* functions. */
/*
- * GiNaC Copyright (C) 1999-2003 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2004 Johannes Gutenberg University Mainz, Germany
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
#include <fstream>
-struct point
+////////////////////////////////////////////////////////////////////////////////
+////////////////////////////////////////////////////////////////////////////////
+// S exam
+////////////////////////////////////////////////////////////////////////////////
+////////////////////////////////////////////////////////////////////////////////
+
+
+/*
+ * The data in the following include file has been produced by the following
+ * Mathematica (V4.1) script:
+ *
+ *
+ * x={2/10,1,14/10,30/10}
+ * y={0,3/10,-14/10}
+ * st = OpenAppend["exam_inifcns_nstdsums_data.raw"]
+ * $NumberMarks = False
+ * Do[
+ * Do[
+ * Do[Write[st, i]; Write[st,j]; Write[st,x[[k]]+I*y[[l]]];
+ * Write[st,Chop[N[PolyLog[i,j,x[[k]]+I*y[[l]]],25]]],{i,3},{j,3}], {k,4}],{l,3}]
+ * Do[
+ * Do[
+ * Do[Write[st, i]; Write[st,j]; Write[st,-x[[k]]+I*y[[l]]];
+ * Write[st,Chop[N[PolyLog[i,j,-x[[k]]+I*y[[l]]],25]]],{i,3},{j,3}], {k,4}], {l,3}]
+ * Close[st]
+ *
+ *
+ * and postprocessed by the following shell script
+ *
+ *
+ * #/bin/sh
+ * IFS=$'\n'
+ * cat exam_inifcns_nstdsums_data.raw | sed -e 's/\*\^/E/g' > exam_inifcns_nstdsums_data.raw2
+ * echo 'const char *data[] = {' > exam_inifcns_nstdsums_data.raw3
+ * for i in `cat exam_inifcns_nstdsums_data.raw2`; do echo \"$i\",; done >> exam_inifcns_nstdsums_data.raw3
+ * echo '"-999"};' >> exam_inifcns_nstdsums.h
+ *
+ *
+ */
+#include "exam_inifcns_nstdsums.h"
+
+
+// signals end of data
+const int ENDMARK = -999;
+
+
+static unsigned inifcns_test_S()
{
- ex x;
- ex res;
-};
+ int digitsbuf = Digits;
+ // precision of data
+ Digits = 22;
+ ex prec = 5 * pow(10, -(int)Digits);
+
+ unsigned result = 0;
+
+ int i = 0;
+ while (true) {
+ ex n(data[i++],symbol());
+ if (n == ENDMARK) {
+ break;
+ }
+ ex p(data[i++],symbol());
+ ex x(data[i++],symbol());
+ ex res(data[i++],symbol());
+ ex res2 = S(n, p, x).evalf();
+ if (abs(res-res2) > prec) {
+ clog << "S(" << n << "," << p << "," << x << ") seems to be wrong:" << endl;
+ clog << "GiNaC : " << res2 << endl;
+ clog << "Reference : " << res << endl;
+ clog << "Abs. Difference : " << res2-res << endl;
+ if (res2 != 0) {
+ ex reldiff = abs((res2-res)/res2);
+ clog << "Rel. Difference : " << reldiff << endl;
+ }
+ result++;
+ }
+ if (i % 80) {
+ cout << "." << flush;
+ }
+ }
+ Digits = digitsbuf;
-const int NDIM = 5;
-const int PDIM = 5;
+ return result;
+}
-typedef vector<point> vp;
-vp pp[NDIM][PDIM];
+////////////////////////////////////////////////////////////////////////////////
+////////////////////////////////////////////////////////////////////////////////
+// H/Li exam
+////////////////////////////////////////////////////////////////////////////////
+////////////////////////////////////////////////////////////////////////////////
