# This library is free software; you can redistribute it and/or
# modify it under the terms of the GNU Library General Public
# License as published by the Free Software Foundation; either
# version 2 of the License, or (at your option) any later version.
#
# This library is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
# GNU Library General Public License for more details.
#
# You should have received a copy of the GNU Library General
# Public License along with this library; if not, write to the
# Free Foundation, Inc., 59 Temple Place, Suite 330, Boston,
# MA  02111-1307  USA

# Copyrights (C)
# for this R-port: 
#   1999 - 2007, Diethelm Wuertz, GPL
#   Diethelm Wuertz <wuertz@itp.phys.ethz.ch>
#   info@rmetrics.org
#   www.rmetrics.org
# for the code accessed (or partly included) from other R-ports:
#   see R's copyright and license files
# for the code accessed (or partly included) from contributed R-ports
# and other sources
#   see Rmetrics's copyright file


################################################################################
# FUNCTION:             ASSETS STATISTICS:
#  assetsLPM             Computes Lower Partial Moments 
################################################################################



assetsLPM = 
function(x, tau = colMeans(x), a = 1.5, ...)
{   # A function implemented by Diethelm Wuertz
    
    # Description:
    #   Computes LPM and CLPM from multivariate time series
    
    # Arguments:
    #   x - a multivariate time series, a data frame, or any other
    #       rectangular object of assets which can be converted into
    #       a matrix by the function 'as.matrix'. Optional Dates are 
    #       rownames, instrument names are column names.
    
    # Note:
    #   The output of this function can be used for portfolio
    #   optimization.
    
    # FUNCTION:
    
    # Transform Input:
    x.mat = as.matrix(x)
    nCol = ncol(x)
    nRow = nrow(x)
    Tau = matrix(rep(tau, nRow), byrow = TRUE, ncol = nCol)
    TauX = Tau-x
    X.max = ((TauX) + abs(TauX))/2
    
    # Compute Lower Partial Moments:
    LPM = colMeans(X.max^a)
    
    # Compute co-LPMs:
    CLPM = diag(0, nCol)
    if (a > 1) {
        for (i in 1:nCol) {
            for (j in 1:nCol) {
                CLPM[i, j] = 
                    mean( (X.max[, i])^(a-1) * TauX[, j] )
            }
            CLPM[i, i] = LPM[i]
        }
    } else if (a == 1) {
        for (i in 1:nCol) {
            for (j in 1:nCol) {
                CLPM[i, j] = 
                    mean( sign( X.max[, i]) * TauX[, j] )
            }
            CLPM[i, i] = LPM[i]
        }
    }
    
    # Result:
    ans = list(mu = LPM, Sigma = CLPM)
    attr(ans, "control") <- c(a = a, tau = tau)
        
    # Return Value:
    ans
}


################################################################################