#!/usr/bin/awk -f

### det.awk
# determinant via LU
# input: square array as delimited text
# output: (scalar) determinant

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

NR == 1 {
    for (y=1; y<=NF; y++)
        ($y ~ number) ? header[y] = "col" y : header[y] = $y
}

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

    ### columns
    for (y=1; y<=nf_max; y++) {
        ### rows
        if ($y !~ number) {
            continue
        }
        else {
            read_data[NR,y] = $y
            col_sum[y] += $y
            row_sum[NR] += $y
        }
    }
}

END {
    print length(row_sum), length(col_sum)
    ### columns
    for (y=1; y<=nf_max; y++) {
        if (y in col_sum) {
            ### rows
            for (x=1; x<=NR; x++) {
                if (x in row_sum) {
                    printf("[" OFMT "," OFMT "]" OFS OFMT OFS OFMT,
                        x, y, read_data[x,y], col_sum[y])
                    if (x < nf_max)
                        printf(OFS)
                }
            }
        }
        printf(ORS)
    }
}