Commit 177ab79a authored by shiy's avatar shiy
Browse files

Ver8: adjusted on ver7, inv = solve(covF,...)

parent 2fbf0645
Env8 <- funEnv(
info = "inv-solve(covF)",
# Initialize the weight -- Find first free weight
initAlgo = function(mu, lB, uB ){
#New-ordered return, lB, uB with decreasing return
w <- c()
index.new <- order(mu,decreasing = TRUE) # new order with decreasing return
lB.new <- lB[index.new]
uB.new <- uB[index.new]
# free weight - starting solution
i.new <- 0
w.new <- lB.new # initialy
while(sum(w.new) < 1) {
i.new <- i.new + 1
w.new[i.new] <- uB.new[i.new]
}
w.new[i.new] <- 1 - sum(w.new[-i.new])
w[index.new] <- w.new #back to original order
i <- index.new[i.new]
list(index = i, weights = w) # return the index of first free asset and vector w
},
# getMatrices --- -------------------------------------------------------------
getMatrices = function(mu, covar, w, f){
# Slice covarF,covarFB,covarB,muF,muB,wF,wB
covarF <- covar[f,f]
muF <- mu[f]
b <- (seq_along(mu))[-f]
covarFB <- covar[f,b]
wB <- w[b]
return(list(covarF = covarF, covarFB = covarFB, muF = muF, wB = wB))
},
computeInv = function(get){
solve(get$covarF, cbind(1, get$muF, get$covarFB %*% get$wB, deparse.level = 0L))
},
# computeW -----------------------------------------------------------------
computeW = function(lam, inv, wB){
# w2 <- inv[,1]; w3 <- inv[,2]; w1 <- inv[,3]
inv.s <- colSums(inv) # g1 <- inv.s[2]; g2 <- inv.s[1]; g4 <- inv.s[3]
#1) compute gamma
g <- (-lam * inv.s[2] + (1- sum(wB) + inv.s[3]))/inv.s[1]
#2) compute free weights
list(wF = - inv[,3] + g * inv[,1] + lam * inv[,2], gamma = g)
},
# computeLambda --------------------------------------------------------------
computeLambda = function(wB, inv, i, bi.input){
inv.s <- colSums(inv)
# c1 <- inv.s[1]; l2 <- inv.s[3]; c2i <- inv[i,2];
# c3 <- inv.s[2]; c4i <- inv[i, 1]; l1 <- sum(wB)
c1 <- inv.s[1]
if(length(bi.input)==1){ # 1.bound to free
c4i <- inv[i, 1]
Ci <- - c1 * inv[i, 2] + inv.s[2] * c4i
if(Ci == 0) 0
((1- sum(wB) + inv.s[3])* c4i- c1 * (bi.input + inv[i, 3]))/Ci # return lambda
} else { # 2.free to bound
c4i <- inv[, 1]
Ci <- - c1 * inv[, 2] + inv.s[2] * c4i
bi <- bi.input[i, 1] # bi.lB
bi[Ci > 0] <- bi.input[i[Ci > 0], 2] # bi.uB
bi[Ci == 0] <- 0
list(lambda = ((1- sum(wB) + inv.s[3]) * c4i- c1 *(bi + inv[, 3]))/Ci,
bi = bi)
# return lambda and boundary
}
},
MS = function(weights_set, mu, covar){
Sig2 <- colSums(weights_set *(covar %*% weights_set) )
cbind(Sig = sqrt(Sig2), Mu = as.vector(t(weights_set) %*% mu))
},
cla.solve = function(cla.input){
options(digits = 3)
# Compute the turning points, free sets and weights
mu <- cla.input$mu
covar <- cla.input$covar
lB <- cla.input$lB
uB <- cla.input$uB
ans <- initAlgo(mu, lB, uB)
f <- ans$index
w <- ans$weights
weights_set <- w # store solution
lambdas <- NA # The first step has no lambda or gamma, add NA instead.
gammas <- NA
free_indices <- list(f)
lam <- 1 # set non-zero lam
while ( lam > 0 && length(f) < length(mu)) {
# 1) case a): Bound one free weight F -> B
l_in <- 0
if(length(f) > 1 ){
compl <- computeLambda(wB = w[-f], inv = inv, # inv from last step k (k >= 1)
i = f, bi.input = cbind(lB, uB))
lam_in <- compl$lambda
bi <- compl$bi
k <- which.max(lam_in)
i_in <- f[k]
bi_in <- bi[k]
l_in <- lam_in[k]
}
# 2) case b): Free one bounded weight B -> F
b <- seq_along(mu)[-f]
inv_list <- lapply(b, function(bi){
get_i <- getMatrices(mu, covar, w, c(f,bi))
computeInv(get_i)
})
fi <- length(f) + 1
lam_out <- sapply(seq_along(b), function(i) {
computeLambda(wB = w[b[-i]], inv = inv_list[[i]],
i = fi, bi.input = w[b[i]])
})
if (length(lambdas) > 1 && any(!(sml <- lam_out < lam*(1-1e-7)))) {## tol
lam_out <- lam_out[sml]
b <- b [sml]
inv_list <- inv_list[sml]
}
k <- which.max(lam_out)
i_out <- b [k] # one only !
l_out <- lam_out[k]
inv_out <- inv_list[[k]]
# 3) decide lambda
lam <- max(l_in, l_out, 0)
if(lam > 0) { # remove i_in from f; or add i_out into f
if(l_in > l_out ){
f <- f[f != i_in]
w[i_in] <- bi_in # set value at the correct boundary
getM <- getMatrices(mu, covar, w, f)
inv <- computeInv(getM)
}
else {
f <- c(f,i_out)
inv <- inv_out
}
compW <- computeW(lam, inv = inv, wB = w[-f])
}
else{ #4) if max(l_in, l_out) < 0, "stop" when at the min var solution!
compW <- computeW(lam = lam, inv = inv, wB = w[-f])
# muF = 0 not necessary, get1 replaced by getM (ie getM from previous step)
}
wF <- compW$wF
g <- compW$gamma
w[f] <- wF[seq_along(f)]
lambdas <- c(lambdas, lam)
weights_set <- cbind(weights_set, w, deparse.level = 0L) # store solution
gammas <- c(gammas, g)
free_indices <- c(free_indices, list(sort(f)))
} #end While
list(weights_set = weights_set,
free_indices = free_indices,
gammas = gammas, lambdas = lambdas,
MS_weight = MS(weights_set = weights_set, mu = mu, covar = covar))
}
)
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