annotate +sbp/+implementations/d1_noneq_10.m @ 1337:bf2554f1825d feature/D2_boundary_opt

Add periodic D1 and D2 operators for orders 8,10,12
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Fri, 13 May 2022 13:28:10 +0200
parents 4cb627c7fb90
children
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
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4cb627c7fb90 Make D1Nonequidistant use the grid generation functions accurate/minimalBoundaryOptimizedGrid and remove grid generation from +implementations
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 267
diff changeset
1 function [D1,H] = d1_noneq_10(N,h)
261
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2
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3 % N: Number of grid points
266
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Martin Almquist <martin.almquist@it.uu.se>
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4 if(N<20)
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5 error('Operator requires at least 20 grid points');
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6 end
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7
261
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diff changeset
8 % BP: Number of boundary points
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9 BP = 10;
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10
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11 %%%% Norm matrix %%%%%%%%
267
f7ac3cd6eeaa Sparsified all implementation files, removed all matlab warnings, fixed small bugs on minimum grid points.
Martin Almquist <martin.almquist@it.uu.se>
parents: 266
diff changeset
12 P = sparse(BP,1);
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13 %#ok<*NASGU>
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14 P0 = 1.0000000000000e-01;
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15 P1 = 5.8980851260667e-01;
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parents:
diff changeset
16 P2 = 9.5666820955973e-01;
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parents:
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17 P3 = 1.1500297411596e+00;
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18 P4 = 1.1232986993248e+00;
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19 P5 = 1.0123020150951e+00;
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20 P6 = 9.9877122702527e-01;
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21 P7 = 1.0000873322761e+00;
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22 P8 = 1.0000045540888e+00;
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23 P9 = 9.9999861455083e-01;
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24
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25 for i = 0:BP-1
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26 P(i+1) = eval(['P' num2str(i)]);
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27 end
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28
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29 H = ones(N,1);
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30 H(1:BP) = P;
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31 H(end-BP+1:end) = flip(P);
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32 H = spdiags(h*H,0,N,N);
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33 %%%%%%%%%%%%%%%%%%%%%%%%%
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34
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35 %%%% Q matrix %%%%%%%%%%%
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36 % interior stencil
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4cb627c7fb90 Make D1Nonequidistant use the grid generation functions accurate/minimalBoundaryOptimizedGrid and remove grid generation from +implementations
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 267
diff changeset
37 order = 10;
4cb627c7fb90 Make D1Nonequidistant use the grid generation functions accurate/minimalBoundaryOptimizedGrid and remove grid generation from +implementations
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parents: 267
diff changeset
38 d = [-1/1260,5/504,-5/84,5/21,-5/6,0,5/6,-5/21,5/84,-5/504,1/1260];
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39 d = repmat(d,N,1);
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40 Q = spdiags(d,-order/2:order/2,N,N);
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41
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42 % Boundaries
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43 Q0_0 = -5.0000000000000e-01;
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44 Q0_1 = 6.7548747038002e-01;
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parents:
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45 Q0_2 = -2.6691978151546e-01;
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46 Q0_3 = 1.4438714982130e-01;
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47 Q0_4 = -7.7273673750760e-02;
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48 Q0_5 = 2.5570078343005e-02;
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49 Q0_6 = 4.2808774693299e-03;
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50 Q0_7 = -8.2902108933389e-03;
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51 Q0_8 = 3.2031176427908e-03;
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52 Q0_9 = -4.4502749689556e-04;
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53 Q0_10 = 0.0000000000000e+00;
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54 Q0_11 = 0.0000000000000e+00;
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55 Q0_12 = 0.0000000000000e+00;
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Martin Almquist <martin.almquist@it.uu.se>
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56 Q0_13 = 0.0000000000000e+00;
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Martin Almquist <martin.almquist@it.uu.se>
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57 Q0_14 = 0.0000000000000e+00;
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Martin Almquist <martin.almquist@it.uu.se>
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58 Q1_0 = -6.7548747038002e-01;
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59 Q1_1 = 0.0000000000000e+00;
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60 Q1_2 = 9.5146052715180e-01;
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61 Q1_3 = -4.2442349882626e-01;
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62 Q1_4 = 2.1538865145190e-01;
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63 Q1_5 = -7.1939778160350e-02;
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64 Q1_6 = -8.2539187832840e-03;
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65 Q1_7 = 1.9930661669090e-02;
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66 Q1_8 = -7.7433256989613e-03;
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67 Q1_9 = 1.0681515760869e-03;
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68 Q1_10 = 0.0000000000000e+00;
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69 Q1_11 = 0.0000000000000e+00;
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70 Q1_12 = 0.0000000000000e+00;
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diff changeset
71 Q1_13 = 0.0000000000000e+00;
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72 Q1_14 = 0.0000000000000e+00;
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73 Q2_0 = 2.6691978151546e-01;
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74 Q2_1 = -9.5146052715180e-01;
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75 Q2_2 = 0.0000000000000e+00;
6009f2712d13 Moved and renamned all implementations.
