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#!/usr/bin/awk -f
### cov.awk
# online covariance algorithm
BEGIN {
OFMT = "%.18g"
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] = $y
printf(header[y])
}
NF > 0 {
if (NF > nf_max)
nf_max = NF
### columns
for (y=1; y<=nf_max; y++) {
if ($y == header[y])
continue
### rows
for (x=1; x<=nf_max; x++) {
count[x,y]++
dx[x,y] = $x - meanx[x,y]
meanx[x,y] += dx[x,y]/count[x,y]
meany[x,y] += ($y - meany[x,y])/count[x,y]
C[x,y] += dx[x,y]*($y - meany[x,y])
cov_pop[x,y] = C[x,y]/count[x,y]
(count[x,y] > 1) ? cov_samp[x,y] = C[x,y]/(count[x,y] - 1) : cov_samp[x,y] = ""
}
}
}
END {
### column headers
printf("cov")
for (y=1; y<=nf_max; y++) {
printf(OFS header[y])
}
printf(ORS)
### columns
for (y=1; y<=nf_max; y++) {
printf(header[y] OFS)
### rows
for (x=1; x<=nf_max; x++) {
printf(OFMT, cov_samp[x,y])
if (x < nf_max)
printf(OFS)
}
printf(ORS)
}
}
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