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annotate +sbp/D1Nonequidistant.m @ 258:a8d89688ba01 operator_remake

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Merged nonequidistant into one class and cleaned up.
author Martin Almquist <martin.almquist@it.uu.se>
date Thu, 08 Sep 2016 13:28:35 +0200
parents
children a94bb3d92aba
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258
a8d89688ba01 Merged nonequidistant into one class and cleaned up.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
1 classdef D1Nonequidistant < sbp.OpSet
a8d89688ba01 Merged nonequidistant into one class and cleaned up.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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2 properties
a8d89688ba01 Merged nonequidistant into one class and cleaned up.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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3 D1 % SBP operator approximating first derivative
a8d89688ba01 Merged nonequidistant into one class and cleaned up.
Martin Almquist <martin.almquist@it.uu.se>
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4 H % Norm matrix
a8d89688ba01 Merged nonequidistant into one class and cleaned up.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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5 HI % H^-1
a8d89688ba01 Merged nonequidistant into one class and cleaned up.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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6 Q % Skew-symmetric matrix
a8d89688ba01 Merged nonequidistant into one class and cleaned up.
Martin Almquist <martin.almquist@it.uu.se>
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7 e_1 % Left boundary operator
a8d89688ba01 Merged nonequidistant into one class and cleaned up.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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8 e_m % Right boundary operator
a8d89688ba01 Merged nonequidistant into one class and cleaned up.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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9 m % Number of grid points.
a8d89688ba01 Merged nonequidistant into one class and cleaned up.
Martin Almquist <martin.almquist@it.uu.se>
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10 h % Step size
a8d89688ba01 Merged nonequidistant into one class and cleaned up.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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11 x % grid
a8d89688ba01 Merged nonequidistant into one class and cleaned up.
Martin Almquist <martin.almquist@it.uu.se>
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12 end
a8d89688ba01 Merged nonequidistant into one class and cleaned up.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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13
a8d89688ba01 Merged nonequidistant into one class and cleaned up.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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14 methods
a8d89688ba01 Merged nonequidistant into one class and cleaned up.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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15 function obj = D1Nonequidistant(m,L,order,option)
a8d89688ba01 Merged nonequidistant into one class and cleaned up.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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16
a8d89688ba01 Merged nonequidistant into one class and cleaned up.
Martin Almquist <martin.almquist@it.uu.se>
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17 default_arg('option','Accurate');
a8d89688ba01 Merged nonequidistant into one class and cleaned up.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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18 % 'Accurate' operators are optimized for accuracy
a8d89688ba01 Merged nonequidistant into one class and cleaned up.
Martin Almquist <martin.almquist@it.uu.se>
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19 % 'Minimal' operators have the smallest possible boundary
a8d89688ba01 Merged nonequidistant into one class and cleaned up.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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20 % closure
a8d89688ba01 Merged nonequidistant into one class and cleaned up.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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21
a8d89688ba01 Merged nonequidistant into one class and cleaned up.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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22 switch option
a8d89688ba01 Merged nonequidistant into one class and cleaned up.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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23
a8d89688ba01 Merged nonequidistant into one class and cleaned up.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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24 case {'Accurate','accurate','A'}
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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25
a8d89688ba01 Merged nonequidistant into one class and cleaned up.
