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#!/usr/bin/awk -f
### quad_reg.awk
# quadratic regression along columns
BEGIN {
OFS = ":"
pi = 4.0*atan2(1.0, 1.0)
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] = $n
}
# read input data
NF > 0 {
(NF > nf_max) ? nf_max = NF : nf_max = nf_max
# columns
for (y=1; y<=nf_max; y++) {
if ($y == header[n])
continue
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
delta0[y] = $y - mean[y]
mean[y] += delta0[y]/count[y]
mean2[y] = sum2[y]/count[y]
delta1[y] = $y - mean[y]
delta2[y] = delta0[y]*delta1[y]
sum_delta[y] += delta1[y]
sum_delta2[y] += delta2[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_xy[x,y] += 1
sum_xy[x,y] += $x*$y
sum_x2y[x,y] += $x*$x*$y
# covariances
if (count_xy[x,y] > 0) {
s_xx[x,y] = sum2[x]/count_xy[x,y] - mean[x]*mean[x]
s_xy[x,y] = sum_xy[x,y]/count_xy[x,y] - mean[x]*mean[y]
s_xx2[x,y] = sum3[x]/count_xy[x,y] - mean[x]*mean2[x]
s_x2x2[x,y] = sum4[x]/count_xy[x,y] - mean2[x]*mean2[x]
s_x2y[x,y] = sum_x2y[x,y]/count_xy[x,y] - mean2[x]*mean[y]
}
else {
s_xx[x,y] = 0
s_xy[x,y] = 0
s_xx2[x,y] = 0
s_x2x2[x,y] = 0
s_x2y[x,y] = 0
}
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] != 0) {
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]*mean2[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] = 1 - sum_err2[x,y]/sum_delta2[y] : r2[x,y] = 0
#print a[x,y],b[x,y],c[x,y],err[x,y],sum_err2[x,y]
# quadratic roots (x-intercepts)
if (c[x,y] != 0) {
D[x,y] = b[x,y]*b[x,y] - 4.0*a[x,y]*c[x,y]
if (D[x,y] >= 0) {
rx0[x,y] = 0.5*(-1.0*b[x,y] - sqrt(D[x,y]))/c[x,y]
rx1[x,y] = 0.5*(-1.0*b[x,y] + sqrt(D[x,y]))/c[x,y]
}
if (D[x,y] < 0) {
rx_real[x,y] = -0.5*b[x,y]/c[x,y]
rx_imag[x,y] = 0.5*sqrt(-1.0*D[x,y])/c[x,y]
rx0[x,y] = rx_real[x,y]
rx1[x,y] = rx_real[x,y]
}
# vertex of parabola
xv[x,y] = -0.5*b[x,y]/c[x,y]
yv[x,y] = -0.25*(b[x,y]*b[x,y])/c[x,y] + a[x,y]
# focus of parabola
xf[x,y] = -0.5*b[x,y]/c[x,y]
yf[x,y] = (4.0*a[x,y]*c[x,y] - b[x,y]*b[x,y] + 1.0)/(4.0*c[x,y])
}
}
}
else
continue
}
}
END {
for (x=1; x<=nf_max; x++) {
for (y=1; y<=nf_max; y++) {
if (x != y) {
printf(OFMT OFS "(%s)" OFS "= (" OFMT ")(%s)^2 + (" OFMT ")(%s) + (" OFMT ")" OFS,
r2[x,y], header[y], c[x,y], header[x], b[x,y], header[x], a[x,y])
printf("[" OFMT "," OFMT "][" OFMT "," OFMT "][" OFMT "," OFMT "]" OFS "[" OFMT "," OFMT "]",
rx0[x,y], (a[x,y] + b[x,y]*rx0[x,y] + c[x,y]*rx0[x,y]*rx0[x,y]),
rx1[x,y], (a[x,y] + b[x,y]*rx1[x,y] + c[x,y]*rx1[x,y]*rx1[x,y]),
0, a[x,y],
xv[x,y], yv[x,y])
printf(OFS "[" OFMT "," OFMT "]", xf[x,y], yf[x,y])
printf(OFS "[" OFMT "]" ORS, (yf[x,y] - yv[x,y]))
}
}
}
}
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