-static unsigned inifcns_consist_S(void)
+static unsigned inifcns_test_HLi()
{
+ int digitsbuf = Digits;
+ Digits = 17;
+ ex prec = 5 * pow(10, -(int)Digits);
+ numeric almostone("0.999999999999999999");
unsigned result = 0;
+
+ lst res;
+
+ res.append(H(lst(2,1),numeric(1)/2).hold() - (zeta(3)/8 - pow(log(2),3)/6));
+ res.append(H(lst(2,1,3),numeric(1)/3).hold() - Li(lst(2,1,3),lst(numeric(1)/3,1,1)).hold());
+ res.append(H(lst(2,1,3),numeric(98)/100).hold() - Li(lst(2,1,3),lst(numeric(98)/100,1,1)).hold());
+ res.append(H(lst(2,1,3),numeric(245)/100).hold() - Li(lst(2,1,3),lst(numeric(245)/100,1,1)).hold());
+ res.append(H(lst(4,1,1,1),numeric(1)/3).hold() - S(3,4,numeric(1)/3).hold());
+ res.append(H(lst(4,1,1,1),numeric(98)/100).hold() - S(3,4,numeric(98)/100).hold());
+ res.append(H(lst(4,1,1,1),numeric(245)/100).hold() - S(3,4,numeric(245)/100).hold());
+ res.append(H(lst(2,2,3),almostone).hold() - zeta(lst(2,2,3)));
+ res.append(H(lst(-3,-1,2,1),almostone).hold() - zeta(lst(3,1,2,1),lst(-1,1,-1,1)));
+ res.append(H(lst(-2,1,3),numeric(1)/3).hold() - -Li(lst(2,1,3),lst(-numeric(1)/3,-1,1)).hold());
+ res.append(H(lst(-2,1,3),numeric(98)/100).hold() - -Li(lst(2,1,3),lst(-numeric(98)/100,-1,1)).hold());
+ res.append(H(lst(-2,1,3),numeric(245)/100).hold() - -Li(lst(2,1,3),lst(-numeric(245)/100,-1,1)).hold());
+ res.append(H(lst(-3,1,-2,0,0),numeric(3)/10).hold() - convert_H_to_Li(lst(-3,1,-2,0,0),numeric(3)/10).eval());
- ifstream in("exam_inifcns_nstdsums_data");
+ 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;
+ }
+
+ Digits = digitsbuf;
- if (!in) {
- clog << "exam_inifcns_nstdsums_data not readable!" << endl;
- return 666;
+ // conjugate test
+ numeric cdif = ex_to<numeric>(H(lst(2,2,1),5.0-5.0*I) - H(lst(2,2,1),5.0+5.0*I));
+ numeric cadd = ex_to<numeric>(H(lst(2,2,1),5.0-5.0*I) + H(lst(2,2,1),5.0+5.0*I));
+ if ((cdif.real() > prec) || (cadd.imag() > prec)) {
+ clog << "complex conjugation test of H({2,2,1},5.0-5.0*I) seems to be wrong: " << cdif << " " << cadd << endl;
+ result++;
}
- string str;
- point ppbuf;
+ return result;
+}
- while (1) {
- getline(in,str);
- if (!in)
- break;
- ex en(str,symbol());
- getline(in,str);
- if (!in)
- break;
- ex ep(str,symbol());
- getline(in,str);
- if (!in)
- break;
- ex x(str,symbol());
- getline(in,str);
- if (!in)
- break;
- ex res(str,symbol());
- numeric n = ex_to<numeric>(en);
- numeric p = ex_to<numeric>(ep);
+////////////////////////////////////////////////////////////////////////////////
+////////////////////////////////////////////////////////////////////////////////
+// zeta exam
+////////////////////////////////////////////////////////////////////////////////
+////////////////////////////////////////////////////////////////////////////////
- ppbuf.x = x;
- ppbuf.res = res;
- pp[n.to_int()-1][p.to_int()-1].push_back(ppbuf);
- }
+static unsigned inifcns_test_zeta()
+{
+ int digitsbuf = Digits;
+
+ unsigned result = 0;
