1 | /// \ingroup newmat |
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2 | ///@{ |
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3 | |
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4 | /// \file sort.cpp |
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5 | /// Sorting functions. |
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6 | |
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7 | // Copyright (C) 1991,2,3,4: R B Davies |
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8 | |
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9 | #define WANT_MATH |
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10 | |
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11 | #include "include.h" |
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12 | |
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13 | #include "newmatap.h" |
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14 | |
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15 | #ifdef use_namespace |
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16 | namespace NEWMAT { |
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17 | #endif |
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18 | |
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19 | #ifdef DO_REPORT |
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20 | #define REPORT { static ExeCounter ExeCount(__LINE__,13); ++ExeCount; } |
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21 | #else |
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22 | #define REPORT {} |
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23 | #endif |
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24 | |
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25 | /******************************** Quick sort ********************************/ |
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26 | |
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27 | // Quicksort. |
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28 | // Essentially the method described in Sedgewick s algorithms in C++ |
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29 | // My version is still partially recursive, unlike Segewick s, but the |
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30 | // smallest segment of each split is used in the recursion, so it should |
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31 | // not overlead the stack. |
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32 | |
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33 | // If the process does not seems to be converging an exception is thrown. |
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34 | |
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35 | |
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36 | #define DoSimpleSort 17 // when to switch to insert sort |
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37 | #define MaxDepth 50 // maximum recursion depth |
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38 | |
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39 | static void MyQuickSortDescending(Real* first, Real* last, int depth); |
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40 | static void InsertionSortDescending(Real* first, const int length, |
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41 | int guard); |
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42 | static Real SortThreeDescending(Real* a, Real* b, Real* c); |
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43 | |
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44 | static void MyQuickSortAscending(Real* first, Real* last, int depth); |
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45 | static void InsertionSortAscending(Real* first, const int length, |
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46 | int guard); |
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47 | |
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48 | |
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49 | void sort_descending(GeneralMatrix& GM) |
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50 | { |
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51 | REPORT |
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52 | Tracer et("sort_descending"); |
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53 | |
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54 | Real* data = GM.Store(); int max = GM.Storage(); |
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55 | |
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56 | if (max > DoSimpleSort) MyQuickSortDescending(data, data + max - 1, 0); |
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57 | InsertionSortDescending(data, max, DoSimpleSort); |
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58 | |
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59 | } |
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60 | |
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61 | static Real SortThreeDescending(Real* a, Real* b, Real* c) |
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62 | { |
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63 | // sort *a, *b, *c; return *b; optimise for already sorted |
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64 | if (*a >= *b) |
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65 | { |
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66 | if (*b >= *c) { REPORT return *b; } |
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67 | else if (*a >= *c) { REPORT Real x = *c; *c = *b; *b = x; return x; } |
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68 | else { REPORT Real x = *a; *a = *c; *c = *b; *b = x; return x; } |
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69 | } |
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70 | else if (*c >= *b) { REPORT Real x = *c; *c = *a; *a = x; return *b; } |
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71 | else if (*a >= *c) { REPORT Real x = *a; *a = *b; *b = x; return x; } |
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72 | else { REPORT Real x = *c; *c = *a; *a = *b; *b = x; return x; } |
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73 | } |
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74 | |
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75 | static void InsertionSortDescending(Real* first, const int length, |
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76 | int guard) |
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77 | // guard gives the length of the sequence to scan to find first |
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78 | // element (eg = length) |
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79 | { |
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80 | REPORT |
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81 | if (length <= 1) return; |
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82 | |
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83 | // scan for first element |
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84 | Real* f = first; Real v = *f; Real* h = f; |
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85 | if (guard > length) { REPORT guard = length; } |
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86 | int i = guard - 1; |
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87 | while (i--) if (v < *(++f)) { v = *f; h = f; } |
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88 | *h = *first; *first = v; |
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89 | |
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90 | // do the sort |
