Mercurial > repos > public > sbplib
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> |
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date | Fri, 13 May 2022 13:28:10 +0200 |
parents | 4cb627c7fb90 |
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rev | line source |
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1286
4cb627c7fb90
Make D1Nonequidistant use the grid generation functions accurate/minimalBoundaryOptimizedGrid and remove grid generation from +implementations
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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1 function [D1,H] = d1_noneq_10(N,h) |
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2 |
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3 % N: Number of grid points |
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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 |
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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 %%%%%%%% |
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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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16 P2 = 9.5666820955973e-01; |
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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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37 order = 10; |
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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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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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56 Q0_13 = 0.0000000000000e+00; |
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57 Q0_14 = 0.0000000000000e+00; |
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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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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; |
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76 Q2_3 = 9.6073770842387e-01; |
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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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100 Q3_12 = 0.0000000000000e+00; |
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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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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; |
6009f2712d13
Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff
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113 Q4_10 = 0.0000000000000e+00; |
6009f2712d13
Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff
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|
114 Q4_11 = 0.0000000000000e+00; |
6009f2712d13
Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff
changeset
|
115 Q4_12 = 0.0000000000000e+00; |
6009f2712d13
Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff
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|
116 Q4_13 = 0.0000000000000e+00; |
6009f2712d13
Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff
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117 Q4_14 = 0.0000000000000e+00; |
6009f2712d13
Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff
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118 Q5_0 = -2.5570078343005e-02; |
6009f2712d13
Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff
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119 Q5_1 = 7.1939778160350e-02; |
6009f2712d13
Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff
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120 Q5_2 = -1.3302097358959e-01; |
6009f2712d13
Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff
changeset
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121 Q5_3 = 2.8541713079648e-01; |
6009f2712d13
Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff
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122 Q5_4 = -8.3519401865051e-01; |
6009f2712d13
Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff
changeset
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123 Q5_5 = 0.0000000000000e+00; |
6009f2712d13
Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff
changeset
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124 Q5_6 = 8.1046389580138e-01; |
6009f2712d13
Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff
changeset
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125 Q5_7 = -2.1879194972141e-01; |
6009f2712d13
Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff
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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
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127 Q5_9 = -9.0146730522360e-03; |
6009f2712d13
Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff
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128 Q5_10 = 7.9365079365079e-04; |
6009f2712d13
Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff
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|
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
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|
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
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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
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|
139 Q6_6 = 0.0000000000000e+00; |
6009f2712d13
Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff
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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
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|
144 Q6_11 = 7.9365079365079e-04; |
6009f2712d13
Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff
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|
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
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|
148 Q7_0 = 8.2902108933389e-03; |
6009f2712d13
Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff
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|
149 Q7_1 = -1.9930661669090e-02; |
6009f2712d13
Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff
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|
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
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|
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
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|
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 %%%%%%%%%%%%%%%%%%%%%%%%%%% |