Martin Almquist <martin.almquist@it.uu.se>
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26 if order == 4
a8d89688ba01 Merged nonequidistant into one class and cleaned up.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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27 [obj.D1,obj.H,obj.x,obj.h] = sbp.D1_4th_4BP_2shifts(m,L);
a8d89688ba01 Merged nonequidistant into one class and cleaned up.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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28 elseif order == 6
a8d89688ba01 Merged nonequidistant into one class and cleaned up.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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29 [obj.D1,obj.H,obj.x,obj.h] = sbp.D1_6th_6BP_3shifts(m,L);
a8d89688ba01 Merged nonequidistant into one class and cleaned up.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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30 elseif order == 8
a8d89688ba01 Merged nonequidistant into one class and cleaned up.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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31 [obj.D1,obj.H,obj.x,obj.h] = sbp.D1_8th_8BP_4shifts(m,L);
a8d89688ba01 Merged nonequidistant into one class and cleaned up.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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32 elseif order == 10
a8d89688ba01 Merged nonequidistant into one class and cleaned up.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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33 [obj.D1,obj.H,obj.x,obj.h] = sbp.D1_10th_10BP_5shifts(m,L);
a8d89688ba01 Merged nonequidistant into one class and cleaned up.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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34 elseif order == 12
a8d89688ba01 Merged nonequidistant into one class and cleaned up.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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35 [obj.D1,obj.H,obj.x,obj.h] = sbp.D1_12th_12BP_6shifts(m,L);
a8d89688ba01 Merged nonequidistant into one class and cleaned up.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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36 else
a8d89688ba01 Merged nonequidistant into one class and cleaned up.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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37 error('Invalid operator order %d.',order);
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Martin Almquist <martin.almquist@it.uu.se>
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38 end
a8d89688ba01 Merged nonequidistant into one class and cleaned up.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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39
a8d89688ba01 Merged nonequidistant into one class and cleaned up.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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40 case {'Minimal','minimal','M'}
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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41
a8d89688ba01 Merged nonequidistant into one class and cleaned up.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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42 if order == 4
a8d89688ba01 Merged nonequidistant into one class and cleaned up.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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43 [obj.D1,obj.H,obj.x,obj.h] = sbp.D1_minimal_4th_3BP_1shifts(m,L);
a8d89688ba01 Merged nonequidistant into one class and cleaned up.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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44 elseif order == 6
a8d89688ba01 Merged nonequidistant into one class and cleaned up.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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45 [obj.D1,obj.H,obj.x,obj.h] = sbp.D1_minimal_6th_5BP_2shifts(m,L);
a8d89688ba01 Merged nonequidistant into one class and cleaned up.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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46 elseif order == 8
a8d89688ba01 Merged nonequidistant into one class and cleaned up.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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47 [obj.D1,obj.H,obj.x,obj.h] = sbp.D1_minimal_8th_6BP_2shifts(m,L);
a8d89688ba01 Merged nonequidistant into one class and cleaned up.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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48 elseif order == 10
a8d89688ba01 Merged nonequidistant into one class and cleaned up.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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49 [obj.D1,obj.H,obj.x,obj.h] = sbp.D1_minimal_10th_8BP_3shifts(m,L);
a8d89688ba01 Merged nonequidistant into one class and cleaned up.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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50 elseif order == 12
a8d89688ba01 Merged nonequidistant into one class and cleaned up.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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51 [obj.D1,obj.H,obj.x,obj.h] = sbp.D1_minimal_12th_10BP_4shifts(m,L);
a8d89688ba01 Merged nonequidistant into one class and cleaned up.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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52 else
a8d89688ba01 Merged nonequidistant into one class and cleaned up.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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53 error('Invalid operator order %d.',order);
a8d89688ba01 Merged nonequidistant into one class and cleaned up.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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54 end
a8d89688ba01 Merged nonequidistant into one class and cleaned up.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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55
a8d89688ba01 Merged nonequidistant into one class and cleaned up.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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56 end
a8d89688ba01 Merged nonequidistant into one class and cleaned up.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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57
a8d89688ba01 Merged nonequidistant into one class and cleaned up.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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58 obj.e_1 = sparse(m,1);
a8d89688ba01 Merged nonequidistant into one class and cleaned up.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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59 obj.e_m = sparse(m,1);
a8d89688ba01 Merged nonequidistant into one class and cleaned up.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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60 obj.e_1(1) = 1;
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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61 obj.e_m(m) = 1;
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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62
a8d89688ba01 Merged nonequidistant into one class and cleaned up.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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63 obj.HI = inv(obj.H);
a8d89688ba01 Merged nonequidistant into one class and cleaned up.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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64 obj.Q = obj.H*obj.D1 - obj.e_m*obj.e_m' + obj.e_0*obj.e_0';
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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65
a8d89688ba01 Merged nonequidistant into one class and cleaned up.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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66 end
a8d89688ba01 Merged nonequidistant into one class and cleaned up.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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67 end
a8d89688ba01 Merged nonequidistant into one class and cleaned up.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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68
a8d89688ba01 Merged nonequidistant into one class and cleaned up.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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69 methods (Static)
a8d89688ba01 Merged nonequidistant into one class and cleaned up.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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70 function lambda = smallestGrid(obj)
a8d89688ba01 Merged nonequidistant into one class and cleaned up.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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71 error('Not implmented')
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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72 end
a8d89688ba01 Merged nonequidistant into one class and cleaned up.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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73 end
a8d89688ba01 Merged nonequidistant into one class and cleaned up.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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74 end
a8d89688ba01 Merged nonequidistant into one class and cleaned up.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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75
a8d89688ba01 Merged nonequidistant into one class and cleaned up.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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76
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parents:
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77
a8d89688ba01 Merged nonequidistant into one class and cleaned up.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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78
a8d89688ba01 Merged nonequidistant into one class and cleaned up.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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79