1 | /************************************************************************* |
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2 | Copyright (c) 1992-2007 The University of Tennessee. All rights reserved. |
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3 | |
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4 | Contributors: |
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5 | * Sergey Bochkanov (ALGLIB project). Translation from FORTRAN to |
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6 | pseudocode. |
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7 | |
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8 | See subroutines comments for additional copyrights. |
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9 | |
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10 | Redistribution and use in source and binary forms, with or without |
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11 | modification, are permitted provided that the following conditions are |
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12 | met: |
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13 | |
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14 | - Redistributions of source code must retain the above copyright |
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15 | notice, this list of conditions and the following disclaimer. |
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16 | |
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17 | - Redistributions in binary form must reproduce the above copyright |
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18 | notice, this list of conditions and the following disclaimer listed |
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19 | in this license in the documentation and/or other materials |
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20 | provided with the distribution. |
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21 | |
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22 | - Neither the name of the copyright holders nor the names of its |
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23 | contributors may be used to endorse or promote products derived from |
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24 | this software without specific prior written permission. |
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25 | |
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26 | THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS |
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27 | "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT |
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28 | LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR |
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29 | A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT |
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30 | OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, |
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31 | SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT |
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32 | LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, |
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33 | DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY |
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34 | THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT |
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35 | (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE |
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36 | OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. |
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37 | *************************************************************************/ |
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38 | |
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39 | #ifndef _rotations_h |
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40 | #define _rotations_h |
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41 | |
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42 | #include "ap.h" |
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43 | #include "amp.h" |
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44 | namespace rotations |
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45 | { |
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46 | template<unsigned int Precision> |
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47 | void applyrotationsfromtheleft(bool isforward, |
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48 | int m1, |
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49 | int m2, |
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50 | int n1, |
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51 | int n2, |
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52 | const ap::template_1d_array< amp::ampf<Precision> >& c, |
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53 | const ap::template_1d_array< amp::ampf<Precision> >& s, |
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54 | ap::template_2d_array< amp::ampf<Precision> >& a, |
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55 | ap::template_1d_array< amp::ampf<Precision> >& work); |
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56 | template<unsigned int Precision> |
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57 | void applyrotationsfromtheright(bool isforward, |
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58 | int m1, |
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59 | int m2, |
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60 | int n1, |
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61 | int n2, |
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62 | const ap::template_1d_array< amp::ampf<Precision> >& c, |
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63 | const ap::template_1d_array< amp::ampf<Precision> >& s, |
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64 | ap::template_2d_array< amp::ampf<Precision> >& a, |
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65 | ap::template_1d_array< amp::ampf<Precision> >& work); |
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66 | template<unsigned int Precision> |
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67 | void generaterotation(amp::ampf<Precision> f, |
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68 | amp::ampf<Precision> g, |
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69 | amp::ampf<Precision>& cs, |
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70 | amp::ampf<Precision>& sn, |
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71 | amp::ampf<Precision>& r); |
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72 | |
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73 | |
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74 | /************************************************************************* |
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75 | Application of a sequence of elementary rotations to a matrix |
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76 | |
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77 | The algorithm pre-multiplies the matrix by a sequence of rotation |
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78 | transformations which is given by arrays C and S. Depending on the value |
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79 | of the IsForward parameter either 1 and 2, 3 and 4 and so on (if IsForward=true) |
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80 | rows are rotated, or the rows N and N-1, N-2 and N-3 and so on, are rotated. |
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81 | |
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82 | Not the whole matrix but only a part of it is transformed (rows from M1 to |
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83 | M2, columns from N1 to N2). Only the elements of this submatrix are changed. |
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84 | |
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85 | Input parameters: |
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86 | IsForward - the sequence of the rotation application. |
