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annotate +scheme/Hypsyst3d.m @ 520:f235284e2eb1 feature/quantumTriangles

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changed sign in penalty parameter
author Ylva Rydin <ylva.rydin@telia.com>
date Mon, 07 Aug 2017 13:20:48 +0200
parents feebfca90080
children
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
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1 classdef Hypsyst3d < scheme.Scheme
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2 properties
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3 m % Number of points in each direction, possibly a vector
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4 n % Size of system
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5 h % Grid spacing
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6 x, y, z % Grid
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7 X, Y, Z% Values of x and y for each grid point
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8 Yx, Zx, Xy, Zy, Xz, Yz %Grid values for boundary surfaces
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9 order % Order accuracy for the approximation
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10 grid
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11
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12 D % non-stabalized scheme operator
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13 A, B, C, E % Symbolic coefficient matrices
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14 Aevaluated,Bevaluated,Cevaluated, Eevaluated
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15
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16 H % Discrete norm
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17 Hx, Hy, Hz % Norms in the x, y and z directions
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18 Hxi,Hyi, Hzi % Kroneckerd norms. 1'*Hx*v corresponds to integration in the x dir.
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19 I_x,I_y, I_z, I_N
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20 e_w, e_e, e_s, e_n, e_b, e_t
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21 params % Parameters for the coeficient matrice
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22 end
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23
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24
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25 methods
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26 % Solving Hyperbolic systems on the form u_t=-Au_x-Bu_y-Cu_z-Eu
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27 function obj = Hypsyst3d(m, lim, order, A, B,C, E, params,operator)
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28 default_arg('E', [])
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29 xlim = lim{1};
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30 ylim = lim{2};
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31 zlim = lim{3};
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32
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33 if length(m) == 1
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34 m = [m m m];
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35 end
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36
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37 obj.A = A;
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38 obj.B = B;
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39 obj.C = C;
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40 obj.E = E;
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41 m_x = m(1);
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42 m_y = m(2);
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43 m_z = m(3);
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44 obj.params = params;
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45
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46 switch operator
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47 case 'upwind'
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48 ops_x = sbp.D1Upwind(m_x,xlim,order);
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49 ops_y = sbp.D1Upwind(m_y,ylim,order);
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50 ops_z = sbp.D1Upwind(m_z,zlim,order);
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51 otherwise
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52 ops_x = sbp.D2Standard(m_x,xlim,order);
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53 ops_y = sbp.D2Standard(m_y,ylim,order);
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54 ops_z = sbp.D2Standard(m_z,zlim,order);
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55 end
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56
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57 obj.x = ops_x.x;
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58 obj.y = ops_y.x;
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59 obj.z = ops_z.x;
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60
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61 obj.X = kr(obj.x,ones(m_y,1),ones(m_z,1));
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62 obj.Y = kr(ones(m_x,1),obj.y,ones(m_z,1));
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63 obj.Z = kr(ones(m_x,1),ones(m_y,1),obj.z);
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64
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65 obj.Yx = kr(obj.y,ones(m_z,1));
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66 obj.Zx = kr(ones(m_y,1),obj.z);
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67 obj.Xy = kr(obj.x,ones(m_z,1));
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68 obj.Zy = kr(ones(m_x,1),obj.z);
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69 obj.Xz = kr(obj.x,ones(m_y,1));
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70 obj.Yz = kr(ones(m_z,1),obj.y);
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71
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72 obj.Aevaluated = obj.evaluateCoefficientMatrix(A, obj.X, obj.Y,obj.Z);
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73 obj.Bevaluated = obj.evaluateCoefficientMatrix(B, obj.X, obj.Y,obj.Z);
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74 obj.Cevaluated = obj.evaluateCoefficientMatrix(C, obj.X, obj.Y,obj.Z);
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75 obj.Eevaluated = obj.evaluateCoefficientMatrix(E, obj.X, obj.Y,obj.Z);
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76
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77 obj.n = length(A(obj.params,0,0,0));
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78
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79 I_n = speye(obj.n);
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80 I_x = speye(m_x);
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81 obj.I_x = I_x;
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82 I_y = speye(m_y);
