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authorwukong <wukong@longaeva>2018-06-13 21:41:39 -0700
committerwukong <wukong@longaeva>2018-06-13 21:41:39 -0700
commit8875b420a873a360a9484778b487394add318a5e (patch)
treed357816354c5d9d4bc3b1db5c43ceda7933b5e3f
parent6bb6be845b6099550e0a530217633e30522093ad (diff)
added shebang, replaced if-elses with shortcut notation, ported online mean and variance calc to mean.awk
Diffstat (limited to '')
-rw-r--r--conv.awk2
-rw-r--r--diff.awk32
-rw-r--r--diff1.awk2
-rw-r--r--hamming.awk2
-rw-r--r--kalman.awk17
-rw-r--r--kalman_init.awk22
-rw-r--r--lin_reg.awk17
-rw-r--r--lin_reg1.awk12
-rw-r--r--lin_reg2.awk17
-rw-r--r--mean.awk37
-rw-r--r--mean_avg.awk22
-rw-r--r--pi.awk6
-rw-r--r--sample.desc.txt78
-rw-r--r--sampledata.txt17495
-rw-r--r--sterling_approx.txt10
-rw-r--r--sum1.awk13
-rw-r--r--sum2.awk10
-rw-r--r--sum3.awk17
-rw-r--r--sum4.awk9
19 files changed, 17701 insertions, 119 deletions
diff --git a/conv.awk b/conv.awk
index 73e176e..2248927 100644
--- a/conv.awk
+++ b/conv.awk
@@ -1,3 +1,5 @@
+#!/usr/bin/awk -f
+
### conv.awk
# [PoC] linear convolution (with hardcoded IR window).
diff --git a/diff.awk b/diff.awk
index 1032659..6dc427d 100644
--- a/diff.awk
+++ b/diff.awk
@@ -1,3 +1,5 @@
+#!/usr/bin/awk -f
+
### diff.awk
# numerical diff along columns
@@ -12,11 +14,16 @@ BEGIN {
NR == 1 {
header_nf = NF
for (n=1; n<=NF; n++) {
- if ($n !~ number)
- header[n] = "d" $n
- else
- header[n] = "col_" n
- printf("%s,", header[n])
+ printf("%s", $n)
+ ($n !~ number) ? dheader[n] = "d" $n : dheader[n] = "dcol_" n
+ if (n <= NF)
+ printf("%s", OFS)
+ }
+
+ for (n=1; n<=NF; n++) {
+ printf("%s", dheader[n])
+ if (n < NF)
+ printf("%s", OFS)
}
}
@@ -26,11 +33,22 @@ NF != 0 {
### iterate over columns
for (y=1; y<=max_nf; y++) {
+ if (match(dheader[y], $y))
+ continue
+ if ($y ~ number)
+ printf("%g", $y)
+ if (y <= max_nf)
+ printf("%s", OFS)
+ }
+
+ for (y=1; y<=max_nf; y++) {
if ($y ~ number) {
data[y] = $y
- diff[y] = data[y] - data_prev[y]
- printf("%g,", diff[y])
+ (data_prev[y] ~ number) ? diff[y] = data[y] - data_prev[y] : diff[y] = "nan"
data_prev[y] = data[y]
+ printf("%g", diff[y])
+ if (y < max_nf)
+ printf("%s", OFS)
}
}
printf("\n")
diff --git a/diff1.awk b/diff1.awk
index e5e8fea..cb86e00 100644
--- a/diff1.awk
+++ b/diff1.awk
@@ -1,3 +1,5 @@
+#!/usr/bin/awk -f
+
### diff.awk
# numerical diff along columns
diff --git a/hamming.awk b/hamming.awk
index c853003..21d241e 100644
--- a/hamming.awk
+++ b/hamming.awk
@@ -1,3 +1,5 @@
+#!/usr/bin/awk -f
+
### hamming.awk
# generate a Hamming window
# https://en.wikipedia.org/wiki/Window_function provides a few values for the
diff --git a/kalman.awk b/kalman.awk