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91 | i = length - 1; f = first; |
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92 | while (i--) |
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93 | { |
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94 | Real* g = f++; h = f; v = *h; |
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95 | while (*g < v) *h-- = *g--; |
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96 | *h = v; |
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97 | } |
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98 | } |
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99 | |
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100 | static void MyQuickSortDescending(Real* first, Real* last, int depth) |
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101 | { |
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102 | REPORT |
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103 | for (;;) |
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104 | { |
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105 | const int length = last - first + 1; |
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106 | if (length < DoSimpleSort) { REPORT return; } |
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107 | if (depth++ > MaxDepth) |
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108 | Throw(ConvergenceException("QuickSortDescending fails: ")); |
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109 | Real* centre = first + length/2; |
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110 | const Real test = SortThreeDescending(first, centre, last); |
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111 | Real* f = first; Real* l = last; |
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112 | for (;;) |
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113 | { |
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114 | while (*(++f) > test) {} |
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115 | while (*(--l) < test) {} |
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116 | if (l <= f) break; |
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117 | const Real temp = *f; *f = *l; *l = temp; |
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118 | } |
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119 | if (f > centre) |
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120 | { REPORT MyQuickSortDescending(l+1, last, depth); last = f-1; } |
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121 | else { REPORT MyQuickSortDescending(first, f-1, depth); first = l+1; } |
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122 | } |
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123 | } |
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124 | |
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125 | void sort_ascending(GeneralMatrix& GM) |
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126 | { |
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127 | REPORT |
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128 | Tracer et("sort_ascending"); |
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129 | |
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130 | Real* data = GM.Store(); int max = GM.Storage(); |
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131 | |
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132 | if (max > DoSimpleSort) MyQuickSortAscending(data, data + max - 1, 0); |
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133 | InsertionSortAscending(data, max, DoSimpleSort); |
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134 | |
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135 | } |
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136 | |
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137 | static void InsertionSortAscending(Real* first, const int length, |
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138 | int guard) |
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139 | // guard gives the length of the sequence to scan to find first |
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140 | // element (eg guard = length) |
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141 | { |
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142 | REPORT |
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143 | if (length <= 1) return; |
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144 | |
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145 | // scan for first element |
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146 | Real* f = first; Real v = *f; Real* h = f; |
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147 | if (guard > length) { REPORT guard = length; } |
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148 | int i = guard - 1; |
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149 | while (i--) if (v > *(++f)) { v = *f; h = f; } |
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150 | *h = *first; *first = v; |
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151 | |
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152 | // do the sort |
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153 | i = length - 1; f = first; |
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154 | while (i--) |
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155 | { |
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156 | Real* g = f++; h = f; v = *h; |
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157 | while (*g > v) *h-- = *g--; |
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158 | *h = v; |
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159 | } |
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160 | } |
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161 | static void MyQuickSortAscending(Real* first, Real* last, int depth) |
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162 | { |
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163 | REPORT |
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164 | for (;;) |
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165 | { |
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166 | const int length = last - first + 1; |
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167 | if (length < DoSimpleSort) { REPORT return; } |
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168 | if (depth++ > MaxDepth) |
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169 | Throw(ConvergenceException("QuickSortAscending fails: ")); |
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170 | Real* centre = first + length/2; |
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171 | const Real test = SortThreeDescending(last, centre, first); |
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172 | Real* f = first; Real* l = last; |
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173 | for (;;) |
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174 | { |
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175 | while (*(++f) < test) {} |
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176 | while (*(--l) > test) {} |
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177 | if (l <= f) break; |
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178 | const Real temp = *f; *f = *l; *l = temp; |
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179 | } |
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180 | if (f > centre) |
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181 | { REPORT MyQuickSortAscending(l+1, last, depth); last = f-1; } |
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182 | else { REPORT MyQuickSortAscending(first, f-1, depth); first = l+1; } |
