renamed fir window generators;

minor edits to whitespace and comments for more consistent style;

30 files changed, 325 insertions, 129 deletions

diff --git a/binom_coeff.awk b/binom_coeff.awk
index a19f464..6896671 100644
--- a/binom_coeff.awk
+++ b/binom_coeff.awk
@@ -1,7 +1,9 @@
-#! /usr/bin/awk -f
+#!/usr/bin/awk -f
 
 ### binomial coeffecient
 # https://rosettacode.org/wiki/Evaluate_binomial_coefficients
+
+
 function binom(n, k) {
     b = 1
     for (i=1; i<(k+1); i++) {
@@ -10,9 +12,11 @@ function binom(n, k) {
     return b
 }
 
+
 BEGIN {
     ARGV[1] ? N = ARGV[1] : N = 1
     ARGV[2] ? K = ARGV[2] : K = 1
     ARGV[3] ? OFMT = "%." ARGV[3] "g" : OFMT = "%g"
     printf(OFMT ORS, binom(N, K))
 }
+
diff --git a/conv.awk b/conv.awk
index b7e48eb..e46dcdf 100644
--- a/conv.awk
+++ b/conv.awk
@@ -3,6 +3,7 @@
 ### conv.awk

 # [PoC] linear convolution (with hardcoded IR window).

 

+

 BEGIN {

     ARGV[1] ? X = ARGV[1] : X = 0

     ARGV[2] ? OFMT = "%." ARGV[2] "g" : OFMT = "%g"

diff --git a/cov.awk b/cov.awk
index c06a447..92e92a8 100644
--- a/cov.awk
+++ b/cov.awk
@@ -3,6 +3,7 @@
 ### cov.awk
 # online covariance algorithm
 
+
 BEGIN {
     OFS = FS
     sign = "[+-]?"
@@ -12,18 +13,20 @@ BEGIN {
     number = "^" sign "(" decimal "|" fraction ")" exponent "$"
 }
 
+
+# column headers
 NR == 1 {
-    for (y=1; y<=NF; y++)
-        ($y ~ number) ? header[y] = "col" y : header[y] = $y
+    for (n=1; n<=NF; n++)
+        ($n ~ number) ? header[n] = "col" n : header[n] = $n
 }
 
+
 NF > 0 {
-    if (NF > nf_max)
-        nf_max = NF
+    (NF > nf_max) ? nf_max = NF : nf_max = nf_max
 
-    ### columns
+    # columns
     for (y=1; y<=nf_max; y++) {
-        ### rows
+        # rows
         for (x=1; x<=nf_max; x++) {
             if ($x !~ number || $x == header[x])
                 continue
@@ -39,18 +42,19 @@ NF > 0 {
     }
 }
 
+
 END {
-    ### column headers
+    # column headers
     printf("cov")
     for (y=1; y<=nf_max; y++) {
         printf(OFS header[y])
     }
     printf(ORS)
 
-    ### columns
+    # columns
     for (y=1; y<=nf_max; y++) {
         printf(header[y] OFS)
-        ### rows
+        # rows
         for (x=1; x<=nf_max; x++) {
             printf(OFMT, cov_samp[x,y])
             if (x < nf_max)
@@ -59,3 +63,4 @@ END {
         printf(ORS)
     }
 }
+
diff --git a/det.awk b/det.awk
index b3e5c1f..e83a9ea 100644
--- a/det.awk
+++ b/det.awk
@@ -5,6 +5,7 @@
 # input: square array as delimited text
 # output: (scalar) determinant
 
+
 BEGIN {
     OFS = "\t"
     sign = "[+-]?"
@@ -14,17 +15,21 @@ BEGIN {
     number = "^" sign "(" decimal "|" fraction ")" exponent "$"
 }
 
+
+# column headers
 NR == 1 {
     for (y=1; y<=NF; y++)
         ($y ~ number) ? header[y] = "col" y : header[y] = $y
 }
 
+
+# read input data
 NF > 0 {
     (NF > nf_max) ? nf_max = NF : nf_max = nf_max
 
-    ### columns
+    # columns
     for (y=1; y<=nf_max; y++) {
-        ### rows
+        # rows
         if ($y !~ number) {
             continue
         }
@@ -36,12 +41,13 @@ NF > 0 {
     }
 }
 