index 18279b1..f67e9de 100644
--- a/kalman.awk
+++ b/kalman.awk
@@ -1,3 +1,5 @@
+#!/usr/bin/awk -f
+
### lin_reg.awk
# simple linear regression between columns
@@ -12,10 +14,7 @@ BEGIN {
NR == 1 {
header_nf = NF
for (n=1; n<=NF; n++) {
- if ($n !~ number)
- header[n] = $n
- else
- header[n] = "col_" n
+ ($n !~ number) ? header[n] = $n : header[n] = "col_" n
}
}
@@ -40,10 +39,7 @@ NF != 0 {
sum_delta2[y] += delta[y]*delta[y]
### sample variance
- if (count[y] - 1)
- var[y] = sum_delta2[y]/(count[y] - 1)
- else
- var[y] = 0
+ (count[y] - 1) ? var[y] = sum_delta2[y]/(count[y] - 1) : var[y] = 0
# x = row, y = col
for (x=1; x<=max_nf; x++) {
@@ -64,10 +60,7 @@ NF != 0 {
# correlation
r_den[x,y] = sqrt(sum_delta2[x]*sum_delta2[y])
- if (r_den[x,y])
- r[x,y] = sum_delta_xy[x,y]/r_den[x,y]
- else
- r[x,y] = 1
+ (r_den[x,y]) ? r[x,y] = sum_delta_xy[x,y]/r_den[x,y] : r[x,y] = 1
ab_den[x,y] = (count[x,y]*sum2[x] - sum[x]*sum[x])
if (ab_den[x,y]) {
diff --git a/kalman_init.awk b/kalman_init.awk
index 331d99a..f1dcac4 100644
--- a/kalman_init.awk
+++ b/kalman_init.awk
@@ -1,4 +1,4 @@
-#!/usr/bin/awk
+#!/usr/bin/awk -f
### kalman.awk
# kalman csv experiemnt
@@ -14,10 +14,7 @@ BEGIN {
NR == 1 {
header_nf = NF
for (n=1; n<=NF; n++) {
- if ($n !~ number)
- header[n] = "d" $n
- else
- header[n] = "col_" n
+ ($n !~ number) ? header[n] = "d" $n : header[n] = "col_" n
}
}
@@ -34,19 +31,13 @@ NF != 0 {
diff[n] = $n - last[n]
diff2[n] = 0.5*($n - 2.0*last[n] + last2[n])
sum[n] = $n + last[n] + last2[n]
- if (count[n])
- mean[n] = sum[n]/count[n]
- else
- mean[n] = sum[n]
+ (count[n]) ? mean[n] = sum[n]/count[n] : mean[n] = sum[n]
delta[n] = $n - mean[n]
delta2[n] = delta[n]*delta[n]
sum_delta[n] = delta[n] + delta_last[n] + delta_last2[n]
sum_delta2[n] = delta2[n] + delta2_last[n] + delta2_last2[n]
- if (count[n] > 1)
- var[n] = sum_delta2[n]/(count[n] - 1)
- else
- var[n] = 0
+ (count[n] > 1) ? var[n] = sum_delta2[n]/(count[n] - 1) : var[n] = 0
if (count[n]) {
meas_err[n] = sqrt(var[n]/count[n])
@@ -57,10 +48,7 @@ NF != 0 {
count[m,n]++
sum_xy[m,n] += 1
delta_xy[m,n] = delta[m]*delta[n]
- if (count[m,n] > 1)
- meas_cov[m,n] = delta[m]*delta[n]/(count[m,n] - 1)
- else
- meas_cov[m,n] = 0
+ (count[m,n] > 1) ? meas_cov[m,n] = delta[m]*delta[n]/(count[m,n] - 1) : meas_cov[m,n] = 0
est_err_last_cov[m,n] = 1
print meas_cov[m,n], est_err_last_cov[m,n]
}
diff --git a/lin_reg.awk b/lin_reg.awk
index 66d8aa6..e1cb722 100644
--- a/lin_reg.awk
+++ b/lin_reg.awk
@@ -1,3 +1,5 @@
+#!/usr/bin/awk -f
+
### lin_reg.awk
# simple linear regression between columns
@@ -12,10 +14,7 @@ BEGIN {
NR == 1 {
header_nf = NF
for (n=1; n<=NF; n++) {
