value (including NaN), the result is +infinity.

  • If a is any value (including NaN) and b is either +infinity or -infinity, the result is +infinity.

  • If a is either +0 or -0, the result is equal to abs(b).

  • If b is either +0 or -0, the result is equal to abs(a).

  • If a is NaN and b is a finite number, the result is NaN.

  • If a is a finite number and b is NaN, the result is NaN.

  • If a is NaN and b is NaN, the result is NaN.

Changed in version 2022.12: Added complex data type support.