+
 END {
     print length(row_sum), length(col_sum)
-    ### columns
+    # columns
     for (y=1; y<=nf_max; y++) {
         if (y in col_sum) {
-            ### rows
+            # rows
             for (x=1; x<=NR; x++) {
                 if (x in row_sum) {
                     printf("[" OFMT "," OFMT "]" OFS OFMT OFS OFMT,
diff --git a/diff.awk b/diff.awk
index bf8b472..83fd0b5 100644
--- a/diff.awk
+++ b/diff.awk
@@ -3,9 +3,9 @@
 ### diff.awk
 # print numerical diff along columns
 
+
 BEGIN {
     OFS = FS
-    # OFMT = "%.9g"
     sign = "[+-]?"
     decimal = "[0-9]+[.]?[0-9]*"
     fraction = "[.][0-9]*"
@@ -13,6 +13,8 @@ BEGIN {
     number = "^" sign "(" decimal "|" fraction ")" exponent "$"
 }
 
+
+# column headers
 NR == 1 {
     # orig data columns
     for (n=1; n<=NF; n++) {
@@ -35,9 +37,9 @@ NR == 1 {
     }
 }
 
-NF {
-    if (NF > nf_max)
-        nf_max = NF
+
+NF > 0 {
+    (NF > nf_max) ? nf_max = NF : nf_max = nf_max
 
     # data columns
     for (n=1; n<=nf_max; n++) {
diff --git a/diff1.awk b/diff1.awk
index 7322e98..a6bf6ec 100644
--- a/diff1.awk
+++ b/diff1.awk
@@ -3,9 +3,9 @@
 ### diff1.awk
 # print numerical diff along columns
 
+
 BEGIN {
     OFS = FS
-    # OFMT = "%.9g"
     sign = "[+-]?"
     decimal = "[0-9]+[.]?[0-9]*"
     fraction = "[.][0-9]*"
@@ -13,6 +13,8 @@ BEGIN {
     number = "^" sign "(" decimal "|" fraction ")" exponent "$"
 }
 
+
+# column headers
 NR == 1 {
     # orig data columns
     for (n=1; n<=NF; n++) {
@@ -29,9 +31,9 @@ NR == 1 {
     }
 }
 
-NF {
-    if (NF > nf_max)
-        nf_max = NF
+
+NF > 0 {
+    (NF > nf_max) ? nf_max = NF : nf_max = nf_max
 
     # data columns
     for (n=1; n<=nf_max; n++) {
diff --git a/em.awk b/em.awk
index c956fa1..2cc6a74 100644
--- a/em.awk
+++ b/em.awk
@@ -1,9 +1,13 @@
 #!/usr/bin/awk -f
 
+### em.awk
+# list of physical EM constants
+
+
 BEGIN {
     ARGV[1] ? OFMT = "%." ARGV[1] "g" : OFMT = "%.12g"
 
-    ### constants
+    # constants
     pi = 4.0*atan2(1,1)         # rad
     c0 = 299792458E0            # m/s, exact
     mu0 = (4.0E-7)*pi           # H/m = (T*m)/A = N/(A^2) = (kg*m)/(A*s)
@@ -11,3 +15,4 @@ BEGIN {
 
     print pi, c0, mu0, epsilon0
 }
+
diff --git a/exp_reg.awk b/exp_reg.awk
index f4ea12c..fac4b8f 100644
--- a/exp_reg.awk
+++ b/exp_reg.awk
@@ -3,6 +3,7 @@
 ### lin_reg.awk
 # simple linear regression between columns
 
+
 BEGIN {
     OFS = ":"
     sign = "[+-]?"
@@ -12,23 +13,25 @@ BEGIN {
     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 {
-    if (NF > nf_max)
-        nf_max = NF
 
-    ### iterate over columns
+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
+            # mean
             count[y] += 1
             data[y] = log($y)
             sum[y] += data[y]
@@ -39,7 +42,7 @@ NF {
             sum_delta[y] += delta1[y]
             sum_delta2[y] += delta0[y]*delta1[y]
 
-            ### sample variance
+            # sample variance
             #(count[y] > 1) ? var[y] = sum_delta2[y]/(count[y] - 1) : var[y] = ""
 
             # x = row, y = col, trendline: y = A + Bx
@@ -92,6 +95,7 @@ NF {
     }
 }
 
+
 END {
     for (y=1; y<=nf_max; y++) {
         for (x=1; x<=nf_max; x++) {
diff --git a/fib.awk b/fib.awk
index 7baef76..01cb8ce 100644
--- a/fib.awk
+++ b/fib.awk
@@ -1,6 +1,9 @@
 #!/usr/bin/awk -f
 
 ### fib.awk
+# print nth Fibonacci number, based on R. Hamming's solution to a diff eqn
+# form of the sequence
+
 
 BEGIN {
     ARGV[1] ? n = ARGV[1] : n = 0
diff --git a/hamming.awk b/fir_window.awk
index acfde97..076e5df 100644
--- a/hamming.awk
+++ b/fir_window.awk
@@ -7,18 +7,18 @@
 # 'a0' and 'a1' parameters of the raised cosine.

