/*===========================================================================
Copyright (C) 2002-2017 Yves Renard.
This file is a part of GetFEM++
GetFEM++ is free software; you can redistribute it and/or modify it
under the terms of the GNU Lesser General Public License as published
by the Free Software Foundation; either version 3 of the License, or
(at your option) any later version along with the GCC Runtime Library
Exception either version 3.1 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 Lesser General Public
License and GCC Runtime Library Exception for more details.
You should have received a copy of the GNU Lesser General Public License
along with this program; if not, write to the Free Software Foundation,
Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA.
===========================================================================*/
#include "getfem/bgeot_poly.h"
using std::endl; using std::cout; using std::cerr;
using std::ends; using std::cin;
std::string horner_print(bgeot::short_type degree, bgeot::power_index &mi,
bgeot::short_type k, bgeot::short_type de) {
char s[1024];
const char *xyz = "xyzabcdefghijklmnop";
if (k == 0) {
sprintf(s, "P[%d]", int(mi.global_index()));
return s;
} else {
std::string str;
//T v = (*(it+k-1)), res = T(0);
for (mi[k-1] = bgeot::short_type(degree-de);
mi[k-1] != bgeot::short_type(-1); (mi[k-1])--) {
//res = horner(mi, k-1, de + mi[k-1], it) + v * res;
if (str.size())
sprintf(s, "%s + %c*(%s)",
horner_print(degree, mi,bgeot::short_type(k-1),bgeot::short_type(de+mi[k-1])).c_str(), xyz[k-1],
str.c_str());
else
sprintf(s, "%s", horner_print(degree, mi,bgeot::short_type(k-1),bgeot::short_type(de+mi[k-1])).c_str());
str = s;
}
mi[k-1] = 0;
return str;
}
}
void dump_poly_eval() {
for (bgeot::short_type dim = 1; dim <= 3; ++dim) {
cout << "case " << dim << ": {\n";
for (unsigned k=0; k < dim; ++k) {
cout << "T " << "xyzZ"[k] << " = it[" << k << "];\n";
}
for (bgeot::short_type dg=2; dg <= 6; ++dg) {
cout << " if (deg == " << dg << ") ";
bgeot::power_index mi(dim);
cout << " return " << horner_print(dg, mi, dim, 0) << ";\n";
}
cout << "} break;\n";
}
}
int main(void)
{
try {
bgeot::base_poly W, Z; W[0] = 1.0;
Z[0] = 2.0;
cout << "rd = " << W.real_degree() << endl;
cout << "W = " << W << endl;
W.direct_product(Z);
cout << "W = " << W << endl;
bgeot::base_poly P(2,2), Q(2,2);
P[2] = 1.0;
Q[3] = 2.0;
cout << "Le nombre de monomes de P est " << P.size() << endl;
cout << "P = " << P << endl;
cout << "Q = " << Q << endl;
cout << "P + Q = " << P + Q << endl;
cout << "P * 2.0 * Q = " << P * 2.0 * Q << endl;
bgeot::base_poly R = P * Q;
cout << "Le nombre de monomes de R est " << R.size() << endl;
cout << "Le degre de R est " << R.degree() << endl;
P.direct_product(Q);
cout << "Produit direct de P et Q : " << P << endl;
Z.direct_product(P);
cout << "Produit direct de P et Z : " << Z << endl;
P = bgeot::base_poly(3,1,1);
P *= 3.0; P *= bgeot::base_poly(3,1,0);
P += bgeot::base_poly(3,1,1);
P *= bgeot::base_poly(3,1,2);
P += bgeot::base_poly(3,1,0);
cout << "P = " << P << " : degree=" << P.degree() << endl;
bgeot::opt_long_scalar_type tab[3];
tab[0] = 1.0; tab[1] = 2.0; tab[2] = -1.0;
cout << "P(1.0, 2.0) = " << P.eval(&(tab[0])) << endl;
for (bgeot::short_type dg=0; dg <= 6; ++dg) {
for (bgeot::short_type dim=0; dim <= 3; ++dim) {
bgeot::base_poly PP(dim, dg);
for (unsigned i=0; i < PP.size(); ++i)
PP[i] = bgeot::opt_long_scalar_type(rand())
/ bgeot::opt_long_scalar_type(RAND_MAX);
std::vector<bgeot::opt_long_scalar_type> X(dim);
for (unsigned i=0; i < dim; ++i) X[i] =
bgeot::opt_long_scalar_type(rand())
/ bgeot::opt_long_scalar_type(RAND_MAX);
bgeot::opt_long_scalar_type a = PP.eval(X.begin());
bgeot::power_index mi(dim);
bgeot::opt_long_scalar_type b = PP.horner(mi,dim,0,X.begin());
cout << "[d=" << dim << ", dg=" << PP.degree()
//<< ", P=" << PP << " -> "
<< a << " == " << b
<< "?\n";
assert(gmm::abs(a-b) < 1e-14);
//cout << "Horner: " << PP.horner_print(mi,dim,0) << "\n";
}
}
cout << "\n--------------------------------------------------------\n";
dump_poly_eval();
cout << "\n--------------------------------------------------------\n";
Q = P;
P *= Q;
cout << "PP = " << P << "\n";
P.derivative(0);
cout << "PP.derivative(0)=" << P << "\n";
bgeot::power_index p(3);
for (int i=0; i < 20; ++i, ++p) {
cout << "i=" << i << ", p=";
for (unsigned k=0; k < p.size(); ++k) cout << p[k] << " ";
cout << "degree=" << p.degree() << ", global_index(p)="
<< p.global_index() << "\n";
}
bgeot::base_poly S(1,2); S[0] = -2; S[1] = 3; S[2] = 1;
cout << "P=" << P << ", S=" << S << " \n";
cout << "P(S,x)=" << bgeot::poly_substitute_var(P,S,0) << "\n";
bgeot::opt_long_scalar_type t0 = gmm::uclock_sec();
std::vector<bgeot::opt_long_scalar_type> v(3);
for (unsigned i=0; i < 100000; ++i) {
for (unsigned k=0; k < v.size(); ++k)
v[k] = bgeot::opt_long_scalar_type(rand())
/ bgeot::opt_long_scalar_type(RAND_MAX);
P.eval(v.begin());
}
cout << "poly eval : " << gmm::uclock_sec() - t0 << "sec \n";
bgeot::base_poly QQ(P); QQ.derivative(1); QQ.derivative(2);
cout << "QQ=" << QQ << "\n";
for (unsigned i=0; i < 100000; ++i) {
QQ.eval(v.begin());
}
cout << "poly eval : " << gmm::uclock_sec() - t0 << "sec \n";
t0 = gmm::uclock_sec();
bgeot::opt_long_scalar_type z=0;
for (unsigned i=0; i < 100000; ++i) {
bgeot::base_poly P2(P);
for (bgeot::short_type k=0; k < P.dim(); ++k) {
P2.derivative(k); z += P2[0];
}
}
cout << "poly derivative : " << gmm::uclock_sec() - t0 << "sec\n";
bgeot::base_poly P2;
std::stringstream ss; ss << P;
P2 = bgeot::read_base_poly(P.dim(), ss);
cout << "P=" << P << "\nread_base_poly=" << P2 << "\n";
assert(P == P2);
}
GMM_STANDARD_CATCH_ERROR;
return 0;
}