#Generic negative exponential function with offset
Ftaf <- function (t, s3, c, b, a, dc) {
.expr1 <- exp(b) 
.expr3 <- t - a
.expr5 <- exp(((-.expr1) * .expr3))
.expr6 <- 1 - .expr5
.value <- c*.expr6 + dc*s3*.expr6

# set gradient attribute
.actualArgs <- as.list(c("c", "b", "a", "dc"))
.grad <- array(0, c(length(.value), 4), list(NULL, c("c", "b", "a", "dc")))
.grad[, "c"] <- .expr6
.grad[, "b"] <- c * (.expr5 * (.expr1 * .expr3))
.grad[, "a"] <- -(c * (.expr5 * .expr1))
.grad[, "dc"] <- ifelse(s3, .expr6, 0)
dimnames(.grad) <- list(NULL, .actualArgs)
attr(.value, "gradient") <- .grad

# return
.value
}