#ifndef around namespace GiNaC { }

[ginac.git] / ginac / inifcns_gamma.cpp

diff --git a/ginac/inifcns_gamma.cpp b/ginac/inifcns_gamma.cpp
index 7bd6669bb8b5eb8c817fd016718c5e3bfdaa2546..2fd58cce517fe04d66c8bf158aa95878de6635ea 100644 (file)
--- a/ginac/inifcns_gamma.cpp
+++ b/ginac/inifcns_gamma.cpp
@@ -1,6 +1,7 @@
 /** @file inifcns_gamma.cpp
  *
- *  Implementation of Gamma function and some related stuff. */
+ *  Implementation of Gamma-function, Polygamma-functions, and some related
+ *  stuff. */
 
 /*
  *  GiNaC Copyright (C) 1999 Johannes Gutenberg University Mainz, Germany
@@ -30,10 +31,12 @@
 #include "power.h"
 #include "symbol.h"
 
+#ifndef NO_GINAC_NAMESPACE
 namespace GiNaC {
+#endif // ndef NO_GINAC_NAMESPACE
 
 //////////
-// gamma function
+// Gamma-function
 //////////
 
 /** Evaluation of gamma(x). Knows about integer arguments, half-integer
@@ -44,21 +47,20 @@ namespace GiNaC {
 static ex gamma_eval(ex const & x)
 {
     if (x.info(info_flags::numeric)) {
-
         // trap integer arguments:
-        if ( x.info(info_flags::integer) ) {
+        if (x.info(info_flags::integer)) {
             // gamma(n+1) -> n! for postitive n
-            if ( x.info(info_flags::posint) ) {
+            if (x.info(info_flags::posint)) {
                 return factorial(ex_to_numeric(x).sub(numONE()));
             } else {
                 return numZERO();  // Infinity. Throw? What?
             }
         }
         // trap half integer arguments:
-        if ( (x*2).info(info_flags::integer) ) {
+        if ((x*2).info(info_flags::integer)) {
             // trap positive x=(n+1/2)
             // gamma(n+1/2) -> Pi^(1/2)*(1*3*..*(2*n-1))/(2^n)
-            if ( (x*2).info(info_flags::posint) ) {
+            if ((x*2).info(info_flags::posint)) {
                 numeric n = ex_to_numeric(x).sub(numHALF());
                 numeric coefficient = doublefactorial(n.mul(numTWO()).sub(numONE()));
                 coefficient = coefficient.div(numTWO().power(n));
@@ -75,7 +77,7 @@ static ex gamma_eval(ex const & x)
     }
     return gamma(x).hold();
 }    
-    
+
 static ex gamma_evalf(ex const & x)
 {
     BEGIN_TYPECHECK
@@ -87,9 +89,9 @@ static ex gamma_evalf(ex const & x)
 
 static ex gamma_diff(ex const & x, unsigned diff_param)
 {
-    ASSERT(diff_param==0);
-
-    return psi(exZERO(),x)*gamma(x);
+    GINAC_ASSERT(diff_param==0);
+    
+    return psi(x)*gamma(x);  // diff(log(gamma(x)),x)==psi(x)
 }
 
 static ex gamma_series(ex const & x, symbol const & s, ex const & point, int order)
@@ -105,20 +107,75 @@ static ex gamma_series(ex const & x, symbol const & s, ex const & point, int ord
 REGISTER_FUNCTION(gamma, gamma_eval, gamma_evalf, gamma_diff, gamma_series);
 
 //////////
-// psi function (aka polygamma function)
+// Psi-function (aka polygamma-function)
+//////////
+
+/** Evaluation of polygamma-function psi(x). 
+ *  Somebody ought to provide some good numerical evaluation some day... */
+static ex psi1_eval(ex const & x)
+{
+    if (x.info(info_flags::numeric)) {
+        if (x.info(info_flags::integer) && !x.info(info_flags::positive))
+            throw (std::domain_error("psi_eval(): simple pole"));
+        if (x.info(info_flags::positive)) {
+            // psi(n) -> 1 + 1/2 +...+ 1/(n-1) - EulerGamma
+            if (x.info(info_flags::integer)) {
+                numeric rat(0);
+                for (numeric i(ex_to_numeric(x)-numONE()); i.is_positive(); --i)
+                    rat += i.inverse();
+                return rat-EulerGamma;
+            }
+            // psi((2m+1)/2) -> 2/(2m+1) + 2/2m +...+ 2/1 - EulerGamma - 2log(2)
+            if ((exTWO()*x).info(info_flags::integer)) {
+                numeric rat(0);
+                for (numeric i((ex_to_numeric(x)-numONE())*numTWO()); i.is_positive(); i-=numTWO())
+                    rat += numTWO()*i.inverse();
+                return rat-EulerGamma-exTWO()*log(exTWO());
+            }
+            if (x.compare(exONE())==1) {
+                // should call numeric, since >1
+            }
+        }
+    }
+    return psi(x).hold();
+}
+
+static ex psi1_evalf(ex const & x)
+{
+    BEGIN_TYPECHECK
+        TYPECHECK(x,numeric)
+    END_TYPECHECK(psi(x))
+    
+    return psi(ex_to_numeric(x));
+}
+
+static ex psi1_diff(ex const & x, unsigned diff_param)
+{
+    GINAC_ASSERT(diff_param==0);
+    
+    return psi(exONE(), x);
+}
+
+const unsigned function_index_psi1 = function::register_new("psi", psi1_eval, psi1_evalf, psi1_diff, NULL);
+
+//////////
+// Psi-functions (aka polygamma-functions)  psi(0,x)==psi(x)
 //////////
 
 /** Evaluation of polygamma-function psi(n,x). 
  *  Somebody ought to provide some good numerical evaluation some day... */
-static ex psi_eval(ex const & n, ex const & x)
+static ex psi2_eval(ex const & n, ex const & x)
 {
+    // psi(0,x) -> psi(x)
+    if (n.is_zero())
+        return psi(x);
     if (n.info(info_flags::numeric) && x.info(info_flags::numeric)) {
         // do some stuff...
     }
     return psi(n, x).hold();
 }    
-    
-static ex psi_evalf(ex const & n, ex const & x)
+
+static ex psi2_evalf(ex const & n, ex const & x)
 {
     BEGIN_TYPECHECK
         TYPECHECK(n,numeric)
@@ -128,18 +185,20 @@ static ex psi_evalf(ex const & n, ex const & x)
     return psi(ex_to_numeric(n), ex_to_numeric(x));
 }
 
-static ex psi_diff(ex const & n, ex const & x, unsigned diff_param)
+static ex psi2_diff(ex const & n, ex const & x, unsigned diff_param)
 {
-    ASSERT(diff_param==0);
+    GINAC_ASSERT(diff_param<2);
     
+    if (diff_param==0) {
+        // d/dn psi(n,x)
+        throw(std::logic_error("cannot diff psi(n,x) with respect to n"));
+    }
+    // d/dx psi(n,x)
     return psi(n+1, x);
 }
 
-static ex psi_series(ex const & n, ex const & x, symbol const & s, ex const & point, int order)
-{
-    throw(std::logic_error("Nobody told me how to series expand the psi function. :-("));
-}
-
-REGISTER_FUNCTION(psi, psi_eval, psi_evalf, psi_diff, psi_series);
+const unsigned function_index_psi2 = function::register_new("psi", psi2_eval, psi2_evalf, psi2_diff, NULL);
 
+#ifndef NO_GINAC_NAMESPACE
 } // namespace GiNaC
+#endif // ndef NO_GINAC_NAMESPACE