1 | // This file is a part of Framsticks SDK. http://www.framsticks.com/ |
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2 | // Copyright (C) 1999-2015 Maciej Komosinski and Szymon Ulatowski. |
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3 | // See LICENSE.txt for details. |
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4 | |
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5 | //////////////////////////////////////////////////////////////////////////////////////// |
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6 | // |
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7 | // IMPORTANT: READ BEFORE DOWNLOADING, COPYING, INSTALLING OR USING. |
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8 | // |
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9 | // By downloading, copying, installing or using the software you agree to this license. |
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10 | // If you do not agree to this license, do not download, install, |
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11 | // copy or use the software. |
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12 | // |
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13 | // |
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14 | // License Agreement |
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15 | // For Open Source Computer Vision Library |
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16 | // |
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17 | // Copyright (C) 2000-2008, Intel Corporation, all rights reserved. |
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18 | // Copyright (C) 2009, Willow Garage Inc., all rights reserved. |
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19 | // Third party copyrights are property of their respective owners. |
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20 | // |
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21 | // Redistribution and use in source and binary forms, with or without modification, |
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22 | // are permitted provided that the following conditions are met: |
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23 | // |
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24 | // * Redistribution's of source code must retain the above copyright notice, |
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25 | // this list of conditions and the following disclaimer. |
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26 | // |
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27 | // * Redistribution's in binary form must reproduce the above copyright notice, |
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28 | // this list of conditions and the following disclaimer in the documentation |
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29 | // and/or other materials provided with the distribution. |
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30 | // |
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31 | // * The name of the copyright holders may not be used to endorse or promote products |
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32 | // derived from this software without specific prior written permission. |
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33 | // |
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34 | // This software is provided by the copyright holders and contributors "as is" and |
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35 | // any express or implied warranties, including, but not limited to, the implied |
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36 | // warranties of merchantability and fitness for a particular purpose are disclaimed. |
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37 | // In no event shall the Intel Corporation or contributors be liable for any direct, |
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38 | // indirect, incidental, special, exemplary, or consequential damages |
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39 | // (including, but not limited to, procurement of substitute goods or services; |
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40 | // loss of use, data, or profits; or business interruption) however caused |
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41 | // and on any theory of liability, whether in contract, strict liability, |
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42 | // or tort (including negligence or otherwise) arising in any way out of |
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43 | // the use of this software, even if advised of the possibility of such damage. |
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44 | // |
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45 | // |
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46 | /* |
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47 | * AutoBuffer from https://github.com/Itseez/opencv/blob/master/modules/core/include/opencv2/core/utility.hpp |
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48 | * VBLAS, JacobiSVDImpl_ from https://github.com/Itseez/opencv/blob/master/modules/core/src/lapack.cpp |
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49 | * changes MK, May 2015: |
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50 | * - "RNG rng(0x12345678)" and "rng.next()" replaced with a local PRBS-7 implementation so that this file does not depend on external random number generators. |
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51 | */ |
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52 | #include <cstdlib> |
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53 | #include <algorithm> |
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54 | #include <cmath> |
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55 | #include <limits> |
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56 | #include <cfloat> |
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57 | //#include <assert.h> |
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58 | #include <math.h> //hypot(), embarcadero |
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59 | #include <stdint.h> //uint8_t |
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60 | #include "lapack.h" |
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61 | |
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62 | |
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63 | #if defined _M_IX86 && defined _MSC_VER && _MSC_VER < 1700 |
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64 | #pragma float_control(precise, on) |
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65 | #endif |
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66 | |
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67 | template<typename _Tp, size_t fixed_size = 1024 / sizeof(_Tp) + 8 > class AutoBuffer |
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68 | { |
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69 | public: |
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70 | typedef _Tp value_type; |
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71 | |
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72 | //! the default constructor |
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73 | AutoBuffer(); |
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74 | //! constructor taking the real buffer size |
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75 | AutoBuffer(size_t _size); |
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76 | |
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77 | //! the copy constructor |
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78 | AutoBuffer(const AutoBuffer<_Tp, fixed_size>& buf); |
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79 | //! the assignment operator |
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80 | AutoBuffer<_Tp, fixed_size>& operator=(const AutoBuffer<_Tp, fixed_size>& buf); |
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81 | |
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82 | //! destructor. calls deallocate() |
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83 | ~AutoBuffer(); |
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84 | |
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85 | //! allocates the new buffer of size _size. if the _size is small enough, stack-allocated buffer is used |
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86 | void allocate(size_t _size); |
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87 | //! deallocates the buffer if it was dynamically allocated |
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88 | void deallocate(); |
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89 | //! resizes the buffer and preserves the content |
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90 | void resize(size_t _size); |
