#!/usr/bin/awk -f

### diff2.awk
# print numerical second diff along columns
#  dy[n]   =  y[n]   -  y[n-1]
#  d2y[n]  =  dy[n]  -  dy[n-1]


BEGIN {
    OFS = FS
    sign = "[+-]?"
    decimal = "[0-9]+[.]?[0-9]*"
    fraction = "[.][0-9]*"
    exponent = "([Ee]" sign "[0-9]+)?"
    number = "^" sign "(" decimal "|" fraction ")" exponent "$"
}


# column headers
NR == 1 {
    # orig data columns
    for (n=1; n<=NF; n++) {
        if ($n !~ number) {
            header[n] = $n
            dheader[n] = "d_" $n
            d2header[n] = "d2_" $n
        }
        else {
            header[n] = "col" n
            dheader[n] = "d_col" n
            d2header[n] = "d2_col" n
        }
        printf(header[n])
        printf(OFS)
    }

    # new diff columns
    for (n=1; n<=NF; n++) {
        printf(dheader[n])
        printf(OFS)
    }

    # new diff2 columns
    for (n=1; n<=NF; n++) {
        printf(d2header[n])
        printf(n < NF ? OFS : ORS)
    }
}


NF > 0 {
    (NF > nf_max) ? nf_max = NF : nf_max = nf_max

    # orig data columns
    for (n=1; n<=nf_max; n++) {
        if ($n == header[n] || $n == dheader[n])
            continue
        if ($n ~ number)
            printf(OFMT, $n)
        else
            printf("")
        printf(OFS)
    }

    # new diff columns
    for (n=1; n<=nf_max; n++) {
        if ($n == header[n] || $n == dheader[n])
            continue
        if ($n ~ number) {
            data[n] = $n
            if (data_prev[n] ~ number)
                diff[n] = data[n] - data_prev[n]
            else
                diff[n] = ""
            data_prev[n] = data[n]
        }
        printf(diff[n])
        printf(OFS)
    }

    # new diff2 columns
    for (n=1; n<=nf_max; n++) {
        if ($n == header[n] || $n == d2header[n])
            continue
        if (diff[n] ~ number) {
            #data[n] = $n
            if (diff_prev[n] ~ number)
                diff2[n] = diff[n] - diff_prev[n]
            else
                diff2[n] = ""
            diff_prev[n] = diff[n]
        }
        printf(diff2[n])
        printf(n < nf_max ? OFS : ORS)
    }
}