norm method

Complex norm([ Norm normType = Norm.frobenius ])

Returns the norm (or length) of this vector.

The norm of a vector is the square root of the sum of the squares of its elements. It gives a measure of the magnitude (or length) of the vector.

Example:

var v = Vector.fromList([3, 4]);
print(v.norm());

Output:

5.0

Explanation: The vector [3, 4] has a norm of 5 because sqrt(33 + 44) = sqrt(9 + 16) = sqrt(25) = 5.

Implementation

Complex norm([Norm normType = Norm.frobenius]) {
  switch (normType) {
    case Norm.frobenius:
      return math
          .sqrt(_data.map((value) => value * value).reduce((a, b) => a + b));
    case Norm.manhattan:
      return _data.map((value) => value.abs()).reduce((a, b) => a + b);
    case Norm.chebyshev:
      return _data
          .map((value) => value.abs())
          .reduce((a, b) => math.max(a, b));
    case Norm.hamming:
      return Complex(_data.where((value) => value != 0).length);
    case Norm.cosine:
      final magnitude = norm(Norm.frobenius);
      final vDot = dot(this);
      return vDot / magnitude;
    // The below norms need more context to implement.
    case Norm.mahalanobis:
      throw UnimplementedError('Mahalanobis norm is not implemented');
    case Norm.spectral:
    case Norm.trace:
    default:
      throw Exception('Invalid norm type');
  }
}