matipl2dpar {dad}

Matrix of L^2 inner products of Gaussian densities

Description

Computes the matrix of the L^2 inner products 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).

Usage

matipl2dpar(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 Gaussian densities.

Value

Positive symmetric matrix whose order is equal to the number of densities, consisting of the pairwise inner products between the Gaussian densities.

Author(s)

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

See Also

l2dpar.

matipl2d for the distance matrix 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))
    
    # Gaussian densities, given parameters
    matipl2dpar(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)
    
    # Gaussian densities, given parameters
    matipl2dpar(mean.X1, var.X1)