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#!/usr/bin/awk -f
### cov.awk
# online covariance algorithm
BEGIN {
OFS = FS
sign = "[+-]?"
decimal = "[0-9]+[.]?[0-9]*"
fraction = "[.][0-9]*"
exponent = "([Ee]" sign "[0-9]+)?"
number = "^" sign "(" decimal "|" fraction ")" exponent "$"
}
# column headers
NR == 1 {
for (n=1; n<=NF; n++)
($n ~ number) ? header[n] = "col" n : header[n] = $n
}
NF > 0 {
(NF > nf_max) ? nf_max = NF : nf_max = nf_max
# columns
for (y=1; y<=nf_max; y++) {
# rows
for (x=1; x<=nf_max; x++) {
if ($x !~ number || $x == header[x])
continue
count[x,y]++
dx[x,y] = $x - meanx[x,y]
dy[x,y] = $y - meany[x,y]
meanx[x,y] += dx[x,y]/count[x,y]
meany[x,y] += dy[x,y]/count[x,y]
C[x,y] += dx[x,y]*dy[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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