 

 

-### Gaussian

+# Gaussian window

 function gaussian(n) {

     # sigma <= 0.5

     sigma = 0.4

-    e[n] = (n)/(sigma*M)

+    en[n] = (n - M)/(sigma*M)

     return exp(-0.5*e[n]*e[n])

 }

 

 

-### Hamming, raised cosine

+# Hamming window (raised cosine)

 function hamming(n) {

-    ### optimal values for equal-ripple

+    # optimal values for equal-ripple

     #a0 = 0.53836

     #a1 = 0.46164

 

@@ -28,7 +28,7 @@ function hamming(n) {
 }

 

 

-### vonHann, raised cosine

+# vonHann (raised cosine)

 function vonhann(n) {

     a0 = 0.5

     a1 = 0.5

@@ -54,6 +54,5 @@ BEGIN {
             print n + M, 1.0

         }

     }

-

 }

 

diff --git a/gaussian.awk b/fir_window_gaussian.awk
index 402ea10..14ebc48 100644
--- a/gaussian.awk
+++ b/fir_window_gaussian.awk
@@ -1,11 +1,11 @@
 #!/usr/bin/awk -f

 

-### gaussian.awk

+### fir_window_gaussian.awk

 # generate a Gaussian window

 # https://en.wikipedia.org/wiki/Window_function

 

 

-### Gaussian

+# Gaussian window

 function gaussian(n) {

     # sigma <= 0.5

     sigma = 0.4

@@ -35,5 +35,5 @@ BEGIN {
             print n, 1.0

         }

     }

-

 }

+

diff --git a/fir_window_hamming.awk b/fir_window_hamming.awk
new file mode 100644
index 0000000..5660754
--- /dev/null
+++ b/fir_window_hamming.awk
@@ -0,0 +1,41 @@
+#!/usr/bin/awk -f

+

+### fir_window_hamming.awk

+# generate a Hamming window

+# R.W. Hamming, 'Digital Filters': H = '0.23 0.54 0.23'

+# https://en.wikipedia.org/wiki/Window_function provides a few values for the

+# 'a0' and 'a1' parameters of the raised cosine.

+

+

+# Hamming window (raised cosine)

+function hamming(n) {

+    # optimal values for equal-ripple

+    #a0 = 0.53836

+    #a1 = 0.46164

+

+    a0 = (25.0/46.0)

+    a1 = (21.0/46.0)

+    return a0 + a1*cos((pi*n)/M)

+}

+

+

+BEGIN {

+

+    ARGV[1] ? N = ARGV[1] : N = 0

+    ARGV[2] ? OFMT = "%." ARGV[2] "g" : OFMT = "%g"

+

+    # window interval goes from -M to M

+    M = 0.5*(N - 1)

+    pi = 4*atan2(1,1)

+

+    for (n=-M; n<=M; n++) {

+        if (N > 1 && M > 0) {

+            w[n] = hamming(n)

+            print n + M, w[n]/M

+        }

+        else {

+            print n + M, 1.0

+        }

+    }

+}

+

diff --git a/fir_window_vonhann.awk b/fir_window_vonhann.awk
new file mode 100644
index 0000000..3c831c7
--- /dev/null
+++ b/fir_window_vonhann.awk
@@ -0,0 +1,35 @@
+#!/usr/bin/awk -f

+

+### fir_window_vonhann.awk

+# https://en.wikipedia.org/wiki/Window_function provides a few values for the

+# 'a0' and 'a1' parameters of the raised cosine.

+

+

+# vonHann (raised cosine)

+function vonhann(n) {

+    a0 = 0.5

+    a1 = 0.5

+    return a0 + a1*cos((pi*n)/M)

+}

+

+

+BEGIN {

+

+    ARGV[1] ? N = ARGV[1] : N = 0

+    ARGV[2] ? OFMT = "%." ARGV[2] "g" : OFMT = "%g"

+

+    # window interval goes from -M to M

+    M = 0.5*(N - 1)

+    pi = 4*atan2(1,1)

+

+    for (n=-M; n<=M; n++) {

+        if (N > 1 && M > 0) {

+            w[n] = hamming(n)

