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annotate +sbp/+implementations/d1_noneq_minimal_10.m @ 1289:2fd2e2337b77 feature/boundary_optimized_grids

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Add utility function for constructing a (possibly multidimensional) grid based on the grid points used by the boundary optimized SBP operators
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Wed, 01 Jul 2020 15:15:30 +0200
parents 4cb627c7fb90
children
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
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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_minimal_10(N,h)
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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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diff changeset
4 if(N<16)
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5 error('Operator requires at least 16 grid points');
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diff changeset
6 end
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7
261
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8 % BP: Number of boundary points
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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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14 P0 = 1.6717213975289e-01;
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15 P1 = 9.3675739171278e-01;
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16 P2 = 1.3035532379753e+00;
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17 P3 = 1.1188461804303e+00;
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18 P4 = 9.6664345922660e-01;
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19 P5 = 1.0083235564392e+00;
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20 P6 = 9.9858767377362e-01;
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21 P7 = 1.0001163606893e+00;
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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);
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31 %%%%%%%%%%%%%%%%%%%%%%%%%
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32
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33 %%%% Q matrix %%%%%%%%%%%
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34 % interior stencil
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parents: 267
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35 order = 10;
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36 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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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 = 6.7349296966214e-01;
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43 Q0_2 = -2.5186401896559e-01;
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44 Q0_3 = 8.3431385420901e-02;
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45 Q0_4 = 2.5480326895984e-02;
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46 Q0_5 = -4.5992420658252e-02;
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47 Q0_6 = 1.7526412909003e-02;
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48 Q0_7 = -2.0746552641799e-03;
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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 Q0_12 = 0.0000000000000e+00;
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54 Q1_0 = -6.7349296966214e-01;
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55 Q1_1 = 0.0000000000000e+00;
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56 Q1_2 = 9.1982892384044e-01;
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57 Q1_3 = -2.7262271754043e-01;
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58 Q1_4 = -5.0992113348238e-02;
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59 Q1_5 = 1.1814647281129e-01;
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60 Q1_6 = -4.6693123378079e-02;
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61 Q1_7 = 5.8255272771571e-03;
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62 Q1_8 = 0.0000000000000e+00;
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63 Q1_9 = 0.0000000000000e+00;
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64 Q1_10 = 0.0000000000000e+00;
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65 Q1_11 = 0.0000000000000e+00;
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66 Q1_12 = 0.0000000000000e+00;
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67 Q2_0 = 2.5186401896559e-01;
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68 Q2_1 = -9.1982892384044e-01;
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69 Q2_2 = 0.0000000000000e+00;
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70 Q2_3 = 7.8566746772741e-01;
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71 Q2_4 = -2.4097806629929e-02;
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72 Q2_5 = -1.5312168858669e-01;
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73 Q2_6 = 6.9451518963875e-02;
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74 Q2_7 = -9.9345865998262e-03;
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75 Q2_8 = 0.0000000000000e+00;
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76 Q2_9 = 0.0000000000000e+00;
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77 Q2_10 = 0.0000000000000e+00;
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78 Q2_11 = 0.0000000000000e+00;
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79 Q2_12 = 0.0000000000000e+00;
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80 Q3_0 = -8.3431385420901e-02;
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81 Q3_1 = 2.7262271754043e-01;
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82 Q3_2 = -7.8566746772741e-01;
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83 Q3_3 = 0.0000000000000e+00;
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84 Q3_4 = 6.2047871210535e-01;
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85 Q3_5 = 1.4776775176509e-02;
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86 Q3_6 = -4.6889652372990e-02;
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87 Q3_7 = 7.3166499053672e-03;
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88 Q3_8 = 7.9365079365079e-04;
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89 Q3_9 = 0.0000000000000e+00;
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90 Q3_10 = 0.0000000000000e+00;
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91 Q3_11 = 0.0000000000000e+00;
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92 Q3_12 = 0.0000000000000e+00;
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93 Q4_0 = -2.5480326895984e-02;
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94 Q4_1 = 5.0992113348238e-02;
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95 Q4_2 = 2.4097806629929e-02;
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96 Q4_3 = -6.2047871210535e-01;
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97 Q4_4 = 0.0000000000000e+00;
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98 Q4_5 = 6.9425006383507e-01;
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99 Q4_6 = -1.5686345740485e-01;
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100 Q4_7 = 4.2609496719925e-02;
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101 Q4_8 = -9.9206349206349e-03;
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102 Q4_9 = 7.9365079365079e-04;
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103 Q4_10 = 0.0000000000000e+00;
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104 Q4_11 = 0.0000000000000e+00;
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105 Q4_12 = 0.0000000000000e+00;
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106 Q5_0 = 4.5992420658252e-02;
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107 Q5_1 = -1.1814647281129e-01;
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108 Q5_2 = 1.5312168858669e-01;
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109 Q5_3 = -1.4776775176509e-02;
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110 Q5_4 = -6.9425006383507e-01;
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111 Q5_5 = 0.0000000000000e+00;
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112 Q5_6 = 8.0719535654891e-01;
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113 Q5_7 = -2.2953297936781e-01;
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114 Q5_8 = 5.9523809523809e-02;
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115 Q5_9 = -9.9206349206349e-03;
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116 Q5_10 = 7.9365079365079e-04;
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117 Q5_11 = 0.0000000000000e+00;
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118 Q5_12 = 0.0000000000000e+00;
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119 Q6_0 = -1.7526412909003e-02;
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120 Q6_1 = 4.6693123378079e-02;
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121 Q6_2 = -6.9451518963875e-02;
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122 Q6_3 = 4.6889652372990e-02;
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123 Q6_4 = 1.5686345740485e-01;
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124 Q6_5 = -8.0719535654891e-01;
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125 Q6_6 = 0.0000000000000e+00;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
126 Q6_7 = 8.3142546796428e-01;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
127 Q6_8 = -2.3809523809524e-01;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
128 Q6_9 = 5.9523809523809e-02;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
129 Q6_10 = -9.9206349206349e-03;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
130 Q6_11 = 7.9365079365079e-04;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
131 Q6_12 = 0.0000000000000e+00;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
132 Q7_0 = 2.0746552641799e-03;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
133 Q7_1 = -5.8255272771571e-03;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
134 Q7_2 = 9.9345865998262e-03;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
135 Q7_3 = -7.3166499053672e-03;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
136 Q7_4 = -4.2609496719925e-02;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
137 Q7_5 = 2.2953297936781e-01;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
138 Q7_6 = -8.3142546796428e-01;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
139 Q7_7 = 0.0000000000000e+00;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
140 Q7_8 = 8.3333333333333e-01;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
141 Q7_9 = -2.3809523809524e-01;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
142 Q7_10 = 5.9523809523809e-02;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
143 Q7_11 = -9.9206349206349e-03;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
144 Q7_12 = 7.9365079365079e-04;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
145 for i = 1:BP
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
146 for j = 1:BP
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
147 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
148 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
149 end
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
150 end
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
151 %%%%%%%%%%%%%%%%%%%%%%%%%%%
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
152
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
153 %%%% Difference operator %%
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
154 D1 = H\Q;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
155 %%%%%%%%%%%%%%%%%%%%%%%%%%%