1 | // -*- C++ -*- |
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2 | /*************************************************************************** |
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3 | * blitz/array/stencilops.h Stencil operators |
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4 | * |
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5 | * Copyright (C) 1997-2001 Todd Veldhuizen <tveldhui@oonumerics.org> |
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6 | * |
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7 | * This program is free software; you can redistribute it and/or |
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8 | * modify it under the terms of the GNU General Public License |
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9 | * as published by the Free Software Foundation; either version 2 |
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10 | * of the License, or (at your option) any later version. |
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11 | * |
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12 | * This program is distributed in the hope that it will be useful, |
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13 | * but WITHOUT ANY WARRANTY; without even the implied warranty of |
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14 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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15 | * GNU General Public License for more details. |
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16 | * |
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17 | * Suggestions: blitz-dev@oonumerics.org |
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18 | * Bugs: blitz-bugs@oonumerics.org |
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19 | * |
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20 | * For more information, please see the Blitz++ Home Page: |
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21 | * http://oonumerics.org/blitz/ |
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22 | * |
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23 | ****************************************************************************/ |
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24 | #ifndef BZ_ARRAYSTENCILOPS_H |
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25 | #define BZ_ARRAYSTENCILOPS_H |
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26 | |
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27 | // NEEDS_WORK: need to factor many of the stencils in terms of the |
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28 | // integer constants, e.g. 16*(A(-1,0)+A(0,-1)+A(0,1)+A(1,0)) |
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29 | |
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30 | #ifndef BZ_ARRAYSTENCILS_H |
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31 | #error <blitz/array/stencilops.h> must be included via <blitz/array/stencils.h> |
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32 | #endif |
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33 | |
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34 | #ifndef BZ_GEOMETRY_H |
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35 | #include <blitz/array/geometry.h> |
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36 | #endif |
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37 | |
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38 | #ifndef BZ_TINYMAT_H |
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39 | #include <blitz/tinymat.h> |
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40 | #endif |
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41 | |
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42 | BZ_NAMESPACE(blitz) |
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43 | |
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44 | #define BZ_DECLARE_STENCIL_OPERATOR1(name,A) \ |
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45 | template<typename T> \ |
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46 | inline _bz_typename T::T_numtype name(T& A) \ |
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47 | { |
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48 | |
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49 | #define BZ_END_STENCIL_OPERATOR } |
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50 | |
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51 | #define BZ_DECLARE_STENCIL_OPERATOR2(name,A,B) \ |
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52 | template<typename T> \ |
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53 | inline _bz_typename T::T_numtype name(T& A, T& B) \ |
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54 | { |
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55 | |
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56 | #define BZ_DECLARE_STENCIL_OPERATOR3(name,A,B,C) \ |
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57 | template<typename T> \ |
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58 | inline _bz_typename T::T_numtype name(T& A, T& B, T& C) \ |
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59 | { |
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60 | |
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61 | // These constants are accurate to 45 decimal places = 149 bits of mantissa |
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62 | const double recip_2 = .500000000000000000000000000000000000000000000; |
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63 | const double recip_4 = .250000000000000000000000000000000000000000000; |
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64 | const double recip_6 = .166666666666666666666666666666666666666666667; |
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65 | const double recip_8 = .125000000000000000000000000000000000000000000; |
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66 | const double recip_12 = .0833333333333333333333333333333333333333333333; |
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67 | const double recip_144 = .00694444444444444444444444444444444444444444444; |
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68 | |
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69 | /**************************************************************************** |
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70 | * Laplacian Operators |
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71 | ****************************************************************************/ |
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72 | |
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73 | BZ_DECLARE_STENCIL_OPERATOR1(Laplacian2D, A) |
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74 | return -4.0 * (*A) |
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75 | + A.shift(-1,0) + A.shift(1,0) |
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76 | + A.shift(-1,1) + A.shift(1,1); |
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77 | BZ_END_STENCIL_OPERATOR |
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78 | |
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79 | BZ_DECLARE_STENCIL_OPERATOR1(Laplacian3D, A) |
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80 | return -6.0 * (*A) |
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81 | + A.shift(-1,0) + A.shift(1,0) |
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82 | + A.shift(-1,1) + A.shift(1,1) |
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83 | + A.shift(-1,2) + A.shift(1,2); |
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84 | BZ_END_STENCIL_OPERATOR |
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85 | |
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86 | BZ_DECLARE_STENCIL_OPERATOR1(Laplacian2D4, A) |
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87 | return -60.0 * (*A) |
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88 | + 16.0 * (A.shift(-1,0) + A.shift(1,0) + A.shift(-1,1) + A.shift(1,1)) |
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89 | - (A.shift(-2,0) + A.shift(2,0) + A.shift(-2,1) + A.shift(2,1)); |
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90 | BZ_END_STENCIL_OPERATOR |
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91 | |
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92 | BZ_DECLARE_STENCIL_OPERATOR1(Laplacian2D4n, A) |
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93 | return Laplacian2D4(A) * recip_12; |
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94 | BZ_END_STENCIL_OPERATOR |
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95 | |
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96 | BZ_DECLARE_STENCIL_OPERATOR1(Laplacian3D4, A) |
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97 | return -90.0 * (*A) |
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98 | + 16.0 * (A.shift(-1,0) + A.shift(1,0) + A.shift(-1,1) + A.shift(1,1) + |