+            print n + M, w[n]/M

+        }

+        else {

+            print n + M, 1.0

+        }

+    }

+}

+

diff --git a/kalman.awk b/kalman.awk
index f68cf81..7b6cb82 100644
--- a/kalman.awk
+++ b/kalman.awk
@@ -1,7 +1,7 @@
 #!/usr/bin/awk -f
 
 ### kalman.awk
-# simple linear regression between columns
+
 
 BEGIN {
     sign = "[+-]?"
@@ -11,6 +11,8 @@ BEGIN {
     number = "^" sign "(" decimal "|" fraction ")" exponent "$"
 }
 
+
+# column headers
 NR == 1 {
     header_nf = NF
     for (n=1; n<=NF; n++) {
@@ -18,31 +20,30 @@ NR == 1 {
     }
 }
 
-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++) {
+NF > 0 {
+    (NF > nf_max) ? nf_max = NF : nf_max = nf_max
+
+    # columns
+    for (y=1; y<=nf_max; y++) {
         if ($y ~ number) {
 
-            ### mean
+            # mean
             count[y] += 1
             sum[y] += $y
             sum2[y] += $y*$y
             mean[y] = sum[y]/count[y]
 
-            ### difference from the mean
+            # difference from the mean
             delta[y] = $y - mean[y]
             sum_delta[y] += delta[y]
             sum_delta2[y] += delta[y]*delta[y]
 
-            ### sample variance
+            # 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++) {
+            for (x=1; x<=nf_max; x++) {
                 count[x,y] += 1
                 sum_xy[x,y] += $x*$y
                 sum_delta_xy[x,y] += delta[x]*delta[y]
@@ -72,7 +73,7 @@ NF != 0 {
                     b[x,y] = 1
                 }
 
-                ### error estimate
+                # 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)
@@ -93,9 +94,10 @@ NF != 0 {
     }
 }
 
+
 END {
-    for (y=1; y<=max_nf; y++) {
-        for (x=1; x<=max_nf; x++) {
+    for (y=1; y<=nf_max; y++) {
+        for (x=1; x<=nf_max; x++) {
             if (x != y && r[x,y]) {
                 printf(OFMT OFS OFMT OFS "(%s)" OFS " = (" OFMT " +/- " OFMT ")(%s)" OFS " + (" OFMT " +/- " OFMT ")"ORS,
                     meas_cov[x,y], est_err_cov[x,y], header[y], b[x,y], b_err[x,y], header[x],
diff --git a/kalman_init.awk b/kalman_init.awk
index 57f7bbd..757d80b 100644
--- a/kalman_init.awk
+++ b/kalman_init.awk
@@ -1,7 +1,8 @@
 #!/usr/bin/awk -f
 
-### kalman.awk
-# kalman csv experiemnt
+### kalman_init.awk
+# kalman filter csv experiemnt
+
 
 BEGIN {
     sign = "[+-]?"
@@ -11,6 +12,8 @@ BEGIN {
     number = "^" sign "(" decimal "|" fraction ")" exponent "$"
 }
 
+
+# column headers
 NR == 1 {
     header_nf = NF
     for (n=1; n<=NF; n++) {
@@ -18,12 +21,12 @@ NR == 1 {
     }
 }
 
-NF != 0 {
+
+NF > 0 {
     print ORS NR ":" OFS $0 ORS
-    if (NF > max_nf)
-        max_nf = NF
+    (NF > nf_max) ? nf_max = NF : nf_max = nf_max
 
-    ### iterate over columns
+    # columns
     for (n=1; n<=max_nf; n++) {
         if ($n ~ number) {
             count[n] = ($n ~ number) + (last[n] ~ number) + (last2[n] ~ number)
@@ -42,7 +45,7 @@ NF != 0 {
                 meas_err[n] = sqrt(var[n]/count[n])
             }
 
-            ### error covariance
+            # error covariance
             for (m=1; m<=max_nf; m++) {
                 count[m,n]++
                 sum_xy[m,n] += 1
@@ -52,7 +55,7 @@ NF != 0 {
                 print meas_cov[m,n], est_err_last_cov[m,n]
             }
 
-            ### kalman gain
+            # kalman gain
             if (count[n] <= 1) {
                 Gk[n] = 1
                 est_err[n] = sqrt(diff[n]*diff[n]) + 2.0*sqrt(diff2[n]*diff2[n])
@@ -61,17 +64,17 @@ NF != 0 {
             else
                 Gk[n] = est_err_last[n]/(est_err_last[n] + meas_err[n])
 
-            ### update estimate and estimated error
+            # update estimate and estimated error
             est[n] = est_last[n] + Gk[n]*($n - est_last[n])
             est_err[n] = (1.0 - Gk[n])*est_err_last[n]
 
