32368e6030a9d92d747ffccf2c2e84c0a1634ecd
[ginac.git] / check / exam_inifcns.cpp
1 /** @file exam_inifcns.cpp
2  *
3  *  This test routine applies assorted tests on initially known higher level
4  *  functions. */
5
6 /*
7  *  GiNaC Copyright (C) 1999-2011 Johannes Gutenberg University Mainz, Germany
8  *
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.
13  *
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.
18  *
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
22  */
23
24 #include "ginac.h"
25 using namespace GiNaC;
26
27 #include <iostream>
28 using namespace std;
29
30 /* Assorted tests on other transcendental functions. */
31 static unsigned inifcns_consist_trans()
32 {
33         using GiNaC::asin; using GiNaC::acos;
34         using GiNaC::asinh; using GiNaC::acosh; using GiNaC::atanh;
35
36         unsigned result = 0;
37         symbol x("x");
38         ex chk;
39         
40         chk = asin(1)-acos(0);
41         if (!chk.is_zero()) {
42                 clog << "asin(1)-acos(0) erroneously returned " << chk
43                      << " instead of 0" << endl;
44                 ++result;
45         }
46         
47         // arbitrary check of type sin(f(x)):
48         chk = pow(sin(acos(x)),2) + pow(sin(asin(x)),2)
49                 - (1+pow(x,2))*pow(sin(atan(x)),2);
50         if (chk != 1-pow(x,2)) {
51                 clog << "sin(acos(x))^2 + sin(asin(x))^2 - (1+x^2)*sin(atan(x))^2 "
52                      << "erroneously returned " << chk << " instead of 1-x^2" << endl;
53                 ++result;
54         }
55         
56         // arbitrary check of type cos(f(x)):
57         chk = pow(cos(acos(x)),2) + pow(cos(asin(x)),2)
58                 - (1+pow(x,2))*pow(cos(atan(x)),2);
59         if (!chk.is_zero()) {
60                 clog << "cos(acos(x))^2 + cos(asin(x))^2 - (1+x^2)*cos(atan(x))^2 "
61                      << "erroneously returned " << chk << " instead of 0" << endl;
62                 ++result;
63         }
64         
65         // arbitrary check of type tan(f(x)):
66         chk = tan(acos(x))*tan(asin(x)) - tan(atan(x));
67         if (chk != 1-x) {
68                 clog << "tan(acos(x))*tan(asin(x)) - tan(atan(x)) "
69                      << "erroneously returned " << chk << " instead of -x+1" << endl;
70                 ++result;
71         }
72         
73         // arbitrary check of type sinh(f(x)):
74         chk = -pow(sinh(acosh(x)),2).expand()*pow(sinh(atanh(x)),2)
75                 - pow(sinh(asinh(x)),2);
76         if (!chk.is_zero()) {
77                 clog << "expand(-(sinh(acosh(x)))^2)*(sinh(atanh(x))^2) - sinh(asinh(x))^2 "
78                      << "erroneously returned " << chk << " instead of 0" << endl;
79                 ++result;
80         }
81         
82         // arbitrary check of type cosh(f(x)):
83         chk = (pow(cosh(asinh(x)),2) - 2*pow(cosh(acosh(x)),2))
84                 * pow(cosh(atanh(x)),2);
85         if (chk != 1) {
86                 clog << "(cosh(asinh(x))^2 - 2*cosh(acosh(x))^2) * cosh(atanh(x))^2 "
87                      << "erroneously returned " << chk << " instead of 1" << endl;
88                 ++result;
89         }
90         
91         // arbitrary check of type tanh(f(x)):
92         chk = (pow(tanh(asinh(x)),-2) - pow(tanh(acosh(x)),2)).expand()
93                 * pow(tanh(atanh(x)),2);
94         if (chk != 2) {
95                 clog << "expand(tanh(acosh(x))^2 - tanh(asinh(x))^(-2)) * tanh(atanh(x))^2 "
96                      << "erroneously returned " << chk << " instead of 2" << endl;
97                 ++result;
98         }
99         
100         // check consistency of log and eta phases:
101         for (int r1=-1; r1<=1; ++r1) {
102                 for (int i1=-1; i1<=1; ++i1) {
103                         ex x1 = r1+I*i1;
104                         if (x1.is_zero())
105                                 continue;
106                         for (int r2=-1; r2<=1; ++r2) {
107                                 for (int i2=-1; i2<=1; ++i2) {
108                                         ex x2 = r2+I*i2;
109                                         if (x2.is_zero())
110                                                 continue;
111                                         if (abs(evalf(eta(x1,x2)-log(x1*x2)+log(x1)+log(x2)))>.1e-12) {
112                                                 clog << "either eta(x,y), log(x), log(y) or log(x*y) is wrong"