- in.close();
-
- vp::iterator it;
- int error = 0;
-
- cout << endl << "Calculating ";
- for (int sum=2; sum<=3; sum++) {
- for (int nn=1; nn<sum; nn++) {
- vp& da = pp[nn-1][sum-nn-1];
- for (it = da.begin(); it!=da.end(); it++) {
- cout << "S(" << nn << "," << sum-nn << "," << it->x << ") " << flush;
- ex res = S(nn,sum-nn,it->x).evalf();
- if (!is_a<numeric>(res)) {
- if ((it->x != -1) || ((sum-nn) == 1)) {
- clog << "S(" << nn << "," << sum-nn << "," << it->x << ") didn't give numerical result!" << endl;
- result++;
- }
- }
- else {
- ex reldiff = abs((it->res-res)/it->res);
- if ((!is_a<numeric>(res)) || (reldiff > numeric("1E-10"))) {
- clog << "S(" << nn << "," << sum-nn << "," << it->x << ") seems to be wrong:" << endl;
- clog << "GiNaC : " << res << endl;
- clog << "Reference : " << it->res << endl;
- clog << "Abs. Difference : " << it->res-res << endl;
- clog << "Rel. Difference : " << reldiff << endl;
- result++;
- }
- }
- }
+ lst res;
+
+ res.append(zeta(lst(2,1)) - zeta(3));
+ res.append(zeta(lst(2,1,1,1,1)) - zeta(6));
+ res.append(zeta(lst(6,3)) - (zeta(9)*83/2 - zeta(2)*zeta(7)*21 - zeta(2)*zeta(2)*zeta(5)*12/5));
+ res.append(zeta(lst(4,2,3)) - (-zeta(9)*59 + zeta(2)*zeta(7)*28 + pow(zeta(2),2)*zeta(5)*4 -
+ pow(zeta(3),3)/3 + pow(zeta(2),3)*zeta(3)*8/21));
+ res.append(zeta(lst(3,1,3,1,3,1,3,1)) - (2*pow(Pi,16)/factorial(18)));
+ res.append(zeta(lst(2),lst(-1)) - -zeta(2)/2);
+ res.append(zeta(lst(1,2),lst(-1,1)) - (-zeta(3)/4 - zeta(lst(1),lst(-1))*zeta(2)/2));
+ res.append(zeta(lst(2,1,1),lst(-1,-1,1)) - (-pow(zeta(2),2)*23/40 - pow(zeta(lst(1),lst(-1)),2)*zeta(2)*3/4
+ - zeta(lst(3,1),lst(-1,1))*3/2 - zeta(lst(1),lst(-1))*zeta(3)*21/8));
+
+ for (lst::const_iterator it = res.begin(); it != res.end(); it++) {
+ Digits = 17;
+ ex prec = 5 * pow(10, -(int)Digits);
+ ex diff = abs((*it).evalf());
+ if (diff > prec) {
+ clog << *it << " seems to be wrong: " << diff << endl;
+ clog << "Digits: " << Digits << endl;
+ result++;
+ }
+ cout << "." << flush;
+ Digits = 40;
+ prec = 5 * pow(10, -(int)Digits);
+ diff = abs((*it).evalf());
+ if (diff > prec) {
+ clog << *it << " seems to be wrong: " << diff << endl;
+ clog << "Digits: " << Digits << endl;
+ result++;
}
+ cout << "." << flush;
+ }
+
+ Digits = digitsbuf;
+ return result;
+}
+
+
+////////////////////////////////////////////////////////////////////////////////
+////////////////////////////////////////////////////////////////////////////////
+// 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;
}
- cout << endl;
return result;
}
cout << "examining consistency of nestedsums functions" << flush;
clog << "----------consistency of nestedsums functions:" << endl;
- result += inifcns_consist_S(); cout << '.' << flush;
+ result += inifcns_test_zeta();
+ result += inifcns_test_S();
+ result += inifcns_test_HLi();
+ result += inifcns_test_LiG();
if (!result) {
cout << " passed " << endl;
return result;
}
-
git://www.ginac.de / ginac.git / blobdiff