/** @file exam_inifcns_nstdsums.cpp * * This test routine applies assorted tests on initially known higher level * functions. */ /* * GiNaC Copyright (C) 1999-2005 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 * the Free Software Foundation; either version 2 of the License, or * (at your option) any later version. * * This program is distributed in the hope that it will be useful, * but WITHOUT ANY WARRANTY; without even the implied warranty of * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the * GNU General Public License for more details. * * You should have received a copy of the GNU General Public License * along with this program; if not, write to the Free Software * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA */ #include "exams.h" #include //////////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////////// // 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() { 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; return result; } //////////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////////// // H/Li exam //////////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////////// 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()); 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; // conjugate test numeric cdif = ex_to(H(lst(2,2,1),5.0-5.0*I) - H(lst(2,2,1),5.0+5.0*I)); numeric cadd = ex_to(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++; } return result; } //////////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////////// // zeta exam //////////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////////// static unsigned inifcns_test_zeta() { int digitsbuf = Digits; unsigned result = 0; 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; } return result; } unsigned exam_inifcns_nstdsums(void) { unsigned result = 0; cout << "examining consistency of nestedsums functions" << flush; clog << "----------consistency of nestedsums functions:" << endl; result += inifcns_test_zeta(); result += inifcns_test_S(); result += inifcns_test_HLi(); result += inifcns_test_LiG(); if (!result) { cout << " passed " << endl; clog << "(no output)" << endl; } else { cout << " failed " << endl; } return result; }