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76 Q2_3 = 9.6073770842387e-01;
6009f2712d13 Moved and renamned all implementations.
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77 Q2_4 = -3.9378595264609e-01;
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78 Q2_5 = 1.3302097358959e-01;
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79 Q2_6 = 8.1200458151489e-05;
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80 Q2_7 = -2.3849770528789e-02;
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81 Q2_8 = 9.6600442856829e-03;
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82 Q2_9 = -1.3234579460680e-03;
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83 Q2_10 = 0.0000000000000e+00;
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84 Q2_11 = 0.0000000000000e+00;
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85 Q2_12 = 0.0000000000000e+00;
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86 Q2_13 = 0.0000000000000e+00;
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87 Q2_14 = 0.0000000000000e+00;
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88 Q3_0 = -1.4438714982130e-01;
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89 Q3_1 = 4.2442349882626e-01;
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90 Q3_2 = -9.6073770842387e-01;
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91 Q3_3 = 0.0000000000000e+00;
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92 Q3_4 = 9.1551097634196e-01;
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93 Q3_5 = -2.8541713079648e-01;
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94 Q3_6 = 4.1398809121293e-02;
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95 Q3_7 = 1.7256059167927e-02;
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96 Q3_8 = -9.4349194803610e-03;
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97 Q3_9 = 1.3875650645663e-03;
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98 Q3_10 = 0.0000000000000e+00;
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99 Q3_11 = 0.0000000000000e+00;
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Martin Almquist <martin.almquist@it.uu.se>
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100 Q3_12 = 0.0000000000000e+00;
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Martin Almquist <martin.almquist@it.uu.se>
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101 Q3_13 = 0.0000000000000e+00;
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102 Q3_14 = 0.0000000000000e+00;
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103 Q4_0 = 7.7273673750760e-02;
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104 Q4_1 = -2.1538865145190e-01;
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105 Q4_2 = 3.9378595264609e-01;
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106 Q4_3 = -9.1551097634196e-01;
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Martin Almquist <martin.almquist@it.uu.se>
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107 Q4_4 = 0.0000000000000e+00;
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108 Q4_5 = 8.3519401865051e-01;
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109 Q4_6 = -2.0586492924974e-01;
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110 Q4_7 = 3.1230261235901e-02;
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111 Q4_8 = -2.0969453466651e-04;
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112 Q4_9 = -5.0965470499782e-04;
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113 Q4_10 = 0.0000000000000e+00;
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Martin Almquist <martin.almquist@it.uu.se>
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114 Q4_11 = 0.0000000000000e+00;
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Martin Almquist <martin.almquist@it.uu.se>
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115 Q4_12 = 0.0000000000000e+00;
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Martin Almquist <martin.almquist@it.uu.se>
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116 Q4_13 = 0.0000000000000e+00;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
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117 Q4_14 = 0.0000000000000e+00;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
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118 Q5_0 = -2.5570078343005e-02;
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119 Q5_1 = 7.1939778160350e-02;
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120 Q5_2 = -1.3302097358959e-01;
6009f2712d13 Moved and renamned all implementations.
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121 Q5_3 = 2.8541713079648e-01;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
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122 Q5_4 = -8.3519401865051e-01;
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Martin Almquist <martin.almquist@it.uu.se>
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123 Q5_5 = 0.0000000000000e+00;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
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124 Q5_6 = 8.1046389580138e-01;
6009f2712d13 Moved and renamned all implementations.
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125 Q5_7 = -2.1879194972141e-01;
6009f2712d13 Moved and renamned all implementations.
