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//==============================================================================
// GridSplineBetaPolynomials.h
//
// Copyright (C) 2010-2013 Tobias Toll and Thomas Ullrich
//
// This file is part of Sartre version: 1.00
//
// 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.
// 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, see <http://www.gnu.org/licenses/>.
//
// Author: Thomas Ullrich
// Last update:
// $Date: 2013-01-14 21:47:05 +0000 (Mon, 14 Jan 2013) $
// $Author: thomas.ullrich@bnl.gov $
//==============================================================================
//
// Definitions for the spline polynomials of the second kind (beta-s)
// in addition, various wrappers (in case they are needed)
//
//
// This algorithm was written by Cristian Lalescu.
// See http://arxiv.org/abs/0905.3564 for details.
// The code here is slightly modified for use in Sartre.
//
//==============================================================================
#ifndef GridSplineBetaPolynomials_h
#define GridSplineBetaPolynomials_h
inline double BETA_n1_q2_j1 (double x) { return ((x>=0 && x<=1) ? (1-x) : 0); }
inline double OMEGA_n1_q2 (double x) { return ((x>=0) ? BETA_n1_q2_j1(x) : BETA_n1_q2_j1(-x)); }
inline double BETA_n3_q4_j1 (double x) { return ((x*((4-3*x)*x+1))/2); }
inline double BETA_n3_q4_j2 (double x) { return (((x-1)*x*x)/2); }
inline double OMEGA_n3_q4_half (double x) { return ((x>=0 && x<=2) ? ((x>=0 && x<=1) ? BETA_n3_q4_j1(1-x) : BETA_n3_q4_j2(2-x)) : 0); }
inline double OMEGA_n3_q4 (double x) { return ((x>=0) ? OMEGA_n3_q4_half(x) : OMEGA_n3_q4_half(-x) ); }
inline double BETA_n5_q4_j1 (double x) { return ((x*(x*(x*(x*(6*x-15)+9)+1)+1))/2); }
inline double BETA_n5_q4_j2 (double x) { return ((x*x*x*((5-2*x)*x-3))/2); }
inline double OMEGA_n5_q4_half (double x) { return ((x>=0 && x<=2) ? ((x>=0 && x<=1) ? BETA_n5_q4_j1(1-x) : BETA_n5_q4_j2(2-x)) : 0); }
inline double OMEGA_n5_q4 (double x) { return ((x>=0) ? OMEGA_n5_q4_half(x) : OMEGA_n5_q4_half(-x) ); }
inline double BETA_n3_q6_j3 (double x) { return (((1-x)*x*x)/12); }
inline double BETA_n3_q6_j2 (double x) { return ((x*(x*(7*x-6)-1))/12); }
inline double BETA_n3_q6_j1 (double x) { return ((x*((5-4*x)*x+2))/3); }
inline double OMEGA_n3_q6_half (double x) { return ((x>=0 && x<=3) ? ((x>=0 && x<=2) ? ((x>=0 && x<=1) ? BETA_n3_q6_j1(1-x) : BETA_n3_q6_j2(2-x)) : BETA_n3_q6_j3(3-x)) : 0); }
inline double OMEGA_n3_q6 (double x) { return ((x>=0) ? OMEGA_n3_q6_half(x) : OMEGA_n3_q6_half(-x)); }
inline double BETA_n5_q6_j3 (double x) { return ((x*x*x*(x*(5*x-12)+7))/24); }
inline double BETA_n5_q6_j2 (double x) { return ((x*(x*(x*((61-25*x)*x-33)-1)-2))/24); }
inline double BETA_n5_q6_j1 (double x) { return ((x*(x*(x*(x*(25*x-62)+33)+8)+8))/12); }
