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annotate +sbp/+implementations/d1_noneq_8.m @ 1337:bf2554f1825d feature/D2_boundary_opt

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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:
rev   line source
1286
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_8(N,h)
261
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parents:
diff changeset
2
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Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
3 % N: Number of grid points
266
bfa130b7abf6 Added error message for too few grid points to all implementation files.
Martin Almquist <martin.almquist@it.uu.se>
parents: 261
diff changeset
4 if(N<16)
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Martin Almquist <martin.almquist@it.uu.se>
parents: 261
diff changeset
5 error('Operator requires at least 16 grid points');
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Martin Almquist <martin.almquist@it.uu.se>
parents: 261
diff changeset
6 end
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parents: 261
diff changeset
7
261
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Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
8 % BP: Number of boundary points
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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9 BP = 8;
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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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parents:
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14 P0 = 1.0758368078310e-01;
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15 P1 = 6.1909685107891e-01;
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parents:
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16 P2 = 9.6971176519117e-01;
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parents:
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17 P3 = 1.1023441350947e+00;
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18 P4 = 1.0244688965833e+00;
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19 P5 = 9.9533550116831e-01;
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parents:
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20 P6 = 1.0008236941028e+00;
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21 P7 = 9.9992060631812e-01;
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22
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23 for i = 0:BP-1
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24 P(i+1) = eval(['P' num2str(i)]);
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25 end
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26
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27 H = ones(N,1);
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28 H(1:BP) = P;
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29 H(end-BP+1:end) = flip(P);
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30 H = spdiags(h*H,0,N,N);
6009f2712d13 Moved and renamned all implementations.
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parents:
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31 %%%%%%%%%%%%%%%%%%%%%%%%%
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32
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33 %%%% Q matrix %%%%%%%%%%%
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parents:
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34 % interior stencil
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 267
diff changeset
35 order = 8;
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
36 d = [1/280,-4/105,1/5,-4/5,0,4/5,-1/5,4/105,-1/280];
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parents:
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37 d = repmat(d,N,1);
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38 Q = spdiags(d,-order/2:order/2,N,N);
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39
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40 % Boundaries
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41 Q0_0 = -5.0000000000000e-01;
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42 Q0_1 = 6.7284756079369e-01;
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parents:
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43 Q0_2 = -2.5969732837062e-01;
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44 Q0_3 = 1.3519390385721e-01;
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parents:
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45 Q0_4 = -6.9678474730984e-02;
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46 Q0_5 = 2.6434024071371e-02;
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47 Q0_6 = -5.5992311465618e-03;
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48 Q0_7 = 4.9954552590464e-04;
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49 Q0_8 = 0.0000000000000e+00;
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50 Q0_9 = 0.0000000000000e+00;
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51 Q0_10 = 0.0000000000000e+00;
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52 Q0_11 = 0.0000000000000e+00;
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53 Q1_0 = -6.7284756079369e-01;
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54 Q1_1 = 0.0000000000000e+00;
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55 Q1_2 = 9.4074021172233e-01;
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parents:
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56 Q1_3 = -4.0511642426516e-01;
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57 Q1_4 = 1.9369192209331e-01;
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58 Q1_5 = -6.8638079843479e-02;
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59 Q1_6 = 1.3146457241484e-02;
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60 Q1_7 = -9.7652615479254e-04;
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61 Q1_8 = 0.0000000000000e+00;
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62 Q1_9 = 0.0000000000000e+00;
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63 Q1_10 = 0.0000000000000e+00;
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64 Q1_11 = 0.0000000000000e+00;
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65 Q2_0 = 2.5969732837062e-01;
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66 Q2_1 = -9.4074021172233e-01;
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67 Q2_2 = 0.0000000000000e+00;
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68 Q2_3 = 9.4316393361096e-01;
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69 Q2_4 = -3.5728039257451e-01;
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70 Q2_5 = 1.1266686855013e-01;
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71 Q2_6 = -1.8334941452280e-02;
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72 Q2_7 = 8.2741521740941e-04;
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73 Q2_8 = 0.0000000000000e+00;
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74 Q2_9 = 0.0000000000000e+00;
