added diff2.awk to estimate numerical second diff;

removed commented out population covariance from cov.awk;
added decimal points to pi estimate in em.awk;

1 files changed, 97 insertions, 0 deletions

diff --git a/diff2.awk b/diff2.awk
new file mode 100644
index 0000000..6086254
--- /dev/null
+++ b/diff2.awk
@@ -0,0 +1,97 @@
+#!/usr/bin/awk -f
+
+### diff2.awk
+# print numerical second diff along columns
+#  dy[n]   =  y[n]   -  y[n-1]
+#  d2y[n]  =  dy[n]  -  dy[n-1]
+
+
+BEGIN {
+    OFS = FS
+    sign = "[+-]?"
+    decimal = "[0-9]+[.]?[0-9]*"
+    fraction = "[.][0-9]*"
+    exponent = "([Ee]" sign "[0-9]+)?"
+    number = "^" sign "(" decimal "|" fraction ")" exponent "$"
+}
+
+
+# column headers
+NR == 1 {
+    # orig data columns
+    for (n=1; n<=NF; n++) {
+        if ($n !~ number) {
+            header[n] = $n
+            dheader[n] = "d_" $n
+            d2header[n] = "d2_" $n
+        }
+        else {
+            header[n] = "col" n
+            dheader[n] = "d_col" n
+            d2header[n] = "d2_col" n
+        }
+        printf(header[n])
+        printf(OFS)
+    }
+
+    # new diff columns
+    for (n=1; n<=NF; n++) {
+        printf(dheader[n])
+        printf(OFS)
+    }
+
+    # new diff2 columns
+    for (n=1; n<=NF; n++) {
+        printf(d2header[n])
+        printf(n < NF ? OFS : ORS)
+    }
+}
+
+
+NF > 0 {
+    (NF > nf_max) ? nf_max = NF : nf_max = nf_max
+
+    # orig data columns
+    for (n=1; n<=nf_max; n++) {
+        if ($n == header[n] || $n == dheader[n])
+            continue
+        if ($n ~ number)
+            printf(OFMT, $n)
+        else
+            printf("")
+        printf(OFS)
+    }
+
+    # new diff columns
+    for (n=1; n<=nf_max; n++) {
+        if ($n == header[n] || $n == dheader[n])
+            continue
+        if ($n ~ number) {
+            data[n] = $n
+            if (data_prev[n] ~ number)
+                diff[n] = data[n] - data_prev[n]
+            else
+                diff[n] = ""
+            data_prev[n] = data[n]
+        }
+        printf(diff[n])
+        printf(OFS)
+    }
+
+    # new diff2 columns
+    for (n=1; n<=nf_max; n++) {
+        if ($n == header[n] || $n == d2header[n])
+            continue
+        if (diff[n] ~ number) {
+            #data[n] = $n
+            if (diff_prev[n] ~ number)
+                diff2[n] = diff[n] - diff_prev[n]
+            else
+                diff2[n] = ""
+            diff_prev[n] = diff[n]
+        }
+        printf(diff2[n])
+        printf(n < nf_max ? OFS : ORS)
+    }
+}
+