- if ($n !~ number)
- header[n] = $n
- else
- header[n] = "col_" n
+ ($n !~ number) ? header[n] = $n : header[n] = "col_" n
}
}
@@ -40,10 +39,7 @@ NF != 0 {
sum_delta2[y] += delta[y]*delta[y]
### sample variance
- if (count[y] - 1)
- var[y] = sum_delta2[y]/(count[y] - 1)
- else
- var[y] = 0
+ (count[y] - 1) ? var[y] = sum_delta2[y]/(count[y] - 1) : var[y] = 0
# x = row, y = col
for (x=1; x<=max_nf; x++) {
@@ -53,10 +49,7 @@ NF != 0 {
# correlation
r_den[x,y] = sqrt(sum_delta2[x]*sum_delta2[y])
- if (r_den[x,y])
- r[x,y] = sum_delta_xy[x,y]/r_den[x,y]
- else
- r[x,y] = 1
+ (r_den[x,y]) ? r[x,y] = sum_delta_xy[x,y]/r_den[x,y] : r[x,y] = 1
ab_den[x,y] = (count[x,y]*sum2[x] - sum[x]*sum[x])
if (ab_den[x,y]) {
diff --git a/lin_reg1.awk b/lin_reg1.awk
index 866cab8..de1189f 100644
--- a/lin_reg1.awk
+++ b/lin_reg1.awk
@@ -1,3 +1,5 @@
+#!/usr/bin/awk -f
+
### lin_reg1.awk
# simple linear regression between individual text columns
@@ -12,10 +14,7 @@ BEGIN {
NR == 1 {
header_nf = NF
for (n=1; n<=NF; n++) {
- if ($n !~ number)
- header[n] = $n
- else
- header[n] = sprintf("col_%g", n)
+ ($n !~ number) ? header[n] = $n : header[n] = sprintf("col_%g", n)
}
}
@@ -45,10 +44,7 @@ NF != 0 {
sum_delta_xy[x,y] += delta[x]*delta[y]
r_den[x,y] = sqrt(sum_delta2[x]*sum_delta2[y])
- if (r_den[x,y])
- r[x,y] = sum_delta_xy[x,y]/r_den[x,y]
- else
- r[x,y] = 0
+ (r_den[x,y]) ? r[x,y] = sum_delta_xy[x,y]/r_den[x,y] : r[x,y] = 0
ab_den[x,y] = (count[x,y]*sum2[x] - sum[x]*sum[x])
if (ab_den[x,y]) {
diff --git a/lin_reg2.awk b/lin_reg2.awk
index 1f9ad31..7553c4e 100644
--- a/lin_reg2.awk
+++ b/lin_reg2.awk
@@ -1,3 +1,5 @@
+#!/usr/bin/awk -f
+
### lin_reg.awk
# simple linear regression between columns
@@ -12,10 +14,7 @@ BEGIN {
NR == 1 {
header_nf = NF
for (n=1; n<=NF; n++) {
- if ($n !~ number)
- header[n] = $n
- else
- header[n] = n
+ ($n !~ number) ? header[n] = $n : header[n] = n
}
}
@@ -40,10 +39,7 @@ NF != 0 {
sum_delta2[y] += delta[y]*delta[y]
### sample variance
- if (count[y] - 1)
- var[y] = sum_delta2[y]/(count[y] - 1)
- else
- var[y] = 0
+ (count[y] - 1) ? var[y] = sum_delta2[y]/(count[y] - 1) : var[y] = 0
# x = row, y = col
for (x=1; x<=max_nf; x++) {
@@ -53,10 +49,7 @@ NF != 0 {
# correlation
r_den[x,y] = sqrt(sum_delta2[x]*sum_delta2[y])
- if (r_den[x,y])
- r[x,y] = sum_delta_xy[x,y]/r_den[x,y]
- else
- r[x,y] = 1
+ (r_den[x,y]) ? r[x,y] = sum_delta_xy[x,y]/r_den[x,y] : r[x,y] = 1
ab_den[x,y] = (count[x,y]*sum2[x] - sum[x]*sum[x])
if (ab_den[x,y]) {
diff --git a/mean.awk b/mean.awk
index 45bedee..c1d31a6 100644
--- a/mean.awk
+++ b/mean.awk
@@ -1,13 +1,34 @@
+#!/usr/bin/awk -f
+
### mean.awk
-# find mean average of a list of numbers.