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99 | A.shift(-1,2) + A.shift(1,2)) |
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100 | - (A.shift(-2,0) + A.shift(2,0) + A.shift(-2,1) + A.shift(2,1) + |
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101 | A.shift(-2,2) + A.shift(2,2)); |
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102 | BZ_END_STENCIL_OPERATOR |
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103 | |
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104 | BZ_DECLARE_STENCIL_OPERATOR1(Laplacian3D4n, A) |
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105 | return Laplacian3D4(A) * recip_12; |
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106 | BZ_END_STENCIL_OPERATOR |
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107 | |
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108 | /**************************************************************************** |
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109 | * Derivatives |
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110 | ****************************************************************************/ |
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111 | |
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112 | #define BZ_DECLARE_DIFF(name) \ |
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113 | template<typename T> \ |
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114 | inline _bz_typename T::T_numtype name(T& A, int dim = firstDim) |
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115 | |
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116 | #define BZ_DECLARE_MULTIDIFF(name) \ |
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117 | template<typename T> \ |
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118 | inline _bz_typename multicomponent_traits<_bz_typename \ |
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119 | T::T_numtype>::T_element name(T& A, int comp, int dim) |
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120 | |
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121 | /**************************************************************************** |
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122 | * Central differences with accuracy O(h^2) |
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123 | ****************************************************************************/ |
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124 | |
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125 | BZ_DECLARE_DIFF(central12) { |
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126 | return A.shift(1,dim) - A.shift(-1,dim); |
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127 | } |
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128 | |
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129 | BZ_DECLARE_DIFF(central22) { |
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130 | return -2.0 * (*A) + A.shift(1,dim) + A.shift(-1,dim); |
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131 | } |
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132 | |
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133 | BZ_DECLARE_DIFF(central32) { |
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134 | return -2.0 * (A.shift(1,dim) - A.shift(-1,dim)) |
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135 | + (A.shift(2,dim) - A.shift(-2,dim)); |
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136 | } |
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137 | |
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138 | BZ_DECLARE_DIFF(central42) { |
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139 | return 6.0 * (*A) |
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140 | - 4.0 * (A.shift(1,dim) + A.shift(-1,dim)) |
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141 | + (A.shift(2,dim) + A.shift(-2,dim)); |
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142 | } |
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143 | |
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144 | /**************************************************************************** |
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145 | * Central differences with accuracy O(h^2) (multicomponent versions) |
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146 | ****************************************************************************/ |
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147 | |
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148 | BZ_DECLARE_MULTIDIFF(central12) { |
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149 | return A.shift(1,dim)[comp] - A.shift(-1,dim)[comp]; |
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150 | } |
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151 | |
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152 | BZ_DECLARE_MULTIDIFF(central22) { |
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153 | return -2.0 * (*A)[comp] |
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154 | + A.shift(1,dim)[comp] + A.shift(-1,dim)[comp]; |
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155 | } |
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156 | |
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157 | BZ_DECLARE_MULTIDIFF(central32) { |
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158 | return -2.0 * (A.shift(1,dim)[comp] - A.shift(-1,dim)[comp]) |
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159 | + (A.shift(2,dim)[comp] - A.shift(-2,dim)[comp]); |
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160 | } |
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161 | |
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162 | BZ_DECLARE_MULTIDIFF(central42) { |
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163 | return 6.0 * (*A)[comp] |
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164 | -4.0 * (A.shift(1,dim)[comp] + A.shift(-1,dim)[comp]) |
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165 | + (A.shift(2,dim)[comp] + A.shift(-2,dim)[comp]); |
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166 | } |
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167 | |
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168 | /**************************************************************************** |
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169 | * Central differences with accuracy O(h^2) (normalized versions) |
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170 | ****************************************************************************/ |
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171 | |
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172 | BZ_DECLARE_DIFF(central12n) { |
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173 | return central12(A,dim) * recip_2; |
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174 | } |
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175 | |
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176 | BZ_DECLARE_DIFF(central22n) { |
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177 | return central22(A,dim); |
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178 | } |
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179 | |
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180 | BZ_DECLARE_DIFF(central32n) { |
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181 | return central32(A,dim) * recip_2; |
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182 | } |
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183 | |
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184 | BZ_DECLARE_DIFF(central42n) { |
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185 | return central42(A,dim); |
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186 | } |
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187 | |
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188 | /**************************************************************************** |
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189 | * Central differences with accuracy O(h^2) (normalized multicomponent) |
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190 | ****************************************************************************/ |
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191 | |
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192 | BZ_DECLARE_MULTIDIFF(central12n) { |
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193 | return central12(A,comp,dim) * recip_2; |
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194 | } |
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195 | |
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196 | BZ_DECLARE_MULTIDIFF(central22n) { |
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197 | return central22(A,comp,dim); |
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198 | } |
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199 | |
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200 | BZ_DECLARE_MULTIDIFF(central32n) { |
