1 /** @file exam_inifcns_nstdsums.cpp
3 * This test routine applies assorted tests on initially known higher level
7 * GiNaC Copyright (C) 1999-2007 Johannes Gutenberg University Mainz, Germany
9 * This program is free software; you can redistribute it and/or modify
10 * it under the terms of the GNU General Public License as published by
11 * the Free Software Foundation; either version 2 of the License, or
12 * (at your option) any later version.
14 * This program is distributed in the hope that it will be useful,
15 * but WITHOUT ANY WARRANTY; without even the implied warranty of
16 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
17 * GNU General Public License for more details.
19 * You should have received a copy of the GNU General Public License
20 * along with this program; if not, write to the Free Software
21 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
29 ////////////////////////////////////////////////////////////////////////////////
30 ////////////////////////////////////////////////////////////////////////////////
32 ////////////////////////////////////////////////////////////////////////////////
33 ////////////////////////////////////////////////////////////////////////////////
37 * The data in the following include file has been produced by the following
38 * Mathematica (V4.1) script:
41 * x={2/10,1,14/10,30/10}
43 * st = OpenAppend["exam_inifcns_nstdsums_data.raw"]
44 * $NumberMarks = False
47 * Do[Write[st, i]; Write[st,j]; Write[st,x[[k]]+I*y[[l]]];
48 * Write[st,Chop[N[PolyLog[i,j,x[[k]]+I*y[[l]]],25]]],{i,3},{j,3}], {k,4}],{l,3}]
51 * Do[Write[st, i]; Write[st,j]; Write[st,-x[[k]]+I*y[[l]]];
52 * Write[st,Chop[N[PolyLog[i,j,-x[[k]]+I*y[[l]]],25]]],{i,3},{j,3}], {k,4}], {l,3}]
56 * and postprocessed by the following shell script
61 * cat exam_inifcns_nstdsums_data.raw | sed -e 's/\*\^/E/g' > exam_inifcns_nstdsums_data.raw2
62 * echo 'const char *data[] = {' > exam_inifcns_nstdsums_data.raw3
63 * for i in `cat exam_inifcns_nstdsums_data.raw2`; do echo \"$i\",; done >> exam_inifcns_nstdsums_data.raw3
64 * echo '"-999"};' >> exam_inifcns_nstdsums.h
68 #include "exam_inifcns_nstdsums.h"
71 // signals end of data
72 const int ENDMARK = -999;
75 static unsigned inifcns_test_S()
77 int digitsbuf = Digits;
80 ex prec = 5 * pow(10, -(int)Digits);
86 ex n(data[i++],symbol());
90 ex p(data[i++],symbol());
91 ex x(data[i++],symbol());
92 ex res(data[i++],symbol());
93 ex res2 = S(n, p, x).evalf();
94 if (abs(res-res2) > prec) {
95 clog << "S(" << n << "," << p << "," << x << ") seems to be wrong:" << endl;
96 clog << "GiNaC : " << res2 << endl;
97 clog << "Reference : " << res << endl;
98 clog << "Abs. Difference : " << res2-res << endl;
100 ex reldiff = abs((res2-res)/res2);
101 clog << "Rel. Difference : " << reldiff << endl;
106 cout << "." << flush;
116 ////////////////////////////////////////////////////////////////////////////////
117 ////////////////////////////////////////////////////////////////////////////////
119 ////////////////////////////////////////////////////////////////////////////////
120 ////////////////////////////////////////////////////////////////////////////////
123 static unsigned inifcns_test_HLi()
125 int digitsbuf = Digits;
127 ex prec = 5 * pow(10, -(int)Digits);
128 numeric almostone("0.999999999999999999");
