R Code: Apply a function to each element of a list (or data frame) or to each element of a list within a list of data while retaining the names attribute of each nested list

lf.compute.data.column <- function(dat.list, func, ...)
{ 
    ## Purpose: Apply a function to each column of a list (e.g. data frame). Retains the names information.  
    ##          Basis for processing more complex data (e.g. a list of a list)
    ## Arguments:
    ##     dat.list: a list of data (e.g. data frame)
    ##     func: a function that computes a vector (may have an argument "name")
    ##     ...: passed to "func"
    ## Return:
    ##    a list of outputs. 
    ## Author: Feiming Chen, Date: 30 Jan 2017, 13:21
    ## ________________________________________________

    this.name <- null2na(names(dat.list))

    mapply(func, 
           dat.list, 
           name = this.name, 
           ..., 
           SIMPLIFY = FALSE
           )
}
if (F) {                                # Unit Test
    dat.list = data.frame(x=rnorm(10), y=rnorm(10))
    lf.compute.data.column(dat.list, mean)
    lf.compute.data.column(dat.list, function(x, ...) { c(a=mean(x), b=sd(x)) })
    lf.compute.data.column(dat.list, function(x, name) { list(a=mean(x), n=name) })
}


lf.compute.data.column.2 <- function(dat.list, func, ...)
{ 
    ## Purpose: Apply a function to a list of a list of data. Retains the names information.  
    ## Arguments:
    ##   dat.list: a list of a list
    ##   func: a function that computes a vector.  (may have an argument "name")
    ## Return: a list of list of results
    ## Author: Feiming Chen, Date:  6 Feb 2017, 12:50
    ## ________________________________________________
    
    this.name <- null2na(names(dat.list))

    mapply(
        function(d, name) {
            if (!is.na(name)) names(d) <- paste0(name, ".", names(d))
            lf.compute.data.column(d, func)
        },
        dat.list, 
        name = this.name, 
        ..., 
        SIMPLIFY = FALSE
    )
}
if (F) {                                # Unit Test
    dat.list.2 = list(test1 = data.frame(x=1:5, y=6:10), test2= data.frame(x=11:15, y=16:20))
    lf.compute.data.column.2(dat.list.2, mean)
    lf.compute.data.column.2(dat.list.2, function(x, ...) { c(m=mean(x), s=sd(x)) })
    lf.compute.data.column.2(dat.list.2, function(x, name) { list(m=mean(x), n=name) })
}

null2na <- function(x) {
    ## if the value of x is NULL(as determined by length test since is.null may
    ## not always work), turn it into NA so that an object
    ## made of it will always exist.
    if (length(x)==0)
        x <- NA
    x
}