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201 | return central32(A,comp,dim) * recip_2; |
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202 | } |
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203 | |
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204 | BZ_DECLARE_MULTIDIFF(central42n) { |
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205 | return central42(A,comp,dim); |
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206 | } |
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207 | |
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208 | /**************************************************************************** |
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209 | * Central differences with accuracy O(h^4) |
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210 | ****************************************************************************/ |
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211 | |
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212 | BZ_DECLARE_DIFF(central14) { |
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213 | return 8.0 * (A.shift(1,dim) - A.shift(-1,dim)) |
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214 | - (A.shift(2,dim) - A.shift(-2,dim)); |
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215 | } |
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216 | |
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217 | BZ_DECLARE_DIFF(central24) { |
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218 | return -30.0 * (*A) |
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219 | + 16.0 * (A.shift(1,dim) + A.shift(-1,dim)) |
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220 | - (A.shift(2,dim) + A.shift(-2,dim)); |
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221 | } |
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222 | |
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223 | BZ_DECLARE_DIFF(central34) { |
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224 | return -13.0 * (A.shift(1,dim) - A.shift(-1,dim)) |
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225 | + 8.0 * (A.shift(2,dim) - A.shift(-2,dim)) |
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226 | - (A.shift(3,dim) - A.shift(-3,dim)); |
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227 | } |
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228 | |
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229 | BZ_DECLARE_DIFF(central44) { |
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230 | return 56.0 * (*A) |
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231 | - 39.0 * (A.shift(1,dim) + A.shift(-1,dim)) |
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232 | + 12.0 * (A.shift(2,dim) + A.shift(-2,dim)) |
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233 | - (A.shift(3,dim) + A.shift(-3,dim)); |
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234 | } |
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235 | |
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236 | /**************************************************************************** |
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237 | * Central differences with accuracy O(h^4) (multicomponent versions) |
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238 | ****************************************************************************/ |
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239 | |
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240 | BZ_DECLARE_MULTIDIFF(central14) { |
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241 | return 8.0 * (A.shift(1,dim)[comp] - A.shift(-1,dim)[comp]) |
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242 | - (A.shift(2,dim)[comp] - A.shift(-2,dim)[comp]); |
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243 | } |
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244 | |
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245 | BZ_DECLARE_MULTIDIFF(central24) { |
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246 | return - 30.0 * (*A)[comp] |
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247 | + 16.0 * (A.shift(1,dim)[comp] + A.shift(-1,dim)[comp]) |
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248 | - (A.shift(2,dim)[comp] + A.shift(-2,dim)[comp]); |
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249 | } |
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250 | |
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251 | BZ_DECLARE_MULTIDIFF(central34) { |
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252 | return -13.0 * (A.shift(1,dim)[comp] - A.shift(-1,dim)[comp]) |
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253 | + 8.0 * (A.shift(2,dim)[comp] - A.shift(-2,dim)[comp]) |
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254 | - (A.shift(3,dim)[comp] - A.shift(-3,dim)[comp]); |
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255 | } |
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256 | |
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257 | BZ_DECLARE_MULTIDIFF(central44) { |
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258 | return 56.0 * (*A)[comp] |
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259 | - 39.0 * (A.shift(1,dim)[comp] + A.shift(-1,dim)[comp]) |
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260 | + 12.0 * (A.shift(2,dim)[comp] + A.shift(-2,dim)[comp]) |
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261 | - (A.shift(3,dim)[comp] + A.shift(-3,dim)[comp]); |
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262 | } |
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263 | |
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264 | /**************************************************************************** |
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265 | * Central differences with accuracy O(h^4) (normalized) |
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266 | ****************************************************************************/ |
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267 | |
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268 | BZ_DECLARE_DIFF(central14n) { |
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269 | return central14(A,dim) * recip_12; |
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270 | } |
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271 | |
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272 | BZ_DECLARE_DIFF(central24n) { |
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273 | return central24(A,dim) * recip_12; |
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274 | } |
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275 | |
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276 | BZ_DECLARE_DIFF(central34n) { |
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277 | return central34(A,dim) * recip_8; |
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278 | } |
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279 | |
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280 | BZ_DECLARE_DIFF(central44n) { |
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281 | return central44(A,dim) * recip_6; |
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282 | } |
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283 | |
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284 | /**************************************************************************** |
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285 | * Central differences with accuracy O(h^4) (normalized, multicomponent) |
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286 | ****************************************************************************/ |
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287 | |
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288 | BZ_DECLARE_MULTIDIFF(central14n) { |
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289 | return central14(A,comp,dim) * recip_12; |
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290 | } |
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291 | |
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292 | BZ_DECLARE_MULTIDIFF(central24n) { |
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293 | return central24(A,comp,dim) * recip_12; |
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294 | } |
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295 | |
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296 | BZ_DECLARE_MULTIDIFF(central34n) { |
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297 | return central34(A,comp,dim) * recip_8; |
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298 | } |
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299 | |
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300 | BZ_DECLARE_MULTIDIFF(central44n) { |
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301 | return central44(A,comp,dim) * recip_6; |
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302 | } |
