- fixed differentiation of gamma(x)

- preliminary support for polygamma-functions psi(n,x)

diff --git a/ginac/inifcns.h b/ginac/inifcns.h
index 42f3838919635a98b95f989e98a2d823d68cfe1c..0ccde8de774a9d2900581d905908fc17b82325cc 100644 (file)
--- a/ginac/inifcns.h
+++ b/ginac/inifcns.h
@@ -82,6 +82,9 @@ DECLARE_FUNCTION_1P(Li3)
 /** Gamma function. */
 DECLARE_FUNCTION_1P(gamma)
 
 /** Gamma function. */
 DECLARE_FUNCTION_1P(gamma)
 

+/** Psi function (aka polygamma-function) */
+DECLARE_FUNCTION_2P(psi)
+    

 /** Factorial function. */
 DECLARE_FUNCTION_1P(factorial)
 
 /** Factorial function. */
 DECLARE_FUNCTION_1P(factorial)
 

diff --git a/ginac/inifcns_gamma.cpp b/ginac/inifcns_gamma.cpp
index fd3c32efef5359475862b5f413c6b543ac97d572..7bd6669bb8b5eb8c817fd016718c5e3bfdaa2546 100644 (file)
--- a/ginac/inifcns_gamma.cpp
+++ b/ginac/inifcns_gamma.cpp
@@ -43,7 +43,7 @@ namespace GiNaC {
  *  @exception fail_numeric("complex_infinity") or something similar... */
 static ex gamma_eval(ex const & x)
 {
  *  @exception fail_numeric("complex_infinity") or something similar... */
 static ex gamma_eval(ex const & x)
 {

-    if ( x.info(info_flags::numeric) ) {
+    if (x.info(info_flags::numeric)) {

 
         // trap integer arguments:
         if ( x.info(info_flags::integer) ) {
 
         // trap integer arguments:
         if ( x.info(info_flags::integer) ) {


@@ -62,14 +62,14 @@ static ex gamma_eval(ex const & x)
                 numeric n = ex_to_numeric(x).sub(numHALF());
                 numeric coefficient = doublefactorial(n.mul(numTWO()).sub(numONE()));
                 coefficient = coefficient.div(numTWO().power(n));
                 numeric n = ex_to_numeric(x).sub(numHALF());
                 numeric coefficient = doublefactorial(n.mul(numTWO()).sub(numONE()));
                 coefficient = coefficient.div(numTWO().power(n));

-                return coefficient * power(Pi,numHALF());
+                return coefficient * pow(Pi,numHALF());

             } else {
                 // trap negative x=(-n+1/2)
                 // gamma(-n+1/2) -> Pi^(1/2)*(-2)^n/(1*3*..*(2*n-1))
                 numeric n = abs(ex_to_numeric(x).sub(numHALF()));
                 numeric coefficient = numeric(-2).power(n);
                 coefficient = coefficient.div(doublefactorial(n.mul(numTWO()).sub(numONE())));;
             } else {
                 // trap negative x=(-n+1/2)
                 // gamma(-n+1/2) -> Pi^(1/2)*(-2)^n/(1*3*..*(2*n-1))
                 numeric n = abs(ex_to_numeric(x).sub(numHALF()));
                 numeric coefficient = numeric(-2).power(n);
                 coefficient = coefficient.div(doublefactorial(n.mul(numTWO()).sub(numONE())));;

-                return coefficient * power(Pi,numHALF());
+                return coefficient*sqrt(Pi);

             }
         }
     }
             }
         }
     }


@@ -89,14 +89,14 @@ static ex gamma_diff(ex const & x, unsigned diff_param)
 {
     ASSERT(diff_param==0);
 
 {
     ASSERT(diff_param==0);
 

-    return power(x, -1);       // FIXME
+    return psi(exZERO(),x)*gamma(x);

 }
 
 static ex gamma_series(ex const & x, symbol const & s, ex const & point, int order)
 {
        // FIXME: Only handle one special case for now...
        if (x.is_equal(s) && point.is_zero()) {
 }
 
 static ex gamma_series(ex const & x, symbol const & s, ex const & point, int order)
 {
        // FIXME: Only handle one special case for now...
        if (x.is_equal(s) && point.is_zero()) {