+# calculate mean average
BEGIN {
- X = ARGV[1]
- inputsize = split(X, Xarr)
- Yarr[n] = 0
- SUM = 0
- for (m=1; m <= inputsize; m++) {
- SUM =+ Xarr[m]
+ sign = "[+-±]?"
+ decimal = "[0-9]+[.]?[0-9]*"
+ fraction = "[.][0-9]*"
+ exponent = "([Ee]" sign "[0-9]+)?"
+ number = "^" sign "(" decimal "|" fraction ")" exponent "$"
+}
+
+# Welford's 'online' algorithm for variance
+NF > 0 {
+ for (m=1; m<=NF; m++) {
+ if (m ~ number) {
+ count += 1
+ delta0 = $m - mean
+ mean = mean + delta0/count
+ delta1 = $m - mean
+ M2 = M2 + delta0*delta1
+ if (count > 1)
+ var = M2/(count - 1)
+ else
+ var = "nan"
+ }
}
- print SUM
+}
+
+END {
+ print "mean", "std_dev", "std_err", "count"
+ print mean, sqrt(var), sqrt(var/count), count
}
diff --git a/mean_avg.awk b/mean_avg.awk
index 9864dae..945ed3c 100644
--- a/mean_avg.awk
+++ b/mean_avg.awk
@@ -1,4 +1,4 @@
-#!/usr/bin/awk
+#!/usr/bin/awk -f
### mean_avg.awk
# average columns of numerical data
@@ -20,7 +20,7 @@ NR == 1 {
}
# Welford's 'online' algorithm for variance
-NF != 0 {
+NF > 0 {
if (NF > max_nf)
max_nf = NF
for (n=1; n <= NF; n++) {
@@ -30,28 +30,18 @@ NF != 0 {
mean[n] = mean[n] + delta0[n]/count[n]
delta1[n] = $n - mean[n]
M2[n] = M2[n] + delta0[n]*delta1[n]
- if (count[n] > 1)
- var[n] = M2[n]/(count[n] - 1)
- else
- var[n] = "0"
+ (count[n] > 1) ? var[n] = M2[n]/(count[n] - 1) : var[n] = "0"
}
}
}
END {
- printf("\n")
- printf("%s, \t%s, %s, %s, %s\n", "col", "mean", "std_dev", "std_err", "count")
+ print "col", "mean", "std_dev", "std_err", "count"
for (n=1; n<=max_nf; n++) {
if (header[n])
- printf("%s, \t", header[n])
+ print header[n], mean[n], sqrt(var[n]), sqrt(var[n]/count[n]), count[n]
else
- printf("col_%g, \t", n)
- if (count[n]) {
- printf("%g, ±%g, ±%g, %g\n",
- mean[n], sqrt(var[n]), sqrt(var[n]/count[n]), count[n])
- }
- else
- printf(",,,,\n")
+ print "col_" n, mean[n], sqrt(var[n]), sqrt(var[n]/count[n]), count[n]
}
}
diff --git a/pi.awk b/pi.awk
index 7ecc4ab..cb476ac 100644
--- a/pi.awk
+++ b/pi.awk
@@ -1,3 +1,4 @@
+#! /usr/bin/awk -f
### pi.awk, https://en.wikipedia.org/wiki/Pi
# In 1706 John Machin used the Gregory–Leibniz series to produce an algorithm
@@ -15,10 +16,7 @@ function pi() {
}
BEGIN {
- if (ARGV[1] > 0)
- fig = ARGV[1]
- else
- fig = 6
+ (ARGV[1] > 0) ? fig = ARGV[1] : fig = 6
str = "%." fig "g\n"
printf(str, pi())
}
diff --git a/sample.desc.txt b/sample.desc.txt
new file mode 100644
index 0000000..d7c1c67
--- /dev/null
+++ b/sample.desc.txt
@@ -0,0 +1,78 @@
+File name: sample.descr.txt
+Author: Paul R. gazis
+Date: 7-APR-2006
+
+This file contains a description of the contents of sample.bin, a
+binary file of sample data for demonstration of the 'viewpoints'
+analysis package, along with a brief description of how that data
+can be used. This file contains a small subset of the Pioneer 10
+data set. The Pioneer 10 and 11 spacecraft, launched in 1972 and
