lexer: when switching to another output stream, clean last read character.
[ginac.git] / check / exam_inifcns_nstdsums.cpp
index f6864aa5f4d7112a95bbdcdf8b642fe4977f5492..ec843da3ab5544ea8b9eda8c0f4c3a8a19d0a541 100644 (file)
@@ -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
  *
  *  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 <iostream>
 #include <fstream>
+#include "ginac.h"
+using namespace std;
+using namespace GiNaC;
+
+
+
+////////////////////////////////////////////////////////////////////////////////
+////////////////////////////////////////////////////////////////////////////////
+//  S exam
+////////////////////////////////////////////////////////////////////////////////
+////////////////////////////////////////////////////////////////////////////////
 
 
 /*
  * 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]
  *
  *    
 #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<point> 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<numeric>(en);
-               ex ep(data[i++],symbol());
-               numeric p = ex_to<numeric>(ep);
+               ex p(data[i++],symbol());
                ex x(data[i++],symbol());
                ex res(data[i++],symbol());
-               
-               ppbuf.x = x;
-               ppbuf.res = res;
+               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
+////////////////////////////////////////////////////////////////////////////////
+////////////////////////////////////////////////////////////////////////////////
+
 
-               pp[n.to_int()-1][p.to_int()-1].push_back(ppbuf);
+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<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++;
+       }
+
+       return result;
+}
+
+
+////////////////////////////////////////////////////////////////////////////////
+////////////////////////////////////////////////////////////////////////////////
+//  zeta exam
+////////////////////////////////////////////////////////////////////////////////
+////////////////////////////////////////////////////////////////////////////////
+
+
+static unsigned inifcns_test_zeta()
+{
+       int digitsbuf = Digits;
        
-       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++;
-                                       }
-                               }
-                       }
+       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;
+}
+
+
+////////////////////////////////////////////////////////////////////////////////
+////////////////////////////////////////////////////////////////////////////////
+//  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;
 }
@@ -144,16 +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();
+}