inline double OMEGA_n5_q6_half (double x) { return ((x>=0 && x<=3) ? ((x>=0 && x<=2) ? ((x>=0 && x<=1) ? BETA_n5_q6_j1(1-x) : BETA_n5_q6_j2(2-x)) : BETA_n5_q6_j3(3-x)) : 0); }
inline double OMEGA_n5_q6 (double x) { return ((x>=0) ? OMEGA_n5_q6_half(x) : OMEGA_n5_q6_half(-x)); }
inline double BETA_n7_q6_j3 (double x) { return ((x*x*x*x*(x*((49-14*x)*x-58)+23))/24); }
inline double BETA_n7_q6_j2 (double x) { return ((x*(x*(x*(x*(x*(x*(70*x-245)+290)-114)+2)-1)-2))/24); }
inline double BETA_n7_q6_j1 (double x) { return ((x*(x*(x*(x*(x*((245-70*x)*x-290)+113)-2)+8)+8))/12); }
inline double OMEGA_n7_q6_half (double x) { return ((x>=0 && x<=3) ? ((x>=0 && x<=2) ? ((x>=0 && x<=1) ? BETA_n7_q6_j1(1-x) : BETA_n7_q6_j2(2-x)) : BETA_n7_q6_j3(3-x)) : 0); }
inline double OMEGA_n7_q6 (double x) { return ((x>=0) ? OMEGA_n7_q6_half(x) : OMEGA_n7_q6_half(-x)); }
inline double BETA_n9_q6_j3 (double x) { return ((x*x*x*x*x*(x*(x*(x*(46*x-207)+354)-273)+80))/24); }
inline double BETA_n9_q6_j2 (double x) { return ((x*(x*(x*(x*(x*(x*(x*((1035-230*x)*x-1770)+1365)-400)+1)+2)-1)-2))/24); }
inline double BETA_n9_q6_j1 (double x) { return ((x*(x*(x*(x*(x*(x*(x*(x*(230*x-1035)+1770)-1365)+400)-2)-2)+8)+8))/12); }
inline double OMEGA_n9_q6_half (double x) { return ((x>=0 && x<=3) ? ((x>=0 && x<=2) ? ((x>=0 && x<=1) ? BETA_n9_q6_j1(1-x) : BETA_n9_q6_j2(2-x)) : BETA_n9_q6_j3(3-x)) : 0); }
inline double OMEGA_n9_q6 (double x) { return ((x>=0) ? OMEGA_n9_q6_half(x) : OMEGA_n9_q6_half(-x)); }
inline double BETA_n3_q8_j4 (double x) { return (((x-1)*x*x)/60); }
inline double BETA_n3_q8_j3 (double x) { return ((x*((7-8*x)*x+1))/60); }
inline double BETA_n3_q8_j2 (double x) { return ((x*(x*(12*x-9)-3))/20); }
inline double BETA_n3_q8_j1 (double x) { return ((x*((6-5*x)*x+3))/4); }
inline double OMEGA_n3_q8_half (double x) { return ((x>=0 && x<=4) ? ((x>=0 && x<=3) ? ((x>=0 && x<=2) ? ((x>=0 && x<=1) ? BETA_n3_q8_j1(1-x) : BETA_n3_q8_j2(2-x)) : BETA_n3_q8_j3(3-x)) : BETA_n3_q8_j4(4-x)):0); }
inline double OMEGA_n3_q8 (double x) { return ((x>=0) ? OMEGA_n3_q8_half(x) : OMEGA_n3_q8_half(-x)); }
inline double BETA_n5_q8_j4 (double x) { return ((x*x*x*((19-8*x)*x-11))/180); }
inline double BETA_n5_q8_j3 (double x) { return ((x*(x*(x*(x*(115*x-270)+147)+2)+6))/360); }
inline double BETA_n5_q8_j2 (double x) { return ((x*(x*(x*((93-39*x)*x-45)-3)-6))/40); }
inline double BETA_n5_q8_j1 (double x) { return ((x*(x*(x*(x*(59*x-145)+68)+27)+27))/36); }
inline double OMEGA_n5_q8_half (double x) { return ((x>=0 && x<=4) ? ((x>=0 && x<=3) ? ((x>=0 && x<=2) ? ((x>=0 && x<=1) ? BETA_n5_q8_j1(1-x) : BETA_n5_q8_j2(2-x)) : BETA_n5_q8_j3(3-x)) : BETA_n5_q8_j4(4-x)):0); }
inline double OMEGA_n5_q8 (double x) { return ((x>=0) ? OMEGA_n5_q8_half(x) : OMEGA_n5_q8_half(-x)); }
inline double BETA_n7_q8_j4 (double x) { return ((x*x*x*x*(x*(x*(89*x-311)+367)-145))/720); }