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303 | |
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304 | /**************************************************************************** |
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305 | * Backward differences with accuracy O(h) |
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306 | ****************************************************************************/ |
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307 | |
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308 | BZ_DECLARE_DIFF(backward11) { |
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309 | return (*A) - A.shift(-1,dim); |
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310 | } |
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311 | |
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312 | BZ_DECLARE_DIFF(backward21) { |
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313 | return (*A) - 2.0 * A.shift(-1,dim) + A.shift(-2,dim); |
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314 | } |
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315 | |
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316 | BZ_DECLARE_DIFF(backward31) { |
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317 | return (*A) - 3.0 * A.shift(-1,dim) + 3.0 * A.shift(-2,dim) |
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318 | - A.shift(-3,dim); |
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319 | } |
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320 | |
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321 | BZ_DECLARE_DIFF(backward41) { |
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322 | return (*A) - 4.0 * A.shift(-1,dim) + 6.0 * A.shift(-2,dim) |
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323 | - 4.0 * A.shift(-3,dim) + A.shift(-4,dim); |
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324 | } |
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325 | |
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326 | /**************************************************************************** |
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327 | * Backward differences with accuracy O(h) (multicomponent versions) |
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328 | ****************************************************************************/ |
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329 | |
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330 | BZ_DECLARE_MULTIDIFF(backward11) { |
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331 | return (*A)[comp] - A.shift(-1,dim)[comp]; |
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332 | } |
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333 | |
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334 | BZ_DECLARE_MULTIDIFF(backward21) { |
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335 | return (*A)[comp] - 2.0 * A.shift(-1,dim)[comp] + A.shift(-2,dim)[comp]; |
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336 | } |
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337 | |
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338 | BZ_DECLARE_MULTIDIFF(backward31) { |
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339 | return (*A)[comp] - 3.0 * A.shift(-1,dim)[comp] + 3.0 * A.shift(-2,dim)[comp] |
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340 | - A.shift(-3,dim)[comp]; |
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341 | } |
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342 | |
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343 | BZ_DECLARE_MULTIDIFF(backward41) { |
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344 | return (*A)[comp] - 4.0 * A.shift(-1,dim)[comp] + 6.0 * A.shift(-2,dim)[comp] |
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345 | - 4.0 * A.shift(-3,dim)[comp] + A.shift(-4,dim)[comp]; |
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346 | } |
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347 | |
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348 | /**************************************************************************** |
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349 | * Backward differences with accuracy O(h) (normalized) |
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350 | ****************************************************************************/ |
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351 | |
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352 | BZ_DECLARE_DIFF(backward11n) { return backward11(A,dim); } |
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353 | BZ_DECLARE_DIFF(backward21n) { return backward21(A,dim); } |
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354 | BZ_DECLARE_DIFF(backward31n) { return backward31(A,dim); } |
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355 | BZ_DECLARE_DIFF(backward41n) { return backward41(A,dim); } |
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356 | |
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357 | /**************************************************************************** |
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358 | * Backward differences with accuracy O(h) (normalized, multicomponent) |
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359 | ****************************************************************************/ |
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360 | |
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361 | BZ_DECLARE_MULTIDIFF(backward11n) { return backward11(A,comp,dim); } |
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362 | BZ_DECLARE_MULTIDIFF(backward21n) { return backward21(A,comp,dim); } |
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363 | BZ_DECLARE_MULTIDIFF(backward31n) { return backward31(A,comp,dim); } |
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364 | BZ_DECLARE_MULTIDIFF(backward41n) { return backward41(A,comp,dim); } |
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365 | |
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366 | /**************************************************************************** |
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367 | * Backward differences with accuracy O(h^2) |
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368 | ****************************************************************************/ |
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369 | |
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370 | BZ_DECLARE_DIFF(backward12) { |
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371 | return 3.0 * (*A) - 4.0 * A.shift(-1,dim) + A.shift(-2,dim); |
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372 | } |
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373 | |
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374 | BZ_DECLARE_DIFF(backward22) { |
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375 | return 2.0 * (*A) - 5.0 * A.shift(-1,dim) + 4.0 * A.shift(-2,dim) |
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376 | - A.shift(-3,dim); |
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377 | } |
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378 | |
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379 | BZ_DECLARE_DIFF(backward32) { |
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380 | return 5.0 * (*A) - 18.0 * A.shift(-1,dim) + 24.0 * A.shift(-2,dim) |
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381 | - 14.0 * A.shift(-3,dim) + 3.0 * A.shift(-4,dim); |
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382 | } |
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383 | |
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384 | BZ_DECLARE_DIFF(backward42) { |
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385 | return 3.0 * (*A) - 14.0 * A.shift(-1,dim) + 26.0 * A.shift(-2,dim) |
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386 | - 24.0 * A.shift(-3,dim) + 11.0 * A.shift(-4,dim) - 2.0 * A.shift(-5,dim); |
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387 | } |
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388 | |
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389 | /**************************************************************************** |
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390 | * Backward differences with accuracy O(h^2) (multicomponent versions) |
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391 | ****************************************************************************/ |
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392 | |
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393 | BZ_DECLARE_MULTIDIFF(backward12) { |
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394 | return 3.0 * (*A)[comp] - 4.0 * A.shift(-1,dim)[comp] |
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395 | + A.shift(-2,dim)[comp]; |
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396 | } |
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397 | |