+1973, respectively, were the first spacecraft to encounter
+Jupiter and Saturn, and in 1983, Pioneer 10 became the first
+man-made object to leave the solar system. The full data Pioneer
+data set is available from the National Space Science Data Center
+(NSSDC)
+
+http://nssdc.gsfc.nasa.gov/
+
+from their FTP site at
+
+ftp://nssdcftp.gsfc.nasa.gov/spacecraft_data/
+
+These data consist of a set of times, trajectory information, and
+hourly averaged solar wind speed, density, temperatures, and flow
+angles described below. They encompass the range of helioncentric
+distances between 1 and 17 AU when Pioneer 10 began to observe
+quasi-periodic co-rotating inbteraction regions associated with
+the interaction of low- and high-speed streams in the solar wind.
+Within these regions, solar wind speed is moderate (of the order
+400-500 km/s) while solar wind densoty and temperature are
+elevated. This is readily apparent if one compares scatter plots
+of speed, density, and temperature observed in 1972 and early 1973,
+when the spacecraft was comparatively close to the Sun, with
+scatter plots at later times and latger distances.
+
+NOTE 1: To compare solar wind densities and temperatures observed
+at different heliocentric distances, it is necessary to account for
+evolutionary effects as the solar wind is convected outward from
+the Sun. This is done by scaling the density, N, by heliocentric
+distance squared, to account for simple radial expansion and by
+scaling the temperature, T, by R^-0.6 to account for the
+empirically observed power-law dependance, which is significantly
+hotter than would be expected for simple adiabatic cooling.
+
+NOTE 2: While 'viewpoints' was NOT originally designed to display
+time series data, it can be used for this purpose.
+
+
+! File name: sample.txt - Hourly averaged Pioneer 10 solar wind parameters, 1972-1978
+! Field Parameter Comments
+! 1 Year - Year of measurement (Spacecraft ephemeris time at Pioneer 10)
+! 2 days-1950 - Time of measurement in days since day 1 of 1950
+! 3 R(AU) - Heliocentric distance of spacecraft in AU
+! 4 Phi - Heliographic longitude of spacecraft
+! 5 Theta - Heliographic latitude of spacecraft
+! 6 V(km/s) - Solar wind speed (km/s)
+! 7 NR2(#/cc) - Solar wind proton density multipled by R(AU)^2 to account for radial expansion
+! 8 TR-.6(K) - Solar wind proton temperature multipled by R(AU)^(-0.6) to account for radial expansion
+! 9 E/W - Solar wind E/W flow angle (+ = in the direction of planetary rotation)
+! 10 N/S - Solar wind N/S flow angle (+ = north of the ecliptic)
+! 11 N(#/cc) - Unmodified solar wind proton density
+! 12 T(K) - Unmodified solar wind proton temperature
+ Year days-1950 R_AU Phi Theta V(km/s) NR2(#/cc) TR-.6(K) E/W N/S N(#/cc) T(K)
+ 1973 8401.0000 3.35613 -66.357 -1.558 323.378 9.230828 4512.5 0.871 -1.960 0.819527 9330.9
