New checks for G and Li functions.
authorJens Vollinga <vollinga@thep.physik.uni-mainz.de>
Tue, 19 Oct 2004 15:18:46 +0000 (15:18 +0000)
committerJens Vollinga <vollinga@thep.physik.uni-mainz.de>
Tue, 19 Oct 2004 15:18:46 +0000 (15:18 +0000)
check/exam_inifcns_nstdsums.cpp

index 35f9ddbbb32dddc698da42963b18ff4cdeeb7b8e..8434fd1e699d28cd3cd1d69506f03b037bd5ddca 100644 (file)
@@ -220,6 +220,73 @@ static unsigned inifcns_test_zeta()
 }
 
 
+////////////////////////////////////////////////////////////////////////////////
+////////////////////////////////////////////////////////////////////////////////
+//  H/Li exam
+////////////////////////////////////////////////////////////////////////////////
+////////////////////////////////////////////////////////////////////////////////
+
+
+static unsigned inifcns_test_LiG()
+{
+       int digitsbuf = Digits;
+       Digits = 17;
+       ex prec = 5 * pow(10, -(int)Digits);
+       numeric almostone("0.99999999999999999999");
+       unsigned result = 0;
+
+       lst res;
+       
+       res.append(Li(lst(4), lst(6)).hold() - Li(4, 6.0));
+       res.append(G(lst(0,0,5.0,0,2.0,0,0,0,3.0),0.5).hold()
+                  + Li(lst(3,2,4), lst(numeric(1,10), numeric(5,2), numeric(2,3))));
+       res.append(Li(lst(2,1,1), lst(almostone, almostone, almostone)) - zeta(lst(2,1,1)));
+
+       // check Li_{1,1} against known expression
+       symbol x("x"), y("y");
+       ex eps = 1e-30*I;
+       ex s1 = Li(lst(1,1),lst(x,y));
+       ex s2 = log(1-1/x/y-eps)*log((1-1/x-eps)/(1/x/y-1/x)) + Li(2,(1-1/x/y-eps)/(1/x-1/x/y))
+                       - log(-1/x/y-eps)*log((-1/x-eps)/(1/x/y-1/x)) - Li(2,(-1/x/y-eps)/(1/x-1/x/y))
+                       - log(-1/x/y-eps)*log(1-1/x-eps) + log(-1/x/y-eps)*log(-1/x-eps);
+       res.append(s1.subs(lst(x==numeric(1)/2, y==3)) - s2.subs(lst(x==numeric(1)/2, y==3)));
+       res.append(s1.subs(lst(x==numeric(3)/2, y==numeric(1)/2)) - s2.subs(lst(x==numeric(3)/2, y==numeric(1)/2)));
+       res.append(s1.subs(lst(x==2, y==numeric(4)/5)) - s2.subs(lst(x==2, y==numeric(4)/5)));
+
+       // shuffle and quasi-shuffle identities
+       res.append(G(lst(0,0.2),1).hold() * G(lst(0.5),1).hold() - G(lst(0.5,0,0.2),1).hold()
+                       - G(lst(0,0.5,0.2),1).hold() - G(lst(0,0.2,0.5),1).hold());
+       res.append(G(lst(0,0.5),1).hold() * G(lst(0.6),1).hold() - G(lst(0,0.5,0.5*0.6),1).hold()
+                       - G(lst(0.6,0,0.5*0.6),1).hold() + G(lst(0,0,0.5*0.6),1).hold());
+       res.append(Li(lst(2),lst(numeric(1,5))).hold() * Li(lst(3),lst(7)).hold() - Li(lst(2,3),lst(numeric(1,5),7)).hold()
+                       - Li(lst(3,2),lst(7,numeric(1,5))).hold() - Li(lst(5),lst(numeric(7,5))).hold());
+       symbol a1, a2, a3, a4;
+       res.append((G(lst(a1,a2),1) * G(lst(a3,a4),1) - G(lst(a1,a2,a3,a4),1)
+                       - G(lst(a1,a3,a2,a4),1) - G(lst(a3,a1,a2,a4),1)
+                       - G(lst(a1,a3,a4,a2),1) - G(lst(a3,a1,a4,a2),1) - G(lst(a3,a4,a1,a2),1))
+                               .subs(lst(a1==numeric(1)/10, a2==numeric(3)/10, a3==numeric(7)/10, a4==5)));
+       res.append(G(lst(-0.009),1).hold() * G(lst(-8,1.4999),1).hold() - G(lst(-0.009,-8,1.4999),1).hold()
+                       - G(lst(-8,-0.009,1.4999),1).hold() - G(lst(-8,1.4999,-0.009),1).hold());
+       res.append(G(lst(sqrt(numeric(1)/2)+I*sqrt(numeric(1)/2)),1).hold() * G(lst(1.51,-0.999),1).hold()
+                       - G(lst(sqrt(numeric(1)/2)+I*sqrt(numeric(1)/2),1.51,-0.999),1).hold()
+                       - G(lst(1.51,sqrt(numeric(1)/2)+I*sqrt(numeric(1)/2),-0.999),1).hold()
+                       - G(lst(1.51,-0.999,sqrt(numeric(1)/2)+I*sqrt(numeric(1)/2)),1).hold());
+       // checks for hoelder convolution which is used if one argument has a distance to one smaller than 0.01 
+       res.append(G(lst(0, 1.2, 1, 1.01), 1).hold() - G(lst(0, 1.2, 1, numeric("1.009999999999999999")), 1).hold());
+
+       for (lst::const_iterator it = res.begin(); it != res.end(); it++) {
+               ex diff = abs((*it).evalf());
+               if (diff > prec) {
+                       clog << *it << " seems to be wrong: " << diff << endl;
+                       result++;
+               }
+               cout << "." << flush;
+       }
+
+       return result;
+}
+
+
 unsigned exam_inifcns_nstdsums(void)
 {
        unsigned result = 0;
@@ -230,6 +297,7 @@ unsigned exam_inifcns_nstdsums(void)
        result += inifcns_test_zeta();
        result += inifcns_test_S();
        result += inifcns_test_HLi();
+       result += inifcns_test_LiG();
        
        if (!result) {
                cout << " passed " << endl;