-            ### visual check
+            # visual check
             printf "meas: " OFS OFMT OFS OFMT OFS OFMT, $n, meas_err[n], count[n]
             printf "d1: " OFS OFMT, diff[n]
             printf "d2: " OFS OFMT, diff2[n]
             printf "est: " OFS OFMT OFS OFMT OFS OFMT, est[n], est_err[n], Gk[n]
 
-            ### update previously remembered values
+            # update previously remembered values
             last2[n] = last[n]
             last[n] = $n
             diff_last2[n] = diff_last[n]
@@ -86,3 +89,4 @@ NF != 0 {
         }
     }
 }
+
diff --git a/lin_reg.awk b/lin_reg.awk
index 5a9df56..3006e8a 100644
--- a/lin_reg.awk
+++ b/lin_reg.awk
@@ -3,6 +3,7 @@
 ### lin_reg.awk
 # simple linear regression between columns
 
+
 BEGIN {
     OFS = ":"
     sign = "[+-]?"
@@ -12,23 +13,26 @@ BEGIN {
     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 {
-    if (NF > nf_max)
-        nf_max = NF
 
-    ### iterate over columns
+# 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
+            # mean
             count[y] += 1
             sum[y] += $y
             sum2[y] += $y*$y
@@ -38,7 +42,7 @@ NF {
             sum_delta[y] += delta1[y]
             sum_delta2[y] += delta0[y]*delta1[y]
 
-            ### sample variance
+            # sample variance
             #(count[y] > 1) ? var[y] = sum_delta2[y]/(count[y] - 1) : var[y] = ""
 
             # x = row, y = col, trendline: y = A + Bx
@@ -91,6 +95,7 @@ NF {
     }
 }
 
+
 END {
     for (y=1; y<=nf_max; y++) {
         for (x=1; x<=nf_max; x++) {
diff --git a/lin_reg1.awk b/lin_reg1.awk
index c657035..7786247 100644
--- a/lin_reg1.awk
+++ b/lin_reg1.awk
@@ -3,6 +3,7 @@
 ### lin_reg1.awk
 # simple linear regression between columns
 
+
 BEGIN {
     sign = "[+-]?"
     decimal = "[0-9]+[.]?[0-9]*"
@@ -11,22 +12,26 @@ BEGIN {
     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 {
-    if (NF > nf_max)
-        nf_max = NF
+    (NF > nf_max) ? nf_max = NF : nf_max = nf_max
 
-    ### iterate over columns
+    # columns
     for (y=1; y<=nf_max; y++) {
         if ($y == header[n])
             continue
+
         if ($y ~ number) {
 
-            ### mean
+            # mean
             count[y] += 1
             sum[y] += $y
             sum2[y] += $y*$y
@@ -62,6 +67,7 @@ NF > 0 {
     }
 }
 
+
 END {
     for (y=1; y<=nf_max; y++) {
         for (x=1; x<=nf_max; x++) {
diff --git a/lin_reg2.awk b/lin_reg2.awk
index 450f0f0..d6097e3 100644
--- a/lin_reg2.awk
+++ b/lin_reg2.awk
@@ -3,6 +3,7 @@
 ### lin_reg2.awk
 # simple linear regression between columns
 
+
 BEGIN {
     sign = "[+-]?"
     decimal = "[0-9]+[.]?[0-9]*"
@@ -11,22 +12,26 @@ BEGIN {
     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 {
-    if (NF > nf_max)
-        nf_max = NF
+    (NF > nf_max) ? nf_max = NF : nf_max = nf_max
 
-    ### iterate over columns
+    # columns
     for (y=1; y<=nf_max; y++) {
         if ($y == header[n])
             continue
+
         if ($y ~ number) {
 
-            ### mean
+            # mean
             count[y] += 1
             sum[y] += $y
             sum2[y] += $y*$y
@@ -75,6 +80,7 @@ NF > 0 {
     }
 }
 
+
 END {
     for (y=1; y<=nf_max; y++) {
         for (x=1; x<=nf_max; x++) {
diff --git a/lpf.awk b/lpf.awk
index aba92e1..638af3c 100644
--- a/lpf.awk
+++ b/lpf.awk
@@ -1,7 +1,8 @@
 #!/usr/bin/awk -f

 

 ### lpf.awk

-# Low Pass Filter with Hardcoded FIR Window

+# low pass filter with hardcoded FIR window

+

 

 BEGIN {

     OFS = FS

@@ -20,19 +21,22 @@ BEGIN {
     window_size = split(H, H_arr, "[ ]*")