+ 1973 8401.0417 3.35641 -66.353 -1.558 324.071 9.638469 5078.6 1.611 -2.156 0.855575 10502.0
+ 1973 8401.0833 3.35669 -66.348 -1.558 318.470 11.603700 5170.5 1.131 -2.431 1.029850 10692.6
+ 1973 8401.1250 3.35697 -66.343 -1.558 320.427 18.037112 4589.0 2.875 -3.245 1.600560 9490.5
+ 1973 8401.2083 3.35753 -66.334 -1.557 323.891 17.943892 6167.9 3.389 -4.430 1.591756 12757.1
+ 1973 8401.2500 3.35781 -66.329 -1.557 314.161 21.142727 6616.6 1.903 -4.754 1.875203 13685.7
+ 1973 8401.2917 3.35809 -66.324 -1.557 313.777 21.553091 7349.5 2.516 -4.421 1.911280 15202.4
+ 1973 8401.3333 3.35837 -66.320 -1.557 315.775 20.507291 6770.0 3.275 -3.545 1.818237 14004.4
+ 1973 8401.3750 3.35865 -66.315 -1.557 314.674 16.684952 5431.6 3.303 -3.288 1.479090 11236.4
+ 1973 8401.4167 3.35893 -66.310 -1.557 309.441 17.818612 5698.4 2.730 -3.644 1.579323 11789.0
+ 1973 8401.5000 3.35949 -66.301 -1.557 307.265 13.367473 5107.7 1.608 -2.427 1.184408 10568.0
+ 1973 8401.5417 3.35978 -66.296 -1.557 307.449 11.578219 4689.9 1.086 -2.623 1.025702 9704.0
+ 1973 8401.5833 3.36006 -66.291 -1.556 307.415 11.215317 4828.1 1.104 -2.634 0.993387 9990.5
+ 1973 8401.6250 3.36034 -66.286 -1.556 307.485 11.281679 4760.3 1.111 -2.637 0.999098 9850.7
+ 1973 8401.6667 3.36062 -66.282 -1.556 308.293 12.167288 4800.8 1.723 -2.613 1.077347 9934.9
+
diff --git a/sampledata.txt b/sampledata.txt
new file mode 100644
index 0000000..9c7e5ed
--- /dev/null
+++ b/sampledata.txt
@@ -0,0 +1,17495 @@
+ Year days-1950 R_AU Phi Theta V(km/s) NR2(#/cc) TR-.6(K) E/W N/S N(#/cc) T(K)
+ 1973 8401.0000 3.35613 -66.357 -1.558 323.378 9.230828 4512.5 0.871 -1.960 0.819527 9330.9
+ 1973 8401.0417 3.35641 -66.353 -1.558 324.071 9.638469 5078.6 1.611 -2.156 0.855575 10502.0
+ 1973 8401.0833 3.35669 -66.348 -1.558 318.470 11.603700 5170.5 1.131 -2.431 1.029850 10692.6
+ 1973 8401.1250 3.35697 -66.343 -1.558 320.427 18.037112 4589.0 2.875 -3.245 1.600560 9490.5
+ 1973 8401.2083 3.35753 -66.334 -1.557 323.891 17.943892 6167.9 3.389 -4.430 1.591756 12757.1
+ 1973 8401.2500 3.35781 -66.329 -1.557 314.161 21.142727 6616.6 1.903 -4.754 1.875203 13685.7
+ 1973 8401.2917 3.35809 -66.324 -1.557 313.777 21.553091 7349.5 2.516 -4.421 1.911280 15202.4
+ 1973 8401.3333 3.35837 -66.320 -1.557 315.775 20.507291 6770.0 3.275 -3.545 1.818237 14004.4
+ 1973 8401.3750 3.35865 -66.315 -1.557 314.674 16.684952 5431.6 3.303 -3.288 1.479090 11236.4
+ 1973 8401.4167 3.35893 -66.310 -1.557 309.441 17.818612 5698.4 2.730 -3.644 1.579323 11789.0
+ 1973 8401.5000 3.35949 -66.301 -1.557 307.265 13.367473 5107.7 1.608 -2.427 1.184408 10568.0
+ 1973 8401.5417 3.35978 -66.296 -1.557 307.449 11.578219 4689.9 1.086 -2.623 1.025702 9704.0
+ 1973 8401.5833 3.36006 -66.291 -1.556 307.415 11.215317 4828.1 1.104 -2.634 0.993387 9990.5