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398 | BZ_DECLARE_MULTIDIFF(backward22) { |
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399 | return 2.0 * (*A)[comp] - 5.0 * A.shift(-1,dim)[comp] |
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400 | + 4.0 * A.shift(-2,dim)[comp] - A.shift(-3,dim)[comp]; |
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401 | } |
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402 | |
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403 | BZ_DECLARE_MULTIDIFF(backward32) { |
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404 | return 5.0 * (*A)[comp] - 18.0 * A.shift(-1,dim)[comp] |
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405 | + 24.0 * A.shift(-2,dim)[comp] - 14.0 * A.shift(-3,dim)[comp] |
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406 | + 3.0 * A.shift(-4,dim)[comp]; |
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407 | } |
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408 | |
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409 | BZ_DECLARE_MULTIDIFF(backward42) { |
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410 | return 3.0 * (*A)[comp] - 14.0 * A.shift(-1,dim)[comp] |
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411 | + 26.0 * A.shift(-2,dim)[comp] - 24.0 * A.shift(-3,dim)[comp] |
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412 | + 11.0 * A.shift(-4,dim)[comp] - 2.0 * A.shift(-5,dim)[comp]; |
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413 | } |
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414 | |
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415 | /**************************************************************************** |
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416 | * Backward differences with accuracy O(h^2) (normalized) |
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417 | ****************************************************************************/ |
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418 | |
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419 | BZ_DECLARE_DIFF(backward12n) { return backward12(A,dim) * recip_2; } |
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420 | BZ_DECLARE_DIFF(backward22n) { return backward22(A,dim); } |
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421 | BZ_DECLARE_DIFF(backward32n) { return backward32(A,dim) * recip_2; } |
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422 | BZ_DECLARE_DIFF(backward42n) { return backward42(A,dim); } |
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423 | |
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424 | /**************************************************************************** |
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425 | * Backward differences with accuracy O(h^2) (normalized, multicomponent) |
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426 | ****************************************************************************/ |
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427 | |
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428 | BZ_DECLARE_MULTIDIFF(backward12n) { return backward12(A,comp,dim) * recip_2; } |
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429 | BZ_DECLARE_MULTIDIFF(backward22n) { return backward22(A,comp,dim); } |
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430 | BZ_DECLARE_MULTIDIFF(backward32n) { return backward32(A,comp,dim) * recip_2; } |
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431 | BZ_DECLARE_MULTIDIFF(backward42n) { return backward42(A,comp,dim); } |
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432 | |
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433 | /**************************************************************************** |
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434 | * Forward differences with accuracy O(h) |
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435 | ****************************************************************************/ |
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436 | |
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437 | BZ_DECLARE_DIFF(forward11) { |
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438 | return -(*A) + A.shift(1,dim); |
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439 | } |
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440 | |
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441 | BZ_DECLARE_DIFF(forward21) { |
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442 | return (*A) - 2.0 * A.shift(1,dim) + A.shift(2,dim); |
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443 | } |
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444 | |
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445 | BZ_DECLARE_DIFF(forward31) { |
---|
446 | return -(*A) + 3.0 * A.shift(1,dim) - 3.0 * A.shift(2,dim) + A.shift(3,dim); |
---|
447 | } |
---|
448 | |
---|
449 | BZ_DECLARE_DIFF(forward41) { |
---|
450 | return (*A) - 4.0 * A.shift(1,dim) + 6.0 * A.shift(2,dim) |
---|
451 | - 4.0 * A.shift(3,dim) + A.shift(4,dim); |
---|
452 | } |
---|
453 | |
---|
454 | /**************************************************************************** |
---|
455 | * Forward differences with accuracy O(h) (multicomponent versions) |
---|
456 | ****************************************************************************/ |
---|
457 | |
---|
458 | BZ_DECLARE_MULTIDIFF(forward11) { |
---|
459 | return -(*A)[comp] + A.shift(1,dim)[comp]; |
---|
460 | } |
---|
461 | |
---|
462 | BZ_DECLARE_MULTIDIFF(forward21) { |
---|
463 | return (*A)[comp] - 2.0 * A.shift(1,dim)[comp] + A.shift(2,dim)[comp]; |
---|
464 | } |
---|
465 | |
---|
466 | BZ_DECLARE_MULTIDIFF(forward31) { |
---|
467 | return -(*A)[comp] + 3.0 * A.shift(1,dim)[comp] - 3.0 * A.shift(2,dim)[comp] |
---|
468 | + A.shift(3,dim)[comp]; |
---|
469 | } |
---|
470 | |
---|
471 | BZ_DECLARE_MULTIDIFF(forward41) { |
---|
472 | return (*A)[comp] - 4.0 * A.shift(1,dim)[comp] + 6.0 * A.shift(2,dim)[comp] |
---|
473 | - 4.0 * A.shift(3,dim)[comp] + A.shift(4,dim)[comp]; |
---|
474 | } |
---|
475 | |
---|
476 | /**************************************************************************** |
---|
477 | * Forward differences with accuracy O(h) (normalized) |
---|
478 | ****************************************************************************/ |
---|
479 | |
---|
480 | BZ_DECLARE_DIFF(forward11n) { return forward11(A,dim); } |
---|
481 | BZ_DECLARE_DIFF(forward21n) { return forward21(A,dim); } |
---|
482 | BZ_DECLARE_DIFF(forward31n) { return forward31(A,dim); } |
---|
483 | BZ_DECLARE_DIFF(forward41n) { return forward41(A,dim); } |
---|
484 | |
---|
485 | /**************************************************************************** |
---|
486 | * Forward differences with accuracy O(h) (multicomponent,normalized) |
---|
487 | ****************************************************************************/ |
---|
488 | |
---|
489 | BZ_DECLARE_MULTIDIFF(forward11n) { return forward11(A,comp,dim); } |
---|
490 | BZ_DECLARE_MULTIDIFF(forward21n) { return forward21(A,comp,dim); } |
---|
491 | BZ_DECLARE_MULTIDIFF(forward31n) { return forward31(A,comp,dim); } |
---|
492 | BZ_DECLARE_MULTIDIFF(forward41n) { return forward41(A,comp,dim); } |
---|
493 | |
---|
494 | /**************************************************************************** |
---|
495 | * Forward differences with accuracy O(h^2) |
---|
496 | ****************************************************************************/ |
---|
497 | |
---|
498 | BZ_DECLARE_DIFF(forward12) { |
---|
499 | return -3.0 * (*A) + 4.0 * A.shift(1,dim) - A.shift(2,dim); |
---|
500 | } |
---|
501 | |
---|
502 | BZ_DECLARE_DIFF(forward22) { |
---|
503 | return 2.0 * (*A) - 5.0 * A.shift(1,dim) + 4.0 * A.shift(2,dim) |
---|
504 | - A.shift(3,dim); |
---|
505 | } |
---|
506 | |
---|
507 | BZ_DECLARE_DIFF(forward32) { |
---|
508 | return -5.0 * (*A) + 18.0 * A.shift(1,dim) - 24.0 * A.shift(2,dim) |
---|
509 | + 14.0 * A.shift(3,dim) - 3.0 * A.shift(4,dim); |
---|
510 | } |
---|
511 | |
---|
512 | BZ_DECLARE_DIFF(forward42) { |
---|
513 | return 3.0 * (*A) - 14.0 * A.shift(1,dim) + 26.0 * A.shift(2,dim) |
---|
514 | - 24.0 * A.shift(3,dim) + 11.0 * A.shift(4,dim) - 2.0 * A.shift(5,dim); |
---|
515 | } |
---|
516 | |
---|
517 | /**************************************************************************** |
---|
518 | * Forward differences with accuracy O(h^2) (multicomponent versions) |
---|
519 | ****************************************************************************/ |
---|
520 | |
---|
521 | BZ_DECLARE_MULTIDIFF(forward12) { |
---|
522 | return -3.0 * (*A)[comp] + 4.0 * A.shift(1,dim)[comp] - A.shift(2,dim)[comp]; |
---|
523 | } |
---|
524 | |
---|
525 | BZ_DECLARE_MULTIDIFF(forward22) { |
---|
526 | return 2.0 * (*A)[comp] - 5.0 * A.shift(1,dim)[comp] |
---|
527 | + 4.0 * A.shift(2,dim)[comp] - A.shift(3,dim)[comp]; |
---|
528 | } |
---|
529 | |
---|
530 | BZ_DECLARE_MULTIDIFF(forward32) { |
---|
531 | return -5.0 * (*A)[comp] + 18.0 * A.shift(1,dim)[comp] |