 }

 

+

+# column headers

 NR == 1 {

     for (y=1; y<=NF; y++)

         ($y ~ number) ? header[y] = "col" y : header[y] = $y

 }

 

+

+# read input data

 NF > 0 {

-    if (NF > nf_max)

-        nf_max = NF

+    (NF > nf_max) ? nf_max = NF : nf_max = nf_max

 

     input_size = window_size

     output_size = (input_size + window_size - 1)

 

-    ### columns

+    # columns

     for (y=1; y<=nf_max; y++) {

         if ($y == header[y])

             printf(header[y] OFS header[y] "_lpf")

@@ -75,15 +79,13 @@ NF > 0 {
             printf(ORS)

 

     }

-

-

-

 }

 

+

 END {

-    ### rows

+    # rows

     for (x=1; x<=window_size; x++) {

-        ### columns

+        # columns

         for (y=1; y<=nf_max; y++) {

             # rotate input buffer

             for (n=1; n<=input_size; n++) {

@@ -93,7 +95,7 @@ END {
             #delete X_arr[y,input_size]

             #input_size = length(X_arr)

             #print length(X_arr)

-            

+

             Y[y] = 0

             for (n=1; n<=window_size; n++) {

                 for (m=1; m<=input_size; m++) {

@@ -120,7 +122,7 @@ END {
                 printf(OFS)

             else

                 printf(ORS)

-            X_arr[input_size] = 0 

+            X_arr[input_size] = 0

         }

     }

 }

diff --git a/ludcmp.awk b/ludcmp.awk
index 6c7807a..8097263 100644
--- a/ludcmp.awk
+++ b/ludcmp.awk
@@ -11,6 +11,7 @@
 # note, matrix indexing begins with 1 and uses i=row, j=col
 # lu = L + U - I
 
+
 # decomposition of A
 function lu_decomp(A, n) {
 
@@ -43,6 +44,7 @@ function lu_decomp(A, n) {
     }
 }
 
+
 # regex to identify strings that look like numbers
 BEGIN {
     OFS = FS
@@ -53,12 +55,14 @@ BEGIN {
     number = "^" sign "(" decimal "|" fraction ")" exponent "$"
 }
 
+
 # column headers
 NR == 1 {
     for (n=1; n<=NF; n++)
         ($n ~ number) ? head[n] = "col" n : head[n] = $n
 }
 
+
 # read input data
 NF {
 
@@ -74,17 +78,17 @@ NF {
             print(matrix[count[n],n])
         }
     }
-
 }
 
+
 END {
     printf(ORS)
     print(NR, max_nf, size)
     printf(ORS)
     lu_decomp(matrix, size)
-
 }
 
+
 ## find solution of Ly = b, for y
 #for (i=0; i<n;, i++) {
 #    sum = 0
diff --git a/lupd.awk b/lupd.awk
index 39bf00c..08e1e30 100644
--- a/lupd.awk
+++ b/lupd.awk
@@ -9,6 +9,7 @@
 # note, matrix indexing begins with 1 and uses i=row, j=col
 # lu = L + U - I
 
+
 # solve A[n,n] * x[n] = b[n]
 function lu_solve(A, b, n) {
 
@@ -56,6 +57,7 @@ function lu_solve(A, b, n) {
 
 }
 
+
 # regex to identify strings that look like numbers
 BEGIN {
     OFS = FS
@@ -66,19 +68,21 @@ BEGIN {
     number = "^" sign "(" decimal "|" fraction ")" exponent "$"
 }
 
+
 # column headers
 NR == 1 {
     for (y=1; y<=NF; y++)
         ($y ~ number) ? header[y] = "col" y : header[y] = $y
 }
 
+
 # read input data
 NF > 0 {
     (NF > nf_max) ? nf_max = NF : nf_max = nf_max
 
-    ### columns
+    # columns
     for (y=1; y<=nf_max; y++) {
-        ### rows
+        # rows
         if ($y !~ number) {
             continue
         }
@@ -90,12 +94,13 @@ NF > 0 {
     }
 }
 
+
 END {
     print length(row_sum), length(col_sum)
-    ### columns
+    # columns
     for (y=1; y<=nf_max; y++) {
         if (y in col_sum) {
-            ### rows
+            # rows
             for (x=1; x<=NR; x++) {
                 if (x in row_sum) {
                     printf("[" OFMT "," OFMT "]" OFS OFMT OFS OFMT,
diff --git a/mean.awk b/mean.awk
index 069db4c..a57922b 100644
--- a/mean.awk
+++ b/mean.awk
@@ -3,6 +3,7 @@
 ### mean.awk

 # calculate mean average of serialized input

 

+

 BEGIN {

     OFS = FS

     #sign = "[+-]?"