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87 | M1,M2 - the range of rows to be transformed. |
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88 | N1, N2 - the range of columns to be transformed. |
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89 | C,S - transformation coefficients. |
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90 | Array whose index ranges within [1..M2-M1]. |
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91 | A - processed matrix. |
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92 | WORK - working array whose index ranges within [N1..N2]. |
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93 | |
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94 | Output parameters: |
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95 | A - transformed matrix. |
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96 | |
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97 | Utility subroutine. |
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98 | *************************************************************************/ |
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99 | template<unsigned int Precision> |
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100 | void applyrotationsfromtheleft(bool isforward, |
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101 | int m1, |
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102 | int m2, |
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103 | int n1, |
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104 | int n2, |
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105 | const ap::template_1d_array< amp::ampf<Precision> >& c, |
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106 | const ap::template_1d_array< amp::ampf<Precision> >& s, |
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107 | ap::template_2d_array< amp::ampf<Precision> >& a, |
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108 | ap::template_1d_array< amp::ampf<Precision> >& work) |
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109 | { |
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110 | int j; |
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111 | int jp1; |
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112 | amp::ampf<Precision> ctemp; |
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113 | amp::ampf<Precision> stemp; |
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114 | amp::ampf<Precision> temp; |
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115 | |
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116 | |
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117 | if( m1>m2 || n1>n2 ) |
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118 | { |
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119 | return; |
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120 | } |
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121 | |
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122 | // |
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123 | // Form P * A |
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124 | // |
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125 | if( isforward ) |
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126 | { |
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127 | if( n1!=n2 ) |
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128 | { |
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129 | |
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130 | // |
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131 | // Common case: N1<>N2 |
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132 | // |
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133 | for(j=m1; j<=m2-1; j++) |
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134 | { |
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135 | ctemp = c(j-m1+1); |
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136 | stemp = s(j-m1+1); |
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137 | if( ctemp!=1 || stemp!=0 ) |
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138 | { |
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139 | jp1 = j+1; |
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140 | ap::vmove(work.getvector(n1, n2), a.getrow(jp1, n1, n2), ctemp); |
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141 | ap::vsub(work.getvector(n1, n2), a.getrow(j, n1, n2), stemp); |
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142 | ap::vmul(a.getrow(j, n1, n2), ctemp); |
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143 | ap::vadd(a.getrow(j, n1, n2), a.getrow(jp1, n1, n2), stemp); |
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144 | ap::vmove(a.getrow(jp1, n1, n2), work.getvector(n1, n2)); |
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145 | } |
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146 | } |
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147 | } |
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148 | else |
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149 | { |
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150 | |
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151 | // |
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152 | // Special case: N1=N2 |
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153 | // |
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154 | for(j=m1; j<=m2-1; j++) |
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155 | { |
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156 | ctemp = c(j-m1+1); |
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157 | stemp = s(j-m1+1); |
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158 | if( ctemp!=1 || stemp!=0 ) |
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159 | { |
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160 | temp = a(j+1,n1); |
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161 | a(j+1,n1) = ctemp*temp-stemp*a(j,n1); |
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162 | a(j,n1) = stemp*temp+ctemp*a(j,n1); |
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163 | } |
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164 | } |
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165 | } |
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166 | } |
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167 | else |
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168 | { |
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169 | if( n1!=n2 ) |
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170 | { |
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171 | |
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172 | // |
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173 | // Common case: N1<>N2 |
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174 | // |
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175 | for(j=m2-1; j>=m1; j--) |
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176 | { |
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177 | ctemp = c(j-m1+1); |
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178 | stemp = s(j-m1+1); |
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179 | if( ctemp!=1 || stemp!=0 ) |
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180 | { |
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181 | jp1 = j+1; |
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182 | ap::vmove(work.getvector(n1, n2), a.getrow(jp1, n1, n2), ctemp); |
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183 | ap::vsub(work.getvector(n1, n2), a.getrow(j, n1, n2), stemp); |
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184 | ap::vmul(a.getrow(j, n1, n2), ctemp); |
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185 | ap::vadd(a.getrow(j, n1, n2), a.getrow(jp1, n1, n2), stemp); |
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186 | ap::vmove(a.getrow(jp1, n1, n2), work.getvector(n1, n2)); |
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187 | } |
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188 | } |
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189 | } |