-               ex e = 1 / s - EulerGamma + s * (power(Pi, 2) / 12 + power(EulerGamma, 2) / 2) + Order(power(s, 2));
+               ex e = 1 / s - EulerGamma + s * (pow(Pi, 2) / 12 + pow(EulerGamma, 2) / 2) + Order(pow(s, 2));

                return e.series(s, point, order);
        } else
                throw(std::logic_error("don't know the series expansion of this particular gamma function"));
                return e.series(s, point, order);
        } else
                throw(std::logic_error("don't know the series expansion of this particular gamma function"));


@@ -104,4 +104,42 @@ 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);
 
 
 REGISTER_FUNCTION(gamma, gamma_eval, gamma_evalf, gamma_diff, gamma_series);
 

+//////////
+// psi function (aka polygamma function)
+//////////
+
+/** 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)
+{
+    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)
+{
+    BEGIN_TYPECHECK
+        TYPECHECK(n,numeric)
+        TYPECHECK(x,numeric)
+    END_TYPECHECK(psi(n,x))
+    
+    return psi(ex_to_numeric(n), ex_to_numeric(x));
+}
+
+static ex psi_diff(ex const & n, ex const & x, unsigned diff_param)
+{
+    ASSERT(diff_param==0);
+    
+    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);
+

 } // namespace GiNaC
 } // namespace GiNaC

diff --git a/ginac/inifcns_trans.cpp b/ginac/inifcns_trans.cpp
index 40968672dcd01dfb715e9e4a08ab92f562797492..ce979686337d9abb435f179ae64117d50ad295ff 100644 (file)
--- a/ginac/inifcns_trans.cpp
+++ b/ginac/inifcns_trans.cpp
@@ -465,13 +465,13 @@ static ex atan2_eval(ex const & y, ex const & x)
 static ex atan2_diff(ex const & y, ex const & x, unsigned diff_param)
 {
     ASSERT(diff_param<2);
 static ex atan2_diff(ex const & y, ex const & x, unsigned diff_param)
 {
     ASSERT(diff_param<2);

-
+    

     if (diff_param==0) {
         // d/dy atan(y,x)
     if (diff_param==0) {
         // d/dy atan(y,x)

-        return power(x*(1+y*y/(x*x)),-1);
+        return pow(x*(1+y*y/(x*x)),-1);

     }
     // d/dx atan(y,x)
     }
     // d/dx atan(y,x)

-    return -y*power(x*x+y*y,-1);
+    return -y*pow(x*x+y*y,-1);

 }
 
 REGISTER_FUNCTION(atan2, atan2_eval, atan2_evalf, atan2_diff, NULL);
 }
 
 REGISTER_FUNCTION(atan2, atan2_eval, atan2_evalf, atan2_diff, NULL);

diff --git a/ginac/numeric.cpp b/ginac/numeric.cpp
index 165ce594c106e6fd66d69415202c9fb7339c9673..ef2784172107f22965381b271e2fafcd92d7bbca 100644 (file)
--- a/ginac/numeric.cpp
+++ b/ginac/numeric.cpp
@@ -1063,10 +1063,18 @@ numeric atanh(numeric const & x)
 }
 
 /** The gamma function.
 }
 
 /** The gamma function.

- *  stub stub stub stub stub stub! */
+ *  This is only a stub! */

 numeric gamma(numeric const & x)
 {
 numeric gamma(numeric const & x)
 {

-    clog << "gamma(): Nobody expects the Spanish inquisition" << endl;
+    clog << "gamma(): Does anybody know good way to calculate this numerically?" << endl;
+    return numeric(0);
+}
+
+/** The psi function (aka polygamma function).
+ *  This is only a stub! */
+numeric psi(numeric const & n, numeric const & x)
+{
+    clog << "psi(): Does anybody know good way to calculate this numerically?" << endl;

     return numeric(0);
 }
 
     return numeric(0);
 }