/** @file powerlaws.cpp * * Tests for power laws. You shouldn't try to draw much inspiration from * this code, it is a sanity check rather deeply rooted in GiNaC's classes. * * GiNaC Copyright (C) 1999 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 * the Free Software Foundation; either version 2 of the License, or * (at your option) any later version. * * This program is distributed in the hope that it will be useful, * but WITHOUT ANY WARRANTY; without even the implied warranty of * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the * GNU General Public License for more details. * * 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 */ #include static unsigned powerlaws1(void) { // (x^a)^b = x^(a*b) symbol x("x"); symbol a("a"); symbol b("b"); ex e1=power(power(x,a),b); if (!(is_ex_exactly_of_type(e1,power) && is_ex_exactly_of_type(e1.op(0),power) && is_ex_exactly_of_type(e1.op(0).op(0),symbol) && is_ex_exactly_of_type(e1.op(0).op(1),symbol) && is_ex_exactly_of_type(e1.op(1),symbol) && e1.is_equal(power(power(x,a),b)) )) { clog << "(x^a)^b, x,a,b symbolic wrong" << endl; clog << "returned: " << e1 << endl; return 1; } ex e2=e1.subs(a==1); if (!(is_ex_exactly_of_type(e2,power) && is_ex_exactly_of_type(e2.op(0),symbol) && is_ex_exactly_of_type(e2.op(1),symbol) && e2.is_equal(power(x,b)) )) { clog << "(x^a)^b, x,b symbolic, a==1 wrong" << endl; clog << "returned: " << e2 << endl; return 1; } ex e3=e1.subs(a==-1); if (!(is_ex_exactly_of_type(e3,power) && is_ex_exactly_of_type(e3.op(0),power) && is_ex_exactly_of_type(e3.op(0).op(0),symbol) && is_ex_exactly_of_type(e3.op(0).op(1),numeric) && is_ex_exactly_of_type(e3.op(1),symbol) && e3.is_equal(power(power(x,-1),b)) )) { clog << "(x^a)^b, x,b symbolic, a==-1 wrong" << endl; clog << "returned: " << e3 << endl; return 1; } ex e4=e1.subs(lst(a==-1,b==2.5)); if (!(is_ex_exactly_of_type(e4,power) && is_ex_exactly_of_type(e4.op(0),power) && is_ex_exactly_of_type(e4.op(0).op(0),symbol) && is_ex_exactly_of_type(e4.op(0).op(1),numeric) && is_ex_exactly_of_type(e4.op(1),numeric) && e4.is_equal(power(power(x,-1),2.5)) )) { clog << "(x^a)^b, x symbolic, a==-1, b==2.5 wrong" << endl; clog << "returned: " << e4 << endl; return 1; } ex e5=e1.subs(lst(a==-0.9,b==2.5)); if (!(is_ex_exactly_of_type(e5,power) && is_ex_exactly_of_type(e5.op(0),symbol) && is_ex_exactly_of_type(e5.op(1),numeric) && e5.is_equal(power(x,numeric(-0.9)*numeric(2.5))) )) { clog << "(x^a)^b, x symbolic, a==-0.9, b==2.5 wrong" << endl; clog << "returned: " << e5 << endl; return 1; } ex e6=e1.subs(lst(a==numeric(3)+numeric(5.3)*I,b==-5)); if (!(is_ex_exactly_of_type(e6,power) && is_ex_exactly_of_type(e6.op(0),symbol) && is_ex_exactly_of_type(e6.op(1),numeric) && e6.is_equal(power(x,numeric(-15)+numeric(5.3)*numeric(-5)*I)) )) { clog << "(x^a)^b, x symbolic, a==3+5.3*I, b==-5 wrong" << endl; clog << "returned: " << e6 << endl; return 1; } return 0; } static unsigned powerlaws2(void) { // (a*x)^b = a^b * x^b symbol x("x"); symbol a("a"); symbol b("b"); ex e1=power(a*x,b); if (!(is_ex_exactly_of_type(e1,power) && is_ex_exactly_of_type(e1.op(0),mul) && (e1.op(0).nops()==2) && is_ex_exactly_of_type(e1.op(0).op(0),symbol) && is_ex_exactly_of_type(e1.op(0).op(1),symbol) && is_ex_exactly_of_type(e1.op(1),symbol) && e1.is_equal(power(a*x,b)) )) { clog << "(a*x)^b, x,a,b symbolic wrong" << endl; clog << "returned: " << e1 << endl; return 1; } ex e2=e1.subs(a==3); if (!(is_ex_exactly_of_type(e2,power) && is_ex_exactly_of_type(e2.op(0),mul) && (e2.op(0).nops()==2) && is_ex_exactly_of_type(e2.op(0).op(0),symbol) && is_ex_exactly_of_type(e2.op(0).op(1),numeric) && is_ex_exactly_of_type(e2.op(1),symbol) && e2.is_equal(power(3*x,b)) )) { clog << "(a*x)^b, x,b symbolic, a==3 wrong" << endl; clog << "returned: " << e2 << endl; return 1; } ex e3=e1.subs(b==-3); if (!