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190 | else |
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191 | { |
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192 | |
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193 | // |
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194 | // Special case: N1=N2 |
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195 | // |
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196 | for(j=m2-1; j>=m1; j--) |
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197 | { |
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198 | ctemp = c(j-m1+1); |
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199 | stemp = s(j-m1+1); |
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200 | if( ctemp!=1 || stemp!=0 ) |
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201 | { |
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202 | temp = a(j+1,n1); |
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203 | a(j+1,n1) = ctemp*temp-stemp*a(j,n1); |
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204 | a(j,n1) = stemp*temp+ctemp*a(j,n1); |
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205 | } |
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206 | } |
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207 | } |
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208 | } |
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209 | } |
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210 | |
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211 | |
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212 | /************************************************************************* |
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213 | Application of a sequence of elementary rotations to a matrix |
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214 | |
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215 | The algorithm post-multiplies the matrix by a sequence of rotation |
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216 | transformations which is given by arrays C and S. Depending on the value |
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217 | of the IsForward parameter either 1 and 2, 3 and 4 and so on (if IsForward=true) |
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218 | rows are rotated, or the rows N and N-1, N-2 and N-3 and so on are rotated. |
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219 | |
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220 | Not the whole matrix but only a part of it is transformed (rows from M1 |
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221 | to M2, columns from N1 to N2). Only the elements of this submatrix are changed. |
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222 | |
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223 | Input parameters: |
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224 | IsForward - the sequence of the rotation application. |
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225 | M1,M2 - the range of rows to be transformed. |
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226 | N1, N2 - the range of columns to be transformed. |
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227 | C,S - transformation coefficients. |
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228 | Array whose index ranges within [1..N2-N1]. |
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229 | A - processed matrix. |
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230 | WORK - working array whose index ranges within [M1..M2]. |
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231 | |
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232 | Output parameters: |
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233 | A - transformed matrix. |
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234 | |
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235 | Utility subroutine. |
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236 | *************************************************************************/ |
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237 | template<unsigned int Precision> |
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238 | void applyrotationsfromtheright(bool isforward, |
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239 | int m1, |
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240 | int m2, |
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241 | int n1, |
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242 | int n2, |
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243 | const ap::template_1d_array< amp::ampf<Precision> >& c, |
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244 | const ap::template_1d_array< amp::ampf<Precision> >& s, |
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245 | ap::template_2d_array< amp::ampf<Precision> >& a, |
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246 | ap::template_1d_array< amp::ampf<Precision> >& work) |
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247 | { |
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248 | int j; |
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249 | int jp1; |
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250 | amp::ampf<Precision> ctemp; |
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251 | amp::ampf<Precision> stemp; |
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252 | amp::ampf<Precision> temp; |
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253 | |
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254 | |
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255 | |
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256 | // |
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257 | // Form A * P' |
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258 | // |
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259 | if( isforward ) |
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260 | { |
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261 | if( m1!=m2 ) |
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262 | { |
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263 | |
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264 | // |
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265 | // Common case: M1<>M2 |
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266 | // |
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267 | for(j=n1; j<=n2-1; j++) |
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268 | { |
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269 | ctemp = c(j-n1+1); |
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270 | stemp = s(j-n1+1); |
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271 | if( ctemp!=1 || stemp!=0 ) |
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272 | { |
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273 | jp1 = j+1; |
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274 | ap::vmove(work.getvector(m1, m2), a.getcolumn(jp1, m1, m2), ctemp); |
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275 | ap::vsub(work.getvector(m1, m2), a.getcolumn(j, m1, m2), stemp); |
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276 | ap::vmul(a.getcolumn(j, m1, m2), ctemp); |
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277 | ap::vadd(a.getcolumn(j, m1, m2), a.getcolumn(jp1, m1, m2), stemp); |
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278 | ap::vmove(a.getcolumn(jp1, m1, m2), work.getvector(m1, m2)); |
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279 | } |
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280 | } |
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281 | } |
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282 | else |
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283 | { |
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284 | |
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285 | // |
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286 | // Special case: M1=M2 |
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287 | // |
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288 | for(j=n1; j<=n2-1; j++) |
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289 | { |
