distance method

Complex distance(Vector other, { DistanceType distance = DistanceType.frobenius, })

Sets all elements of this vector to value.

Example:

var v = Vector.fromList([1, 2, 3]);
v.setAll(0);
print(v);

Output:

[0, 0, 0]

Returns the Euclidean distance between this vector and other.

The distance is given by the formula sqrt(sum((this[i] - other[i])^2)) for all i.

Throws an ArgumentError if the vectors have different lengths.

Example:

var v1 = Vector.fromList([1, 2, 3]);
var v2 = Vector.fromList([4, 5, 6]);
print(v1.distance(v2));

Output:

5.196152422706632

Implementation

// void setAll(num value) {
//   for (var i = 0; i < length; i++) {
//     this[i] = value;
//   }
// }

/// Returns the Euclidean distance between this vector and [other].
///
/// The distance is given by the formula `sqrt(sum((this[i] - other[i])^2))` for all i.
///
/// Throws an `ArgumentError` if the vectors have different lengths.
///
/// Example:
/// ```dart
/// var v1 = Vector.fromList([1, 2, 3]);
/// var v2 = Vector.fromList([4, 5, 6]);
/// print(v1.distance(v2));
/// ```
///
/// Output:
/// ```
/// 5.196152422706632
/// ```
Complex distance(Vector other,
    {DistanceType distance = DistanceType.frobenius}) {
  if (length != other.length) {
    throw ArgumentError(
        "Vectors must have the same length for distance calculation.");
  }

  Complex sumSquare = Complex.zero();
  Complex sumAbs = Complex.zero();
  Complex maxAbs = Complex.zero();
  Complex dotProduct = Complex.zero();
  Complex sumSquare1 = Complex.zero();
  Complex sumSquare2 = Complex.zero();
  Complex hammingDistance = Complex.zero();

  for (int i = 0; i < _data.length; i++) {
    final diff = _data[i] - other[i];
    final absDiff = diff.abs();

    sumSquare += diff * diff;
    sumAbs += absDiff;
    maxAbs = math.max(maxAbs, absDiff);
    dotProduct += _data[i] * other[i];
    sumSquare1 += _data[i] * _data[i];
    sumSquare2 += other[i] * other[i];
    hammingDistance += _data[i] != other[i] ? Complex.one() : Complex.zero();
  }

  switch (distance) {
    case DistanceType.frobenius:
      return math.sqrt(sumSquare);
    case DistanceType.manhattan:
      return sumAbs;
    case DistanceType.chebyshev:
      return maxAbs;
    case DistanceType.mahalanobis:
      // We need a covariance matrix and its inverse to compute Mahalanobis distance
      return Complex.nan(); // placeholder value indicating unimplemented
    case DistanceType.cosine:
      final magnitude1 = math.sqrt(sumSquare1);
      final magnitude2 = math.sqrt(sumSquare2);
      return Complex.one() - (dotProduct / (magnitude1 * magnitude2));
    case DistanceType.hamming:
      return hammingDistance;
    case DistanceType.spectral:
    // For vectors, we consider spectral norm as its magnitude
    //return math.sqrt(sumSquare);
    case DistanceType.trace:
    // For vectors, we consider trace norm as the sum of its elements
    //return sumAbs;
    default:
      throw Exception('Invalid distance type');
  }
}