From: Richard Kreckel <Richard.Kreckel@uni-mainz.de>
Date: Mon, 29 Nov 1999 22:50:42 +0000 (+0000)
Subject: - changed function::diff() to be more tolerant by checking first if the
X-Git-Tag: release_0-5-0~105
X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=commitdiff_plain;h=be0485a03e9886496eeb7e8cdc2cc5c95b848632;hp=a87e6ee6d794b99dcf3946e7dde969edafeb3295

- changed function::diff() to be more tolerant by checking first if the
  nth argument when differentiated is non-zero and *then* building the sum.
- added support for overloaded polygamma functions psi(x) and psi(n,x).
- changed return code of atan2_diff to be somewhat simpler and adjusted
  check/differentiation.cpp to account for this.
---

diff --git a/check/differentiation.cpp b/check/differentiation.cpp
index 611342d0..0d963fed 100644
--- a/check/differentiation.cpp
+++ b/check/differentiation.cpp
@@ -234,10 +234,16 @@ static unsigned differentiation5(void)
          pow(y*b+pow(y,2)*x+a,-2)*pow(y,2))*
         pow(1+pow(a*x+b+y*pow(x,2),2)*pow(y*b+pow(y,2)*x+a,-2),-1);
     */
+    /*
     d = pow(1+pow(a*x+b+y*pow(x,2),2)*pow(y*b+pow(y,2)*x+a,-2),-1)
         *pow(y*b+pow(y,2)*x+a,-1)*(a+2*y*x)
         +pow(y,2)*(-a*x-b-y*pow(x,2))*
         pow(pow(y*b+pow(y,2)*x+a,2)+pow(a*x+b+y*pow(x,2),2),-1);
+    */
+    d = pow(y,2)*pow(pow(b+y*pow(x,2)+x*a,2)+pow(y*b+pow(y,2)*x+a,2),-1)*
+        (-b-y*pow(x,2)-x*a)+
+        pow(pow(b+y*pow(x,2)+x*a,2)+pow(y*b+pow(y,2)*x+a,2),-1)*
+        (y*b+pow(y,2)*x+a)*(2*y*x+a);
     result += check_diff(e, x, d);
     
     return result;
diff --git a/ginac/diff.cpp b/ginac/diff.cpp
index 7b4d489b..2661fddb 100644
--- a/ginac/diff.cpp
+++ b/ginac/diff.cpp
@@ -175,17 +175,22 @@ ex power::diff(symbol const & s) const
 ex function::diff(symbol const & s) const
 {
     exvector new_seq;
-
-    if (serial == function_index_Order) {
-
+    
+    if (serial==function_index_Order) {
         // Order Term function only differentiates the argument
         return Order(seq[0].diff(s));
-
     } else {
-
         // Chain rule
+        ex arg_diff;
         for (unsigned i=0; i!=seq.size(); i++) {
-            new_seq.push_back(mul(pdiff(i), seq[i].diff(s)));
+            arg_diff = seq[i].diff(s);
+            // We apply the chain rule only when it makes sense.  This is not
+            // just for performance reasons but also to allow functions to
+            // throw when differentiated with respect to one of its arguments
+            // without running into trouble with our automatic full
+            // differentiation:
+            if (!arg_diff.is_zero())
+                new_seq.push_back(mul(pdiff(i), arg_diff));
         }
     }
     return add(new_seq);
diff --git a/ginac/inifcns.h b/ginac/inifcns.h
index ee737818..725c1ee7 100644
--- a/ginac/inifcns.h
+++ b/ginac/inifcns.h
@@ -87,8 +87,16 @@ DECLARE_FUNCTION_1P(zeta)
 DECLARE_FUNCTION_1P(gamma)
 
 /** Psi-function (aka polygamma-function). */
+extern unsigned function_index_psi1;
+inline function psi(ex const & p1) {
+    return function(function_index_psi1, p1);
+}
+extern unsigned function_index_psi2;
+inline function psi(ex const & p1, ex const & p2) {
+    return function(function_index_psi2, p1, p2);
+}
 //DECLARE_FUNCTION_1P(psi)
-DECLARE_FUNCTION_2P(psi)
+//DECLARE_FUNCTION_2P(psi)
     