133 res.append(H(lst(2,1),numeric(1)/2).hold() - (zeta(3)/8 - pow(log(2),3)/6));
134 res.append(H(lst(2,1,3),numeric(1)/3).hold() - Li(lst(2,1,3),lst(numeric(1)/3,1,1)).hold());
135 res.append(H(lst(2,1,3),numeric(98)/100).hold() - Li(lst(2,1,3),lst(numeric(98)/100,1,1)).hold());
136 res.append(H(lst(2,1,3),numeric(245)/100).hold() - Li(lst(2,1,3),lst(numeric(245)/100,1,1)).hold());
137 res.append(H(lst(4,1,1,1),numeric(1)/3).hold() - S(3,4,numeric(1)/3).hold());
138 res.append(H(lst(4,1,1,1),numeric(98)/100).hold() - S(3,4,numeric(98)/100).hold());
139 res.append(H(lst(4,1,1,1),numeric(245)/100).hold() - S(3,4,numeric(245)/100).hold());
140 res.append(H(lst(2,2,3),almostone).hold() - zeta(lst(2,2,3)));
141 res.append(H(lst(-3,-1,2,1),almostone).hold() - zeta(lst(3,1,2,1),lst(-1,1,-1,1)));
142 res.append(H(lst(-2,1,3),numeric(1)/3).hold() - -Li(lst(2,1,3),lst(-numeric(1)/3,-1,1)).hold());
143 res.append(H(lst(-2,1,3),numeric(98)/100).hold() - -Li(lst(2,1,3),lst(-numeric(98)/100,-1,1)).hold());
144 res.append(H(lst(-2,1,3),numeric(245)/100).hold() - -Li(lst(2,1,3),lst(-numeric(245)/100,-1,1)).hold());
145 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());
147 for (lst::const_iterator it = res.begin(); it != res.end(); it++) {
148 ex diff = abs((*it).evalf());
150 clog << *it << " seems to be wrong: " << diff << endl;
153 cout << "." << flush;
159 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));
160 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));
161 if ((cdif.real() > prec) || (cadd.imag() > prec)) {
162 clog << "complex conjugation test of H({2,2,1},5.0-5.0*I) seems to be wrong: " << cdif << " " << cadd << endl;
170 ////////////////////////////////////////////////////////////////////////////////
171 ////////////////////////////////////////////////////////////////////////////////
173 ////////////////////////////////////////////////////////////////////////////////
174 ////////////////////////////////////////////////////////////////////////////////
177 static unsigned inifcns_test_zeta()
179 int digitsbuf = Digits;
185 res.append(zeta(lst(2,1)) - zeta(3));
186 res.append(zeta(lst(2,1,1,1,1)) - zeta(6));
187 res.append(zeta(lst(6,3)) - (zeta(9)*83/2 - zeta(2)*zeta(7)*21 - zeta(2)*zeta(2)*zeta(5)*12/5));
188 res.append(zeta(lst(4,2,3)) - (-zeta(9)*59 + zeta(2)*zeta(7)*28 + pow(zeta(2),2)*zeta(5)*4 -
189 pow(zeta(3),3)/3 + pow(zeta(2),3)*zeta(3)*8/21));
190 res.append(zeta(lst(3,1,3,1,3,1,3,1)) - (2*pow(Pi,16)/factorial(18)));
191 res.append(zeta(lst(2),lst(-1)) - -zeta(2)/2);
192 res.append(zeta(lst(1,2),lst(-1,1)) - (-zeta(3)/4 - zeta(lst(1),lst(-1))*zeta(2)/2));
193 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
194 - zeta(lst(3,1),lst(-1,1))*3/2 - zeta(lst(1),lst(-1))*zeta(3)*21/8));
196 for (lst::const_iterator it = res.begin(); it != res.end(); it++) {
198 ex prec = 5 * pow(10, -(int)Digits);
199 ex diff = abs((*it).evalf());
201 clog << *it << " seems to be wrong: " << diff << endl;
202 clog << "Digits: " << Digits << endl;
205 cout << "." << flush;
207 prec = 5 * pow(10, -(int)Digits);
208 diff = abs((*it).evalf());
210 clog << *it << " seems to be wrong: " << diff << endl;
211 clog << "Digits: " << Digits << endl;
214 cout << "." << flush;
223 ////////////////////////////////////////////////////////////////////////////////
224 ////////////////////////////////////////////////////////////////////////////////
