action portfoliooptimizer_post_assets_correlation_matrix_distance {
  label: "Correlation Matrix Distance"
  description: "Compute the distance between an asset correlation matrix and a reference correlation matrix, using one of the following distance metrics:\n* Euclidean distance (default), which is the distance induced by [the Frobenius norm](https://en.wikipedia.org/wiki/Matrix_norm#Frobenius_norm)\n* Correlation matrix distance, defined in the first reference, which corresponds to [the cosine distance](https://en.wikipedia.org/wiki/Cosine_similarity) between the two vectorized asset correlation matrices\n* Bures distance, defined in the second reference\n\n References\n * [M. Herdin, N. Czink, H. Ozcelik and E. Bonek, Correlation matrix distance, a meaningful measure for evaluation of non-stationary MIMO channels, 2005 IEEE 61st Vehicular Technology Conference, 2005, pp. 136-140 Vol. 1](https://ieeexplore.ieee.org/document/1543265)\n * [Rajendra Bhatia, Tanvi Jain, Yongdo Lim, On the Bures–Wasserstein distance between positive definite matrices, Expositiones Mathematicae, Volume 37, Issue 2, 2019](https://www.sciencedirect.com/science/article/pii/S0723086918300021)\n"
  provider: portfoliooptimizer
  method: POST
  path: "/assets/correlation/matrix/distance"
  encoding: json
  input: {
    required: ["assets", "assetsCorrelationMatrix", "referenceCorrelationMatrix"]
    properties: {
      assets: {
        type: "integer"
      }
      assetsCorrelationMatrix: {
        type: "array"
        description: "assetsCorrelationMatrix[i][j] is the correlation between the asset i and the asset j"
        items: {
          type: "array"
          items: {
            type: "number"
          }
        }
      }
      distanceMetric: {
        type: "string"
        description: "The distance metric to use to compute the distance between the asset correlation matrix and the reference correlation matrix"
        enum: ["euclidean", "correlationMatrix", "bures"]
      }
      referenceCorrelationMatrix: {
        type: "array"
        description: "referenceCorrelationMatrix[i][j] is the reference correlation between the asset i and the asset j"
        items: {
          type: "array"
          items: {
            type: "number"
          }
        }
      }
    }
  }
  output: {
    type: "object"
    required: ["assetsCorrelationMatrixDistance"]
    properties: {
      assetsCorrelationMatrixDistance: {
        type: "number"
        description: "The computed distance between the two correlation matrices"
      }
    }
  }
}