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83 obj.I_y = I_y;
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84 I_z = speye(m_z);
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85 obj.I_z = I_z;
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86 I_N = kr(I_n,I_x,I_y,I_z);
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87
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88 obj.Hxi = kr(I_n, ops_x.HI, I_y,I_z);
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89 obj.Hx = ops_x.H;
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90 obj.Hyi = kr(I_n, I_x, ops_y.HI,I_z);
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91 obj.Hy = ops_y.H;
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92 obj.Hzi = kr(I_n, I_x,I_y, ops_z.HI);
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93 obj.Hz = ops_z.H;
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94
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95 obj.e_w = kr(I_n, ops_x.e_l, I_y,I_z);
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96 obj.e_e = kr(I_n, ops_x.e_r, I_y,I_z);
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97 obj.e_s = kr(I_n, I_x, ops_y.e_l,I_z);
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98 obj.e_n = kr(I_n, I_x, ops_y.e_r,I_z);
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99 obj.e_b = kr(I_n, I_x, I_y, ops_z.e_l);
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100 obj.e_t = kr(I_n, I_x, I_y, ops_z.e_r);
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101
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102 obj.m = m;
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103 obj.h = [ops_x.h ops_y.h ops_x.h];
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104 obj.order = order;
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105
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106 switch operator
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107 case 'upwind'
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108 alphaA = max(abs(eig(A(params,obj.x(end),obj.y(end),obj.z(end)))));
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109 alphaB = max(abs(eig(B(params,obj.x(end),obj.y(end),obj.z(end)))));
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110 alphaC = max(abs(eig(C(params,obj.x(end),obj.y(end),obj.z(end)))));
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111
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112 Ap = (obj.Aevaluated+alphaA*I_N)/2;
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113 Am = (obj.Aevaluated-alphaA*I_N)/2;
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114 Dpx = kr(I_n, ops_x.Dp, I_y,I_z);
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115 Dmx = kr(I_n, ops_x.Dm, I_y,I_z);
369
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diff changeset
116 obj.D = -Am*Dpx;
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diff changeset
117 temp = Ap*Dmx;
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diff changeset
118 obj.D = obj.D-temp;
355
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diff changeset
119 clear Ap Am Dpx Dmx
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diff changeset
120
354
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diff changeset
121 Bp = (obj.Bevaluated+alphaB*I_N)/2;
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parents: 352
diff changeset
122 Bm = (obj.Bevaluated-alphaB*I_N)/2;
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parents: 352
diff changeset
123 Dpy = kr(I_n, I_x, ops_y.Dp,I_z);
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diff changeset
124 Dmy = kr(I_n, I_x, ops_y.Dm,I_z);
369
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diff changeset
125 temp = Bm*Dpy;
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diff changeset
126 obj.D = obj.D-temp;
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diff changeset
127 temp = Bp*Dmy;
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diff changeset
128 obj.D = obj.D-temp;
355
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diff changeset
129 clear Bp Bm Dpy Dmy
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diff changeset
130
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diff changeset
131
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diff changeset
132 Cp = (obj.Cevaluated+alphaC*I_N)/2;
369
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diff changeset
133 Cm = (obj.Cevaluated-alphaC*I_N)/2;
354
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parents: 352
diff changeset
134 Dpz = kr(I_n, I_x, I_y,ops_z.Dp);
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parents: 352
diff changeset
135 Dmz = kr(I_n, I_x, I_y,ops_z.Dm);
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diff changeset
136
369
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diff changeset
137 temp = Cm*Dpz;
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diff changeset
138 obj.D = obj.D-temp;
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diff changeset
139 temp = Cp*Dmz;
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diff changeset
140 obj.D = obj.D-temp;
355
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parents: 354
diff changeset
141 clear Cp Cm Dpz Dmz
369
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diff changeset
142 obj.D = obj.D-obj.Eevaluated;
355
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parents: 354
diff changeset
143
369
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diff changeset
144 case 'standard'
354
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diff changeset
145 D1_x = kr(I_n, ops_x.D1, I_y,I_z);
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parents: 352
diff changeset
146 D1_y = kr(I_n, I_x, ops_y.D1,I_z);
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diff changeset
147 D1_z = kr(I_n, I_x, I_y,ops_z.D1);
369
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diff changeset
148 obj.D = -obj.Aevaluated*D1_x-obj.Bevaluated*D1_y-obj.Cevaluated*D1_z-obj.Eevaluated;
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diff changeset
149 otherwise
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parents: 368
diff changeset
150 error('Opperator not supported');
354
dbac99d2c318 Removed inv(Vi) to save time
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parents: 352
diff changeset
151 end
349
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diff changeset
152 end
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diff changeset
153
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parents:
diff changeset
154 % Closure functions return the opertors applied to the own doamin to close the boundary
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parents:
diff changeset
155 % Penalty functions return the opertors to force the solution. In the case of an interface it returns the operator applied to the other doamin.