inline double BETA_n7_q8_j3 (double x) { return ((x*(x*(x*(x*(x*((2178-623*x)*x-2566)+1010)-15)+4)+12))/720); }
inline double BETA_n7_q8_j2 (double x) { return ((x*(x*(x*(x*(x*(x*(623*x-2179)+2565)-995)+40)-18)-36))/240); }
inline double BETA_n7_q8_j1 (double x) { return ((x*(x*(x*(x*(x*((2180-623*x)*x-2566)+976)-39)+108)+108))/144); }
inline double OMEGA_n7_q8_half (double x) { return ((x>=0 && x<=4) ? ((x>=0 && x<=3) ? ((x>=0 && x<=2) ? ((x>=0 && x<=1) ? BETA_n7_q8_j1(1-x) : BETA_n7_q8_j2(2-x)) : BETA_n7_q8_j3(3-x)) : BETA_n7_q8_j4(4-x)):0); }
inline double OMEGA_n7_q8 (double x) { return ((x>=0) ? OMEGA_n7_q8_half(x) : OMEGA_n7_q8_half(-x)); }
inline double BETA_n9_q8_j4 (double x) { return ((x*x*x*x*x*(x*(x*((1305-290*x)*x-2231)+1719)-503))/720); }
inline double BETA_n9_q8_j3 (double x) { return ((x*(x*(x*(x*(x*(x*(x*(x*(2030*x-9135)+15617)-12032)+3524)-5)-15)+4)+12))/720); }
inline double BETA_n9_q8_j2 (double x) { return ((x*(x*(x*(x*(x*(x*(x*((9135-2030*x)*x-15617)+12031)-3525)+20)+40)-18)-36))/240); }
inline double BETA_n9_q8_j1 (double x) { return ((x*(x*(x*(x*(x*(x*(x*(x*(2030*x-9135)+15617)-12030)+3524)-39)-39)+108)+108))/144); }
inline double OMEGA_n9_q8_half (double x) { return ((x>=0 && x<=4) ? ((x>=0 && x<=3) ? ((x>=0 && x<=2) ? ((x>=0 && x<=1) ? BETA_n9_q8_j1(1-x) : BETA_n9_q8_j2(2-x)) : BETA_n9_q8_j3(3-x)) : BETA_n9_q8_j4(4-x)):0); }
inline double OMEGA_n9_q8 (double x) { return ((x>=0) ? OMEGA_n9_q8_half(x) : OMEGA_n9_q8_half(-x)); }
inline double BETA_n11_q8_j4 (double x) { return ((x*x*x*x*x*x*(x*(x*(x*(x*(1006*x-5533)+12285)-13785)+7829)-1802))/720); }
inline double BETA_n11_q8_j3 (double x) { return ((x*(x*(x*(x*(x*(x*(x*(x*(x*((38731-7042*x)*x-85995)+96495)-54803)+12615)+3)-5)-15)+4)+12))/720); }
inline double BETA_n11_q8_j2 (double x) { return ((x*(x*(x*(x*(x*(x*(x*(x*(x*(x*(7042*x-38731)+85995)-96495)+54803)-12616)-4)+20)+40)-18)-36))/240); }
inline double BETA_n11_q8_j1 (double x) { return ((x*(x*(x*(x*(x*(x*(x*(x*(x*((38731-7042*x)*x-85995)+96495)-54803)+12617)+3)-39)-39)+108)+108))/144); }
inline double OMEGA_n11_q8_half(double x) { return ((x>=0 && x<=4) ? ((x>=0 && x<=3) ? ((x>=0 && x<=2) ? ((x>=0 && x<=1) ? BETA_n11_q8_j1(1-x) : BETA_n11_q8_j2(2-x)) : BETA_n11_q8_j3(3-x)) : BETA_n11_q8_j4(4-x)):0); }
inline double OMEGA_n11_q8 (double x) { return ((x>=0) ? OMEGA_n11_q8_half(x) : OMEGA_n11_q8_half(-x)); }
inline double BETA_n13_q8_j4 (double x) { return ((x*x*x*x*x*x*x*(x*(x*(x*(x*((23426-3604*x)*x-63866)+93577)-77815)+34869)-6587))/720); }
inline double BETA_n13_q8_j3 (double x) { return ((x*(x*(x*(x*(x*(x*(x*(x*(x*(x*(x*(x*(25228*x-163982)+447062)-655039)+544705)-244083)+46109)+1)+3)-5)-15)+4)+12))/720); }
inline double BETA_n13_q8_j2 (double x) { return ((x*(x*(x*(x*(x*(x*(x*(x*(x*(x*(x*((163982-25228*x)*x-447062)+655039)-544705)+244083)-46109)-2)-4)+20)+40)-18)-36))/240); }
