DGtal  1.0.0
testMPolynomial.cpp
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1
30 #include <iostream>
32 #include <iomanip>
33 #include <sstream>
34 #include "DGtal/base/Common.h"
35 #include "DGtal/math/MPolynomial.h"
38
39 using namespace std;
40 using namespace DGtal;
41
43 // Functions for testing class Signal.
45
49 template <typename Ring>
52 {
54  = mmonomial<Ring>( 3, 1, 0 )
55  + mmonomial<Ring>( 1, 0, 3 )
56  + mmonomial<Ring>( 0, 3, 1 )
57  + mmonomial<Ring>( 0, 0, 3 )
58  + ((Ring)5) * mmonomial<Ring>( 0, 0, 1 );
59  return p;
60 }
61
62 double
63 durchblickC( const double & x, const double & y, const double z )
64 {
65  return x*x*x*y + x*z*z*z + y*y*y*z + z*z*z + 5.0 * z;
66 }
67
72 bool testMPolynomialSpeed( double step = 0.01 )
73 {
74  unsigned int nbok = 0;
75  unsigned int nb = 0;
76
77  trace.beginBlock ( "Testing block ... Evaluation speed of mpolynomials (naive)" );
78  trace.info() << setprecision( 15 ) << "step is " << step << std::endl;
79  trace.info() << "approximately " << 8.0/(step*step*step) << " computations." << std::endl;
80  MPolynomial<3, double> P = durchblick<double>();
81  double total = 0.0;
82  for ( double x = -1.0; x < 1.0; x += step )
83  {
84  for ( double y = -1.0; y < 1.0; y += step )
85  {
86  for ( double z = -1.0; z < 1.0; z += step )
87  total += P(x)(y)(z);
88  }
89  }
90  trace.info() << "Total = " << total << std::endl;
91  trace.endBlock();
92
93  trace.beginBlock ( "Testing block ... Evaluation speed of mpolynomials" );
94  //MPolynomial<3, double> P = durchblick<double>();
95  double total1 = 0.0;
96  for ( double x = -1.0; x < 1.0; x += step )
97  {
98  MPolynomial<2, double> PX = P( x );
99  for ( double y = -1.0; y < 1.0; y += step )
100  {
101  MPolynomial<1, double> PXY = PX( y );
102  for ( double z = -1.0; z < 1.0; z += step )
103  total1 += PXY( z );
104  }
105  }
106  trace.info() << "Total1 = " << total1 << std::endl;
107  trace.endBlock();
108
109  trace.beginBlock ( "Testing block ... Same computation in C." );
110  double total2 = 0.0;
111  for ( double x = -1.0; x < 1.0; x += step )
112  {
113  for ( double y = -1.0; y < 1.0; y += step )
114  {
115  for ( double z = -1.0; z < 1.0; z += step )
116  total2 += durchblickC( x, y, z );
117  }
118  }
119  trace.info() << "Total2 = " << total2 << std::endl;
120  trace.endBlock();
121  nbok += fabs( total1 - total ) < 1e-8 ? 1 : 0;
122  nb++;
123  trace.info() << "(" << nbok << "/" << nb << ") "
124  << "fabs( total1 - total ) < 1e-8" << std::endl;
125  nbok += fabs( total2 - total ) < 1e-8 ? 1 : 0;
126  nb++;
127  trace.info() << "(" << nbok << "/" << nb << ") "
128  << "fabs( total2 - total ) < 1e-8" << std::endl;
129
130  trace.info() << "For information, ImaGene::Polynomial3 takes 164ms for step=0.01 and 1604ms for step = 0.005." << std::endl;
131  return nbok == nb;
132 }
133
139 {
140  unsigned int nbok = 0;
141  unsigned int nb = 0;
142
143  trace.beginBlock ( "Testing block ..." );
144
145  MPolynomial<2, int> f = mmonomial<int>(1, 2) + 3 * mmonomial<int>(4, 5);
146  trace.info() << f << std::endl;