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diff changeset
156 % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'.
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parents:
diff changeset
157 % type is a string specifying the type of boundary condition if there are several.
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parents:
diff changeset
158 % data is a function returning the data that should be applied at the boundary.
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parents:
diff changeset
159 function [closure, penalty] = boundary_condition(obj,boundary,type,L)
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parents:
diff changeset
160 default_arg('type','char');
369
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parents: 368
diff changeset
161 BM = boundary_matrices(obj,boundary);
349
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parents:
diff changeset
162 switch type
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parents:
diff changeset
163 case{'c','char'}
354
dbac99d2c318 Removed inv(Vi) to save time
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parents: 352
diff changeset
164 [closure,penalty] = boundary_condition_char(obj,BM);
349
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parents:
diff changeset
165 case{'general'}
354
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parents: 352
diff changeset
166 [closure,penalty] = boundary_condition_general(obj,BM,boundary,L);
349
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diff changeset
167 otherwise
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diff changeset
168 error('No such boundary condition')
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diff changeset
169 end
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diff changeset
170 end
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diff changeset
171
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parents:
diff changeset
172 function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary)
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parents:
diff changeset
173 error('An interface function does not exist yet');
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diff changeset
174 end
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diff changeset
175
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diff changeset
176 function N = size(obj)
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diff changeset
177 N = obj.m;
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diff changeset
178 end
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diff changeset
179
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diff changeset
180 function [ret] = evaluateCoefficientMatrix(obj, mat, X, Y, Z)
354
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diff changeset
181 params = obj.params;
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diff changeset
182 side = max(length(X),length(Y));
349
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diff changeset
183 if isa(mat,'function_handle')
354
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diff changeset
184 [rows,cols] = size(mat(params,0,0,0));
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parents: 352
diff changeset
185 matVec = mat(params,X',Y',Z');
369
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diff changeset
186 matVec = sparse(matVec);
349
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parents:
diff changeset
187 else
354
dbac99d2c318 Removed inv(Vi) to save time
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parents: 352
diff changeset
188 matVec = mat;
369
9d1fc984f40d Added some comments and cleaned up the code a little
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diff changeset
189 [rows,cols] = size(matVec);
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parents: 368
diff changeset
190 side = max(length(X),length(Y));
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diff changeset
191 cols = cols/side;
349
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diff changeset
192 end
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diff changeset
193
369
9d1fc984f40d Added some comments and cleaned up the code a little
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diff changeset
194 ret = cell(rows,cols);
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diff changeset
195 for ii = 1:rows
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diff changeset
196 for jj = 1:cols
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diff changeset
197 ret{ii,jj} = diag(matVec(ii,(jj-1)*side+1:jj*side));
349
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diff changeset
198 end
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diff changeset
199 end
369
9d1fc984f40d Added some comments and cleaned up the code a little
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diff changeset
200 ret = cell2mat(ret);
349
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diff changeset
201 end
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diff changeset
202
369
9d1fc984f40d Added some comments and cleaned up the code a little