113                                                      << " at x==" << x1 << ", y==" << x2 << endl;
114                                                 ++result;
115                                         }
116                                 }
117                         }
118                 }
119         }
120                 
121         return result;
122 }
123
124 /* Simple tests on the tgamma function.  We stuff in arguments where the results
125  * exists in closed form and check if it's ok. */
126 static unsigned inifcns_consist_gamma()
127 {
128         using GiNaC::tgamma;
129         unsigned result = 0;
130         ex e;
131         
132         e = tgamma(1);
133         for (int i=2; i<8; ++i)
134                 e += tgamma(ex(i));
135         if (e != numeric(874)) {
136                 clog << "tgamma(1)+...+tgamma(7) erroneously returned "
137                      << e << " instead of 874" << endl;
138                 ++result;
139         }
140         
141         e = tgamma(1);
142         for (int i=2; i<8; ++i)
143                 e *= tgamma(ex(i));     
144         if (e != numeric(24883200)) {
145                 clog << "tgamma(1)*...*tgamma(7) erroneously returned "
146                      << e << " instead of 24883200" << endl;
147                 ++result;
148         }
149         
150         e = tgamma(ex(numeric(5, 2)))*tgamma(ex(numeric(9, 2)))*64;
151         if (e != 315*Pi) {
152                 clog << "64*tgamma(5/2)*tgamma(9/2) erroneously returned "
153                      << e << " instead of 315*Pi" << endl;
154                 ++result;
155         }
156         
157         e = tgamma(ex(numeric(-13, 2)));
158         for (int i=-13; i<7; i=i+2)
159                 e += tgamma(ex(numeric(i, 2)));
160         e = (e*tgamma(ex(numeric(15, 2)))*numeric(512));
161         if (e != numeric(633935)*Pi) {
162                 clog << "512*(tgamma(-13/2)+...+tgamma(5/2))*tgamma(15/2) erroneously returned "
163                      << e << " instead of 633935*Pi" << endl;
164                 ++result;
165         }
166         
167         return result;
168 }
169
170 /* Simple tests on the Psi-function (aka polygamma-function).  We stuff in
171    arguments where the result exists in closed form and check if it's ok. */
172 static unsigned inifcns_consist_psi()
173 {
174         using GiNaC::log;
175         using GiNaC::tgamma;
176
177         unsigned result = 0;
178         symbol x;
179         ex e, f;
180         
181         // We check psi(1) and psi(1/2) implicitly by calculating the curious
182         // little identity tgamma(1)'/tgamma(1) - tgamma(1/2)'/tgamma(1/2) == 2*log(2).
183         e += (tgamma(x).diff(x)/tgamma(x)).subs(x==numeric(1));
184         e -= (tgamma(x).diff(x)/tgamma(x)).subs(x==numeric(1,2));
185         if (e!=2*log(2)) {
186                 clog << "tgamma(1)'/tgamma(1) - tgamma(1/2)'/tgamma(1/2) erroneously returned "
187                      << e << " instead of 2*log(2)" << endl;
188                 ++result;
189         }
190         
191         return result;
192 }
193
194 /* Simple tests on the Riemann Zeta function.  We stuff in arguments where the
195  * result exists in closed form and check if it's ok.  Of course, this checks
196  * the Bernoulli numbers as a side effect. */
197 static unsigned inifcns_consist_zeta()
198 {
199         unsigned result = 0;
200         ex e;
201         
202         for (int i=0; i<13; i+=2)
203                 e += zeta(i)/pow(Pi,i);
204         if (e!=numeric(-204992279,638512875)) {
205                 clog << "zeta(0) + zeta(2) + ... + zeta(12) erroneously returned "
206                      << e << " instead of -204992279/638512875" << endl;
207                 ++result;
208         }
209         
210         e = 0;
211         for (int i=-1; i>-16; i--)
212                 e += zeta(i);
213         if (e!=numeric(487871,1633632)) {
214                 clog << "zeta(-1) + zeta(-2) + ... + zeta(-15) erroneously returned "
215                      << e << " instead of 487871/1633632" << endl;
216                 ++result;
217         }
218         
219         return result;
220 }
221
222 static unsigned inifcns_consist_abs()
223 {
224         unsigned result = 0;
225         realsymbol a("a"), b("b"), x("x"), y("y");
226         possymbol p("p");
227         symbol z("z");
228
229         if (!abs(exp(x+I*y)).eval().is_equal(exp(x)))
230                 ++result;
231
232         if (!abs(pow(p,a+I*b)).eval().is_equal(pow(p,a)))