---|
532 | - 24.0 * A.shift(2,dim)[comp] + 14.0 * A.shift(3,dim)[comp] |
---|
533 | - 3.0 * A.shift(4,dim)[comp]; |
---|
534 | } |
---|
535 | |
---|
536 | BZ_DECLARE_MULTIDIFF(forward42) { |
---|
537 | return 3.0 * (*A)[comp] - 14.0 * A.shift(1,dim)[comp] |
---|
538 | + 26.0 * A.shift(2,dim)[comp] - 24.0 * A.shift(3,dim)[comp] |
---|
539 | + 11.0 * A.shift(4,dim)[comp] - 2.0 * A.shift(5,dim)[comp]; |
---|
540 | } |
---|
541 | |
---|
542 | |
---|
543 | /**************************************************************************** |
---|
544 | * Forward differences with accuracy O(h^2) (normalized) |
---|
545 | ****************************************************************************/ |
---|
546 | |
---|
547 | BZ_DECLARE_DIFF(forward12n) { return forward12(A,dim) * recip_2; } |
---|
548 | BZ_DECLARE_DIFF(forward22n) { return forward22(A,dim); } |
---|
549 | BZ_DECLARE_DIFF(forward32n) { return forward32(A,dim) * recip_2; } |
---|
550 | BZ_DECLARE_DIFF(forward42n) { return forward42(A,dim); } |
---|
551 | |
---|
552 | /**************************************************************************** |
---|
553 | * Forward differences with accuracy O(h^2) (normalized) |
---|
554 | ****************************************************************************/ |
---|
555 | |
---|
556 | BZ_DECLARE_MULTIDIFF(forward12n) { return forward12(A,comp,dim) * recip_2; } |
---|
557 | BZ_DECLARE_MULTIDIFF(forward22n) { return forward22(A,comp,dim); } |
---|
558 | BZ_DECLARE_MULTIDIFF(forward32n) { return forward32(A,comp,dim) * recip_2; } |
---|
559 | BZ_DECLARE_MULTIDIFF(forward42n) { return forward42(A,comp,dim); } |
---|
560 | |
---|
561 | /**************************************************************************** |
---|
562 | * Gradient operators |
---|
563 | ****************************************************************************/ |
---|
564 | |
---|
565 | template<typename T> |
---|
566 | inline TinyVector<_bz_typename T::T_numtype,2> grad2D(T& A) { |
---|
567 | return TinyVector<_bz_typename T::T_numtype,2>( |
---|
568 | central12(A,firstDim), |
---|
569 | central12(A,secondDim)); |
---|
570 | } |
---|
571 | |
---|
572 | template<typename T> |
---|
573 | inline TinyVector<_bz_typename T::T_numtype,2> grad2D4(T& A) { |
---|
574 | return TinyVector<_bz_typename T::T_numtype,2>( |
---|
575 | central14(A,firstDim), |
---|
576 | central14(A,secondDim)); |
---|
577 | } |
---|
578 | |
---|
579 | template<typename T> |
---|
580 | inline TinyVector<_bz_typename T::T_numtype,3> grad3D(T& A) { |
---|
581 | return TinyVector<_bz_typename T::T_numtype,3>( |
---|
582 | central12(A,firstDim), |
---|
583 | central12(A,secondDim), |
---|
584 | central12(A,thirdDim)); |
---|
585 | } |
---|
586 | |
---|
587 | template<typename T> |
---|
588 | inline TinyVector<_bz_typename T::T_numtype,3> grad3D4(T& A) { |
---|
589 | return TinyVector<_bz_typename T::T_numtype,3>( |
---|
590 | central14(A,firstDim), |
---|
591 | central14(A,secondDim), |
---|
592 | central14(A,thirdDim)); |
---|
593 | } |
---|
594 | |
---|
595 | template<typename T> |
---|
596 | inline TinyVector<_bz_typename T::T_numtype,2> grad2Dn(T& A) { |
---|
597 | return TinyVector<_bz_typename T::T_numtype,2>( |
---|
598 | central12n(A,firstDim), |
---|
599 | central12n(A,secondDim)); |
---|
600 | } |
---|
601 | |
---|
602 | template<typename T> |
---|
603 | inline TinyVector<_bz_typename T::T_numtype,2> grad2D4n(T& A) { |
---|
604 | return TinyVector<_bz_typename T::T_numtype,2>( |
---|
605 | central14n(A,firstDim), |
---|
606 | central14n(A,secondDim)); |
---|
607 | } |
---|
608 | |
---|
609 | template<typename T> |
---|
610 | inline TinyVector<_bz_typename T::T_numtype,3> grad3Dn(T& A) { |
---|
611 | return TinyVector<_bz_typename T::T_numtype,3>( |
---|
612 | central12n(A,firstDim), |
---|
613 | central12n(A,secondDim), |
---|
614 | central12n(A,thirdDim)); |
---|
615 | } |
---|
616 | |
---|
617 | template<typename T> |
---|
618 | inline TinyVector<_bz_typename T::T_numtype,3> grad3D4n(T& A) { |
---|
619 | return TinyVector<_bz_typename T::T_numtype,3>( |
---|
620 | central14n(A,firstDim), |
---|
621 | central14n(A,secondDim), |
---|
622 | central14n(A,thirdDim)); |
---|
623 | } |
---|
624 | |
---|
625 | /**************************************************************************** |
---|
626 | * Grad-squared operators |
---|
627 | ****************************************************************************/ |
---|
628 | |
---|
629 | template<typename T> |
---|
630 | inline TinyVector<_bz_typename T::T_numtype,2> gradSqr2D(T& A) { |
---|
631 | return TinyVector<_bz_typename T::T_numtype,2>( |
---|
632 | central22(A,firstDim), |
---|
633 | central22(A,secondDim)); |
---|
634 | } |
---|
635 | |
---|
636 | template<typename T> |
---|
637 | inline TinyVector<_bz_typename T::T_numtype,2> gradSqr2D4(T& A) { |
---|
638 | return TinyVector<_bz_typename T::T_numtype,2>( |
---|
639 | central24(A,firstDim), |
---|
640 | central24(A,secondDim)); |
---|
641 | } |
---|
642 | |
---|
643 | template<typename T> |
---|
644 | inline TinyVector<_bz_typename T::T_numtype,3> gradSqr3D(T& A) { |
---|
645 | return TinyVector<_bz_typename T::T_numtype,3>( |
---|
646 | central22(A,firstDim), |
---|
647 | central22(A,secondDim), |
---|
648 | central22(A,thirdDim)); |
---|
649 | } |
---|
650 | |
---|
651 | template<typename T> |
---|
652 | inline TinyVector<_bz_typename T::T_numtype,3> gradSqr3D4(T& A) { |
---|
653 | return TinyVector<_bz_typename T::T_numtype,3>( |
---|
654 | central24(A,firstDim), |
---|
655 | central24(A,secondDim), |
---|
656 | central24(A,thirdDim)); |
---|
657 | } |
---|
658 | |
---|
659 | /**************************************************************************** |
---|
660 | * Grad-squared operators (normalized) |
---|
661 | ****************************************************************************/ |
---|
662 | |
---|
663 | template<typename T> |
---|
664 | inline TinyVector<_bz_typename T::T_numtype,2> gradSqr2Dn(T& A) { |
---|
665 | return gradSqr2D(A); |
---|
666 | } |
---|
667 | |
---|
668 | template<typename T> |
---|
669 | inline TinyVector<_bz_typename T::T_numtype,2> gradSqr2D4n(T& A) { |
---|
670 | return TinyVector<_bz_typename T::T_numtype,2>( |
---|
671 | central24(A,firstDim) * recip_12, |
---|
672 | central24(A,secondDim) * recip_12); |
---|
673 | } |
---|
674 | |
---|
675 | template<typename T> |
---|
676 | inline TinyVector<_bz_typename T::T_numtype,3> gradSqr3Dn(T& A) { |
---|
677 | return gradSqr3D(A); |
---|
678 | } |
---|
679 | |
---|
680 | template<typename T> |
---|
681 | inline TinyVector<_bz_typename T::T_numtype,3> gradSqr3D4n(T& A) { |
---|
682 | return TinyVector<_bz_typename T::T_numtype,3>( |
---|
683 | central24(A,firstDim) * recip_12, |
---|
684 | central24(A,secondDim) * recip_12, |
---|
685 | central24(A,thirdDim) * recip_12); |
---|
686 | } |
---|
687 | |
---|
688 | /**************************************************************************** |
---|
689 | * Gradient operators on a vector field |
---|
690 | ****************************************************************************/ |
---|
691 | |
---|
692 | template<typename T> |
---|
693 | inline TinyMatrix<_bz_typename multicomponent_traits<_bz_typename |
---|
694 | T::T_numtype>::T_element, 3, 3> |
---|
695 | Jacobian3D(T& A) |
---|
696 | { |
---|
697 | const int x=0, y=1, z=2; |
---|
698 | const int u=0, v=1, w=2; |
---|
699 | |
---|
700 | TinyMatrix<_bz_typename multicomponent_traits<_bz_typename |
---|
701 | T::T_numtype>::T_element, 3, 3> grad; |
---|
702 | |
---|
703 | grad(u,x) = central12(A,u,x); |
---|
704 | grad(u,y) = central12(A,u,y); |
---|
705 | grad(u,z) = central12(A,u,z); |
---|
706 | grad(v,x) = central12(A,v,x); |
---|
707 | grad(v,y) = central12(A,v,y); |
---|
708 | grad(v,z) = central12(A,v,z); |
---|
709 | grad(w,x) = central12(A,w,x); |
---|
710 | grad(w,y) = central12(A,w,y); |
---|
711 | grad(w,z) = central12(A,w,z); |
---|
712 | |
---|
713 | return grad; |
---|
714 | } |
---|
715 | |
---|
716 | template<typename T> |
---|
717 | inline TinyMatrix<_bz_typename multicomponent_traits<_bz_typename |
---|
718 | T::T_numtype>::T_element, 3, 3> |
---|
719 | Jacobian3Dn(T& A) |
---|
720 | { |
---|
721 | const int x=0, y=1, z=2; |
---|
722 | const int u=0, v=1, w=2; |
---|
723 | |
---|
724 | TinyMatrix<_bz_typename multicomponent_traits<_bz_typename |
---|
725 | T::T_numtype>::T_element, 3, 3> grad; |
---|
726 | |
---|
727 | grad(u,x) = central12n(A,u,x); |
---|
728 | grad(u,y) = central12n(A,u,y); |
---|
729 | grad(u,z) = central12n(A,u,z); |
---|
730 | grad(v,x) = central12n(A,v,x); |
---|
731 | grad(v,y) = central12n(A,v,y); |
---|
732 | grad(v,z) = central12n(A,v,z); |
---|
733 | grad(w,x) = central12n(A,w,x); |
---|
734 | grad(w,y) = central12n(A,w,y); |
---|
735 | grad(w,z) = central12n(A,w,z); |
---|
736 | |
---|
737 | return grad; |
---|
738 | } |
---|
739 | |
---|
740 | template<typename T> |
---|
741 | inline TinyMatrix<_bz_typename multicomponent_traits<_bz_typename |
---|
742 | T::T_numtype>::T_element, 3, 3> |
---|
743 | Jacobian3D4(T& A) |
---|
744 | { |
---|
745 | const int x=0, y=1, z=2; |