(is_ex_exactly_of_type(e3,mul) && (e3.nops()==2) && is_ex_exactly_of_type(e3.op(0),power) && is_ex_exactly_of_type(e3.op(1),power) && e3.is_equal(power(a,-3)*power(x,-3)) )) { clog << "(a*x)^b, x,a symbolic, b==-3 wrong" << endl; clog << "returned: " << e3 << endl; return 1; } ex e4=e1.subs(b==4.5); if (!(is_ex_exactly_of_type(e4,power) && is_ex_exactly_of_type(e4.op(0),mul) && (e4.op(0).nops()==2) && is_ex_exactly_of_type(e4.op(0).op(0),symbol) && is_ex_exactly_of_type(e4.op(0).op(1),symbol) && is_ex_exactly_of_type(e4.op(1),numeric) && e4.is_equal(power(a*x,4.5)) )) { clog << "(a*x)^b, x,a symbolic, b==4.5 wrong" << endl; clog << "returned: " << e4 << endl; return 1; } ex e5=e1.subs(lst(a==3.2,b==3+numeric(5)*I)); if (!(is_ex_exactly_of_type(e5,mul) && (e5.nops()==2) && is_ex_exactly_of_type(e5.op(0),power) && is_ex_exactly_of_type(e5.op(1),numeric) && e5.is_equal(power(x,3+numeric(5)*I)* power(numeric(3.2),3+numeric(5)*I)) )) { clog << "(a*x)^b, x symbolic, a==3.2, b==3+5*I wrong" << endl; clog << "returned: " << e5 << endl; return 1; } ex e6=e1.subs(lst(a==-3.2,b==3+numeric(5)*I)); if (!(is_ex_exactly_of_type(e6,mul) && (e6.nops()==2) && is_ex_exactly_of_type(e6.op(0),power) && is_ex_exactly_of_type(e6.op(1),numeric) && e6.is_equal(power(-x,3+numeric(5)*I)* power(numeric(3.2),3+numeric(5)*I)) )) { clog << "(a*x)^b, x symbolic, a==-3.2, b==3+5*I wrong" << endl; clog << "returned: " << e6 << endl; return 1; } ex e7=e1.subs(lst(a==3+numeric(5)*I,b==3.2)); if (!(is_ex_exactly_of_type(e7,power) && is_ex_exactly_of_type(e7.op(0),mul) && (e7.op(0).nops()==2) && is_ex_exactly_of_type(e7.op(0).op(0),symbol) && is_ex_exactly_of_type(e7.op(0).op(1),numeric) && is_ex_exactly_of_type(e7.op(1),numeric) && e7.is_equal(power((3+numeric(5)*I)*x,3.2)) )) { clog << "(a*x)^b, x symbolic, a==3+5*I, b==3.2 wrong" << endl; clog << "returned: " << e7 << endl; return 1; } return 0; } static unsigned powerlaws3(void) { // numeric evaluation ex e1=power(numeric(4),numeric(1)/numeric(2)); if (e1 != 2) { clog << "4^(1/2) wrongly returned " << e1 << endl; return 1; } ex e2=power(numeric(27),numeric(2)/numeric(3)); if (e2 != 9) { clog << "27^(2/3) wrongly returned " << e2 << endl; return 1; } ex e3=power(numeric(5),numeric(1)/numeric(2)); if (!(is_ex_exactly_of_type(e3,power) && e3.op(0).is_equal(numeric(5)) && e3.op(1).is_equal(numeric(1)/numeric(2)) )) { clog << "5^(1/2) wrongly returned " << e3 << endl; return 1; } ex e4=power(numeric(5),evalf(numeric(1)/numeric(2))); if (!(is_ex_exactly_of_type(e4,numeric))) { clog << "5^(0.5) wrongly returned " << e4 << endl; return 1; } ex e5=power(evalf(numeric(5)),numeric(1)/numeric(2)); if (!(is_ex_exactly_of_type(e5,numeric))) { clog << "5.0^(1/2) wrongly returned " << e5 << endl; return 1; } return 0; } static unsigned powerlaws4(void) { // test for mul::eval() symbol a("a"); symbol b("b"); symbol c("c"); ex f1=power(a*b,ex(1)/ex(2)); ex f2=power(a*b,ex(3)/ex(2)); ex f3=c; exvector v; v.push_back(f1); v.push_back(f2); v.push_back(f3); ex e1=mul(v); if (e1!=a*a*b*b*c) { clog << "(a*b)^(1/2)*(a*b)^(3/2)*c wrongly returned " << e1 << endl; return 1; } return 0; } unsigned powerlaws(void) { unsigned result = 0; cout << "checking power laws..." << flush; clog << "---------power laws:" << endl; result += powerlaws1(); result += powerlaws2(); result += powerlaws3(); result += powerlaws4(); if (!result) { cout << " passed "; clog << "(no output)" << endl; } else { cout << " failed "; } return result; }