233                 ++result;
234
235         // also checks that abs(p)=p
236         if (!abs(pow(p,a+I*b)).eval().is_equal(pow(p,a)))
237                 ++result;
238
239         if (!abs(pow(x+I*y,a)).eval().is_equal(pow(abs(x+I*y),a)))
240                 ++result;
241
242         // it is not necessary a simplification if the following is really evaluated
243         if (!abs(pow(x+I*y,a+I*b)).eval().is_equal(abs(pow(x+I*y,a+I*b))))
244                 ++result;
245
246         // check expansion of abs
247         if (!abs(-7*z*a*p).expand(expand_options::expand_transcendental).is_equal(7*abs(z)*abs(a)*p))
248                 ++result;
249
250         if (!abs(z.conjugate()).eval().is_equal(abs(z)))
251                 ++result;
252
253         if (!abs(step(z)).eval().is_equal(step(z)))
254                 ++result;
255
256         if (!abs(p).info(info_flags::positive) || !abs(a).info(info_flags::real))
257                 ++result;
258
259         if (abs(a).info(info_flags::positive) || !abs(a).info(info_flags::real))
260                 ++result;
261
262         if (abs(z).info(info_flags::positive) || !abs(z).info(info_flags::real))
263                 ++result;
264
265         return result;
266 }
267
268 static unsigned inifcns_consist_exp()
269 {
270         unsigned result = 0;
271         symbol a("a"), b("b");
272
273         if (!exp(a+b).expand(expand_options::expand_transcendental).is_equal(exp(a)*exp(b)))
274                 ++result;
275
276         // shall not be expanded since the arg is not add
277         if (!exp(pow(a+b,2)).expand(expand_options::expand_transcendental).is_equal(exp(pow(a+b,2))))
278                 ++result;
279
280         // expand now
281         if (!exp(pow(a+b,2)).expand(expand_options::expand_function_args | expand_options::expand_transcendental)
282                 .is_equal(exp(a*a)*exp(b*b)*exp(2*a*b)))
283                 ++result;
284
285         return result;
286 }
287
288 static unsigned inifcns_consist_log()
289 {
290         unsigned result = 0;
291         symbol z("a"), w("b");
292         realsymbol a("a"), b("b");
293         possymbol p("p"), q("q");
294
295         // do not expand
296         if (!log(z*w).expand(expand_options::expand_transcendental).is_equal(log(z*w)))
297                 ++result;
298
299         // do not expand
300         if (!log(a*b).expand(expand_options::expand_transcendental).is_equal(log(a*b)))
301                 ++result;
302
303         // shall expand
304         if (!log(p*q).expand(expand_options::expand_transcendental).is_equal(log(p) + log(q)))
305                 ++result;
306
307         // a bit more complicated
308         ex e1 = log(-7*p*pow(q,3)*a*pow(b,2)*z*w).expand(expand_options::expand_transcendental);
309         ex e2 = log(7)+log(p)+log(pow(q,3))+log(-z*a*w*pow(b,2));
310         if (!e1.is_equal(e2))
311                 ++result;
312
313         if (!ex(log(pow(p,a))).is_equal(a*log(p)))
314                 ++result;
315
316         // shall not do for non-real powers
317         if (ex(log(pow(p,z))).is_equal(z*log(p)))
318                 ++result;
319
320         // shall not do for non-positive basis
321         if (ex(log(pow(a,b))).is_equal(b*log(a)))
322                 ++result;
323
324         return result;
325 }
326
327 static unsigned inifcns_consist_various()
328 {
329         unsigned result = 0;
330         symbol n;
331         
332         if ( binomial(n, 0) != 1 ) {
333                 clog << "ERROR: binomial(n,0) != 1" << endl;            
334                 ++result;
335         }
336         
337         return result;
338 }
339
340 unsigned exam_inifcns()
341 {
342         unsigned result = 0;
343         
344         cout << "examining consistency of symbolic functions" << flush;
345         
346         result += inifcns_consist_trans();  cout << '.' << flush;
347         result += inifcns_consist_gamma();  cout << '.' << flush;
348         result += inifcns_consist_psi();  cout << '.' << flush;
349         result += inifcns_consist_zeta();  cout << '.' << flush;
350         result += inifcns_consist_abs();  cout << '.' << flush;
351         result += inifcns_consist_exp();  cout << '.' << flush;
352         result += inifcns_consist_log();  cout << '.' << flush;
353         result += inifcns_consist_various();  cout << '.' << flush;
354         
355         return result;
356 }
357
358 int main(int argc, char** argv)
359 {
360         return exam_inifcns();
361 }