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annotate +sbp/+implementations/d1_noneq_minimal_10.m @ 1031:2ef20d00b386 feature/advectionRV

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For easier comparison, return both the first order and residual viscosity when evaluating the residual. Add the first order and residual viscosity to the state of the RungekuttaRV time steppers
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Thu, 17 Jan 2019 10:25:06 +0100
parents f7ac3cd6eeaa
children 4cb627c7fb90
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
261
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Martin Almquist <martin.almquist@it.uu.se>
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diff changeset
1 function [D1,H,x,h] = d1_noneq_minimal_10(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 = 3;
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18 order = 10;
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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 = 5.8556160757529e-01;
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23 x2 = 1.7473267488572e+00;
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24 x3 = 3.0000000000000e+00;
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25 x4 = 4.0000000000000e+00;
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26 x5 = 5.0000000000000e+00;
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27 x6 = 6.0000000000000e+00;
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28 x7 = 7.0000000000000e+00;
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29 x8 = 8.0000000000000e+00;
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30
267
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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 %%%%%%%%
267
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46 P = sparse(BP,1);
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47 %#ok<*NASGU>
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48 P0 = 1.6717213975289e-01;
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49 P1 = 9.3675739171278e-01;
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50 P2 = 1.3035532379753e+00;
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51 P3 = 1.1188461804303e+00;
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52 P4 = 9.6664345922660e-01;
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53 P5 = 1.0083235564392e+00;
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54 P6 = 9.9858767377362e-01;
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55 P7 = 1.0001163606893e+00;
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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 = 6.7349296966214e-01;
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90 Q0_2 = -2.5186401896559e-01;
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91 Q0_3 = 8.3431385420901e-02;
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92 Q0_4 = 2.5480326895984e-02;
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93 Q0_5 = -4.5992420658252e-02;
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94 Q0_6 = 1.7526412909003e-02;
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95 Q0_7 = -2.0746552641799e-03;
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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 Q0_12 = 0.0000000000000e+00;
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101 Q1_0 = -6.7349296966214e-01;
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102 Q1_1 = 0.0000000000000e+00;
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103 Q1_2 = 9.1982892384044e-01;
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104 Q1_3 = -2.7262271754043e-01;
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105 Q1_4 = -5.0992113348238e-02;
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106 Q1_5 = 1.1814647281129e-01;
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107 Q1_6 = -4.6693123378079e-02;
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108 Q1_7 = 5.8255272771571e-03;
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109 Q1_8 = 0.0000000000000e+00;
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110 Q1_9 = 0.0000000000000e+00;
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111 Q1_10 = 0.0000000000000e+00;
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112 Q1_11 = 0.0000000000000e+00;
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113 Q1_12 = 0.0000000000000e+00;
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114 Q2_0 = 2.5186401896559e-01;
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115 Q2_1 = -9.1982892384044e-01;
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116 Q2_2 = 0.0000000000000e+00;
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117 Q2_3 = 7.8566746772741e-01;
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118 Q2_4 = -2.4097806629929e-02;
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119 Q2_5 = -1.5312168858669e-01;
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120 Q2_6 = 6.9451518963875e-02;
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121 Q2_7 = -9.9345865998262e-03;
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122 Q2_8 = 0.0000000000000e+00;
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123 Q2_9 = 0.0000000000000e+00;
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124 Q2_10 = 0.0000000000000e+00;
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125 Q2_11 = 0.0000000000000e+00;
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126 Q2_12 = 0.0000000000000e+00;
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127 Q3_0 = -8.3431385420901e-02;
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128 Q3_1 = 2.7262271754043e-01;
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129 Q3_2 = -7.8566746772741e-01;
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130 Q3_3 = 0.0000000000000e+00;
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parents:
diff changeset
131 Q3_4 = 6.2047871210535e-01;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
132 Q3_5 = 1.4776775176509e-02;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
133 Q3_6 = -4.6889652372990e-02;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
134 Q3_7 = 7.3166499053672e-03;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
135 Q3_8 = 7.9365079365079e-04;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
136 Q3_9 = 0.0000000000000e+00;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
137 Q3_10 = 0.0000000000000e+00;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
138 Q3_11 = 0.0000000000000e+00;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
139 Q3_12 = 0.0000000000000e+00;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
140 Q4_0 = -2.5480326895984e-02;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
141 Q4_1 = 5.0992113348238e-02;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
142 Q4_2 = 2.4097806629929e-02;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
143 Q4_3 = -6.2047871210535e-01;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
144 Q4_4 = 0.0000000000000e+00;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
145 Q4_5 = 6.9425006383507e-01;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
146 Q4_6 = -1.5686345740485e-01;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
147 Q4_7 = 4.2609496719925e-02;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
148 Q4_8 = -9.9206349206349e-03;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
149 Q4_9 = 7.9365079365079e-04;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
150 Q4_10 = 0.0000000000000e+00;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
151 Q4_11 = 0.0000000000000e+00;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
152 Q4_12 = 0.0000000000000e+00;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
153 Q5_0 = 4.5992420658252e-02;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
154 Q5_1 = -1.1814647281129e-01;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
155 Q5_2 = 1.5312168858669e-01;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
156 Q5_3 = -1.4776775176509e-02;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
157 Q5_4 = -6.9425006383507e-01;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
158 Q5_5 = 0.0000000000000e+00;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
159 Q5_6 = 8.0719535654891e-01;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
160 Q5_7 = -2.2953297936781e-01;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
161 Q5_8 = 5.9523809523809e-02;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
162 Q5_9 = -9.9206349206349e-03;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
163 Q5_10 = 7.9365079365079e-04;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
164 Q5_11 = 0.0000000000000e+00;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
165 Q5_12 = 0.0000000000000e+00;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
166 Q6_0 = -1.7526412909003e-02;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
167 Q6_1 = 4.6693123378079e-02;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
168 Q6_2 = -6.9451518963875e-02;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
169 Q6_3 = 4.6889652372990e-02;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
170 Q6_4 = 1.5686345740485e-01;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
171 Q6_5 = -8.0719535654891e-01;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
172 Q6_6 = 0.0000000000000e+00;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
173 Q6_7 = 8.3142546796428e-01;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
174 Q6_8 = -2.3809523809524e-01;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
175 Q6_9 = 5.9523809523809e-02;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
176 Q6_10 = -9.9206349206349e-03;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
177 Q6_11 = 7.9365079365079e-04;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
178 Q6_12 = 0.0000000000000e+00;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
179 Q7_0 = 2.0746552641799e-03;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
180 Q7_1 = -5.8255272771571e-03;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
181 Q7_2 = 9.9345865998262e-03;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
182 Q7_3 = -7.3166499053672e-03;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
183 Q7_4 = -4.2609496719925e-02;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
184 Q7_5 = 2.2953297936781e-01;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
185 Q7_6 = -8.3142546796428e-01;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
186 Q7_7 = 0.0000000000000e+00;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
187 Q7_8 = 8.3333333333333e-01;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
188 Q7_9 = -2.3809523809524e-01;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
189 Q7_10 = 5.9523809523809e-02;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
190 Q7_11 = -9.9206349206349e-03;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
191 Q7_12 = 7.9365079365079e-04;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
192 for i = 1:BP
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
193 for j = 1:BP
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
194 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
195 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
196 end
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 %%%%%%%%%%%%%%%%%%%%%%%%%%%
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 %%%% Difference operator %%
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
201 D1 = H\Q;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
202 %%%%%%%%%%%%%%%%%%%%%%%%%%%