Modelica.ComplexMath.Vectors

Information

This library provides functions operating on vectors of Complex numbers.

Package Content

Name	Description
norm	Returns the p-norm of a complex vector
length	Return length of a complex vector
normalize	Return normalized complex vector such that length = 1 and prevent zero-division for zero vector
reverse	Reverse vector elements (e.g., v[1] becomes last element)
sort	Sort elements of complex vector

Modelica.ComplexMath.Vectors.norm

Information

Syntax

Vectors.norm(v);
Vectors.norm(v,p=2);   // 1 ≤ p ≤ ∞

Description

The function call "Vectors.norm(v)" returns the Euclidean norm "sqrt(v*v)" of vector v. With the optional second argument "p", any other p-norm can be computed:

Besides the Euclidean norm (p=2), also the 1-norm and the infinity-norm are sometimes used:

Note, for any vector norm the following inequality holds:

norm(v1+v2,p) ≤ norm(v1,p) + norm(v2,p)

Example

  v = {2, -4, -2, -1};
  norm(v,1);    // = 9
  norm(v,2);    // = 5
  norm(v);      // = 5
  norm(v,10.5); // = 4.00052597412635
  norm(v,Modelica.Constants.inf);  // = 4

See also

Matrices.norm

Inputs

Name	Description
v[:]	Vector
p	Type of p-norm (often used: 1, 2, or Modelica.Constants.inf)

Outputs

Name	Description
result	p-norm of vector v

Modelica.ComplexMath.Vectors.length

Information

Syntax

Vectors.length(v);

Description

The function call "Vectors.length(v)" returns the Euclidean length "sqrt(v*v)" of vector v. The function call is equivalent to Vectors.norm(v). The advantage of length(v) over norm(v)"is that function length(..) is implemented in one statement and therefore the function is usually automatically inlined. Further symbolic processing is therefore possible, which is not the case with function norm(..).

Example

  v = {2, -4, -2, -1};
  length(v);  // = 5

See also

Vectors.norm

Inputs

Name	Description
v[:]	Vector

Outputs

Name	Description
result	Length of vector v

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

Inputs

Name	Description
v[:]	Vector
eps	if |v| < eps then result = v

Outputs

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

Modelica.ComplexMath.Vectors.reverse

Information

Syntax

Vectors.reverse(v);

Description

Example

  reverse({1,2,3,4});  // = {4,3,2,1}

Inputs

Name	Description
v[:]	Vector

Outputs

Name	Description
result[size(v, 1)]	Elements of vector v in reversed order

Modelica.ComplexMath.Vectors.sort

Information

Syntax

           sorted_v = Vectors.sort(v);
(sorted_v, indices) = Vectors.sort(v, ascending=true);

Description

Function sort(..) sorts a Real vector v in ascending order and returns the result in sorted_v. If the optional argument "ascending" is false, the vector is sorted in descending order. In the optional second output argument the indices of the sorted vector with respect to the original vector are given, such that sorted_v = v[indices].

Example

  (v2, i2) := Vectors.sort({-1, 8, 3, 6, 2});
       -> v2 = {-1, 2, 3, 6, 8}
          i2 = {1, 5, 3, 4, 2}

Inputs

Name	Description
v[:]	Vector to be sorted
ascending	= true if ascending order, otherwise descending order
sortFrequency	= true, if sorting is first for imaginary then for real value; = false, if sorting is for absolute value

Outputs

Name	Description
sorted_v[size(v, 1)]	Sorted vector
indices[size(v, 1)]	sorted_v = v[indices]