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#############################################################################
# Copyright (c) 2012 Christophe Dutang
#
# This program is free software; you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation; either version 2 of the License, or
# (at your option) any later version.
#
# This program 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 General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program; if not, write to the
# Free Software Foundation, Inc.,
# 59 Temple Place, Suite 330, Boston, MA 02111-1307, USA
#
#############################################################################
### utility functions for constrained equations in GNE
###
### R functions
###
#functions of the Constrained Equation Reformulation of the GNEP
#z = (x, lam, w)
#with size (n, m, m)
funCER <- function(z, dimx, dimlam,
grobj, arggrobj,
constr, argconstr,
grconstr, arggrconstr,
dimmu, joint, argjoint,
grjoint, arggrjoint,
echo=FALSE)
{
arg <- testargfunCER(z, dimx, dimlam, grobj, arggrobj, constr, argconstr, grconstr, arggrconstr,
dimmu, joint, argjoint, grjoint, arggrjoint, echo)
dimx <- arg$dimx
dimlam <- arg$dimlam
dimmu <- arg$dimmu
n <- sum(arg$dimx)
m <- sum(arg$dimlam)
x <- z[1:n]
lam <- z[(n+1):(n+m)]
mu <- z[(n+m+1):(n+m+dimmu)]
w <- z[-(1:(n+m+dimmu))]
part1 <- funSSR(z[1:(n+m+dimmu)], dimx, dimlam, grobj, arggrobj, constr, argconstr, grconstr, arggrconstr,
compl=phiFB, argcompl=NULL, dimmu, joint, argjoint, grjoint, arggrjoint)[1:n]
Constri <- function(i) arg$constr(z, i, arg$argconstr)
if(!is.null(arg$grconstr))
{
part2a <- unlist(sapply(1:arg$nplayer, Constri)) + w[1:m]
part3a <- lam * w[1:m]
}else
part2a <- part3a <- NULL
if(!is.null(arg$joint))
{
part2b <- arg$joint(x, arg$argjoint) + w[m+1:dimmu]
part3b <- mu * w[m+1:dimmu]
}else
part2b <- part3b <- NULL
c( part1, part2a, part2b, part3a, part3b )
}
#z = (x, lam, w)
#with size (n, m, m)
jacCER <- function(z, dimx, dimlam,
heobj, argheobj,
constr, argconstr,
grconstr, arggrconstr,
heconstr, argheconstr,
dimmu, joint, argjoint,
grjoint, arggrjoint,
hejoint, arghejoint,
echo=FALSE)
{
arg <- testargjacCER(z, dimx, dimlam, heobj, argheobj, constr, argconstr, grconstr, arggrconstr,
heconstr, argheconstr, dimmu, joint, argjoint, grjoint, arggrjoint,
hejoint, arghejoint, echo)
dimx <- arg$dimx
dimlam <- arg$dimlam
dimmu <- arg$dimmu
n <- sum(arg$dimx)
m <- sum(arg$dimlam)
p <- dimmu
x <- z[1:n]
lam <- z[(n+1):(n+m)]
mu <- z[(n+m+1):(n+m+p)]
w1 <- z[(n+m+p+1):(n+m+p+m)]
w2 <- z[(n+2*m+p+1):(n+2*m+2*p)]
nplayer <- arg$nplayer
#1st row is the begin index, 2nd row the end index
index4lam <- rbind( cumsum(dimlam) - dimlam + 1, cumsum(dimlam) )
index4x <- rbind( cumsum(dimx) - dimx + 1, cumsum(dimx) )
GrjConstri <- function(i)
{
#i index for player
sapply(index4x[1,i]:index4x[2,i], function(j) arg$grconstr(z, i, j, arg$arggrconstr))
}
jacconstrij <- function(i, j)
{
#i index for player, j index for x_j
arg$grconstr(z, i, j, arg$arggrconstr)
}
jacjointj <- function(j)
{
#j index for x_j
arg$grjoint(z, j, arg$arggrjoint)
}
partSSR <- jacSSR(z[1:(n+m+p)], dimx, dimlam, heobj, argheobj, constr, argconstr, grconstr, arggrconstr,
heconstr, argheconstr, gcompla=GrAphiFB, gcomplb=GrBphiFB, argcompl=NULL,
dimmu, joint, argjoint, grjoint, arggrjoint, hejoint, arghejoint)
#Hessian matrix of the Lagrangian
ggL <- partSSR[1:n, 1:n]
#gradient of the constraint function
if(!is.null(arg$heconstr))
gG <- partSSR[1:n, n+ 1:m]
#gradient of the joint function
if(!is.null(arg$hejoint))
gH <- partSSR[1:n, n+m+ 1:p]
#Jacobian of the constraint function
jacG <- matrix(0, m, n)
if(!is.null(arg$heconstr))
for(i in 1:nplayer)
for(j in 1:sum(dimx))
jacG[index4lam[1,i]:index4lam[2,i] , j] <- jacconstrij(i,j)
#Jacobian of the joint function
jacH <- matrix(0, p, n)
if(!is.null(arg$hejoint))
for(j in 1:sum(dimx))
jacH[, j] <- jacjointj(j)
m0mm <- matrix(0, m, m)
m0pp <- matrix(0, p, p)
m0mp <- matrix(0, m, p)
m0mn <- matrix(0, m, n)
m0pn <- matrix(0, p, n)
if(!is.null(arg$hejoint) && !is.null(arg$heconstr))
res <- rbind(cbind(ggL, gG, gH, t(m0mn), t(m0pn)),
cbind(jacG, m0mm, m0mp, diag(m), m0mp),
cbind(jacH, t(m0mp), m0pp, t(m0mp), diag(p)),
cbind(m0mn, diag(w1), m0mp, diag(lam), m0mp),
cbind(m0pn, t(m0mp), diag(w2), t(m0mp), diag(mu))
)
else if(is.null(arg$hejoint) && !is.null(arg$heconstr))
res <- rbind(cbind(ggL, gG, t(m0mn)),
cbind(jacG, m0mm, diag(m)),
cbind(m0mn, diag(w1), diag(lam))
)
else if(!is.null(arg$hejoint) && is.null(arg$heconstr))
res <- rbind(cbind(ggL, gH, t(m0pn)),
cbind(jacH, m0pp, diag(p)),
cbind(m0pn, diag(w2), diag(mu))
)
else
res <- ggL
return(res)
}
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