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diff changeset
203 function [BM] = boundary_matrices(obj,boundary)
9d1fc984f40d Added some comments and cleaned up the code a little
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diff changeset
204 params = obj.params;
349
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diff changeset
205
cd6a29ab3746 A 3D is added and an attempt to imlement 3D transfinit interpolation has been initialized
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parents:
diff changeset
206 switch boundary
cd6a29ab3746 A 3D is added and an attempt to imlement 3D transfinit interpolation has been initialized
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diff changeset
207 case {'w','W','west'}
369
9d1fc984f40d Added some comments and cleaned up the code a little
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parents: 368
diff changeset
208 BM.e_ = obj.e_w;
9d1fc984f40d Added some comments and cleaned up the code a little
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parents: 368
diff changeset
209 mat = obj.A;
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diff changeset
210 BM.boundpos = 'l';
9d1fc984f40d Added some comments and cleaned up the code a little
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parents: 368
diff changeset
211 BM.Hi = obj.Hxi;
9d1fc984f40d Added some comments and cleaned up the code a little
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parents: 368
diff changeset
212 [BM.V,BM.Vi,BM.D,signVec] = obj.matrixDiag(mat,obj.X(1),obj.Yx,obj.Zx);
9d1fc984f40d Added some comments and cleaned up the code a little
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parents: 368
diff changeset
213 BM.side = length(obj.Yx);
349
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parents:
diff changeset
214 case {'e','E','east'}
369
9d1fc984f40d Added some comments and cleaned up the code a little
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parents: 368
diff changeset
215 BM.e_ = obj.e_e;
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parents: 368
diff changeset
216 mat = obj.A;
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diff changeset
217 BM.boundpos = 'r';
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diff changeset
218 BM.Hi = obj.Hxi;
9d1fc984f40d Added some comments and cleaned up the code a little
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parents: 368
diff changeset
219 [BM.V,BM.Vi,BM.D,signVec] = obj.matrixDiag(mat,obj.X(end),obj.Yx,obj.Zx);
9d1fc984f40d Added some comments and cleaned up the code a little
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diff changeset
220 BM.side = length(obj.Yx);
349
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parents:
diff changeset
221 case {'s','S','south'}
369
9d1fc984f40d Added some comments and cleaned up the code a little
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parents: 368
diff changeset
222 BM.e_ = obj.e_s;
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parents: 368
diff changeset
223 mat = obj.B;
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diff changeset
224 BM.boundpos = 'l';
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parents: 368
diff changeset
225 BM.Hi = obj.Hyi;
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parents: 368
diff changeset
226 [BM.V,BM.Vi,BM.D,signVec] = obj.matrixDiag(mat,obj.Xy,obj.Y(1),obj.Zy);
9d1fc984f40d Added some comments and cleaned up the code a little
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diff changeset
227 BM.side = length(obj.Xy);
349
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diff changeset
228 case {'n','N','north'}
369
9d1fc984f40d Added some comments and cleaned up the code a little
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diff changeset
229 BM.e_ = obj.e_n;
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diff changeset
230 mat = obj.B;
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diff changeset
231 BM.boundpos = 'r';
9d1fc984f40d Added some comments and cleaned up the code a little
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diff changeset
232 BM.Hi = obj.Hyi;
9d1fc984f40d Added some comments and cleaned up the code a little
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diff changeset
233 [BM.V,BM.Vi,BM.D,signVec] = obj.matrixDiag(mat,obj.Xy,obj.Y(end),obj.Zy);
9d1fc984f40d Added some comments and cleaned up the code a little
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diff changeset
234 BM.side = length(obj.Xy);
349
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diff changeset
235 case{'b','B','Bottom'}
369
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diff changeset
236 BM.e_ = obj.e_b;
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diff changeset
237 mat = obj.C;
9d1fc984f40d Added some comments and cleaned up the code a little
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diff changeset
238 BM.boundpos = 'l';
9d1fc984f40d Added some comments and cleaned up the code a little
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parents: 368
diff changeset
239 BM.Hi = obj.Hzi;
9d1fc984f40d Added some comments and cleaned up the code a little
