1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
|
// This file is part of ff3d - http://www.freefem.org/ff3d
// Copyright (C) 2007 Driss Yakoubi
// 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, 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.
// $Id: LegendreBasis.cpp,v 1.2 2007/05/03 18:42:10 yakoubix Exp $
#include <LegendreBasis.hpp>
#include <iostream>
#include <Types.hpp>
#include <vector>
LegendreBasis::
LegendreBasis(const size_t& degree)
: __degree(degree)
{
;
}
LegendreBasis::
~LegendreBasis()
{
;
}
void LegendreBasis::
getValues(const real_t& x,
Vector<real_t>& values) const
{
values[0] = 1;
if (__degree == 0) return ;
values[1] = x;
for (size_t n=1; n<values.size()-1; ++n) {
values[n+1] = ((2*n+1)*x*values[n]-n*values[n-1]) / (n+1);
}
}
void LegendreBasis::
getDerivativeValues(const real_t& x,
Vector<real_t>& derivateValues) const
{
derivateValues[0]= 0;
if (__degree == 0) return ;
derivateValues[1]= 1;
if (__degree == 1) return ;
Vector<real_t> values(derivateValues.size()-1);
getValues(x,values);
for (size_t n=1; n<derivateValues.size()-1; ++n) {
derivateValues[n+1]
= ((2*n+1)*(x*derivateValues[n]+values[n])
- n*derivateValues[n-1])
/ (n+1);
}
}
real_t LegendreBasis::
getValue(const real_t& x,
const size_t& i) const
{
Vector<real_t> values(__degree+1);
this->getValues(x,values);
return values[i];
}
real_t LegendreBasis::
getDerivativeValue(const real_t& x,
const size_t& i) const
{
Vector<real_t> derivateValues(__degree+1);
this->getDerivativeValues(x, derivateValues);
return derivateValues[i];
}
|