226 ////////////////////////////////////////////////////////////////////////////////
227 ////////////////////////////////////////////////////////////////////////////////
230 static unsigned inifcns_test_LiG()
232 int digitsbuf = Digits;
234 ex prec = 5 * pow(10, -(int)Digits);
235 numeric almostone("0.99999999999999999999");
240 res.append(Li(lst(4), lst(6)).hold() - Li(4, 6.0));
241 res.append(G(lst(0,0,5.0,0,2.0,0,0,0,3.0),0.5).hold()
242 + Li(lst(3,2,4), lst(numeric(1,10), numeric(5,2), numeric(2,3))));
243 res.append(Li(lst(2,1,1), lst(almostone, almostone, almostone)) - zeta(lst(2,1,1)));
245 // check Li_{1,1} against known expression
246 symbol x("x"), y("y");
248 ex s1 = Li(lst(1,1),lst(x,y));
249 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))
250 - 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))
251 - log(-1/x/y-eps)*log(1-1/x-eps) + log(-1/x/y-eps)*log(-1/x-eps);
252 res.append(s1.subs(lst(x==numeric(1)/2, y==3)) - s2.subs(lst(x==numeric(1)/2, y==3)));
253 res.append(s1.subs(lst(x==numeric(3)/2, y==numeric(1)/2)) - s2.subs(lst(x==numeric(3)/2, y==numeric(1)/2)));
254 res.append(s1.subs(lst(x==2, y==numeric(4)/5)) - s2.subs(lst(x==2, y==numeric(4)/5)));
256 // shuffle and quasi-shuffle identities
257 res.append(G(lst(0,0.2),1).hold() * G(lst(0.5),1).hold() - G(lst(0.5,0,0.2),1).hold()
258 - G(lst(0,0.5,0.2),1).hold() - G(lst(0,0.2,0.5),1).hold());
259 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()
260 - G(lst(0.6,0,0.5*0.6),1).hold() + G(lst(0,0,0.5*0.6),1).hold());
261 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()
262 - Li(lst(3,2),lst(7,numeric(1,5))).hold() - Li(lst(5),lst(numeric(7,5))).hold());
263 symbol a1, a2, a3, a4;
264 res.append((G(lst(a1,a2),1) * G(lst(a3,a4),1) - G(lst(a1,a2,a3,a4),1)
265 - G(lst(a1,a3,a2,a4),1) - G(lst(a3,a1,a2,a4),1)
266 - G(lst(a1,a3,a4,a2),1) - G(lst(a3,a1,a4,a2),1) - G(lst(a3,a4,a1,a2),1))
267 .subs(lst(a1==numeric(1)/10, a2==numeric(3)/10, a3==numeric(7)/10, a4==5)));
268 res.append(G(lst(-0.009),1).hold() * G(lst(-8,1.4999),1).hold() - G(lst(-0.009,-8,1.4999),1).hold()
269 - G(lst(-8,-0.009,1.4999),1).hold() - G(lst(-8,1.4999,-0.009),1).hold());
270 res.append(G(lst(sqrt(numeric(1)/2)+I*sqrt(numeric(1)/2)),1).hold() * G(lst(1.51,-0.999),1).hold()
271 - G(lst(sqrt(numeric(1)/2)+I*sqrt(numeric(1)/2),1.51,-0.999),1).hold()
272 - G(lst(1.51,sqrt(numeric(1)/2)+I*sqrt(numeric(1)/2),-0.999),1).hold()
273 - G(lst(1.51,-0.999,sqrt(numeric(1)/2)+I*sqrt(numeric(1)/2)),1).hold());
274 // checks for hoelder convolution which is used if one argument has a distance to one smaller than 0.01
275 res.append(G(lst(0, 1.2, 1, 1.01), 1).hold() - G(lst(0, 1.2, 1, numeric("1.009999999999999999")), 1).hold());
277 for (lst::const_iterator it = res.begin(); it != res.end(); it++) {
278 ex diff = abs((*it).evalf());
280 clog << *it << " seems to be wrong: " << diff << endl;
283 cout << "." << flush;
290 unsigned exam_inifcns_nstdsums(void)
294 cout << "examining consistency of nestedsums functions" << flush;
295 clog << "----------consistency of nestedsums functions:" << endl;
297 result += inifcns_test_zeta();
298 result += inifcns_test_S();
299 result += inifcns_test_HLi();
300 result += inifcns_test_LiG();
303 cout << " passed " << endl;
304 clog << "(no output)" << endl;
306 cout << " failed " << endl;