---|
746 | const int u=0, v=1, w=2; |
---|
747 | |
---|
748 | TinyMatrix<_bz_typename multicomponent_traits<_bz_typename |
---|
749 | T::T_numtype>::T_element, 3, 3> grad; |
---|
750 | |
---|
751 | grad(u,x) = central14(A,u,x); |
---|
752 | grad(u,y) = central14(A,u,y); |
---|
753 | grad(u,z) = central14(A,u,z); |
---|
754 | grad(v,x) = central14(A,v,x); |
---|
755 | grad(v,y) = central14(A,v,y); |
---|
756 | grad(v,z) = central14(A,v,z); |
---|
757 | grad(w,x) = central14(A,w,x); |
---|
758 | grad(w,y) = central14(A,w,y); |
---|
759 | grad(w,z) = central14(A,w,z); |
---|
760 | |
---|
761 | return grad; |
---|
762 | } |
---|
763 | |
---|
764 | template<typename T> |
---|
765 | inline TinyMatrix<_bz_typename multicomponent_traits<_bz_typename |
---|
766 | T::T_numtype>::T_element, 3, 3> |
---|
767 | Jacobian3D4n(T& A) |
---|
768 | { |
---|
769 | const int x=0, y=1, z=2; |
---|
770 | const int u=0, v=1, w=2; |
---|
771 | |
---|
772 | TinyMatrix<_bz_typename multicomponent_traits<_bz_typename |
---|
773 | T::T_numtype>::T_element, 3, 3> grad; |
---|
774 | |
---|
775 | grad(u,x) = central14n(A,u,x); |
---|
776 | grad(u,y) = central14n(A,u,y); |
---|
777 | grad(u,z) = central14n(A,u,z); |
---|
778 | grad(v,x) = central14n(A,v,x); |
---|
779 | grad(v,y) = central14n(A,v,y); |
---|
780 | grad(v,z) = central14n(A,v,z); |
---|
781 | grad(w,x) = central14n(A,w,x); |
---|
782 | grad(w,y) = central14n(A,w,y); |
---|
783 | grad(w,z) = central14n(A,w,z); |
---|
784 | |
---|
785 | return grad; |
---|
786 | } |
---|
787 | |
---|
788 | /**************************************************************************** |
---|
789 | * Curl operators |
---|
790 | ****************************************************************************/ |
---|
791 | |
---|
792 | // O(h^2) curl, using central difference |
---|
793 | |
---|
794 | template<typename T> |
---|
795 | inline TinyVector<_bz_typename T::T_numtype,3> |
---|
796 | curl(T& vx, T& vy, T& vz) { |
---|
797 | const int x = firstDim, y = secondDim, z = thirdDim; |
---|
798 | |
---|
799 | return TinyVector<_bz_typename T::T_numtype,3>( |
---|
800 | central12(vz,y)-central12(vy,z), |
---|
801 | central12(vx,z)-central12(vz,x), |
---|
802 | central12(vy,x)-central12(vx,y)); |
---|
803 | } |
---|
804 | |
---|
805 | // Normalized O(h^2) curl, using central difference |
---|
806 | template<typename T> |
---|
807 | inline TinyVector<_bz_typename T::T_numtype,3> |
---|
808 | curln(T& vx, T& vy, T& vz) { |
---|
809 | const int x = firstDim, y = secondDim, z = thirdDim; |
---|
810 | |
---|
811 | return TinyVector<_bz_typename T::T_numtype,3>( |
---|
812 | (central12(vz,y)-central12(vy,z)) * recip_2, |
---|
813 | (central12(vx,z)-central12(vz,x)) * recip_2, |
---|
814 | (central12(vy,x)-central12(vx,y)) * recip_2); |
---|
815 | } |
---|
816 | |
---|
817 | // Multicomponent curl |
---|
818 | template<typename T> |
---|
819 | inline _bz_typename T::T_numtype curl(T& A) { |
---|
820 | const int x = firstDim, y = secondDim, z = thirdDim; |
---|
821 | |
---|
822 | return _bz_typename T::T_numtype( |
---|
823 | central12(A,z,y)-central12(A,y,z), |
---|
824 | central12(A,x,z)-central12(A,z,x), |
---|
825 | central12(A,y,x)-central12(A,x,y)); |
---|
826 | } |
---|
827 | |
---|
828 | // Normalized multicomponent curl |
---|
829 | template<typename T> |
---|
830 | inline _bz_typename T::T_numtype curln(T& A) { |
---|
831 | const int x = firstDim, y = secondDim, z = thirdDim; |
---|
832 | |
---|
833 | return _bz_typename T::T_numtype( |
---|
834 | (central12(A,z,y)-central12(A,y,z)) * recip_2, |
---|
835 | (central12(A,x,z)-central12(A,z,x)) * recip_2, |
---|
836 | (central12(A,y,x)-central12(A,x,y)) * recip_2); |
---|
837 | } |
---|
838 | |
---|
839 | // O(h^4) curl, using 4th order central difference |
---|
840 | template<typename T> |
---|
841 | inline TinyVector<_bz_typename T::T_numtype,3> |
---|
842 | curl4(T& vx, T& vy, T& vz) { |
---|
843 | const int x = firstDim, y = secondDim, z = thirdDim; |
---|
844 | |
---|
845 | return TinyVector<_bz_typename T::T_numtype,3>( |
---|
846 | central14(vz,y)-central14(vy,z), |
---|
847 | central14(vx,z)-central14(vz,x), |
---|
848 | central14(vy,x)-central14(vx,y)); |
---|
849 | } |
---|
850 | |
---|
851 | // O(h^4) curl, using 4th order central difference (multicomponent version) |
---|
852 | template<typename T> |
---|
853 | inline _bz_typename T::T_numtype |
---|
854 | curl4(T& A) { |
---|
855 | const int x = firstDim, y = secondDim, z = thirdDim; |
---|
856 | |
---|
857 | return _bz_typename T::T_numtype( |
---|
858 | central14(A,z,y)-central14(A,y,z), |
---|
859 | central14(A,x,z)-central14(A,z,x), |
---|
860 | central14(A,y,x)-central14(A,x,y)); |
---|
861 | } |
---|
862 | |
---|
863 | // Normalized O(h^4) curl, using 4th order central difference |
---|
864 | template<typename T> |
---|
865 | inline TinyVector<_bz_typename T::T_numtype,3> |
---|
866 | curl4n(T& vx, T& vy, T& vz) { |
---|
867 | const int x = firstDim, y = secondDim, z = thirdDim; |
---|
868 | |
---|
869 | return TinyVector<_bz_typename T::T_numtype,3>( |
---|
870 | (central14(vz,y)-central14(vy,z)) * recip_2, |
---|
871 | (central14(vx,z)-central14(vz,x)) * recip_2, |
---|
872 | (central14(vy,x)-central14(vx,y)) * recip_2); |
---|
873 | } |
---|
874 | |
---|
875 | // O(h^4) curl, using 4th order central difference (normalized multicomponent) |
---|
876 | template<typename T> |
---|
877 | inline _bz_typename T::T_numtype |
---|
878 | curl4n(T& A) { |
---|
879 | const int x = firstDim, y = secondDim, z = thirdDim; |
---|
880 | |
---|
881 | return _bz_typename T::T_numtype( |
---|
882 | (central14(A,z,y)-central14(A,y,z)) * recip_2, |
---|
883 | (central14(A,x,z)-central14(A,z,x)) * recip_2, |
---|
884 | (central14(A,y,x)-central14(A,x,y)) * recip_2); |
---|
885 | } |
---|
886 | |
---|
887 | |
---|
888 | |
---|
889 | // Two-dimensional curl |
---|
890 | |
---|
891 | template<typename T> |
---|
892 | inline _bz_typename T::T_numtype |
---|
893 | curl(T& vx, T& vy) { |
---|
894 | const int x = firstDim, y = secondDim; |
---|
895 | |
---|
896 | return central12(vy,x)-central12(vx,y); |
---|
897 | } |
---|
898 | |
---|
899 | template<typename T> |
---|
900 | inline _bz_typename T::T_numtype |
---|
901 | curln(T& vx, T& vy) { |
---|
902 | const int x = firstDim, y = secondDim; |
---|
903 | |
---|
904 | return (central12(vy,x)-central12(vx,y)) * recip_2; |
---|
905 | } |
---|
906 | |
---|
907 | // Multicomponent curl |
---|
908 | template<typename T> |
---|
909 | inline _bz_typename T::T_numtype::T_numtype curl2D(T& A) { |
---|
910 | const int x = firstDim, y = secondDim; |
---|
911 | return central12(A,y,x)-central12(A,x,y); |
---|
912 | } |
---|
913 | |
---|
914 | template<typename T> |
---|
915 | inline _bz_typename T::T_numtype::T_numtype curl2Dn(T& A) { |
---|
916 | const int x = firstDim, y = secondDim; |
---|
917 | return (central12(A,y,x)-central12(A,x,y)) * recip_2; |
---|
918 | } |
---|
919 | |
---|
920 | |
---|
921 | // 4th order versions |
---|
922 | |
---|
923 | template<typename T> |
---|
924 | inline _bz_typename T::T_numtype |
---|
925 | curl4(T& vx, T& vy) { |
---|
926 | const int x = firstDim, y = secondDim; |
---|
927 | |
---|
928 | return central14(vy,x)-central14(vx,y); |
---|
929 | } |
---|
930 | |
---|
931 | template<typename T> |
---|
932 | inline _bz_typename T::T_numtype |
---|
933 | curl4n(T& vx, T& vy) { |
---|
934 | const int x = firstDim, y = secondDim; |
---|
935 | |
---|
936 | return (central14(vy,x)-central14(vx,y)) * recip_12; |
---|
937 | } |
---|
938 | |
---|
939 | // Multicomponent curl |
---|
940 | template<typename T> |
---|
941 | inline _bz_typename T::T_numtype::T_numtype curl2D4(T& A) { |
---|
942 | const int x = firstDim, y = secondDim; |
---|
943 | return central14(A,y,x)-central14(A,x,y); |
---|
944 | } |
---|
945 | |
---|
946 | template<typename T> |
---|
947 | inline _bz_typename T::T_numtype::T_numtype curl2D4n(T& A) { |
---|
948 | const int x = firstDim, y = secondDim; |
---|
949 | return (central14(A,y,x)-central14(A,x,y)) * recip_12; |
---|
950 | } |
---|
951 | |
---|
952 | /**************************************************************************** |
---|
953 | * Divergence |
---|
954 | ****************************************************************************/ |
---|
955 | |
---|
956 | |
---|
957 | BZ_DECLARE_STENCIL_OPERATOR2(div,vx,vy) |
---|
958 | return central12(vx,firstDim) + central12(vy,secondDim); |
---|
959 | BZ_END_STENCIL_OPERATOR |
---|
960 | |
---|
961 | BZ_DECLARE_STENCIL_OPERATOR2(divn,vx,vy) |
---|
962 | return (central12(vx,firstDim) + central12(vy,secondDim)) |
---|
963 | * recip_2; |
---|
964 | BZ_END_STENCIL_OPERATOR |
---|
965 | |
---|
966 | BZ_DECLARE_STENCIL_OPERATOR2(div4,vx,vy) |
---|
967 | return central14(vx,firstDim) + central14(vy,secondDim); |
---|
968 | BZ_END_STENCIL_OPERATOR |
---|
969 | |
---|
970 | BZ_DECLARE_STENCIL_OPERATOR2(div4n,vx,vy) |
---|
971 | return (central14(vx,firstDim) + central14(vy,secondDim)) |
---|
972 | * recip_12; |
---|
973 | BZ_END_STENCIL_OPERATOR |
---|
974 | |
---|
975 | BZ_DECLARE_STENCIL_OPERATOR3(div,vx,vy,vz) |