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parents: 368
diff changeset
240 [BM.V,BM.Vi,BM.D,signVec] = obj.matrixDiag(mat,obj.Xz,obj.Yz,obj.Z(1));
9d1fc984f40d Added some comments and cleaned up the code a little
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parents: 368
diff changeset
241 BM.side = length(obj.Xz);
349
cd6a29ab3746 A 3D is added and an attempt to imlement 3D transfinit interpolation has been initialized
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diff changeset
242 case{'t','T','Top'}
369
9d1fc984f40d Added some comments and cleaned up the code a little
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parents: 368
diff changeset
243 BM.e_ = obj.e_t;
9d1fc984f40d Added some comments and cleaned up the code a little
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diff changeset
244 mat = obj.C;
9d1fc984f40d Added some comments and cleaned up the code a little
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parents: 368
diff changeset
245 BM.boundpos = 'r';
9d1fc984f40d Added some comments and cleaned up the code a little
Ylva Rydin <ylva.rydin@telia.com>
parents: 368
diff changeset
246 BM.Hi = obj.Hzi;
9d1fc984f40d Added some comments and cleaned up the code a little
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parents: 368
diff changeset
247 [BM.V,BM.Vi,BM.D,signVec] = obj.matrixDiag(mat,obj.Xz,obj.Yz,obj.Z(end));
9d1fc984f40d Added some comments and cleaned up the code a little
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parents: 368
diff changeset
248 BM.side = length(obj.Xz);
349
cd6a29ab3746 A 3D is added and an attempt to imlement 3D transfinit interpolation has been initialized
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diff changeset
249 end
369
9d1fc984f40d Added some comments and cleaned up the code a little
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parents: 368
diff changeset
250 BM.pos = signVec(1); BM.zeroval=signVec(2); BM.neg=signVec(3);
349
cd6a29ab3746 A 3D is added and an attempt to imlement 3D transfinit interpolation has been initialized
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diff changeset
251 end
cd6a29ab3746 A 3D is added and an attempt to imlement 3D transfinit interpolation has been initialized
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diff changeset
252
369
9d1fc984f40d Added some comments and cleaned up the code a little
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diff changeset
253 % Characteristic bouyndary consitions
349
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diff changeset
254 function [closure, penalty]=boundary_condition_char(obj,BM)
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diff changeset
255 side = BM.side;
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diff changeset
256 pos = BM.pos;
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diff changeset
257 neg = BM.neg;
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diff changeset
258 zeroval=BM.zeroval;
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diff changeset
259 V = BM.V;
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diff changeset
260 Vi = BM.Vi;
369
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diff changeset
261 Hi = BM.Hi;
9d1fc984f40d Added some comments and cleaned up the code a little
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diff changeset
262 D = BM.D;
9d1fc984f40d Added some comments and cleaned up the code a little
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diff changeset
263 e_ = BM.e_;
349
cd6a29ab3746 A 3D is added and an attempt to imlement 3D transfinit interpolation has been initialized
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diff changeset
264
cd6a29ab3746 A 3D is added and an attempt to imlement 3D transfinit interpolation has been initialized
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diff changeset
265 switch BM.boundpos
cd6a29ab3746 A 3D is added and an attempt to imlement 3D transfinit interpolation has been initialized
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diff changeset
266 case {'l'}
354
dbac99d2c318 Removed inv(Vi) to save time
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parents: 352
diff changeset
267 tau = sparse(obj.n*side,pos);
dbac99d2c318 Removed inv(Vi) to save time
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parents: 352
diff changeset
268 Vi_plus = Vi(1:pos,:);
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parents: 352
diff changeset
269 tau(1:pos,:) = -abs(D(1:pos,1:pos));
dbac99d2c318 Removed inv(Vi) to save time
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parents: 352
diff changeset
270 closure = Hi*e_*V*tau*Vi_plus*e_';
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parents: 352
diff changeset
271 penalty = -Hi*e_*V*tau*Vi_plus;
349
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diff changeset
272 case {'r'}
354
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parents: 352
diff changeset
273 tau = sparse(obj.n*side,neg);
dbac99d2c318 Removed inv(Vi) to save time
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parents: 352
diff changeset
