#!/usr/bin/awk -f

### mean_avg.awk
# average columns of numerical data

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++) {
        if ($n !~ number)
            header[n] = $n
    }
}

# Welford's 'online' algorithm for variance
NF > 0 {
    if (NF > max_nf)
        max_nf = NF
    for (n=1; n <= NF; n++) {
        if ($n ~ number) {
            count[n] += 1
            delta0[n] = $n - mean[n]
            mean[n] = mean[n] + delta0[n]/count[n]
            delta1[n] = $n - mean[n]
            M2[n] = M2[n] + delta0[n]*delta1[n]
            (count[n] > 1) ? var[n] = M2[n]/(count[n] - 1) : var[n] = "0"
        }
    }
}

END {
    print "col", "mean", "std_dev", "std_err", "count"
    for (n=1; n<=max_nf; n++) {
        if (header[n])
            print header[n], mean[n], sqrt(var[n]), sqrt(var[n]/count[n]), count[n]
        else
            print "col_" n, mean[n], sqrt(var[n]), sqrt(var[n]/count[n]), count[n]
    }
}