1 | /// \ingroup newmat |
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2 | ///@{ |
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3 | |
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4 | /// \file hholder.cpp |
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5 | /// QR related decompositions |
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6 | /// QRZ, QRZT decompositions |
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7 | /// QR update and extend orthogonal functions |
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8 | |
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9 | // Copyright (C) 1991,2,3,4: R B Davies |
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10 | |
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11 | #define WANT_MATH |
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12 | //#define WANT_STREAM |
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13 | |
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14 | #include "include.h" |
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15 | |
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16 | #include "newmatap.h" |
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17 | |
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18 | #ifdef use_namespace |
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19 | namespace NEWMAT { |
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20 | #endif |
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21 | |
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22 | #ifdef DO_REPORT |
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23 | #define REPORT { static ExeCounter ExeCount(__LINE__,16); ++ExeCount; } |
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24 | #else |
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25 | #define REPORT {} |
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26 | #endif |
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27 | |
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28 | |
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29 | /*************************** QR decompositions ***************************/ |
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30 | |
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31 | inline Real square(Real x) { return x*x; } |
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32 | |
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33 | void QRZT(Matrix& X, LowerTriangularMatrix& L) |
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34 | { |
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35 | REPORT |
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36 | Tracer et("QRZT(1)"); |
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37 | int n = X.Ncols(); int s = X.Nrows(); L.resize(s); |
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38 | if (n == 0 || s == 0) { L = 0.0; return; } |
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39 | Real* xi = X.Store(); int k; |
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40 | for (int i=0; i<s; i++) |
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41 | { |
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42 | Real sum = 0.0; |
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43 | Real* xi0=xi; k=n; while(k--) { sum += square(*xi++); } |
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44 | sum = sqrt(sum); |
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45 | if (sum == 0.0) |
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46 | { |
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47 | REPORT |
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48 | k=n; while(k--) { *xi0++ = 0.0; } |
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49 | for (int j=i; j<s; j++) L.element(j,i) = 0.0; |
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50 | } |
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51 | else |
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52 | { |
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53 | L.element(i,i) = sum; |
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54 | Real* xj0=xi0; k=n; while(k--) { *xj0++ /= sum; } |
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55 | for (int j=i+1; j<s; j++) |
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56 | { |
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57 | sum=0.0; |
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58 | xi=xi0; Real* xj=xj0; k=n; while(k--) { sum += *xi++ * *xj++; } |
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59 | xi=xi0; k=n; while(k--) { *xj0++ -= sum * *xi++; } |
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60 | L.element(j,i) = sum; |
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61 | } |
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62 | } |
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63 | } |
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64 | } |
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65 | |
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66 | void QRZT(const Matrix& X, Matrix& Y, Matrix& M) |
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67 | { |
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68 | REPORT |
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69 | Tracer et("QRZT(2)"); |
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70 | int n = X.Ncols(); int s = X.Nrows(); int t = Y.Nrows(); |
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71 | if (Y.Ncols() != n) |
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72 | { Throw(ProgramException("Unequal row lengths",X,Y)); } |
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73 | M.resize(t,s); |
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74 | Real* xi = X.Store(); int k; |
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75 | for (int i=0; i<s; i++) |
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76 | { |
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77 | Real* xj0 = Y.Store(); Real* xi0 = xi; |
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78 | for (int j=0; j<t; j++) |
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79 | { |
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80 | Real sum=0.0; |
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81 | xi=xi0; