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annotate +sbp/+implementations/d1_noneq_8.m @ 267:f7ac3cd6eeaa operator_remake

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Sparsified all implementation files, removed all matlab warnings, fixed small bugs on minimum grid points.
author Martin Almquist <martin.almquist@it.uu.se>
date Fri, 09 Sep 2016 14:53:41 +0200
parents bfa130b7abf6
children 4cb627c7fb90
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
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261
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
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diff changeset
1 function [D1,H,x,h] = d1_noneq_8(N,L)
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2
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3 % L: Domain length
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4 % N: Number of grid points
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5 if(nargin < 2)
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6 L = 1;
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7 end
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8
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9 if(N<16)
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10 error('Operator requires at least 16 grid points');
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11 end
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12
261
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13 % BP: Number of boundary points
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14 % m: Number of nonequidistant spacings
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15 % order: Accuracy of interior stencil
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16 BP = 8;
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17 m = 4;
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18 order = 8;
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19
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20 %%%% Non-equidistant grid points %%%%%
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21 x0 = 0.0000000000000e+00;
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22 x1 = 3.8118550247622e-01;
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23 x2 = 1.1899550868338e+00;
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24 x3 = 2.2476300175641e+00;
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25 x4 = 3.3192851303204e+00;
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26 x5 = 4.3192851303204e+00;
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27 x6 = 5.3192851303204e+00;
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28 x7 = 6.3192851303204e+00;
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29 x8 = 7.3192851303204e+00;
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30
267
f7ac3cd6eeaa Sparsified all implementation files, removed all matlab warnings, fixed small bugs on minimum grid points.
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diff changeset
31 xb = sparse(m+1,1);
261
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32 for i = 0:m
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33 xb(i+1) = eval(['x' num2str(i)]);
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34 end
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35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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36
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37 %%%% Compute h %%%%%%%%%%
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38 h = L/(2*xb(end) + N-1-2*m);
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39 %%%%%%%%%%%%%%%%%%%%%%%%%
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40
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41 %%%% Define grid %%%%%%%%
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42 x = h*[xb; linspace(xb(end)+1,L/h-xb(end)-1,N-2*(m+1))'; L/h-flip(xb) ];
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43 %%%%%%%%%%%%%%%%%%%%%%%%%
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44
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45 %%%% Norm matrix %%%%%%%%
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f7ac3cd6eeaa Sparsified all implementation files, removed all matlab warnings, fixed small bugs on minimum grid points.
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46 P = sparse(BP,1);
261
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47 %#ok<*NASGU>
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48 P0 = 1.0758368078310e-01;
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49 P1 = 6.1909685107891e-01;
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50 P2 = 9.6971176519117e-01;
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51 P3 = 1.1023441350947e+00;
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52 P4 = 1.0244688965833e+00;
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53 P5 = 9.9533550116831e-01;
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54 P6 = 1.0008236941028e+00;
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55 P7 = 9.9992060631812e-01;
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56
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57 for i = 0:BP-1
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58 P(i+1) = eval(['P' num2str(i)]);
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59 end
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60
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61 H = ones(N,1);
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62 H(1:BP) = P;
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63 H(end-BP+1:end) = flip(P);
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64 H = spdiags(h*H,0,N,N);
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65 %%%%%%%%%%%%%%%%%%%%%%%%%
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66
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67 %%%% Q matrix %%%%%%%%%%%
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68
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69 % interior stencil
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70 switch order
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71 case 2
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72 d = [-1/2,0,1/2];
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73 case 4
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74 d = [1/12,-2/3,0,2/3,-1/12];
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75 case 6
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76 d = [-1/60,3/20,-3/4,0,3/4,-3/20,1/60];
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77 case 8
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78 d = [1/280,-4/105,1/5,-4/5,0,4/5,-1/5,4/105,-1/280];
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79 case 10
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80 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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81 case 12
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82 d = [1/5544,-1/385,1/56,-5/63,15/56,-6/7,0,6/7,-15/56,5/63,-1/56,1/385,-1/5544];
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83 end
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84 d = repmat(d,N,1);
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85 Q = spdiags(d,-order/2:order/2,N,N);
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86
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87 % Boundaries
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88 Q0_0 = -5.0000000000000e-01;
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89 Q0_1 = 6.7284756079369e-01;
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90 Q0_2 = -2.5969732837062e-01;
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91 Q0_3 = 1.3519390385721e-01;
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92 Q0_4 = -6.9678474730984e-02;
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93 Q0_5 = 2.6434024071371e-02;
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94 Q0_6 = -5.5992311465618e-03;
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95 Q0_7 = 4.9954552590464e-04;
