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#!/usr/bin/awk -f
### lin_reg.awk
# simple linear regression between columns
BEGIN {
sign = "[+-]?"
decimal = "[0-9]+[.]?[0-9]*"
fraction = "[.][0-9]*"
exponent = "([Ee]" sign "[0-9]+)?"
number = "^" sign "(" decimal "|" fraction ")" exponent "$"
}
NR == 1 {
header_nf = NF
for (n=1; n<=NF; n++) {
($n !~ number) ? header[n] = $n : header[n] = "col_" n
}
}
NF != 0 {
#printf("\n%s: %s", NR, $0)
if (NF > max_nf)
max_nf = NF
### iterate over columns
for (y=1; y<=max_nf; y++) {
if ($y ~ number) {
### mean
count[y] += 1
sum[y] += $y
sum2[y] += $y*$y
mean[y] = sum[y]/count[y]
### difference from the mean
delta[y] = $y - mean[y]
sum_delta[y] += delta[y]
sum_delta2[y] += delta[y]*delta[y]
### sample variance
(count[y] - 1) ? var[y] = sum_delta2[y]/(count[y] - 1) : var[y] = 0
# x = row, y = col
for (x=1; x<=max_nf; x++) {
count[x,y] += 1
sum_xy[x,y] += $x*$y
sum_delta_xy[x,y] += delta[x]*delta[y]
# correlation
r_den[x,y] = sqrt(sum_delta2[x]*sum_delta2[y])
(r_den[x,y]) ? r[x,y] = sum_delta_xy[x,y]/r_den[x,y] : r[x,y] = 1
ab_den[x,y] = (count[x,y]*sum2[x] - sum[x]*sum[x])
if (ab_den[x,y]) {
a[x,y] = (sum[y]*sum2[x] - sum[x]*sum_xy[x,y])/ab_den[x,y]
b[x,y] = (count[x,y]*sum_xy[x,y] - sum[x]*sum[y])/ab_den[x,y]
}
else {
a[x,y] = 0
b[x,y] = 1
}
### error estimate
err_den[x,y] = count[x,y]*(count[x,y] - 2)
if (count[x,y] > 2) {
err[x,y] = $y - (a[x,y] + b[x,y]*$x)
sum_err2[x,y] += err[x,y]*err[x,y]
}
b_err_den[x,y] = (count[x,y] - 2)*sum_delta2[x]
if (b_err_den[x,y])
b_err[x,y] = sqrt(sum_err2[x,y]/b_err_den[x,y])
a_err_den[x,y] = count[x,y]*b_err_den[x,y]
if (a_err_den[x,y])
a_err[x,y] = sqrt(sum2[x]/count[x,y])*b_err[x,y]
}
}
else
continue
}
}
END {
for (y=1; y<=max_nf; y++) {
for (x=1; x<=max_nf; x++) {
if (x != y && r[x,y]) {
printf("\n %g \t (%s) \t = (%g +/- %g)(%s) \t + (%g +/- %g)",
10.0*log(r[x,y]*r[x,y])/log(10), header[y], b[x,y], b_err[x,y], header[x],
a[x,y], a_err[x,y])
}
}
}
}
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