@@ -12,8 +13,9 @@ BEGIN {
     number = "^[+-]?([0-9]+[.]?[0-9]*|[.][0-9]*)([Ee][+-]?[0-9]+)?$"

 }

 

+

 # Welford's 'online' algorithm for variance

-NF {

+NF > 0 {

     for (n=1; n<=NF; n++) {

         if ($n ~ number) {

             count += 1

@@ -29,6 +31,7 @@ NF {
     }

 }

 

+

 END {

     print "mean", "std_err", "std_dev", "range", "min", "max", "total", "count"

     print mean, sqrt(var/count), sqrt(var), range, min, max, (mean*count), count

diff --git a/mean_avg.awk b/mean_avg.awk
index bef984d..05c93f1 100644
--- a/mean_avg.awk
+++ b/mean_avg.awk
@@ -5,6 +5,7 @@
 # input: delimited data as text
 # output: list of univariate summary stats
 
+
 BEGIN {
     OFS = FS
     #sign = "[+-]?"
@@ -14,15 +15,19 @@ BEGIN {
     number = "^[+-]?([0-9]+[.]?[0-9]*|[.][0-9]*)([Ee][+-]?[0-9]+)?$"
 }
 
+
+# column headers
 NR == 1 {
     for (n=1; n<=NF; n++)
         ($n ~ number) ? header[n] = "col" n : header[n] = $n
 }
 
+
 # Welford's 'online' algorithm for variance
-NF {
-    if (NF > max_nf)
-        max_nf = NF
+NF > 0 {
+    (NF > nf_max) ? nf_max = NF : nf_max = nf_max
+
+    # columns
     for (n=1; n <= NF; n++) {
         if ($n ~ number) {
             count[n] += 1
@@ -38,6 +43,7 @@ NF {
     }
 }
 
+
 END {
     print "col", "mean", "std_err", "std_dev", "range", "min", "max", "total", "count"
     for (n=1; n<=max_nf; n++) {
diff --git a/pi.awk b/pi.awk
index 69eb36e..0a529f8 100644
--- a/pi.awk
+++ b/pi.awk
@@ -1,4 +1,4 @@
-#! /usr/bin/awk -f
+#!/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
@@ -11,11 +11,14 @@
 # Ferguson–the best approximation achieved without the aid of a calculating
 # device.
 
+
 function pi() {
     return 4*(4*atan2(1,5) - atan2(1,239))
 }
 
+
 BEGIN {
     ARGV[1] ? OFMT = "%." ARGV[1] "g" : OFMT = "%g"
     printf(OFMT ORS, pi())
 }
+
diff --git a/quad_reg.awk b/quad_reg.awk
index edd0c6f..2682a0f 100644
--- a/quad_reg.awk
+++ b/quad_reg.awk
@@ -3,6 +3,7 @@
 ### quad_reg.awk
 # quadratic regression along columns
 
+
 BEGIN {
     OFS = ":"
     pi = 4.0*atan2(1.0, 1.0)
@@ -13,22 +14,26 @@ BEGIN {
     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 {
-    if (NF > nf_max)
-        nf_max = NF
+    (NF > nf_max) ? nf_max = NF : nf_max = nf_max
 
-    ### iterate over columns
+    # columns
     for (y=1; y<=nf_max; y++) {
         if ($y == header[n])
             continue
+
         if ($y ~ number) {
 
-            ### mean
+            # mean
             count[y] += 1
             sum[y] += $y
             sum2[y] += $y*$y
@@ -42,7 +47,7 @@ NF > 0 {
             sum_delta[y] += delta1[y]
             sum_delta2[y] += delta2[y]
 
-            ### sample variance
+            # 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
@@ -115,6 +120,7 @@ NF > 0 {
     }
 }
 
+
 END {
     for (x=1; x<=nf_max; x++) {
         for (y=1; y<=nf_max; y++) {
diff --git a/sterling_approx.awk b/sterling_approx.awk
index cb5f563..4b0741e 100644
--- a/sterling_approx.awk
+++ b/sterling_approx.awk
@@ -1,21 +1,20 @@
 #!/usr/bin/awk -f
 
-
+### sterling_approx.awk
 # 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) ...
+#   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) ...
 
