.Modelica.ComplexMath.Vectors.normalize

Information

Syntax

Vectors.normalize(v);
Vectors.normalize(v,eps=100*Modelica.Constants.eps);

Description

The function call "Vectors.normalize(v)" returns the unit vector "v/length(v)" of vector v. If length(v) is close to zero (more precisely, if length(v) < eps), v is returned in order to avoid a division by zero. For many applications this is useful, because often the unit vector e = v/length(v) is used to compute a vector x*e, where the scalar x is in the order of length(v), i.e., x*e is small, when length(v) is small and then it is fine to replace e by v to avoid a division by zero.

Since the function is implemented in one statement, it is usually inlined and therefore symbolic processing is possible.

Example

normalize({1,2,3});  // = {0.267, 0.534, 0.802}
normalize({0,0,0});  // = {0,0,0}

See also

Vectors.length

Interface

function normalize
  extends Modelica.Icons.Function;
  input Complex v[:] "Vector";
  input Real eps = 100*Modelica.Constants.eps "if |v| < eps then result = v";
  output Complex result[size(v, 1)] "Input vector v normalized to length=1";
end normalize;