+ 1973 8401.6250 3.36034 -66.286 -1.556 307.485 11.281679 4760.3 1.111 -2.637 0.999098 9850.7
+ 1973 8401.6667 3.36062 -66.282 -1.556 308.293 12.167288 4800.8 1.723 -2.613 1.077347 9934.9
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+ 1977 10217.1667 14.66631 49.969 3.076 388.790 25.896810 2026.4 1.010 -0.636 0.120394 10151.2
+ 1977 10217.2083 14.66664 49.970 3.076 389.618 22.125381 2052.8 1.405 -0.764 0.102856 10283.8
+ 1977 10217.2500 14.66697 49.971 3.076 391.328 20.534497 2152.4 1.596 0.149 0.095456 10782.5
+ 1977 10217.2917 14.66730 49.971 3.076 391.421 21.659696 2055.1 2.005 -0.491 0.100682 10295.6
+ 1977 10217.3333 14.66764 49.972 3.076 385.698 16.644485 1650.3 1.077 1.132 0.077366 8267.4
+ 1977 10217.3750 14.66797 49.973 3.076 386.583 17.320379 1874.4 0.970 1.301 0.080504 9390.6
+ 1977 10217.4167 14.66830 49.974 3.076 383.761 14.532918 2022.4 1.567 0.608 0.067545 10132.1
+ 1977 10218.0000 14.67296 49.983 3.076 384.156 11.191501 2161.1 1.508 0.473 0.051982 10828.8
+ 1977 10218.0417 14.67329 49.984 3.076 385.926 16.026266 2597.3 2.338 -1.605 0.074435 13014.8
+ 1977 10218.0833 14.67363 49.985 3.076 387.114 13.545488 2154.7 1.552 -0.538 0.062910 10797.2
+ 1977 10218.1250 14.67396 49.986 3.076 389.410 24.625663 2389.9 0.803 -1.618 0.114365 11975.8
+ 1977 10218.2083 14.67463 49.987 3.076 394.808 11.498982 2302.8 0.767 -1.268 0.053398 11539.8
+ 1977 10218.2500 14.67497 49.988 3.076 393.425 7.002256 2532.2 0.697 -1.218 0.032515 12689.5
+ 1977 10218.2917 14.67530 49.988 3.076 393.576 10.872460 2518.2 0.742 -1.238 0.050484 12619.5
+ 1977 10218.3333 14.67564 49.989 3.076 393.286 11.337949 2497.6 1.013 -1.596 0.052643 12516.4
+ 1977 10218.3750 14.67597 49.990 3.076 377.955 14.782243 2231.6 0.994 -1.353 0.068632 11183.8
+ 1977 10218.4167 14.67631 49.991 3.076 377.978 12.371798 2203.5 0.990 -1.349 0.057438 11042.7
+ 1977 10219.2083 14.68265 50.004 3.076 379.679 5.979977 2222.4 1.500 -1.197 0.027739 11140.4
+ 1977 10219.3333 14.68364 50.006 3.076 381.258 9.649594 2222.3 0.788 -1.186 0.044755 11140.4
+ 1977 10219.3750 14.68397 50.007 3.076 376.372 10.690175 2413.3 2.066 -0.854 0.049579 12098.2
+ 1977 10220.2083 14.69060 50.021 3.077 385.879 3.588766 3819.4 0.707 -1.613 0.016629 19152.4
+ 1977 10225.2500 14.73094 50.107 3.077 362.736 2.649794 840.3 0.505 0.444 0.012211 4220.4
+ 1977 10226.4583 14.74062 50.127 3.078 363.659 2.843186 769.1 -0.469 0.089 0.013085 3864.6
+
diff --git a/sterling_approx.txt b/sterling_approx.txt
new file mode 100644
index 0000000..5cb3f6e
--- /dev/null
+++ b/sterling_approx.txt
@@ -0,0 +1,10 @@
+
+# https://en.wikipedia.org/wiki/Sterling_Approximation
+# An alternative approximation for the Gamma function stated by Srinivasa
+# Ramanujan (Ramanujan 1988) is
+
+ Gamma(1+x) ~= sqrt(pi)((x/e)^x)(8x^3 + 4x^2 + x + 1/30)^(1/6)
+
+# for x >= 0. The equivalent approximation for ln(n!) has an asymptotic error
+# of 1/(1400*n^3) ...
