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// Copyright (C) 2016 EDF
// All Rights Reserved
// This code is published under the GNU Lesser General Public License (GNU LGPL)
#include <cmath>
#include "Polynomials1D.h"
using namespace std;
namespace StOpt
{
double Canonical::F(double p_x, int p_n) const
{
return pow(p_x, p_n);
}
double Canonical::DF(double p_x, int p_n) const
{
if (p_n == 0) return 0.;
return p_n * pow(p_x, p_n - 1);
}
double Canonical::D2F(double p_x, int p_n) const
{
if (p_n <= 1) return 0.;
return p_n * (p_n - 1) * pow(p_x, p_n - 2);
}
double Hermite::FRec(double p_x, int p_n, int p_n0, double &p_fn0, double &p_fn0_1) const
{
if (p_n == p_n0)
{
return p_fn0;
}
else
{
double save = p_fn0;
p_fn0 = p_x * p_fn0 - p_n0 * p_fn0_1;
p_fn0_1 = save;
return FRec(p_x, p_n, p_n0 + 1, p_fn0, p_fn0_1);
}
}
double Hermite::F(double p_x, int p_n) const
{
double val = p_x;
double val2;
switch (p_n)
{
case 0 :
return 1;
case 1 :
return val;
case 2 :
return val * val - 1.;
case 3 :
return (val * val - 3.) * val;
case 4 :
val2 = val * val;
return (val2 - 6.) * val2 + 3;
case 5 :
val2 = val * val;
return ((val2 - 10) * val2 + 15.) * val;
case 6 :
val2 = val * val;
return ((val2 - 15.) * val2 + 45.) * val2 - 15.;
case 7:
val2 = val * val;
return (((val2 - 21.) * val2 + 105.) * val2 - 105) * val;
default:
double Fn0 = F(p_x, 7);
double Fn0_1 = F(p_x, 6);
return FRec(p_x, p_n, 7, Fn0, Fn0_1);
}
}
double Hermite::DF(double p_x, int p_n) const
{
if (p_n == 0) return 0.;
else return p_n * F(p_x, p_n - 1);
}
double Hermite::D2F(double p_x, int p_n) const
{
if (p_n == 0 || p_n == 1) return 0.;
return p_n * (p_n - 1) * F(p_x, p_n - 2);
}
double Tchebychev::FRec(double p_x, int p_n, int p_n0, double &p_fn0, double &p_fn0_1) const
{
if (p_n == p_n0)
{
return p_fn0;
}
else
{
double save = p_fn0;
p_fn0 = 2 * p_x * p_fn0 - p_fn0_1;
p_fn0_1 = save;
return FRec(p_x, p_n, p_n0 + 1, p_fn0, p_fn0_1);
}
}
double Tchebychev::F(double p_x, int p_n) const
{
double val = p_x;
double val2, val3, val4;
switch (p_n)
{
case 0 :
return 1.;
case 1 :
return val;
case 2 :
return 2. * val * val - 1.;
case 3 :
return (4. * val * val - 3.) * val;
case 4 :
val2 = val * val;
return 8. * val2 * val2 - 8. * val2 + 1.;
break;
case 5 :
val2 = val * val;
val3 = val2 * val;
return 16. * val3 * val2 - 20. * val3 + 5.* val;
case 6 :
val2 = val * val;
val4 = val2 * val2;
return 32. * val4 * val2 - 48. * val4 + 18. * val2 - 1;
case 7 :
val2 = val * val;
val3 = val2 * val;
val4 = val2 * val2;
return (64. * val4 - 112. * val2 + 56) * val3 - 7. * val;
default :
double Fn0 = F(p_x, 7);
double Fn0_1 = F(p_x, 6);
return FRec(p_x, p_n, 7, Fn0, Fn0_1);
}
}
double Tchebychev::DFRec(double p_x, int p_n, int p_n0, double &p_dfn0, double &p_dfn0_1) const
{
if (p_n == p_n0)
{
return p_dfn0;
}
else
{
double save = p_dfn0;
p_dfn0 = 2 * p_x * double(p_n0 + 1.0) / double(p_n0) * p_dfn0 - double(p_n0 + 1.) / double(p_n0 - 1.) * p_dfn0_1;
p_dfn0_1 = save;
return DFRec(p_x, p_n, p_n0 + 1, p_dfn0, p_dfn0_1);
}
}
double Tchebychev::DF(double p_x, int p_n) const
{
double val = p_x;
double val2, val4;
switch (p_n)
{
case 0 :
return 0.;
case 1 :
return 1.;
case 2 :
return 4. * val;
case 3 :
return (12. * val * val - 3.);
case 4 :
return (32. * val * val - 16.) * val;
case 5 :
val2 = val * val;
return 80. * val2 * val2 - 60. * val2 + 5.;
case 6 :
val2 = val * val;
val4 = val2 * val2;
return (192. * val4 - 192. * val2 + 36.) * val;
case 7 :
val2 = val * val;
val4 = val2 * val2;
return (448. * val4 - 560. * val2 + 168) * val2 - 7.;
default :
double Dfn0 = DF(p_x, 7);
double Dfn0_1 = DF(p_x, 6);
return DFRec(p_x, p_n, 7, Dfn0, Dfn0_1);
}
}
double Tchebychev::D2FRec(double p_x, int p_n, int p_n0, double &D2fn0, double &D2fn0_1) const
{
if (p_n == p_n0)
{
return D2fn0;
}
else
{
double save = D2fn0;
D2fn0 = 2 * p_x * D2fn0 - D2fn0_1 + 4 * DF(p_x, p_n0);
D2fn0_1 = save;
return D2FRec(p_x, p_n, p_n0 + 1, D2fn0, D2fn0_1);
}
}
double Tchebychev::D2F(double p_x, int p_n) const
{
double val = p_x;
double val2, val4;
switch (p_n)
{
case 0 :
return 0.;
case 1 :
return 0.;
case 2 :
return 4.;
case 3 :
return 24. * val;
case 4 :
return (96. * val * val - 16.);
case 5 :
val2 = val * val;
return 320. * val2 * val - 120. * val;
case 6 :
val2 = val * val;
val4 = val2 * val2;
return (960. * val4 - 576. * val2 + 36.);
case 7 :
val2 = val * val;
val4 = val2 * val2;
return (2688. * val4 - 2240. * val2 + 336) * val;
default :
double D2fn0_1 = D2F(p_x, 6);
double D2fn0 = D2F(p_x, 7);
return D2FRec(p_x, p_n, 7, D2fn0, D2fn0_1);
}
}
}
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