X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=check%2Fexam_inifcns_nstdsums.cpp;h=ec843da3ab5544ea8b9eda8c0f4c3a8a19d0a541;hp=0ad9f1a80fc1e34d08285dca689a8c852a277e1e;hb=85dbe3f2049dce7d43a1bd956d622f4ff5c0c156;hpb=bab935d3cbaccc2f1a77d16d712271063d085d42 diff --git a/check/exam_inifcns_nstdsums.cpp b/check/exam_inifcns_nstdsums.cpp index 0ad9f1a8..ec843da3 100644 --- a/check/exam_inifcns_nstdsums.cpp +++ b/check/exam_inifcns_nstdsums.cpp @@ -4,7 +4,7 @@ * functions. */ /* - * GiNaC Copyright (C) 1999-2003 Johannes Gutenberg University Mainz, Germany + * GiNaC Copyright (C) 1999-2008 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 @@ -18,104 +18,348 @@ * * 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., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA + * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA */ -#include "exams.h" - +#include #include +#include "ginac.h" +using namespace std; +using namespace GiNaC; + + + +//////////////////////////////////////////////////////////////////////////////// +//////////////////////////////////////////////////////////////////////////////// +// 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; -struct point +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 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(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++; } - 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(en); - numeric p = ex_to(ep); +//////////////////////////////////////////////////////////////////////////////// +//////////////////////////////////////////////////////////////////////////////// +// zeta exam +//////////////////////////////////////////////////////////////////////////////// +//////////////////////////////////////////////////////////////////////////////// + - ppbuf.x = x; - ppbuf.res = res; +static unsigned inifcns_test_zeta() +{ + int digitsbuf = Digits; + + unsigned result = 0; - pp[n.to_int()-1][p.to_int()-1].push_back(ppbuf); + 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; } - in.close(); - - vp::iterator it; - int error = 0; - - cout << endl << "Calculating "; - for (int sum=2; sum<=3; sum++) { - for (int nn=1; nnx << ") " << flush; - ex res = S(nn,sum-nn,it->x).evalf(); - if (!is_a(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(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++; - } - } - } + 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; +} + + +//////////////////////////////////////////////////////////////////////////////// +//////////////////////////////////////////////////////////////////////////////// +// legacy exam - checking for historical bugs +//////////////////////////////////////////////////////////////////////////////// +//////////////////////////////////////////////////////////////////////////////// + + +static unsigned inifcns_test_legacy() +{ + Digits = 17; + ex prec = 5 * pow(10, -(int)Digits); + + unsigned result = 0; + + ex r1 = zeta(lst(1,1,1,1,1,1),lst(-1,-1,-1,1,1,1)); + if ((r1.evalf() - numeric("-0.0012588769028204890704")) > prec) { + clog << "zeta({1,1,1,1,1,1},{-1,-1,-1,1,1,1}) seems to be wrong." << endl; + result++; + } + + ex x1 = exp(2*Pi*I/13).evalf(); + ex x2 = exp(24*Pi*I/13).evalf(); + ex r2 = Li(lst(2),lst(x1)).hold().evalf(); + ex r3 = Li(lst(2),lst(x2)).hold().evalf(); + if ( abs(r2-conjugate(r3)) > prec ) { + clog << "Legacy test 2 seems to be wrong." << endl; + result++; + } + + ex x3 = exp(5*Pi*I/3).evalf(); + ex r4 = Li(lst(3),lst(x3)).hold().evalf(); + if ( abs(r4 - numeric("0.40068563438653142847-0.95698384815740185713*I")) > prec ) { + clog << "Legacy test 3 seems to be wrong." << endl; + result++; + } + + Digits = 100; + prec = 5 * pow(10, -(int)Digits); + ex x0 = 1.; + x1 = exp(Pi*I/3).evalf(); + x2 = exp(2*Pi*I/3).evalf(); + x3 = -1.; + ex x4 = exp(4*Pi*I/3).evalf(); + ex x5 = exp(5*Pi*I/3).evalf(); + + ex r5 = Li(lst(1,1,1,1),lst(x2,x4,x3,x0)).hold().evalf(); + ex r6 = Li(lst(1,1,1,1),lst(x4,x2,x3,x0)).hold().evalf(); + if ( abs(r5-conjugate(r6)) > prec ) { + clog << "Legacy test 4 seems to be wrong." << endl; + result++; + } + + ex r7 = Li(lst(1,2,1),lst(x3,x2,x4)).hold().evalf() + +Li(lst(1,1,2),lst(x3,x2,x4)).hold().evalf() + +Li(lst(1,1,1,1),lst(x3,x0,x2,x4)).hold().evalf() + +Li(lst(1,1,1,1),lst(x3,x2,x0,x4)).hold().evalf() + +Li(lst(1,1,1,1),lst(x3,x2,x4,x0)).hold().evalf() + +Li(lst(1,2,1),lst(x2,x1,x0)).hold().evalf() + +Li(lst(1,1,2),lst(x2,x3,x4)).hold().evalf() + +Li(lst(1,1,1,1),lst(x2,x4,x3,x0)).hold().evalf() + +Li(lst(1,1,1,1),lst(x2,x3,x4,x0)).hold().evalf() + +Li(lst(1,1,1,1),lst(x2,x3,x0,x4)).hold().evalf() + +Li(lst(2,2),lst(x5,x4)).hold().evalf() + +Li(lst(2,1,1),lst(x5,x0,x4)).hold().evalf() + +Li(lst(2,1,1),lst(x5,x4,x0)).hold().evalf() + -Li(lst(1,1),lst(x3,x0)).hold().evalf()*Li(lst(1,1),lst(x2,x4)).hold().evalf(); + if ( abs(r7) > prec ) { + clog << "Legacy test 5 seems to be wrong." << endl; + result++; } - cout << endl; return result; } @@ -126,17 +370,17 @@ unsigned exam_inifcns_nstdsums(void) unsigned result = 0; cout << "examining consistency of nestedsums functions" << flush; - clog << "----------consistency of nestedsums functions:" << endl; - - result += inifcns_consist_S(); cout << '.' << flush; - if (!result) { - cout << " passed " << endl; - clog << "(no output)" << endl; - } else { - cout << " failed " << endl; - } + result += inifcns_test_zeta(); + result += inifcns_test_S(); + result += inifcns_test_HLi(); + result += inifcns_test_LiG(); + result += inifcns_test_legacy(); return result; } +int main(int argc, char** argv) +{ + return exam_inifcns_nstdsums(); +}