+
diff --git a/sum1.awk b/sum1.awk
index 02b7d6a..2f5a041 100644
--- a/sum1.awk
+++ b/sum1.awk
@@ -1,3 +1,5 @@
+#!/usr/bin/awk -f
+
### sum1.awk, print column sums
# input: rows of numbers
# output: sum of each column
@@ -6,16 +8,13 @@
{
for (i=1; i<=NF; i++)
sum[i] += $i
- if (NF > maxfld)
- maxfld = NF
+ if (NF > nf_max)
+ nf_max = NF
}
END {
- for (i=1; i<=maxfld; i++) {
+ for (i=1; i<=nf_max; i++) {
printf("%g", sum[i])
- if (i < maxfld)
- printf(" ")
- else
- printf("\n")
+ (i < nf_max) ? printf(" ") : printf("\n")
}
}
diff --git a/sum2.awk b/sum2.awk
index 0b2aad3..1df83ae 100644
--- a/sum2.awk
+++ b/sum2.awk
@@ -1,16 +1,18 @@
+#!/usr/bin/awk -f
+
### sum2.awk, print column sums
# check that each line has the same number of fields as line one
-NR==1 { nfld = NF }
+NR==1 { nf_max = NF }
{
for (i=1; i<=NF; i++)
sum[i] += $i
- if (NF != nfld)
- print "line " NR " has " NF " entries, not " nfld
+ if (NF != nf_max)
+ print "line " NR " has " NF " entries, not " nf_max
}
END {
for (i=1; i<=NF; i++)
- printf("%g%s", sum[i], i < nfld ? " " : "\n")
+ printf("%g%s", sum[i], i < nf_max ? " " : "\n")
}
diff --git a/sum3.awk b/sum3.awk
index b4100a7..8ceda8b 100644
--- a/sum3.awk
+++ b/sum3.awk
@@ -1,8 +1,16 @@
+#!/usr/bin/awk -f
+
### sum3.awk, print sums of numeric columns
# input: rows of integers and strings
# output: sums of numeric columns
# assumes every line has same layout
+
+function isnum(n) {
+ return n ~ /^[+-]?[0-9]+$/
+}
+
+
NR==1 {
nfld = NF
for (i=1; i<=NF; i++)
@@ -17,15 +25,8 @@ NR==1 {
END {
for (i=1; i<=nfld; i++) {
- if (numcol[i])
- printf("%g", sum[i])
- else
- printf("--")
+ (numcol[i]) ? printf("%g", sum[i]) : printf("--")
printf(i < nfld ? " " : "\n")
}
}
-function isnum(n) {
- return n ~ /^[+-]?[0-9]+$/
-}
-
diff --git a/sum4.awk b/sum4.awk
index c592409..518f6e5 100644
--- a/sum4.awk
+++ b/sum4.awk
@@ -1,3 +1,5 @@
+#!/usr/bin/awk -f
+
### sum4.awk, print sums of numeric columns
# input: rows of integers and strings
# output: sums of numeric columns
@@ -12,7 +14,7 @@ function isnum(n) {
}
NR==1 {
- nfldz = NF
+ nf_max = NF
for (i=1; i<=NF; i++) {
if (!isnum($i))
header[i] = $i
@@ -27,11 +29,10 @@ NR==1 {
}
END {
- for (i=1; i<=nfldz; i++) {
+ for (i=1; i<=nf_max; i++) {
if (header[i])
printf("%s: \t", header[i])
- #if (numcol[i])
printf("%g\n", sum[i])
- printf(i < nfldz ? "" : "\n")
+ printf(i < nf_max ? "" : "\n")
}
}
generated by cgit v1.2.3 (git 2.25.1) at 2026-03-18 09:10:46 +0000