inline double BETA_n13_q8_j1 (double x) { return ((x*(x*(x*(x*(x*(x*(x*(x*(x*(x*(x*(x*(25228*x-163982)+447062)-655039)+544705)-244083)+46109)+3)+3)-39)-39)+108)+108))/144); }
inline double OMEGA_n13_q8_half(double x) { return ((x>=0 && x<=4) ? ((x>=0 && x<=3) ? ((x>=0 && x<=2) ? ((x>=0 && x<=1) ? BETA_n13_q8_j1(1-x) : BETA_n13_q8_j2(2-x)) : BETA_n13_q8_j3(3-x)) : BETA_n13_q8_j4(4-x)):0); }
inline double OMEGA_n13_q8 (double x) { return ((x>=0) ? OMEGA_n13_q8_half(x) : OMEGA_n13_q8_half(-x)); }
/********************************/
// (probably inefficient) wrappers
inline double BETA_n3_q4 (int grid_point, double x)
{
switch(grid_point)
{
case -1: return BETA_n3_q4_j2(1-x);
case 0: return BETA_n3_q4_j1(1-x);
case 1: return BETA_n3_q4_j1(x);
case 2: return BETA_n3_q4_j2(x);
default: return 0;
}
}
inline double BETA_n5_q4 (int grid_point, double x)
{
switch(grid_point)
{
case -1: return BETA_n5_q4_j2(1-x);
case 0: return BETA_n5_q4_j1(1-x);
case 1: return BETA_n5_q4_j1(x);
case 2: return BETA_n5_q4_j2(x);
default: return 0;
}
}
inline double BETA_n3_q6 (int grid_point, double x)
{
switch(grid_point)
{
case -2: return BETA_n3_q6_j3(1-x);
case -1: return BETA_n3_q6_j2(1-x);
case 0: return BETA_n3_q6_j1(1-x);
case 1: return BETA_n3_q6_j1(x);
case 2: return BETA_n3_q6_j2(x);
case 3: return BETA_n3_q6_j3(x);
default: return 0;
}
}
inline double BETA_n5_q6 (int grid_point, double x)
{
switch(grid_point)
{
case -2: return BETA_n5_q6_j3(1-x);
case -1: return BETA_n5_q6_j2(1-x);
case 0: return BETA_n5_q6_j1(1-x);
case 1: return BETA_n5_q6_j1(x);
case 2: return BETA_n5_q6_j2(x);
case 3: return BETA_n5_q6_j3(x);
default: return 0;
}
}
inline double BETA_n7_q6 (int grid_point, double x)
{
switch(grid_point)
{
case -2: return BETA_n7_q6_j3(1-x);
case -1: return BETA_n7_q6_j2(1-x);
case 0: return BETA_n7_q6_j1(1-x);
case 1: return BETA_n7_q6_j1(x);
case 2: return BETA_n7_q6_j2(x);
case 3: return BETA_n7_q6_j3(x);
default: return 0;
}
}
inline double BETA_n9_q6 (int grid_point, double x)
{
switch(grid_point)
{
case -2: return BETA_n9_q6_j3(1-x);
case -1: return BETA_n9_q6_j2(1-x);
case 0: return BETA_n9_q6_j1(1-x);
case 1: return BETA_n9_q6_j1(x);
case 2: return BETA_n9_q6_j2(x);
case 3: return BETA_n9_q6_j3(x);
default: return 0;
}
}
inline double BETA_n3_q8 (int grid_point, double x)
{
switch(grid_point)
{
case -3: return BETA_n3_q8_j4(1-x);
case -2: return BETA_n3_q8_j3(1-x);
case -1: return BETA_n3_q8_j2(1-x);
case 0: return BETA_n3_q8_j1(1-x);
case 1: return BETA_n3_q8_j1(x);
case 2: return BETA_n3_q8_j2(x);
case 3: return BETA_n3_q8_j3(x);
case 4: return BETA_n3_q8_j4(x);
default: return 0;
}
}
inline double BETA_n5_q8 (int grid_point, double x)
{
switch(grid_point)
{
case -3: return BETA_n5_q8_j4(1-x);
case -2: return BETA_n5_q8_j3(1-x);
case -1: return BETA_n5_q8_j2(1-x);
case 0: return BETA_n5_q8_j1(1-x);
case 1: return BETA_n5_q8_j1(x);