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75 Q2_10 = 0.0000000000000e+00;
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76 Q2_11 = 0.0000000000000e+00;
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77 Q3_0 = -1.3519390385721e-01;
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78 Q3_1 = 4.0511642426516e-01;
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79 Q3_2 = -9.4316393361096e-01;
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80 Q3_3 = 0.0000000000000e+00;
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81 Q3_4 = 8.7694387866575e-01;
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82 Q3_5 = -2.4698058719506e-01;
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83 Q3_6 = 4.7291642094198e-02;
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84 Q3_7 = -4.0135203618880e-03;
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85 Q3_8 = 0.0000000000000e+00;
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86 Q3_9 = 0.0000000000000e+00;
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87 Q3_10 = 0.0000000000000e+00;
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88 Q3_11 = 0.0000000000000e+00;
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89 Q4_0 = 6.9678474730984e-02;
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90 Q4_1 = -1.9369192209331e-01;
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91 Q4_2 = 3.5728039257451e-01;
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92 Q4_3 = -8.7694387866575e-01;
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93 Q4_4 = 0.0000000000000e+00;
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94 Q4_5 = 8.1123946853807e-01;
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95 Q4_6 = -2.0267150541446e-01;
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96 Q4_7 = 3.8680398901392e-02;
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97 Q4_8 = -3.5714285714286e-03;
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98 Q4_9 = 0.0000000000000e+00;
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99 Q4_10 = 0.0000000000000e+00;
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100 Q4_11 = 0.0000000000000e+00;
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101 Q5_0 = -2.6434024071371e-02;
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102 Q5_1 = 6.8638079843479e-02;
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103 Q5_2 = -1.1266686855013e-01;
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104 Q5_3 = 2.4698058719506e-01;
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105 Q5_4 = -8.1123946853807e-01;
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106 Q5_5 = 0.0000000000000e+00;
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107 Q5_6 = 8.0108544742793e-01;
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108 Q5_7 = -2.0088756283071e-01;
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109 Q5_8 = 3.8095238095238e-02;
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110 Q5_9 = -3.5714285714286e-03;
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111 Q5_10 = 0.0000000000000e+00;
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112 Q5_11 = 0.0000000000000e+00;
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113 Q6_0 = 5.5992311465618e-03;
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114 Q6_1 = -1.3146457241484e-02;
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115 Q6_2 = 1.8334941452280e-02;
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116 Q6_3 = -4.7291642094198e-02;
6009f2712d13 Moved and renamned all implementations.
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117 Q6_4 = 2.0267150541446e-01;
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118 Q6_5 = -8.0108544742793e-01;
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119 Q6_6 = 0.0000000000000e+00;
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120 Q6_7 = 8.0039405922650e-01;
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121 Q6_8 = -2.0000000000000e-01;
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122 Q6_9 = 3.8095238095238e-02;
6009f2712d13 Moved and renamned all implementations.
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123 Q6_10 = -3.5714285714286e-03;
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124 Q6_11 = 0.0000000000000e+00;
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Martin Almquist <martin.almquist@it.uu.se>
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125 Q7_0 = -4.9954552590464e-04;
6009f2712d13 Moved and renamned all implementations.
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126 Q7_1 = 9.7652615479254e-04;
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127 Q7_2 = -8.2741521740941e-04;
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128 Q7_3 = 4.0135203618880e-03;
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129 Q7_4 = -3.8680398901392e-02;
6009f2712d13 Moved and renamned all implementations.
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130 Q7_5 = 2.0088756283071e-01;
6009f2712d13 Moved and renamned all implementations.
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131 Q7_6 = -8.0039405922650e-01;
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132 Q7_7 = 0.0000000000000e+00;
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Martin Almquist <martin.almquist@it.uu.se>
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133 Q7_8 = 8.0000000000000e-01;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
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134 Q7_9 = -2.0000000000000e-01;
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Martin Almquist <martin.almquist@it.uu.se>
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135 Q7_10 = 3.8095238095238e-02;
6009f2712d13 Moved and renamned all implementations.
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parents:
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136 Q7_11 = -3.5714285714286e-03;
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Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
137 for i = 1:BP
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Martin Almquist <martin.almquist@it.uu.se>
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138 for j = 1:BP
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
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139 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:
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140 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:
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141 end
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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142 end
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
143 %%%%%%%%%%%%%%%%%%%%%%%%%%%
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
144
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
145 %%%% Difference operator %%
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
146 D1 = H\Q;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
147 %%%%%%%%%%%%%%%%%%%%%%%%%%%