matwassersteinpar function

Matrix of 2-Wasserstein distances between Gaussian densities

Computes the matrix of the 2-Wasserstein distances between several multivariate ($p > 1$) or univariate ($p = 1$) Gaussian densities, given their parameters (mean vectors and covariance matrices if the densities are multivariate, or means and variances if univariate), using wassersteinpar.

matwassersteinpar(meanL, varL)

Arguments

• meanL: list of the means ($p = 1$) or vector means ($p > 1$) of the Gaussian densities.
• varL: list of the variances ($p = 1$) or covariance matrices ($p > 1$) of the probability densities.

Returns

Positive symmetric matrix whose order is equal to the number of densities, consisting of the pairwise 2-Wasserstein distances between the Gaussian densities.

Author(s)

Rachid Boumaza, Pierre Santagostini, Smail Yousfi, Gilles Hunault, Sabine Demotes-Mainard

See Also

wasserstein.

matwasserstein for the matrix of 2-Wasserstein distances between probability densities which are estimated from the data.

Examples

data(roses)
    
    # Multivariate:
    X <- roses[,c("Sha","Den","Sym","rose")]
    summary(X)
    mean.X <- as.list(by(X[, 1:3], X$rose, colMeans))
    var.X <- as.list(by(X[, 1:3], X$rose, var))
    matwassersteinpar(mean.X, var.X)

    # Univariate :
    X1 <- roses[,c("Sha","rose")]
    summary(X1)
    mean.X1 <- by(X1$Sha, X1$rose, mean)
    var.X1 <- by(X1$Sha, X1$rose, var)
    matwassersteinpar(mean.X1, var.X1)