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91 | //! returns the current buffer size |
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92 | size_t size() const; |
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93 | //! returns pointer to the real buffer, stack-allocated or head-allocated |
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94 | operator _Tp* (); |
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95 | //! returns read-only pointer to the real buffer, stack-allocated or head-allocated |
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96 | operator const _Tp* () const; |
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97 | |
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98 | protected: |
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99 | //! pointer to the real buffer, can point to buf if the buffer is small enough |
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100 | _Tp* ptr; |
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101 | //! size of the real buffer |
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102 | size_t sz; |
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103 | //! pre-allocated buffer. At least 1 element to confirm C++ standard reqirements |
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104 | _Tp buf[(fixed_size > 0) ? fixed_size : 1]; |
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105 | }; |
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106 | |
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107 | /////////////////////////////// AutoBuffer implementation //////////////////////////////////////// |
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108 | |
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109 | template<typename _Tp, size_t fixed_size> inline |
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110 | AutoBuffer<_Tp, fixed_size>::AutoBuffer() |
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111 | { |
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112 | ptr = buf; |
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113 | sz = fixed_size; |
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114 | } |
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115 | |
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116 | template<typename _Tp, size_t fixed_size> inline |
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117 | AutoBuffer<_Tp, fixed_size>::AutoBuffer(size_t _size) |
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118 | { |
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119 | ptr = buf; |
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120 | sz = fixed_size; |
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121 | allocate(_size); |
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122 | } |
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123 | |
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124 | template<typename _Tp, size_t fixed_size> inline |
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125 | AutoBuffer<_Tp, fixed_size>::AutoBuffer(const AutoBuffer<_Tp, fixed_size>& abuf) |
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126 | { |
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127 | ptr = buf; |
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128 | sz = fixed_size; |
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129 | allocate(abuf.size()); |
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130 | for (size_t i = 0; i < sz; i++) |
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131 | ptr[i] = abuf.ptr[i]; |
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132 | } |
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133 | |
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134 | template<typename _Tp, size_t fixed_size> inline AutoBuffer<_Tp, fixed_size>& |
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135 | AutoBuffer<_Tp, fixed_size>::operator=(const AutoBuffer<_Tp, fixed_size>& abuf) |
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136 | { |
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137 | if (this != &abuf) |
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138 | { |
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139 | deallocate(); |
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140 | allocate(abuf.size()); |
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141 | for (size_t i = 0; i < sz; i++) |
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142 | ptr[i] = abuf.ptr[i]; |
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143 | } |
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144 | return *this; |
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145 | } |
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146 | |
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147 | template<typename _Tp, size_t fixed_size> inline |
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148 | AutoBuffer<_Tp, fixed_size>::~AutoBuffer() |
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149 | { |
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150 | deallocate(); |
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151 | } |
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152 | |
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153 | template<typename _Tp, size_t fixed_size> inline void |
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154 | AutoBuffer<_Tp, fixed_size>::allocate(size_t _size) |
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155 | { |
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156 | if (_size <= sz) |
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157 | { |
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158 | sz = _size; |
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159 | return; |
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160 | } |
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161 | deallocate(); |
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162 | if (_size > fixed_size) |
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163 | { |
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164 | ptr = new _Tp[_size]; |
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165 | sz = _size; |
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166 | } |
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167 | } |
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168 | |
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169 | template<typename _Tp, size_t fixed_size> inline void |
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170 | AutoBuffer<_Tp, fixed_size>::deallocate() |
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171 | { |
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172 | if (ptr != buf) |
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173 | { |
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174 | delete[] ptr; |
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175 | ptr = buf; |
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176 | sz = fixed_size; |
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177 | } |
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178 | } |
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179 | |
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180 | template<typename _Tp, size_t fixed_size> inline void |
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181 | AutoBuffer<_Tp, fixed_size>::resize(size_t _size) |
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182 | { |
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183 | if (_size <= sz) |
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184 | { |
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185 | sz = _size; |
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186 | return; |
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187 | } |
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188 | //size_t i, prevsize = sz, minsize = MIN(prevsize, _size); |
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189 | size_t i, prevsize = sz, minsize = prevsize < _size ? prevsize : _size; |
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190 | _Tp* prevptr = ptr; |
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191 | |
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192 | ptr = _size > fixed_size ? new _Tp[_size] : buf; |
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193 | sz = _size; |
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194 | |
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195 | if (ptr != prevptr) |
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196 | for (i = 0; i < minsize; i++) |
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197 | ptr[i] = prevptr[i]; |
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198 | for (i = prevsize; i < _size; i++) |
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199 | ptr[i] = _Tp(); |