274 tau((pos+zeroval)+1:obj.n*side,:) = -abs(D((pos+zeroval)+1:obj.n*side,(pos+zeroval)+1:obj.n*side));
dbac99d2c318 Removed inv(Vi) to save time
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parents: 352
diff changeset
275 Vi_minus = Vi((pos+zeroval)+1:obj.n*side,:);
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parents: 352
diff changeset
276 closure = Hi*e_*V*tau*Vi_minus*e_';
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parents: 352
diff changeset
277 penalty = -Hi*e_*V*tau*Vi_minus;
349
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diff changeset
278 end
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diff changeset
279 end
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diff changeset
280
369
9d1fc984f40d Added some comments and cleaned up the code a little
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parents: 368
diff changeset
281 % General boundary condition in the form Lu=g(x)
9d1fc984f40d Added some comments and cleaned up the code a little
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parents: 368
diff changeset
282 function [closure,penalty] = boundary_condition_general(obj,BM,boundary,L)
349
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diff changeset
283 side = BM.side;
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diff changeset
284 pos = BM.pos;
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diff changeset
285 neg = BM.neg;
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diff changeset
286 zeroval=BM.zeroval;
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diff changeset
287 V = BM.V;
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diff changeset
288 Vi = BM.Vi;
369
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diff changeset
289 Hi = BM.Hi;
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parents: 368
diff changeset
290 D = BM.D;
9d1fc984f40d Added some comments and cleaned up the code a little
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parents: 368
diff changeset
291 e_ = BM.e_;
9d1fc984f40d Added some comments and cleaned up the code a little
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parents: 368
diff changeset
292
349
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diff changeset
293 switch boundary
354
dbac99d2c318 Removed inv(Vi) to save time
Ylva Rydin <ylva.rydin@telia.com>
parents: 352
diff changeset
294 case {'w','W','west'}
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parents: 352
diff changeset
295 L = obj.evaluateCoefficientMatrix(L,obj.x(1),obj.Yx,obj.Zx);
349
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parents:
diff changeset
296 case {'e','E','east'}
354
dbac99d2c318 Removed inv(Vi) to save time
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parents: 352
diff changeset
297 L = obj.evaluateCoefficientMatrix(L,obj.x(end),obj.Yx,obj.Zx);
349
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diff changeset
298 case {'s','S','south'}
354
dbac99d2c318 Removed inv(Vi) to save time
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parents: 352
diff changeset
299 L = obj.evaluateCoefficientMatrix(L,obj.Xy,obj.y(1),obj.Zy);
349
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diff changeset
300 case {'n','N','north'}
369
9d1fc984f40d Added some comments and cleaned up the code a little
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parents: 368
diff changeset
301 L = obj.evaluateCoefficientMatrix(L,obj.Xy,obj.y(end),obj.Zy);% General boundary condition in the form Lu=g(x)
349
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parents:
diff changeset
302 case {'b','B','bottom'}
354
dbac99d2c318 Removed inv(Vi) to save time
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parents: 352
diff changeset
303 L = obj.evaluateCoefficientMatrix(L,obj.Xz,obj.Yz,obj.z(1));
dbac99d2c318 Removed inv(Vi) to save time
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parents: 352
diff changeset
304 case {'t','T','top'}
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parents: 352
diff changeset
305 L = obj.evaluateCoefficientMatrix(L,obj.Xz,obj.Yz,obj.z(end));
349
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parents:
diff changeset
306 end
cd6a29ab3746 A 3D is added and an attempt to imlement 3D transfinit interpolation has been initialized
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parents:
diff changeset
307
cd6a29ab3746 A 3D is added and an attempt to imlement 3D transfinit interpolation has been initialized
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parents:
diff changeset
308 switch BM.boundpos
cd6a29ab3746 A 3D is added and an attempt to imlement 3D transfinit interpolation has been initialized
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parents:
diff changeset
309 case {'l'}
354
dbac99d2c318 Removed inv(Vi) to save time
Ylva Rydin <ylva.rydin@telia.com>
parents: 352
diff changeset
310 tau = sparse(obj.n*side,pos);
dbac99d2c318 Removed inv(Vi) to save time
Ylva Rydin <ylva.rydin@telia.com>
parents: 352
diff changeset
311 Vi_plus = Vi(1:pos,:);
dbac99d2c318 Removed inv(Vi) to save time
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parents: 352
diff changeset
312 Vi_minus = Vi(pos+zeroval+1:obj.n*side,:);
