From 2478df378bbdbae452288eb3aa16928e168b7fc2 Mon Sep 17 00:00:00 2001 From: Jens Vollinga Date: Mon, 1 Dec 2003 23:03:07 +0000 Subject: [PATCH] * Improved exams for S * Added exams for zeta, H and Li --- check/exam_inifcns_nstdsums.cpp | 200 +++-- check/exam_inifcns_nstdsums.h | 1388 +++++++++---------------------- 2 files changed, 545 insertions(+), 1043 deletions(-) diff --git a/check/exam_inifcns_nstdsums.cpp b/check/exam_inifcns_nstdsums.cpp index f6864aa5..df8a4193 100644 --- a/check/exam_inifcns_nstdsums.cpp +++ b/check/exam_inifcns_nstdsums.cpp @@ -26,22 +26,30 @@ #include +//////////////////////////////////////////////////////////////////////////////// +//////////////////////////////////////////////////////////////////////////////// +// S exam +//////////////////////////////////////////////////////////////////////////////// +//////////////////////////////////////////////////////////////////////////////// + + /* * The data in the following include file has been produced by the following * Mathematica (V4.1) script: * * - * x={0.2,0.7 ,1,1.4,3.0 } - * y={0,0.3,-0.8,3.0} + * 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,N[PolyLog[i,j,x[[k]]+I*y[[l]]]]],{i,3},{j,3}], {k,5}],{l,4}] + * 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,N[PolyLog[i,j,-x[[k]]+I*y[[l]]]]],{i,3},{j,3}], {k,5}], {l,4}] + * Write[st,Chop[N[PolyLog[i,j,-x[[k]]+I*y[[l]]],25]]],{i,3},{j,3}], {k,4}], {l,3}] * Close[st] * * @@ -60,80 +68,145 @@ #include "exam_inifcns_nstdsums.h" -// adjust this if you want to process more S(n,p,x) data -const int MAX_NDIM = 5; -const int MAX_PDIM = 5; - // signals end of data const int ENDMARK = -999; -struct point -{ - ex x; - ex res; -}; - -typedef vector vp; - -vp pp[MAX_NDIM][MAX_PDIM]; - - -static unsigned inifcns_consist_S(void) +static unsigned inifcns_test_S() { + int digitsbuf = Digits; + // precision of data + Digits = 22; + ex prec = 5 * pow(10, -(int)Digits); + unsigned result = 0; - point ppbuf; int i = 0; while (true) { - ex en(data[i++],symbol()); - if (en == ENDMARK) { + ex n(data[i++],symbol()); + if (n == ENDMARK) { break; } - numeric n = ex_to(en); - ex ep(data[i++],symbol()); - numeric p = ex_to(ep); + ex p(data[i++],symbol()); ex x(data[i++],symbol()); ex res(data[i++],symbol()); - - ppbuf.x = x; - ppbuf.res = res; - - pp[n.to_int()-1][p.to_int()-1].push_back(ppbuf); + 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; - 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++; - } - } - } + 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; + + 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; } -// cout << endl; + + Digits = digitsbuf; return result; } @@ -146,7 +219,12 @@ unsigned exam_inifcns_nstdsums(void) cout << "examining consistency of nestedsums functions" << flush; clog << "----------consistency of nestedsums functions:" << endl; - result += inifcns_consist_S(); cout << '.' << flush; + cout << "zeta" << flush; + result += inifcns_test_zeta(); + cout << "S" << flush; + result += inifcns_test_S(); + cout << "H/Li" << flush; + result += inifcns_test_HLi(); if (!result) { cout << " passed " << endl; diff --git a/check/exam_inifcns_nstdsums.h b/check/exam_inifcns_nstdsums.h index 63765048..c2919573 100644 --- a/check/exam_inifcns_nstdsums.h +++ b/check/exam_inifcns_nstdsums.h @@ -1,1442 +1,866 @@ -const char *data[] = { +string data[] = { "1", "1", -"0.2", -"0.2110037754397048", +"1/5", +"0.2110037754397047726111851", "1", "2", -"0.2", -"0.01154815698320566", +"1/5", +"0.01154815698320587834851847", "1", "3", -"0.2", -"0.0005671604269052999", +"1/5", +"0.0005671604269057464369336278", "2", "1", -"0.2", -"0.20532419573331034", +"1/5", +"0.2053241957333103187906279", "2", "2", -"0.2", -"0.005496394299313416", +"1/5", +"0.005496394299313416180783147", "2", "3", -"0.2", -"0.00017753669051818812", +"1/5", +"0.0001775366905181881667796781", "3", "1", -"0.2", -"0.2026055828608338", +"1/5", +"0.2026055828608337918073629", "3", "2", -"0.2", -"0.002660800832970403", +"1/5", +"0.002660800832970401591293284", "3", "3", -"0.2", -"0.00005648589591441389", +"1/5", +"0.00005648589591441390456209617", "1", "1", -"0.7", -"0.8893776242860387", -"1", -"2", -"0.7", -"0.23849649036813148", -"1", -"3", -"0.7", -"0.06009077565899523", -"2", -"1", -"0.7", -"0.7800639342576615", -"2", -"2", -"0.7", -"0.09243937841078567", -"2", -"3", -"0.7", -"0.014300985013200635", -"3", -"1", -"0.7", -"0.7362172409491383", -"3", -"2", -"0.7", -"0.039617343952161696", -"3", -"3", -"0.7", -"0.0037691167701794487", -"1", -"1", -"1", -"1.6449340668482262", -"1", -"2", -"1", -"1.202056903159594", -"1", -"3", -"1", -"1.082323233711138", -"2", -"1", -"1", -"1.202056903159594", -"2", -"2", -"1", -"0.2705808084277845", -"2", -"3", -"1", -"0.09655115998944441", -"3", "1", -"1", -"1.082323233711138", -"3", -"2", -"1", -"0.09655115998944441", -"3", -"3", -"1", -"0.017489853169012193", -"1", -"1", -"1.4", -"2.3190730363096606 - 1.057058706706129*I", +"1.644934066848226436472415", "1", "2", -"1.4", -"0.40012821735085136 - 2.117870033958637*I", "1", -"3", -"1.4", -"-1.3069420677518375 - 0.9582504865992156*I", -"2", +"1.202056903159594285399738", "1", -"1.4", -"1.8988811512408845 - 0.17783545364266917*I", -"2", -"2", -"1.4", -"0.6147866145423271 - 0.4503460612959742*I", -"2", -"3", -"1.4", -"0.02364313457019307 - 0.39576490835181133*I", "3", "1", -"1.4", -"1.5981814495570066 - 0.01994556427923233*I", -"3", +"1.082323233711138191516004", "2", -"1.4", -"0.2551667236941566 - 0.057444069764028605*I", -"3", -"3", -"1.4", -"0.06183658590898977 - 0.06413563191670146*I", -"1", -"1", -"3.", -"2.320180423313098 - 3.451392295223203*I", -"1", -"2", -"3.", -"-3.2830549733147327 - 2.1213489928333162*I", -"1", -"3", -"3.", -"-1.3089568016095854 + 2.735768992719805*I", -"2", -"1", -"3.", -"3.7421225942407315 - 1.8958709942733214*I", -"2", -"2", -"3.", -"-0.48051063523149495 - 2.3025389502658458*I", -"2", -"3", -"3.", -"-1.3402534089764055 + 0.27122772589982036*I", -"3", -"1", -"3.", -"3.7485098910701 - 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