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200 | |
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201 | if (prevptr != buf) |
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202 | delete[] prevptr; |
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203 | } |
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204 | |
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205 | template<typename _Tp, size_t fixed_size> inline size_t |
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206 | AutoBuffer<_Tp, fixed_size>::size() const |
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207 | { |
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208 | return sz; |
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209 | } |
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210 | |
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211 | template<typename _Tp, size_t fixed_size> inline |
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212 | AutoBuffer<_Tp, fixed_size>::operator _Tp* () |
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213 | { |
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214 | return ptr; |
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215 | } |
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216 | |
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217 | template<typename _Tp, size_t fixed_size> inline |
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218 | AutoBuffer<_Tp, fixed_size>::operator const _Tp* () const |
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219 | { |
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220 | return ptr; |
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221 | } |
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222 | |
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223 | template<typename T> struct VBLAS |
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224 | { |
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225 | |
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226 | int dot(const T*, const T*, int, T*) const |
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227 | { |
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228 | return 0; |
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229 | } |
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230 | |
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231 | int givens(T*, T*, int, T, T) const |
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232 | { |
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233 | return 0; |
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234 | } |
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235 | |
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236 | int givensx(T*, T*, int, T, T, T*, T*) const |
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237 | { |
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238 | return 0; |
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239 | } |
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240 | }; |
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241 | |
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242 | template<typename _Tp> void |
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243 | JacobiSVDImpl_(_Tp* At, size_t astep, _Tp* _W, _Tp* Vt, size_t vstep, |
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244 | int m, int n, int n1, double minval, _Tp eps) |
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245 | { |
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246 | VBLAS<_Tp> vblas; |
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247 | AutoBuffer<double> Wbuf(n); |
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248 | double* W = Wbuf; |
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249 | int i, j, k, iter, max_iter = std::max(m, 30); |
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250 | _Tp c, s; |
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251 | double sd; |
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252 | astep /= sizeof(At[0]); |
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253 | vstep /= sizeof(Vt[0]); |
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254 | |
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255 | for (i = 0; i < n; i++) |
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256 | { |
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257 | for (k = 0, sd = 0; k < m; k++) |
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258 | { |
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259 | _Tp t = At[i * astep + k]; |
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260 | sd += (double)t*t; |
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261 | } |
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262 | W[i] = sd; |
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263 | |
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264 | if (Vt) |
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265 | { |
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266 | for (k = 0; k < n; k++) |
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267 | Vt[i * vstep + k] = 0; |
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268 | Vt[i * vstep + i] = 1; |
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269 | } |
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270 | } |
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271 | |
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272 | for (iter = 0; iter < max_iter; iter++) |
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273 | { |
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274 | bool changed = false; |
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275 | |
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276 | for (i = 0; i < n - 1; i++) |
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277 | for (j = i + 1; j < n; j++) |
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278 | { |
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279 | _Tp *Ai = At + i*astep, *Aj = At + j*astep; |
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280 | double a = W[i], p = 0, b = W[j]; |
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281 | |
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282 | for (k = 0; k < m; k++) |
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283 | p += (double)Ai[k] * Aj[k]; |
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284 | |
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285 | if (std::abs(p) <= eps * std::sqrt((double)a * b)) |
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286 | continue; |
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287 | |
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288 | p *= 2; |
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289 | double beta = a - b, gamma = hypot((double)p, beta); |
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290 | if (beta < 0) |
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291 | { |
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292 | double delta = (gamma - beta)*0.5; |
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293 | s = (_Tp)std::sqrt(delta / gamma); |
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294 | c = (_Tp)(p / (gamma * s * 2)); |
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295 | } |
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296 | else |
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297 | { |
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298 | c = (_Tp)std::sqrt((gamma + beta) / (gamma * 2)); |
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299 | s = (_Tp)(p / (gamma * c * 2)); |
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300 | } |
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301 | |
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302 | a = b = 0; |
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303 | for (k = 0; k < m; k++) |
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304 | { |
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305 | _Tp t0 = c * Ai[k] + s * Aj[k]; |
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306 | _Tp t1 = -s * Ai[k] + c * Aj[k]; |
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307 | Ai[k] = t0; |
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308 | Aj[k] = t1; |
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309 | |
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310 | a += (double)t0*t0; |
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311 | b += (double)t1*t1; |
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312 | } |
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313 | W[i] = a; |
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314 | W[j] = b; |
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315 | |
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316 | changed = true; |
