const rawMetrics = (() => {
  const RMS = {
    name: "RMS Deviation (σ)",
    display: p => String.raw`
      \sigma\left(${p}\right) = \sqrt{I\left(${p}\right) - 2\vec{q}\cdot\vec{\mu}\left(${p}\right) + \left|\left|\vec{q}\right|\right|^2}
    `,
    evaluate: (data, target) => math.sqrt(data.inertia - 2 * vectorDot(data.mu.vector, target.vector) + target.sqMag),
  };

  const meanOfAngle = {
    name: "Mean of Angular Difference (Θ)",
    display: p => String.raw`
      \Theta\left(${p}\right) = \cos^{-1}\left( \hat{q}\cdot\vec{\nu}\left(${p}\right) \right)
    `,
    evaluate: (data, target) => rad2deg * Math.acos(vectorDot(data.nu.vector, target.unit)),
  };

  const angleOfMean = {
    name: "Angular Difference of Mean (θ)",
    display: p => String.raw`
      \theta\left(${p}\right) = \cos^{-1}\left( \hat{q}\cdot\hat{\mu}\left(${p}\right) \right)
    `,
    evaluate: (data, target) => rad2deg * Math.acos(vectorDot(data.mu.unit, target.unit)),
  };

  const hue = {
    name: "Hue Difference of Mean (ϕ)",
    display: p => String.raw`
      \phi\left(${p}\right) = \angle \left(\vec{q}_{\perp}, \vec{\mu}\left(${p}\right)_{\perp} \right)
    `,
    evaluate: (data, target) => angleDiff(data.mu.hue, target.hue),
  }

  const euclidean = {
    name: "Euclidean Distance to Mean (δ)",
    display: p => String.raw`
      \delta\left(${p}\right) = \left|\left| \vec{q} - \vec{\mu}\left(${p}\right) \right|\right|
    `,
    evaluate: (data, target) => vectorDist(data.mu.vector, target.vector),
  };

  const chebyshev = {
    name: "Chebyshev Distance to Mean (Ч)",
    display: p => String.raw`
      Ч\left(${p}\right) = \max_{i} \left| \vec{\mu}\left(${p}\right)_i - \vec{q}_i \right|
    `,
    evaluate: (data, target) => Math.max(...data.mu.vector.map((x, i) => Math.abs(x - target.vector[i]))),
  };

  const inertia = {
    name: "Inertia (I)",
    display: p => String.raw`
      I\left(${p}\right) = \frac{1}{\left|${p}\right|} \sum_{p\in ${p}}{\left|\left|\vec{p}\right|\right|^2}
    `,
    evaluate: data => data.inertia,
  };
  
  const size = {
    name: "Size (N)",
    display: p => String.raw`
      N\left(${p}\right) = \left|${p}\right|
    `,
    evaluate: data => data.size,
  };

  return [RMS, meanOfAngle, angleOfMean, hue, euclidean, chebyshev, inertia, size];
})();

const applyMetrics = (data, target)  => ({
  sigma: rawMetrics[0].evaluate(data, target),
  bigTheta: rawMetrics[1].evaluate(data, target),
  theta: rawMetrics[2].evaluate(data, target),
  phi: rawMetrics[3].evaluate(data, target),
  delta: rawMetrics[4].evaluate(data, target),
  ch: rawMetrics[5].evaluate(data, target),
  inertia: rawMetrics[6].evaluate(data),
  size: rawMetrics[7].evaluate(data),
});