---|
976 | return central12(vx,firstDim) + central12(vy,secondDim) |
---|
977 | + central12(vz,thirdDim); |
---|
978 | BZ_END_STENCIL_OPERATOR |
---|
979 | |
---|
980 | BZ_DECLARE_STENCIL_OPERATOR3(divn,vx,vy,vz) |
---|
981 | return (central12(vx,firstDim) + central12(vy,secondDim) |
---|
982 | + central12(vz,thirdDim)) * recip_2; |
---|
983 | BZ_END_STENCIL_OPERATOR |
---|
984 | |
---|
985 | BZ_DECLARE_STENCIL_OPERATOR3(div4,vx,vy,vz) |
---|
986 | return central14(vx,firstDim) + central14(vy,secondDim) |
---|
987 | + central14(vz,thirdDim); |
---|
988 | BZ_END_STENCIL_OPERATOR |
---|
989 | |
---|
990 | BZ_DECLARE_STENCIL_OPERATOR3(div4n,vx,vy,vz) |
---|
991 | return (central14(vx,firstDim) + central14(vy,secondDim) |
---|
992 | + central14(vz,thirdDim)) * recip_12; |
---|
993 | BZ_END_STENCIL_OPERATOR |
---|
994 | |
---|
995 | template<typename T> |
---|
996 | inline _bz_typename T::T_numtype::T_numtype |
---|
997 | div2D(T& A) |
---|
998 | { |
---|
999 | const int x = firstDim, y = secondDim; |
---|
1000 | return central12(A,x,x) + central12(A,y,y); |
---|
1001 | } |
---|
1002 | |
---|
1003 | template<typename T> |
---|
1004 | inline _bz_typename T::T_numtype::T_numtype |
---|
1005 | div2D4(T& A) |
---|
1006 | { |
---|
1007 | const int x = firstDim, y = secondDim; |
---|
1008 | return central14(A,x,x) + central14(A,y,y); |
---|
1009 | } |
---|
1010 | |
---|
1011 | template<typename T> |
---|
1012 | inline _bz_typename T::T_numtype::T_numtype |
---|
1013 | div2Dn(T& A) |
---|
1014 | { |
---|
1015 | const int x = firstDim, y = secondDim; |
---|
1016 | return (central12(A,x,x) + central12(A,y,y)) * recip_2; |
---|
1017 | } |
---|
1018 | |
---|
1019 | template<typename T> |
---|
1020 | inline _bz_typename T::T_numtype::T_numtype |
---|
1021 | div2D4n(T& A) |
---|
1022 | { |
---|
1023 | const int x = firstDim, y = secondDim; |
---|
1024 | return (central14(A,x,x) + central14(A,y,y)) * recip_12; |
---|
1025 | } |
---|
1026 | |
---|
1027 | template<typename T> |
---|
1028 | inline _bz_typename T::T_numtype::T_numtype |
---|
1029 | div3D(T& A) |
---|
1030 | { |
---|
1031 | const int x = firstDim, y = secondDim, z = thirdDim; |
---|
1032 | return central12(A,x,x) + central12(A,y,y) + central12(A,z,z); |
---|
1033 | } |
---|
1034 | |
---|
1035 | template<typename T> |
---|
1036 | inline _bz_typename T::T_numtype::T_numtype |
---|
1037 | div3D4(T& A) |
---|
1038 | { |
---|
1039 | const int x = firstDim, y = secondDim, z = thirdDim; |
---|
1040 | return central14(A,x,x) + central14(A,y,y) + central14(A,z,z); |
---|
1041 | } |
---|
1042 | |
---|
1043 | template<typename T> |
---|
1044 | inline _bz_typename T::T_numtype::T_numtype |
---|
1045 | div3Dn(T& A) |
---|
1046 | { |
---|
1047 | const int x = firstDim, y = secondDim, z = thirdDim; |
---|
1048 | return (central12(A,x,x) + central12(A,y,y) + central12(A,z,z)) * recip_2; |
---|
1049 | } |
---|
1050 | |
---|
1051 | template<typename T> |
---|
1052 | inline _bz_typename T::T_numtype::T_numtype |
---|
1053 | div3D4n(T& A) |
---|
1054 | { |
---|
1055 | const int x = firstDim, y = secondDim, z = thirdDim; |
---|
1056 | return (central14(A,x,x) + central14(A,y,y) + central14(A,z,z)) * recip_12; |
---|
1057 | } |
---|
1058 | |
---|
1059 | /**************************************************************************** |
---|
1060 | * Mixed Partial derivatives |
---|
1061 | ****************************************************************************/ |
---|
1062 | |
---|
1063 | template<typename T> |
---|
1064 | inline _bz_typename T::T_numtype |
---|
1065 | mixed22(T& A, int x, int y) |
---|
1066 | { |
---|
1067 | return A.shift(-1,x,-1,y) - A.shift(-1,x,1,y) |
---|
1068 | - A.shift(1,x,-1,y) + A.shift(1,x,1,y); |
---|
1069 | } |
---|
1070 | |
---|
1071 | template<typename T> |
---|
1072 | inline _bz_typename T::T_numtype |
---|
1073 | mixed22n(T& A, int x, int y) |
---|
1074 | { |
---|
1075 | return mixed22(A,x,y) * recip_4; |
---|
1076 | } |
---|
1077 | |
---|
1078 | template<typename T> |
---|
1079 | inline _bz_typename T::T_numtype |
---|
1080 | mixed24(T& A, int x, int y) |
---|
1081 | { |
---|
1082 | return 64.0 * (A.shift(-1,x,-1,y) - A.shift(-1,x,1,y) - |
---|
1083 | A.shift(1,x,-1,y) + A.shift(1,x,1,y)) |
---|
1084 | + (A.shift(-2,x,1,y) - A.shift(-1,x,2,y) - |
---|
1085 | A.shift(1,x,2,y) - A.shift(2,x,1,y) + |
---|
1086 | A.shift(2,x,-1,y) + A.shift(1,x,-2,y) - |
---|
1087 | A.shift(-1,x,-2,y) + A.shift(-2,x,-1,y)) |
---|
1088 | + 8.0 * (A.shift(-1,x,1,y) + A.shift(-1,x,2,y) - |
---|
1089 | A.shift(2,x,-2,y) + A.shift(2,x,2,y)); |
---|
1090 | } |
---|
1091 | |
---|
1092 | template<typename T> |
---|
1093 | inline _bz_typename T::T_numtype |
---|
1094 | mixed24n(T& A, int x, int y) |
---|
1095 | { |
---|
1096 | return mixed24(A,x,y) * recip_144; |
---|
1097 | } |
---|
1098 | |
---|
1099 | /**************************************************************************** |
---|
1100 | * Smoothers |
---|
1101 | ****************************************************************************/ |
---|
1102 | |
---|
1103 | // NEEDS_WORK-- put other stencil operators here: |
---|
1104 | // Average5pt2D |
---|
1105 | // Average7pt3D |
---|
1106 | // etc. |
---|
1107 | |
---|
1108 | /**************************************************************************** |
---|
1109 | * Stencil operators with geometry (experimental) |
---|
1110 | ****************************************************************************/ |
---|
1111 | |
---|
1112 | template<typename T> |
---|
1113 | inline _bz_typename multicomponent_traits<_bz_typename |
---|
1114 | T::T_numtype>::T_element div3DVec4(T& A, |
---|
1115 | const UniformCubicGeometry<3>& geom) |
---|
1116 | { |
---|
1117 | const int x = 0, y = 1, z = 2; |
---|
1118 | |
---|
1119 | return (central14(A, x, firstDim) + central14(A, y, secondDim) |
---|
1120 | + central14(A, z, thirdDim)) * recip_12 * geom.recipSpatialStep(); |
---|
1121 | } |
---|
1122 | |
---|
1123 | template<typename T> |
---|
1124 | inline _bz_typename T::T_numtype Laplacian3D4(T& A, |
---|
1125 | const UniformCubicGeometry<3>& geom) |
---|
1126 | { |
---|
1127 | return Laplacian3D4n(A) * geom.recipSpatialStepPow2(); |
---|
1128 | } |
---|
1129 | |
---|
1130 | template<typename T> |
---|
1131 | inline _bz_typename T::T_numtype Laplacian3DVec4(T& A, |
---|
1132 | const UniformCubicGeometry<3>& geom) |
---|
1133 | { |
---|
1134 | typedef _bz_typename T::T_numtype vector3d; |
---|
1135 | typedef _bz_typename multicomponent_traits<vector3d>::T_element |
---|
1136 | T_element; |
---|
1137 | const int u = 0, v = 1, w = 2; |
---|
1138 | const int x = 0, y = 1, z = 2; |
---|
1139 | |
---|
1140 | // central24 is a 5-point stencil |
---|
1141 | // This is a 9*5 = 45 point stencil |
---|
1142 | |
---|
1143 | T_element t1 = (central24(A,u,x) + central24(A,u,y) + central24(A,u,z)) |
---|
1144 | * recip_12 * geom.recipSpatialStepPow2(); |
---|
1145 | |
---|
1146 | T_element t2 = (central24(A,v,x) + central24(A,v,y) + central24(A,v,z)) |
---|
1147 | * recip_12 * geom.recipSpatialStepPow2(); |
---|
1148 | |
---|
1149 | T_element t3 = (central24(A,w,x) + central24(A,w,y) + central24(A,w,z)) |
---|
1150 | * recip_12 * geom.recipSpatialStepPow2(); |
---|
1151 | |
---|
1152 | return vector3d(t1,t2,t3); |
---|
1153 | } |
---|
1154 | |
---|
1155 | template<typename T> |
---|
1156 | inline TinyMatrix<_bz_typename multicomponent_traits<_bz_typename |
---|
1157 | T::T_numtype>::T_element, 3, 3> |
---|
1158 | grad3DVec4(T& A, const UniformCubicGeometry<3>& geom) |
---|
1159 | { |
---|
1160 | const int x=0, y=1, z=2; |
---|
1161 | const int u=0, v=1, w=2; |
---|
1162 | |
---|
1163 | TinyMatrix<_bz_typename multicomponent_traits<_bz_typename |
---|
1164 | T::T_numtype>::T_element, 3, 3> grad; |
---|
1165 | |
---|
1166 | // This is a 9*4 = 36 point stencil |
---|
1167 | grad(u,x) = central14n(A,u,x) * geom.recipSpatialStep(); |
---|
1168 | grad(u,y) = central14n(A,u,y) * geom.recipSpatialStep(); |
---|
1169 | grad(u,z) = central14n(A,u,z) * geom.recipSpatialStep(); |
---|
1170 | grad(v,x) = central14n(A,v,x) * geom.recipSpatialStep(); |
---|
1171 | grad(v,y) = central14n(A,v,y) * geom.recipSpatialStep(); |
---|
1172 | grad(v,z) = central14n(A,v,z) * geom.recipSpatialStep(); |
---|
1173 | grad(w,x) = central14n(A,w,x) * geom.recipSpatialStep(); |
---|
1174 | grad(w,y) = central14n(A,w,y) * geom.recipSpatialStep(); |
---|
1175 | grad(w,z) = central14n(A,w,z) * geom.recipSpatialStep(); |
---|
1176 | |
---|
1177 | return grad; |
---|
1178 | } |
---|
1179 | |
---|
1180 | template<typename T> |
---|
1181 | inline TinyVector<_bz_typename T::T_numtype,3> grad3D4(T& A, |
---|
1182 | const UniformCubicGeometry<3>& geom) { |
---|
1183 | return TinyVector<_bz_typename T::T_numtype,3>( |
---|
1184 | central14(A,firstDim) * recip_12 * geom.recipSpatialStep(), |
---|
1185 | central14(A,secondDim) * recip_12 * geom.recipSpatialStep(), |
---|
1186 | central14(A,thirdDim) * recip_12 * geom.recipSpatialStep()); |
---|
1187 | } |
---|
1188 | |
---|
1189 | BZ_NAMESPACE_END |
---|
1190 | |
---|
1191 | #endif // BZ_ARRAYSTENCILOPS_H |
---|
1192 | |
---|