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290 | ctemp = c(j-n1+1); |
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291 | stemp = s(j-n1+1); |
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292 | if( ctemp!=1 || stemp!=0 ) |
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293 | { |
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294 | temp = a(m1,j+1); |
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295 | a(m1,j+1) = ctemp*temp-stemp*a(m1,j); |
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296 | a(m1,j) = stemp*temp+ctemp*a(m1,j); |
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297 | } |
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298 | } |
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299 | } |
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300 | } |
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301 | else |
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302 | { |
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303 | if( m1!=m2 ) |
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304 | { |
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305 | |
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306 | // |
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307 | // Common case: M1<>M2 |
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308 | // |
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309 | for(j=n2-1; j>=n1; j--) |
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310 | { |
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311 | ctemp = c(j-n1+1); |
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312 | stemp = s(j-n1+1); |
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313 | if( ctemp!=1 || stemp!=0 ) |
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314 | { |
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315 | jp1 = j+1; |
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316 | ap::vmove(work.getvector(m1, m2), a.getcolumn(jp1, m1, m2), ctemp); |
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317 | ap::vsub(work.getvector(m1, m2), a.getcolumn(j, m1, m2), stemp); |
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318 | ap::vmul(a.getcolumn(j, m1, m2), ctemp); |
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319 | ap::vadd(a.getcolumn(j, m1, m2), a.getcolumn(jp1, m1, m2), stemp); |
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320 | ap::vmove(a.getcolumn(jp1, m1, m2), work.getvector(m1, m2)); |
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321 | } |
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322 | } |
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323 | } |
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324 | else |
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325 | { |
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326 | |
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327 | // |
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328 | // Special case: M1=M2 |
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329 | // |
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330 | for(j=n2-1; j>=n1; j--) |
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331 | { |
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332 | ctemp = c(j-n1+1); |
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333 | stemp = s(j-n1+1); |
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334 | if( ctemp!=1 || stemp!=0 ) |
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335 | { |
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336 | temp = a(m1,j+1); |
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337 | a(m1,j+1) = ctemp*temp-stemp*a(m1,j); |
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338 | a(m1,j) = stemp*temp+ctemp*a(m1,j); |
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339 | } |
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340 | } |
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341 | } |
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342 | } |
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343 | } |
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344 | |
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345 | |
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346 | /************************************************************************* |
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347 | The subroutine generates the elementary rotation, so that: |
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348 | |
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349 | [ CS SN ] . [ F ] = [ R ] |
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350 | [ -SN CS ] [ G ] [ 0 ] |
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351 | |
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352 | CS**2 + SN**2 = 1 |
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353 | *************************************************************************/ |
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354 | template<unsigned int Precision> |
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355 | void generaterotation(amp::ampf<Precision> f, |
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356 | amp::ampf<Precision> g, |
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357 | amp::ampf<Precision>& cs, |
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358 | amp::ampf<Precision>& sn, |
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359 | amp::ampf<Precision>& r) |
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360 | { |
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361 | amp::ampf<Precision> f1; |
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362 | amp::ampf<Precision> g1; |
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363 | |
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364 | |
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365 | if( g==0 ) |
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366 | { |
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367 | cs = 1; |
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368 | sn = 0; |
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369 | r = f; |
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370 | } |
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371 | else |
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372 | { |
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373 | if( f==0 ) |
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374 | { |
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375 | cs = 0; |
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376 | sn = 1; |
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377 | r = g; |
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378 | } |
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379 | else |
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380 | { |
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381 | f1 = f; |
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382 | g1 = g; |
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383 | r = amp::sqrt<Precision>(amp::sqr<Precision>(f1)+amp::sqr<Precision>(g1)); |
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384 | cs = f1/r; |
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385 | sn = g1/r; |
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386 | if( amp::abs<Precision>(f)>amp::abs<Precision>(g) && cs<0 ) |
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387 | { |
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388 | cs = -cs; |
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389 | sn = -sn; |
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390 | r = -r; |
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391 | } |
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392 | } |
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393 | } |
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394 | } |
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395 | } // namespace |
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396 | |
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397 | #endif |
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