case 2: return BETA_n5_q8_j2(x);
case 3: return BETA_n5_q8_j3(x);
case 4: return BETA_n5_q8_j4(x);
default: return 0;
}
}
inline double BETA_n7_q8 (int grid_point, double x)
{
switch(grid_point)
{
case -3: return BETA_n7_q8_j4(1-x);
case -2: return BETA_n7_q8_j3(1-x);
case -1: return BETA_n7_q8_j2(1-x);
case 0: return BETA_n7_q8_j1(1-x);
case 1: return BETA_n7_q8_j1(x);
case 2: return BETA_n7_q8_j2(x);
case 3: return BETA_n7_q8_j3(x);
case 4: return BETA_n7_q8_j4(x);
default: return 0;
}
}
inline double BETA_n9_q8 (int grid_point, double x)
{
switch(grid_point)
{
case -3: return BETA_n9_q8_j4(1-x);
case -2: return BETA_n9_q8_j3(1-x);
case -1: return BETA_n9_q8_j2(1-x);
case 0: return BETA_n9_q8_j1(1-x);
case 1: return BETA_n9_q8_j1(x);
case 2: return BETA_n9_q8_j2(x);
case 3: return BETA_n9_q8_j3(x);
case 4: return BETA_n9_q8_j4(x);
default: return 0;
}
}
inline double BETA_n11_q8 (int grid_point, double x)
{
switch(grid_point)
{
case -3: return BETA_n11_q8_j4(1-x);
case -2: return BETA_n11_q8_j3(1-x);
case -1: return BETA_n11_q8_j2(1-x);
case 0: return BETA_n11_q8_j1(1-x);
case 1: return BETA_n11_q8_j1(x);
case 2: return BETA_n11_q8_j2(x);
case 3: return BETA_n11_q8_j3(x);
case 4: return BETA_n11_q8_j4(x);
default: return 0;
}
}
inline double BETA_n13_q8 (int grid_point, double x)
{
switch(grid_point)
{
case -3: return BETA_n13_q8_j4(1-x);
case -2: return BETA_n13_q8_j3(1-x);
case -1: return BETA_n13_q8_j2(1-x);
case 0: return BETA_n13_q8_j1(1-x);
case 1: return BETA_n13_q8_j1(x);
case 2: return BETA_n13_q8_j2(x);
case 3: return BETA_n13_q8_j3(x);
case 4: return BETA_n13_q8_j4(x);
default: return 0;
}
}
inline double BETA_q4 (int spline_order, int grid_point, double x)
{
switch(spline_order)
{
case 3: return BETA_n3_q4(grid_point,x);
case 5: return BETA_n5_q4(grid_point,x);
default: return 0;
}
}
inline double BETA_q6 (int spline_order, int grid_point, double x)
{
switch(spline_order)
{
case 3: return BETA_n3_q6(grid_point,x);
case 5: return BETA_n5_q6(grid_point,x);
case 7: return BETA_n7_q6(grid_point,x);
case 9: return BETA_n9_q6(grid_point,x);
default: return 0;
}
}
inline double BETA_q8 (int spline_order, int grid_point, double x)
{
switch(spline_order)
{
case 3: return BETA_n3_q8(grid_point,x);
case 5: return BETA_n5_q8(grid_point,x);
case 7: return BETA_n7_q8(grid_point,x);
case 9: return BETA_n9_q8(grid_point,x);
case 11: return BETA_n11_q8(grid_point,x);
case 13: return BETA_n13_q8(grid_point,x);
default: return 0;
}
}
inline double BETA (int spline_order, int grid_size, int grid_point, double x)
{
switch(grid_size)
{
case 4: return BETA_q4(spline_order, grid_point, x);
case 6: return BETA_q6(spline_order, grid_point, x);
case 8: return BETA_q8(spline_order, grid_point, x);
default: return 0;
}
}
#endif//__BETA_POLYNOMIALS_H__

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