147  int e = f(4)(2);
148  trace.info() << e << std::endl;
149  nbok += e == 24592 ? 1 : 0;
150  nb++;
151  trace.info() << derivative<1>(f) << std::endl;
152  MPolynomial<1, int> g = f(2), h = f(3);
153  trace.info() << g << " and " << h << std::endl;
154  trace.info() << gcd<double>(g, h) << std::endl; // cast polynomials to MPolynomial<1, double> first; otherwise,
155  // result will be incorrect since int is not a field
156  trace.info() << gcd(g, h) << std::endl; // to prove our point, check for yourself that the result is
157  // X_0^5 instead of X_0^2
158  nbok += gcd<double>(g,h) == mmonomial<double>(2) ? 1 : 0;
159  nb++;
160  MPolynomial<1, double> l = f(mmonomial<double>(1) - 1)(mmonomial<double>(1) - 2);
161  trace.info() << l << std::endl;
162  trace.info() << derivative<0>(l) << std::endl;
163  trace.info() << gcd(l, derivative<0>(l)) << " (gcd of two previous polys is 1)" << std::endl;
164  nbok += gcd(l, derivative<0>(l)) == 1.0 * mmonomial<double>(0) ? 1 : 0;
165  nb++;
166  trace.info() << "Durchblick (x3y+xz3+y3z+z3+5z)= " << durchblick<double>() << std::endl;
167  trace.endBlock();
168  MPolynomial<3, double> Q = mmonomial<double>( 0, 0, 0 )
169  + mmonomial<double>( 1, 2, 0 ) + mmonomial<double>( 4, 1, 1 );
170  std::cout << "Q(x,y,z)=1+xy^2+x^4yz = " << Q << std::endl;
171  std::cout << " degree = " << Q.degree() << std::endl;
173  std::cout << " Q[0] = " << Q[ 0 ] << std::endl;
174  std::cout << " Q[1] = " << Q[ 1 ] << std::endl;
175  std::cout << " Q[2] = " << Q[ 2 ] << std::endl;
176  std::cout << " Q[3] = " << Q[ 3 ] << std::endl;
177  std::cout << " Q[4] = " << Q[ 4 ] << std::endl;
178  std::cout << " dQ/dx = " << derivative<0>(Q) << std::endl;
179  std::cout << " dQ/dy = " << derivative<1>(Q) << std::endl;
180  std::cout << " dQ/dz = " << derivative<2>(Q) << std::endl;
182  P = Xe_k<3,double>( 2, 7 ) + Xe_k<3,double>( 1, 3 );
183  trace.info() << "P=" << P << std::endl;
184  return nbok == nb;
185 }
186
187
189 // Standard services - public :
190
191 int main( int /*argc*/, char** /*argv*/ )
192 {
193  trace.beginBlock ( "Testing class MPolynomial" );
194
195  bool res = testMPolynomial()
196  && testMPolynomialSpeed( 0.05 );
197  trace.emphase() << ( res ? "Passed." : "Error." ) << endl;
198  trace.endBlock();
199  return res ? 0 : 1;
200 }
201 // //
void beginBlock(const std::string &keyword="")
MPolynomial< 3, Ring, std::allocator< Ring > > durchblick()
int main(int, char **)
bool testMPolynomial()
Trace trace
Definition: Common.h:144
double endBlock()
Aim: Represents a multivariate polynomial, i.e. an element of , where K is some ring or field.
Definition: MPolynomial.h:58
bool testMPolynomialSpeed(double step=0.01)
std::ostream & emphase()
int degree() const
Definition: MPolynomial.h:1109
MPolynomial< 1, Ring, Alloc > gcd(const MPolynomial< 1, Ring, Alloc > &f, const MPolynomial< 1, Ring, Alloc > &g)
Definition: MPolynomial.h:2047
DGtal is the top-level namespace which contains all DGtal functions and types.
std::ostream & info()
double durchblickC(const double &x, const double &y, const double z)