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183 | } |
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184 | } |
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185 | |
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186 | //********* sort diagonal matrix & rearrange matrix columns **************** |
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187 | |
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188 | // used by SVD |
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189 | |
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190 | // these are for sorting singular values - should be updated with faster |
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191 | // sorts that handle exchange of columns better |
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192 | // however time is probably not significant compared with SVD time |
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193 | |
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194 | void SortSV(DiagonalMatrix& D, Matrix& U, bool ascending) |
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195 | { |
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196 | REPORT |
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197 | Tracer trace("SortSV_DU"); |
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198 | int m = U.Nrows(); int n = U.Ncols(); |
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199 | if (n != D.Nrows()) Throw(IncompatibleDimensionsException(D,U)); |
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200 | Real* u = U.Store(); |
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201 | for (int i=0; i<n; i++) |
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202 | { |
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203 | int k = i; Real p = D.element(i); |
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204 | if (ascending) |
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205 | { |
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206 | for (int j=i+1; j<n; j++) |
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207 | { if (D.element(j) < p) { k = j; p = D.element(j); } } |
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208 | } |
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209 | else |
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210 | { |
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211 | for (int j=i+1; j<n; j++) |
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212 | { if (D.element(j) > p) { k = j; p = D.element(j); } } |
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213 | } |
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214 | if (k != i) |
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215 | { |
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216 | D.element(k) = D.element(i); D.element(i) = p; int j = m; |
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217 | Real* uji = u + i; Real* ujk = u + k; |
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218 | if (j) for(;;) |
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219 | { |
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220 | p = *uji; *uji = *ujk; *ujk = p; |
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221 | if (!(--j)) break; |
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222 | uji += n; ujk += n; |
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223 | } |
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224 | } |
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225 | } |
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226 | } |
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227 | |
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228 | void SortSV(DiagonalMatrix& D, Matrix& U, Matrix& V, bool ascending) |
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229 | { |
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230 | REPORT |
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231 | Tracer trace("SortSV_DUV"); |
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232 | int mu = U.Nrows(); int mv = V.Nrows(); int n = D.Nrows(); |
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233 | if (n != U.Ncols()) Throw(IncompatibleDimensionsException(D,U)); |
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234 | if (n != V.Ncols()) Throw(IncompatibleDimensionsException(D,V)); |
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235 | Real* u = U.Store(); Real* v = V.Store(); |
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236 | for (int i=0; i<n; i++) |
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237 | { |
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238 | int k = i; Real p = D.element(i); |
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239 | if (ascending) |
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240 | { |
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241 | for (int j=i+1; j<n; j++) |
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242 | { if (D.element(j) < p) { k = j; p = D.element(j); } } |
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243 | } |
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244 | else |
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245 | { |
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246 | for (int j=i+1; j<n; j++) |
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247 | { if (D.element(j) > p) { k = j; p = D.element(j); } } |
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248 | } |
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249 | if (k != i) |
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250 | { |
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251 | D.element(k) = D.element(i); D.element(i) = p; |
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252 | Real* uji = u + i; Real* ujk = u + k; |
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253 | Real* vji = v + i; Real* vjk = v + k; |
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254 | int j = mu; |
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255 | if (j) for(;;) |
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256 | { |
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257 | p = *uji; *uji = *ujk; *ujk = p; if (!(--j)) break; |
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258 | uji += n; ujk += n; |
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259 | } |
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260 | j = mv; |
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261 | if (j) for(;;) |
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262 | { |
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263 | p = *vji; *vji = *vjk; *vjk = p; if (!(--j)) break; |
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264 | vji += n; vjk += n; |
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265 | } |
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266 | } |
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267 | } |
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268 | } |
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269 | |
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270 | |
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271 | |
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272 | |
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273 | #ifdef use_namespace |
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274 | } |
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275 | #endif |
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276 | |
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277 | ///@} |
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