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#!/usr/bin/awk -f
### quad_reg.awk
# simple linear regression between columns
BEGIN {
OFMT="%.9g"
sign = "[+-]?"
decimal = "[0-9]+[.]?[0-9]*"
fraction = "[.][0-9]*"
exponent = "([Ee]" sign "[0-9]+)?"
number = "^" sign "(" decimal "|" fraction ")" exponent "$"
}
NR == 1 {
for (n=1; n<=NF; n++)
($n ~ number) ? header[n] = "col" n : header[n] = $n
}
NF > 0 {
if (NF > nf_max)
nf_max = NF
### iterate over columns
for (y=1; y<=nf_max; y++) {
if ($y ~ number) {
### mean
count[y] += 1
sum[y] += $y
sum2[y] += $y*$y
sum3[y] += $y*$y*$y
sum4[y] += $y*$y*$y*$y
mean[y] = sum[y]/count[y]
mean2[y] = sum2[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] = ""
# x = row, y = col, trendline: y = A + Bx + Cx^2
for (x=1; x<=nf_max; x++) {
count[x,y] += 1
sum_xy[x,y] += $x*$y
sum_x2y[x,y] += $x*$x*$y
sum_delta_xy[x,y] += delta[x]*delta[y]
# covariances
if (count[x,y] > 1) {
s_xx[x,y] = sum2[x]/(count[x,y]) - mean[x]*mean[x]
s_xy[x,y] = sum_xy[x,y]/(count[x,y]) - mean[x]*mean[y]
s_xx2[x,y] = sum3[x]/(count[x,y]) - mean[x]*mean2[x]
s_x2x2[x,y] = sum4[x]/(count[x,y]) - mean2[x]*mean2[x]
s_x2y[x,y] = sum_x2y[x]/(count[x,y]) - mean2[x]*mean[y]
}
bc_den[x,y] = (s_xx[x,y]*s_x2x2[x,y] - s_xx2[x,y]*s_xx2[x,y])
if (bc_den[x,y]) {
c[x,y] = (s_x2y[x,y]*s_xx[x,y] - s_xy[x,y]*s_xx2[x,y])/bc_den[x,y]
b[x,y] = (s_xy[x,y]*s_x2x2[x,y] - s_x2y[x,y]*s_xx2[x,y])/bc_den[x,y]
}
else {
c[x,y] = 0
b[x,y] = 0
}
a[x,y] = mean[y] - b[x,y]*mean[x] - c[x,y]*mean[x]*mean[x]
# error estimate
err[x,y] = ($y - (a[x,y] + b[x,y]*$x + c[x,y]*$x*$x))
sum_err2[x,y] += err[x,y]*err[x,y]
# correlation
sum_delta2[y] ? r2[x,y] = sum_err2[x,y]/sum_delta2[y] : r2[x,y] = 1
}
}
else
continue
}
}
END {
for (x=1; x<=nf_max; x++) {
for (y=1; y<=nf_max; y++) {
if (x != y && r2[x,y]) {
printf(OFMT OFS "(%s)" OFS " = (" OFMT ")(%s)^2" OFS " + (" OFMT ")(%s)" OFS " + (" OFMT ")" ORS,
10.0*log(r2[x,y])/log(10), header[y], c[x,y], header[x], b[x,y], header[x], a[x,y])
}
}
}
}
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