 /** Factorial function. */
 DECLARE_FUNCTION_1P(factorial)
diff --git a/ginac/inifcns_gamma.cpp b/ginac/inifcns_gamma.cpp
index bb3a74e0..a208592f 100644
--- a/ginac/inifcns_gamma.cpp
+++ b/ginac/inifcns_gamma.cpp
@@ -46,19 +46,19 @@ 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 +75,7 @@ static ex gamma_eval(ex const & x)
     }
     return gamma(x).hold();
 }    
-    
+
 static ex gamma_evalf(ex const & x)
 {
     BEGIN_TYPECHECK
@@ -89,7 +89,7 @@ static ex gamma_diff(ex const & x, unsigned diff_param)
 {
     GINAC_ASSERT(diff_param==0);
     
-    return psi(exZERO(),x)*gamma(x);  // diff(log(gamma(x)),x)==psi(0,x)
+    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)
@@ -108,17 +108,57 @@ REGISTER_FUNCTION(gamma, gamma_eval, gamma_evalf, gamma_diff, gamma_series);
 // 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)) {
+        // do some stuff...
+    }
+    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);
+}
+
+static ex psi1_series(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. :-("));
+}
+
+unsigned function_index_psi1 = function::register_new("psi", psi1_eval, psi1_evalf, psi1_diff, psi1_series);
+
+//////////
+// 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).hold();
     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 +168,23 @@ 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)
 {
-    GINAC_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)
+static ex psi2_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. :-("));
+    throw(std::logic_error("Nobody told me how to series expand the psi functions. :-("));
 }
 
-REGISTER_FUNCTION(psi, psi_eval, psi_evalf, psi_diff, psi_series);
+unsigned function_index_psi2 = function::register_new("psi", psi2_eval, psi2_evalf, psi2_diff, psi2_series);
 
 } // namespace GiNaC
diff --git a/ginac/inifcns_trans.cpp b/ginac/inifcns_trans.cpp
index 70eccdce..db502ca9 100644
--- a/ginac/inifcns_trans.cpp
+++ b/ginac/inifcns_trans.cpp
@@ -468,10 +468,10 @@ static ex atan2_diff(ex const & y, ex const & x, unsigned diff_param)
     
     if (diff_param==0) {
         // d/dy atan(y,x)
-        return pow(x*(1+y*y/(x*x)),-1);
+        return x*pow(pow(x,2)+pow(y,2),-1);
     }
     // d/dx atan(y,x)
-    return -y*pow(x*x+y*y,-1);
+    return -y*pow(pow(x,2)+pow(y,2),-1);
 }
 
 REGISTER_FUNCTION(atan2, atan2_eval, atan2_evalf, atan2_diff, NULL);
diff --git a/ginac/numeric.cpp b/ginac/numeric.cpp
index bb2762a2..1cc1fa69 100644
--- a/ginac/numeric.cpp
+++ b/ginac/numeric.cpp
@@ -1084,6 +1084,14 @@ numeric gamma(numeric const & x)
 
 /** The psi function (aka polygamma function).
  *  This is only a stub! */
+numeric psi(numeric const & x)
+{
+    clog << "psi(): Does anybody know good way to calculate this numerically?" << endl;
+    return numeric(0);
+}
+
+/** The psi functions (aka polygamma functions).
+ *  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;
diff --git a/ginac/numeric.h b/ginac/numeric.h
index 88b7d953..13c790fc 100644
--- a/ginac/numeric.h
+++ b/ginac/numeric.h
@@ -241,6 +241,7 @@ numeric acosh(numeric const & x);
 numeric atanh(numeric const & x);
 numeric zeta(numeric const & x);
 numeric gamma(numeric const & x);
+numeric psi(numeric const & x);
 numeric psi(numeric const & n, numeric const & x);
 numeric factorial(numeric const & n);
 numeric doublefactorial(numeric const & n);