dbac99d2c318 Removed inv(Vi) to save time
Ylva Rydin <ylva.rydin@telia.com>
parents: 352
diff changeset
313 V_plus = V(:,1:pos);
dbac99d2c318 Removed inv(Vi) to save time
Ylva Rydin <ylva.rydin@telia.com>
parents: 352
diff changeset
314 V_minus = V(:,(pos+zeroval)+1:obj.n*side);
349
cd6a29ab3746 A 3D is added and an attempt to imlement 3D transfinit interpolation has been initialized
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parents:
diff changeset
315
354
dbac99d2c318 Removed inv(Vi) to save time
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parents: 352
diff changeset
316 tau(1:pos,:) = -abs(D(1:pos,1:pos));
dbac99d2c318 Removed inv(Vi) to save time
Ylva Rydin <ylva.rydin@telia.com>
parents: 352
diff changeset
317 R = -inv(L*V_plus)*(L*V_minus);
dbac99d2c318 Removed inv(Vi) to save time
Ylva Rydin <ylva.rydin@telia.com>
parents: 352
diff changeset
318 closure = Hi*e_*V*tau*(Vi_plus-R*Vi_minus)*e_';
dbac99d2c318 Removed inv(Vi) to save time
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parents: 352
diff changeset
319 penalty = -Hi*e_*V*tau*inv(L*V_plus)*L;
349
cd6a29ab3746 A 3D is added and an attempt to imlement 3D transfinit interpolation has been initialized
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parents:
diff changeset
320 case {'r'}
354
dbac99d2c318 Removed inv(Vi) to save time
Ylva Rydin <ylva.rydin@telia.com>
parents: 352
diff changeset
321 tau = sparse(obj.n*side,neg);
dbac99d2c318 Removed inv(Vi) to save time
Ylva Rydin <ylva.rydin@telia.com>
parents: 352
diff changeset
322 tau((pos+zeroval)+1:obj.n*side,:) = -abs(D((pos+zeroval)+1:obj.n*side,(pos+zeroval)+1:obj.n*side));
dbac99d2c318 Removed inv(Vi) to save time
Ylva Rydin <ylva.rydin@telia.com>
parents: 352
diff changeset
323 Vi_plus = Vi(1:pos,:);
dbac99d2c318 Removed inv(Vi) to save time
Ylva Rydin <ylva.rydin@telia.com>
parents: 352
diff changeset
324 Vi_minus = Vi((pos+zeroval)+1:obj.n*side,:);
349
cd6a29ab3746 A 3D is added and an attempt to imlement 3D transfinit interpolation has been initialized
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parents:
diff changeset
325
354
dbac99d2c318 Removed inv(Vi) to save time
Ylva Rydin <ylva.rydin@telia.com>
parents: 352
diff changeset
326 V_plus = V(:,1:pos);
dbac99d2c318 Removed inv(Vi) to save time
Ylva Rydin <ylva.rydin@telia.com>
parents: 352
diff changeset
327 V_minus = V(:,(pos+zeroval)+1:obj.n*side);
dbac99d2c318 Removed inv(Vi) to save time
Ylva Rydin <ylva.rydin@telia.com>
parents: 352
diff changeset
328 R = -inv(L*V_minus)*(L*V_plus);
dbac99d2c318 Removed inv(Vi) to save time
Ylva Rydin <ylva.rydin@telia.com>
parents: 352
diff changeset
329 closure = Hi*e_*V*tau*(Vi_minus-R*Vi_plus)*e_';
dbac99d2c318 Removed inv(Vi) to save time
Ylva Rydin <ylva.rydin@telia.com>
parents: 352
diff changeset
330 penalty = -Hi*e_*V*tau*inv(L*V_minus)*L;
349
cd6a29ab3746 A 3D is added and an attempt to imlement 3D transfinit interpolation has been initialized
Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
331 end
cd6a29ab3746 A 3D is added and an attempt to imlement 3D transfinit interpolation has been initialized
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parents:
diff changeset
332 end
cd6a29ab3746 A 3D is added and an attempt to imlement 3D transfinit interpolation has been initialized
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parents:
diff changeset
333
369
9d1fc984f40d Added some comments and cleaned up the code a little
Ylva Rydin <ylva.rydin@telia.com>
parents: 368
diff changeset
334 % Function that diagonalizes a symbolic matrix A as A=V*D*Vi
9d1fc984f40d Added some comments and cleaned up the code a little
Ylva Rydin <ylva.rydin@telia.com>
parents: 368
diff changeset
335 % D is a diagonal matrix with the eigenvalues on A on the diagonal sorted by their sign
9d1fc984f40d Added some comments and cleaned up the code a little
Ylva Rydin <ylva.rydin@telia.com>
parents: 368
diff changeset
336 % [d+ ]
9d1fc984f40d Added some comments and cleaned up the code a little
Ylva Rydin <ylva.rydin@telia.com>
parents: 368
diff changeset
337 % D = [ d0 ]
9d1fc984f40d Added some comments and cleaned up the code a little
Ylva Rydin <ylva.rydin@telia.com>
parents: 368
diff changeset
338 % [ d-]
9d1fc984f40d Added some comments and cleaned up the code a little
Ylva Rydin <ylva.rydin@telia.com>
parents: 368
diff changeset
339 % signVec is a vector specifying the number of possitive, zero and negative eigenvalues of D
349
cd6a29ab3746 A 3D is added and an attempt to imlement 3D transfinit interpolation has been initialized
Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
340 function [V,Vi, D,signVec]=matrixDiag(obj,mat,x,y,z)
354
dbac99d2c318 Removed inv(Vi) to save time
Ylva Rydin <ylva.rydin@telia.com>
parents: 352
diff changeset
341 params = obj.params;
349
cd6a29ab3746 A 3D is added and an attempt to imlement 3D transfinit interpolation has been initialized
Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
342 syms xs ys zs
354
dbac99d2c318 Removed inv(Vi) to save time
Ylva Rydin <ylva.rydin@telia.com>
parents: 352
diff changeset
343 [V, D] = eig(mat(params,xs,ys,zs));
dbac99d2c318 Removed inv(Vi) to save time
Ylva Rydin <ylva.rydin@telia.com>
