#!/usr/bin/awk -f

### diff.awk
# numerical diff along columns

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

NR == 1 {
    header_nf = NF
    for (n=1; n<=NF; n++) {
        printf("%s", $n)
        ($n !~ number) ?  dheader[n] = "d" $n : dheader[n] = "dcol_" n
        if (n <= NF)
            printf("%s", OFS)
    }

    for (n=1; n<=NF; n++) {
        printf("%s", dheader[n])
        if (n < NF)
            printf("%s", OFS)
    }
}

NF != 0 {
    if (NF > max_nf)
        max_nf = NF

    ### iterate over columns
    for (y=1; y<=max_nf; y++) {
        if (match(dheader[y], $y))
            continue
        if ($y ~ number)
            printf("%g", $y)
        if (y <= max_nf)
            printf("%s", OFS)
    }

    for (y=1; y<=max_nf; y++) {
        if ($y ~ number) {
            data[y] = $y
            (data_prev[y] ~ number) ?  diff[y] = data[y] - data_prev[y] : diff[y] = "nan"
            data_prev[y] = data[y]
            printf("%g", diff[y])
            if (y < max_nf)
                printf("%s", OFS)
        }
    }
    printf("\n")
}