This information is part of the Modelica Standard Library maintained by the Modelica Association.

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

result = normalize(v, eps)

v	Type: Complex[:] Description: Vector
eps	Default Value: 100 * Modelica.Constants.eps Type: Real Description: if |v| < eps then result = v

result	Type: Complex[size(v, 1)] Description: Input vector v normalized to length=1