parents: 352
diff changeset
344 Vi=inv(V);
dbac99d2c318 Removed inv(Vi) to save time
Ylva Rydin <ylva.rydin@telia.com>
parents: 352
diff changeset
345 xs = x;
dbac99d2c318 Removed inv(Vi) to save time
Ylva Rydin <ylva.rydin@telia.com>
parents: 352
diff changeset
346 ys = y;
dbac99d2c318 Removed inv(Vi) to save time
Ylva Rydin <ylva.rydin@telia.com>
parents: 352
diff changeset
347 zs = z;
349
cd6a29ab3746 A 3D is added and an attempt to imlement 3D transfinit interpolation has been initialized
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parents:
diff changeset
348
cd6a29ab3746 A 3D is added and an attempt to imlement 3D transfinit interpolation has been initialized
Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
349
354
dbac99d2c318 Removed inv(Vi) to save time
Ylva Rydin <ylva.rydin@telia.com>
parents: 352
diff changeset
350 side = max(length(x),length(y));
dbac99d2c318 Removed inv(Vi) to save time
Ylva Rydin <ylva.rydin@telia.com>
parents: 352
diff changeset
351 Dret = zeros(obj.n,side*obj.n);
dbac99d2c318 Removed inv(Vi) to save time
Ylva Rydin <ylva.rydin@telia.com>
parents: 352
diff changeset
352 Vret = zeros(obj.n,side*obj.n);
dbac99d2c318 Removed inv(Vi) to save time
Ylva Rydin <ylva.rydin@telia.com>
parents: 352
diff changeset
353 Viret= zeros(obj.n,side*obj.n);
369
9d1fc984f40d Added some comments and cleaned up the code a little
Ylva Rydin <ylva.rydin@telia.com>
parents: 368
diff changeset
354
349
cd6a29ab3746 A 3D is added and an attempt to imlement 3D transfinit interpolation has been initialized
Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
355 for ii=1:obj.n
cd6a29ab3746 A 3D is added and an attempt to imlement 3D transfinit interpolation has been initialized
Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
356 for jj=1:obj.n
354
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diff changeset
357 Dret(jj,(ii-1)*side+1:side*ii) = eval(D(jj,ii));
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diff changeset
358 Vret(jj,(ii-1)*side+1:side*ii) = eval(V(jj,ii));
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parents: 352
diff changeset
359 Viret(jj,(ii-1)*side+1:side*ii) = eval(Vi(jj,ii));
349
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360 end
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parents:
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361 end
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362
354
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parents: 352
diff changeset
363 D = sparse(Dret);
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parents: 352
diff changeset
364 V = sparse(Vret);
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parents: 352
diff changeset
365 Vi = sparse(Viret);
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parents: 352
diff changeset
366 V = obj.evaluateCoefficientMatrix(V,x,y,z);
dbac99d2c318 Removed inv(Vi) to save time
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parents: 352
diff changeset
367 Vi= obj.evaluateCoefficientMatrix(Vi,x,y,z);
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parents: 352
diff changeset
368 D = obj.evaluateCoefficientMatrix(D,x,y,z);
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parents: 352
diff changeset
369 DD = diag(D);
349
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diff changeset
370
354
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parents: 352
diff changeset
371 poseig = (DD>0);
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Ylva Rydin <ylva.rydin@telia.com>
parents: 352
diff changeset
372 zeroeig = (DD==0);
dbac99d2c318 Removed inv(Vi) to save time
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parents: 352
diff changeset
373 negeig = (DD<0);
349
cd6a29ab3746 A 3D is added and an attempt to imlement 3D transfinit interpolation has been initialized
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parents:
diff changeset
374
354
dbac99d2c318 Removed inv(Vi) to save time
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parents: 352
diff changeset
375 D = diag([DD(poseig); DD(zeroeig); DD(negeig)]);
dbac99d2c318 Removed inv(Vi) to save time
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parents: 352
diff changeset
376 V = [V(:,poseig) V(:,zeroeig) V(:,negeig)];
dbac99d2c318 Removed inv(Vi) to save time
Ylva Rydin <ylva.rydin@telia.com>
parents: 352
diff changeset
377 Vi= [Vi(poseig,:); Vi(zeroeig,:); Vi(negeig,:)];
dbac99d2c318 Removed inv(Vi) to save time
Ylva Rydin <ylva.rydin@telia.com>
parents: 352
diff changeset
378 signVec = [sum(poseig),sum(zeroeig),sum(negeig)];
349
cd6a29ab3746 A 3D is added and an attempt to imlement 3D transfinit interpolation has been initialized
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parents:
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379 end
cd6a29ab3746 A 3D is added and an attempt to imlement 3D transfinit interpolation has been initialized
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parents:
diff changeset
380 end
cd6a29ab3746 A 3D is added and an attempt to imlement 3D transfinit interpolation has been initialized
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parents:
diff changeset
381 end