 
-### sterling_approx.awk
-# https://en.wikipedia.org/wiki/Stirling%27s_approximation
 
 function pwr(x, p) {
     return p ? exp(p*log(x)) : 1
 }
 
+
 BEGIN {
     ARGV[1] ? n = ARGV[1] : n = 0
     ARGV[2] ? OFMT = "%." ARGV[2] "g" : OFMT = "%g"
@@ -26,3 +25,4 @@ BEGIN {
     }
     printf(OFMT ORS, f)
 }
+
diff --git a/sum1.awk b/sum1.awk
index 8f1419b..9266789 100644
--- a/sum1.awk
+++ b/sum1.awk
@@ -5,15 +5,35 @@
 # output: sum of each column
 #   missing entries are treated as zeros
 
-BEGIN { OFS = FS }
 
-{
-    if (NF > nf_max)
-        nf_max = NF
+function isnum(n) {
+    sign = "[+-]?"
+    decimal = "[0-9]+[.]?[0-9]*"
+    fraction = "[.][0-9]+"
+    exponent = "([Ee]" sign "[0-9]+)?"
+    number = "^" sign "(" decimal "|" fraction ")" exponent "$"
+    return n ~ number
+}
+
+
+BEGIN {
+    OFS = FS
+}
+
+
+NR == 1 {
+    for (i=1; i<=NF; i++)
+        isnum($i) ? header[i] = "col" i : header[i] = $i
+}
+
+
+NF > 0 {
+    (NF > nf_max) ? nf_max = NF : nf_max = nf_max
     for (i=1; i<=NF; i++)
         sum[i] += $i
 }
 
+
 END {
     for (i=1; i<=nf_max; i++) {
         printf(OFMT, sum[i])
diff --git a/sum2.awk b/sum2.awk
index 694c047..4fcf3b6 100644
--- a/sum2.awk
+++ b/sum2.awk
@@ -3,18 +3,27 @@
 ### sum2.awk, print column sums
 # check that each line has the same number of fields as line one
 
-BEGIN { OFS = FS }
 
-NR == 1 { nf_max = NF }
+BEGIN {
+    OFS = FS
+}
+
+
+NR == 1 {
+    for (i=1; i<=NF; i++)
+        isnum($i) ? header[i] = "col" i : header[i] = $i
+}
+
 
-{
+NF > 0 {
+    (NF > nf_max) ? nf_max = NF : nf_max = nf_max
     for (i=1; i<=NF; i++)
         sum[i] += $i
-    if (NF != nf_max)
-        print "line " NR " has " NF " entries, not " nf_max
 }
 
+
 END {
     for (i=1; i<=nf_max; i++)
         printf(OFMT "%s", sum[i], i < nf_max ? OFS : ORS)
 }
+
diff --git a/sum3.awk b/sum3.awk
index 3e4661f..7f11a49 100644
--- a/sum3.awk
+++ b/sum3.awk
@@ -11,24 +11,29 @@ function isnum(n) {
 }
 
 
-BEGIN { OFS = FS }
+BEGIN {
+    OFS = FS
+}
+
 
 NR == 1 {
-    nfld = NF
     for (i=1; i<=NF; i++)
         numcol[i] = isnum($i)
 }
 
-{
+
+NF > 0 {
+    (NF > nf_max) ? nf_max = NF : nf_max = nf_max
     for (i=1; i<=NF; i++)
         if (numcol[i])
             sum[i] += $i
 }
 
+
 END {
-    for (i=1; i<=nfld; i++) {
+    for (i=1; i<=nf_max; i++) {
         printf(numcol[i] ? sum[i] : "--")
-        printf(i < nfld ? OFS : ORS)
+        printf(i < nf_max ? OFS : ORS)
     }
 }
 
diff --git a/sum4.awk b/sum4.awk
index aa3f044..3e61843 100644
--- a/sum4.awk
+++ b/sum4.awk
@@ -15,17 +15,19 @@ function isnum(n) {
 }
 
 
-BEGIN { OFS = FS }
+BEGIN {
+    OFS = FS
+}
+
 
 NR == 1 {
-    nf_max = NF
     for (i=1; i<=NF; i++)
         isnum($i) ? header[i] = "col" i : header[i] = $i
 }
 
-{
-    if (NF > nf_max)
-        nf_max = NF
+
+NF > 0 {
+    (NF > nf_max) ? nf_max = NF : nf_max = nf_max
     for (i=1; i<=NF; i++) {
         if ($i == header[i])
             continue
@@ -36,6 +38,7 @@ NR == 1 {
     }
 }
 
+
 END {
     for (i=1; i<=nf_max; i++) {
         printf((header[i]) ? header[i] OFS : OFS)