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317 | |
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318 | if (Vt) |
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319 | { |
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320 | _Tp *Vi = Vt + i*vstep, *Vj = Vt + j*vstep; |
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321 | k = vblas.givens(Vi, Vj, n, c, s); |
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322 | |
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323 | for (; k < n; k++) |
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324 | { |
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325 | _Tp t0 = c * Vi[k] + s * Vj[k]; |
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326 | _Tp t1 = -s * Vi[k] + c * Vj[k]; |
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327 | Vi[k] = t0; |
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328 | Vj[k] = t1; |
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329 | } |
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330 | } |
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331 | } |
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332 | if (!changed) |
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333 | break; |
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334 | } |
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335 | |
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336 | for (i = 0; i < n; i++) |
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337 | { |
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338 | for (k = 0, sd = 0; k < m; k++) |
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339 | { |
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340 | _Tp t = At[i * astep + k]; |
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341 | sd += (double)t*t; |
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342 | } |
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343 | W[i] = std::sqrt(sd); |
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344 | } |
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345 | |
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346 | for (i = 0; i < n - 1; i++) |
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347 | { |
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348 | j = i; |
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349 | for (k = i + 1; k < n; k++) |
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350 | { |
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351 | if (W[j] < W[k]) |
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352 | j = k; |
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353 | } |
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354 | if (i != j) |
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355 | { |
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356 | std::swap(W[i], W[j]); |
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357 | if (Vt) |
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358 | { |
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359 | for (k = 0; k < m; k++) |
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360 | std::swap(At[i * astep + k], At[j * astep + k]); |
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361 | |
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362 | for (k = 0; k < n; k++) |
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363 | std::swap(Vt[i * vstep + k], Vt[j * vstep + k]); |
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364 | } |
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365 | } |
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366 | } |
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367 | |
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368 | for (i = 0; i < n; i++) |
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369 | _W[i] = (_Tp)W[i]; |
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370 | |
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371 | if (!Vt) |
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372 | return; |
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373 | |
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374 | uint8_t rndstate = 0x02; //PRBS-7 from http://en.wikipedia.org/wiki/Pseudorandom_binary_sequence |
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375 | for (i = 0; i < n1; i++) |
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376 | { |
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377 | sd = i < n ? W[i] : 0; |
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378 | |
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379 | while (sd <= minval) |
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380 | { |
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381 | // if we got a zero singular value, then in order to get the corresponding left singular vector |
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382 | // we generate a random vector, project it to the previously computed left singular vectors, |
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383 | // subtract the projection and normalize the difference. |
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384 | const _Tp val0 = (_Tp)(1. / m); |
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385 | for (k = 0; k < m; k++) |
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386 | { |
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387 | int rndbit = (((rndstate >> 6) ^ (rndstate >> 5)) & 1); |
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388 | rndstate = ((rndstate << 1) | rndbit) & 0x7f; |
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389 | _Tp val = rndbit == 0 ? val0 : -val0; |
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390 | At[i * astep + k] = val; |
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391 | } |
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392 | for (iter = 0; iter < 2; iter++) |
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393 | { |
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394 | for (j = 0; j < i; j++) |
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395 | { |
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396 | sd = 0; |
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397 | for (k = 0; k < m; k++) |
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398 | sd += At[i * astep + k] * At[j * astep + k]; |
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399 | _Tp asum = 0; |
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400 | for (k = 0; k < m; k++) |
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401 | { |
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402 | _Tp t = (_Tp)(At[i * astep + k] - sd * At[j * astep + k]); |
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403 | At[i * astep + k] = t; |
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404 | asum += std::abs(t); |
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405 | } |
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406 | asum = asum ? 1 / asum : 0; |
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407 | for (k = 0; k < m; k++) |
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408 | At[i * astep + k] *= asum; |
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409 | } |
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410 | } |
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411 | sd = 0; |
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412 | for (k = 0; k < m; k++) |
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413 | { |
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414 | _Tp t = At[i * astep + k]; |
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415 | sd += (double)t*t; |
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416 | } |
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417 | sd = std::sqrt(sd); |
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418 | } |
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419 | |
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420 | s = (_Tp)(1 / sd); |
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421 | for (k = 0; k < m; k++) |
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422 | At[i * astep + k] *= s; |
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423 | } |
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424 | } |
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425 | |
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426 | void Lapack::JacobiSVD(double* At, size_t astep, double* W, double* Vt, size_t vstep, int m, int n, int n1 = -1) |
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427 | { |
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428 | JacobiSVDImpl_(At, astep, W, Vt, vstep, m, n, !Vt ? 0 : n1 < 0 ? n : n1, DBL_MIN, DBL_EPSILON * 10); |
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429 | } |
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