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96 Q0_8 = 0.0000000000000e+00;
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97 Q0_9 = 0.0000000000000e+00;
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98 Q0_10 = 0.0000000000000e+00;
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99 Q0_11 = 0.0000000000000e+00;
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100 Q1_0 = -6.7284756079369e-01;
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101 Q1_1 = 0.0000000000000e+00;
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102 Q1_2 = 9.4074021172233e-01;
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103 Q1_3 = -4.0511642426516e-01;
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104 Q1_4 = 1.9369192209331e-01;
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105 Q1_5 = -6.8638079843479e-02;
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106 Q1_6 = 1.3146457241484e-02;
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107 Q1_7 = -9.7652615479254e-04;
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108 Q1_8 = 0.0000000000000e+00;
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109 Q1_9 = 0.0000000000000e+00;
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110 Q1_10 = 0.0000000000000e+00;
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111 Q1_11 = 0.0000000000000e+00;
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112 Q2_0 = 2.5969732837062e-01;
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113 Q2_1 = -9.4074021172233e-01;
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114 Q2_2 = 0.0000000000000e+00;
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115 Q2_3 = 9.4316393361096e-01;
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116 Q2_4 = -3.5728039257451e-01;
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117 Q2_5 = 1.1266686855013e-01;
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118 Q2_6 = -1.8334941452280e-02;
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119 Q2_7 = 8.2741521740941e-04;
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120 Q2_8 = 0.0000000000000e+00;
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121 Q2_9 = 0.0000000000000e+00;
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122 Q2_10 = 0.0000000000000e+00;
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123 Q2_11 = 0.0000000000000e+00;
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124 Q3_0 = -1.3519390385721e-01;
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125 Q3_1 = 4.0511642426516e-01;
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126 Q3_2 = -9.4316393361096e-01;
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127 Q3_3 = 0.0000000000000e+00;
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128 Q3_4 = 8.7694387866575e-01;
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129 Q3_5 = -2.4698058719506e-01;
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130 Q3_6 = 4.7291642094198e-02;
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parents:
diff changeset
131 Q3_7 = -4.0135203618880e-03;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
132 Q3_8 = 0.0000000000000e+00;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
133 Q3_9 = 0.0000000000000e+00;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
134 Q3_10 = 0.0000000000000e+00;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
135 Q3_11 = 0.0000000000000e+00;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
136 Q4_0 = 6.9678474730984e-02;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
137 Q4_1 = -1.9369192209331e-01;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
138 Q4_2 = 3.5728039257451e-01;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
139 Q4_3 = -8.7694387866575e-01;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
140 Q4_4 = 0.0000000000000e+00;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
141 Q4_5 = 8.1123946853807e-01;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
142 Q4_6 = -2.0267150541446e-01;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
143 Q4_7 = 3.8680398901392e-02;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
144 Q4_8 = -3.5714285714286e-03;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
145 Q4_9 = 0.0000000000000e+00;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
146 Q4_10 = 0.0000000000000e+00;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
147 Q4_11 = 0.0000000000000e+00;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
148 Q5_0 = -2.6434024071371e-02;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
149 Q5_1 = 6.8638079843479e-02;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
150 Q5_2 = -1.1266686855013e-01;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
151 Q5_3 = 2.4698058719506e-01;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
152 Q5_4 = -8.1123946853807e-01;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
153 Q5_5 = 0.0000000000000e+00;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
154 Q5_6 = 8.0108544742793e-01;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
155 Q5_7 = -2.0088756283071e-01;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
156 Q5_8 = 3.8095238095238e-02;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
157 Q5_9 = -3.5714285714286e-03;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
158 Q5_10 = 0.0000000000000e+00;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
159 Q5_11 = 0.0000000000000e+00;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
160 Q6_0 = 5.5992311465618e-03;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
161 Q6_1 = -1.3146457241484e-02;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
162 Q6_2 = 1.8334941452280e-02;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
163 Q6_3 = -4.7291642094198e-02;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
164 Q6_4 = 2.0267150541446e-01;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
165 Q6_5 = -8.0108544742793e-01;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
166 Q6_6 = 0.0000000000000e+00;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
167 Q6_7 = 8.0039405922650e-01;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
168 Q6_8 = -2.0000000000000e-01;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
169 Q6_9 = 3.8095238095238e-02;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
170 Q6_10 = -3.5714285714286e-03;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
171 Q6_11 = 0.0000000000000e+00;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
172 Q7_0 = -4.9954552590464e-04;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
173 Q7_1 = 9.7652615479254e-04;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
174 Q7_2 = -8.2741521740941e-04;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
175 Q7_3 = 4.0135203618880e-03;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
176 Q7_4 = -3.8680398901392e-02;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
177 Q7_5 = 2.0088756283071e-01;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
178 Q7_6 = -8.0039405922650e-01;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
179 Q7_7 = 0.0000000000000e+00;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
180 Q7_8 = 8.0000000000000e-01;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
181 Q7_9 = -2.0000000000000e-01;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
182 Q7_10 = 3.8095238095238e-02;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
183 Q7_11 = -3.5714285714286e-03;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
184 for i = 1:BP
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
185 for j = 1:BP
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
186 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
187 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
188 end
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
189 end
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
190 %%%%%%%%%%%%%%%%%%%%%%%%%%%
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
191
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
192 %%%% Difference operator %%
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
193 D1 = H\Q;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
194 %%%%%%%%%%%%%%%%%%%%%%%%%%%