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126 Q5_8 = 5.2977237804899e-02;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
127 Q5_9 = -9.0146730522360e-03;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
128 Q5_10 = 7.9365079365079e-04;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
129 Q5_11 = 0.0000000000000e+00;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
130 Q5_12 = 0.0000000000000e+00;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
131 Q5_13 = 0.0000000000000e+00;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
132 Q5_14 = 0.0000000000000e+00;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
133 Q6_0 = -4.2808774693299e-03;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
134 Q6_1 = 8.2539187832840e-03;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
135 Q6_2 = -8.1200458151489e-05;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
136 Q6_3 = -4.1398809121293e-02;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
137 Q6_4 = 2.0586492924974e-01;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
138 Q6_5 = -8.1046389580138e-01;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
139 Q6_6 = 0.0000000000000e+00;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
140 Q6_7 = 8.2787884456005e-01;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
141 Q6_8 = -2.3582460382545e-01;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
142 Q6_9 = 5.9178678209520e-02;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
143 Q6_10 = -9.9206349206349e-03;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
144 Q6_11 = 7.9365079365079e-04;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
145 Q6_12 = 0.0000000000000e+00;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
146 Q6_13 = 0.0000000000000e+00;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
147 Q6_14 = 0.0000000000000e+00;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
148 Q7_0 = 8.2902108933389e-03;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
149 Q7_1 = -1.9930661669090e-02;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
150 Q7_2 = 2.3849770528789e-02;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
151 Q7_3 = -1.7256059167927e-02;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
152 Q7_4 = -3.1230261235901e-02;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
153 Q7_5 = 2.1879194972141e-01;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
154 Q7_6 = -8.2787884456005e-01;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
155 Q7_7 = 0.0000000000000e+00;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
156 Q7_8 = 8.3301028859275e-01;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
157 Q7_9 = -2.3804321850015e-01;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
158 Q7_10 = 5.9523809523809e-02;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
159 Q7_11 = -9.9206349206349e-03;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
160 Q7_12 = 7.9365079365079e-04;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
161 Q7_13 = 0.0000000000000e+00;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
162 Q7_14 = 0.0000000000000e+00;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
163 Q8_0 = -3.2031176427908e-03;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
164 Q8_1 = 7.7433256989613e-03;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
165 Q8_2 = -9.6600442856829e-03;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
166 Q8_3 = 9.4349194803610e-03;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
167 Q8_4 = 2.0969453466651e-04;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
168 Q8_5 = -5.2977237804899e-02;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
169 Q8_6 = 2.3582460382545e-01;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
170 Q8_7 = -8.3301028859275e-01;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
171 Q8_8 = 0.0000000000000e+00;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
172 Q8_9 = 8.3333655748509e-01;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
173 Q8_10 = -2.3809523809524e-01;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
174 Q8_11 = 5.9523809523809e-02;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
175 Q8_12 = -9.9206349206349e-03;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
176 Q8_13 = 7.9365079365079e-04;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
177 Q8_14 = 0.0000000000000e+00;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
178 Q9_0 = 4.4502749689556e-04;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
179 Q9_1 = -1.0681515760869e-03;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
180 Q9_2 = 1.3234579460680e-03;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
181 Q9_3 = -1.3875650645663e-03;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
182 Q9_4 = 5.0965470499782e-04;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
183 Q9_5 = 9.0146730522360e-03;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
184 Q9_6 = -5.9178678209520e-02;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
185 Q9_7 = 2.3804321850015e-01;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
186 Q9_8 = -8.3333655748509e-01;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
187 Q9_9 = 0.0000000000000e+00;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
188 Q9_10 = 8.3333333333333e-01;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
189 Q9_11 = -2.3809523809524e-01;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
190 Q9_12 = 5.9523809523809e-02;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
191 Q9_13 = -9.9206349206349e-03;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
192 Q9_14 = 7.9365079365079e-04;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
193 for i = 1:BP
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
194 for j = 1:BP
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
195 Q(i,j) = eval(['Q' num2str(i-1) '_' num2str(j-1)]);
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
196 Q(N+1-i,N+1-j) = -eval(['Q' num2str(i-1) '_' num2str(j-1)]);
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
197 end
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
198 end
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
199 %%%%%%%%%%%%%%%%%%%%%%%%%%%
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
200
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
201 %%%% Difference operator %%
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
202 D1 = H\Q;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
203 %%%%%%%%%%%%%%%%%%%%%%%%%%%