Data update

Task/Thieles-interpolation-formula/Jq/thieles-interpolation-formula.jq

@@ -0,0 +1,42 @@
+def N: 32;
+
+# Input: {x,y,r}
+# Output: update r and set .result
+def rho($i; $n):
+  if $n < 0 then .result = 0
+  elif $n == 0 then .result = .y[$i]
+  else (((N - 1 - $n) * (N - $n) / 2) + $i) as $idx
+  | if (.r[$idx] == null)
+    then
+      rho($i; $n - 1)       | .result as $r1
+      | rho($i + 1; $n - 1) | .result as $r2
+      | rho($i + 1; $n - 2) | .result as $r3
+      | .r[$idx] = (.x[$i] - .x[$i + $n]) / ($r1 - $r2) + $r3
+    end
+  | .result = .r[$idx]
+  end;
+
+# Input: {x,y,r}
+# Output: update r and set .result
+def thiele($xin; $n):
+  if $n > N - 1 then .result = 1
+  else
+     rho(0; $n)             | .result as $r1
+     | rho(0; $n -2)        | .result as $r2
+     | thiele($xin; $n + 1) | .result as $t
+     | .result = ($r1 - $r2) + ($xin - .x[$n]) / $t
+  end;
+
+# Output: {xval, tsin, tcos, ttan}
+def init($step):
+  reduce range(0; N) as $i ({};
+    ($i * $step) as $x
+    | .xval[$i] = $x
+    | .tsin[$i] = ($x|sin)
+    | .tcos[$i] = ($x|cos)
+    | .ttan[$i] = .tsin[$i] / .tcos[$i] ) ;
+
+init(0.05)
+| ({r: [], x: .tsin, y: .xval} | 6 * thiele(0.5; 0).result),
+  ({r: [], x: .tcos, y: .xval} | 3 * thiele(0.5; 0).result),
+  ({r: [], x: .ttan, y: .xval} | 4 * thiele(1.0; 0).result)