Changes between Version 7 and Version 8 of Piecewise

Timestamp:

Jun 13, 2014, 2:42:01 PM (11 years ago)

Author:

Pedro Gea

Comment:

--

Piecewise

@@ -157 +157 @@
 }}}
 y comprobar que: {{{Sum_k(P_k(x)) == x}}}.
+
+----
+
+== [Implementación] ==
+
+Se propone una implementación del particionamiento {{{P_k(x)}}} a partir de los valores: {{{ (x, xI:=x_k, xS:=x_{k+1}) }}} 
+
+=== TOL ===
+
+{{{
+#!java
+//////////////////////////////////////////////////////////////////////////////
+Real Piecewise(Real x, Real xI, Real xS)
+//////////////////////////////////////////////////////////////////////////////
+{
+  Case(xI<0 & xS<0, Case(x<xI, xI-xS, x<xS, x-xS, True, 0),
+    xI<=0 & xS>=0, Case(x<xI, xI, x>xS, xS, True, x), 
+    xI>0 & xS>0, Case(x<xI, 0, x<xS, x-xI, True, xS-xI))
+};
+}}}
+
+Véase [source:trunk/ExtLib/fun_piecewise.tol].
+
+=== SQL ===
+
+{{{
+#!sql
+CREATE FUNCTION piecewise(x NUMERIC, xI NUMERIC, xS NUMERIC) RETURNS NUMERIC
+  AS $$ SELECT CASE 
+  WHEN $1 IS NULL THEN NULL
+  WHEN $2 IS NULL AND $3 IS NULL THEN $1                                                 -- (-inf, inf)
+  WHEN $2 IS NULL AND $3<0 THEN (CASE WHEN $1<$3 THEN $1-$3 ELSE 0 END)                  -- (-inf, neg)
+  WHEN $2 IS NULL AND $3>=0 THEN (CASE WHEN $1>$3 THEN $3 ELSE $1 END)                   -- (-inf, pos|0)
+  WHEN $2<=0 AND $3 IS NULL THEN (CASE WHEN $1<$2 THEN $2 ELSE $1 END)                   -- (neg|0, inf)
+  WHEN $2>0 AND $3 IS NULL THEN (CASE WHEN $1<$2 THEN 0 ELSE $1-$2 END)                  -- (pos, inf)
+  WHEN $2<0 AND $3<0 THEN (CASE WHEN $1<$2 THEN $2-$3 WHEN $1<$3 THEN $1-$3 ELSE 0 END)  -- (neg, neg)
+  WHEN $2<=0 AND $3>=0 THEN (CASE WHEN $1<$2 THEN $2 WHEN $1>$3 THEN $3 ELSE $1 END)     -- (neg|0, pos|0)
+  WHEN $2>0 AND $3>0 THEN (CASE WHEN $1<$2 THEN 0 WHEN $1<$3 THEN $1-$2 ELSE $3-$2 END)  -- (pos, pos)
+  END $$
+  LANGUAGE SQL;
+}}}