## simulate a matrix A
## with 3 columns, each containing an exponential decay
t <- seq(0, 2, by = .04)
k <- c(.5, .6, 1)
A <- matrix(nrow = 51, ncol = 3)
Acolfunc <- function(k, t) exp(-k*t)
for(i in 1:3) A[,i] <- Acolfunc(k[i],t)
## simulate a matrix X
## with 3 columns, each containing a Gaussian shape
## 2 of the Gaussian shapes are non-negative and 1 is non-positive
X <- matrix(nrow = 51, ncol = 3)
wavenum <- seq(18000,28000, by=200)
location <- c(25000, 22000, 20000)
delta <- c(3000,3000,3000)
Xcolfunc <- function(wavenum, location, delta)
exp( - log(2) * (2 * (wavenum - location)/delta)^2)
for(i in 1:3) X[,i] <- Xcolfunc(wavenum, location[i], delta[i])
X[,2] <- -X[,2]
## set seed for reproducibility
set.seed(3300)
## simulated data is the product of A and X with some
## spherical Gaussian noise added
matdat <- A %*% t(X) + .005 * rnorm(nrow(A) * nrow(X))
## estimate the rows of X using NNNPLS criteria
nnnpls_sol <- function(matdat, A) {
X <- matrix(0, nrow = 51, ncol = 3)
for(i in 1:ncol(matdat))
X[i,] <- coef(nnnpls(A,matdat[,i],con=c(1,-1,1)))
X
}
X_nnnpls <- nnnpls_sol(matdat,A)
if (FALSE) {
## can solve the same problem with L-BFGS-B algorithm
## but need starting values for x and
## impose a very low/high bound where none is desired
bfgs_sol <- function(matdat, A) {
startval <- rep(0, ncol(A))
fn1 <- function(par1, b, A) sum( ( b - A %*% par1)^2)
X <- matrix(0, nrow = 51, ncol = 3)
for(i in 1:ncol(matdat))
X[i,] <- optim(startval, fn = fn1, b=matdat[,i], A=A,
lower=rep(0, -1000, 0), upper=c(1000,0,1000),
method="L-BFGS-B")$par
X
}
X_bfgs <- bfgs_sol(matdat,A)
## the RMS deviation under NNNPLS is less than under L-BFGS-B
sqrt(sum((X - X_nnnpls)^2)) < sqrt(sum((X - X_bfgs)^2))
## and L-BFGS-B is much slower
system.time(nnnpls_sol(matdat,A))
system.time(bfgs_sol(matdat,A))
## can also solve the same problem by reformulating it as a
## quadratic program (this requires the quadprog package; if you
## have quadprog installed, uncomment lines below starting with
## only 1 "#" )
# library(quadprog)
# quadprog_sol <- function(matdat, A) {
# X <- matrix(0, nrow = 51, ncol = 3)
# bvec <- rep(0, ncol(A))
# Dmat <- crossprod(A,A)
# Amat <- diag(c(1,-1,1))
# for(i in 1:ncol(matdat)) {
# dvec <- crossprod(A,matdat[,i])
# X[i,] <- solve.QP(dvec = dvec, bvec = bvec, Dmat=Dmat,
# Amat=Amat)$solution
# }
# X
# }
# X_quadprog <- quadprog_sol(matdat,A)
## the RMS deviation under NNNPLS is about the same as under quadprog
# sqrt(sum((X - X_nnnpls)^2))
# sqrt(sum((X - X_quadprog)^2))
## and quadprog requires about the same amount of time
# system.time(nnnpls_sol(matdat,A))
# system.time(quadprog_sol(matdat,A))
}
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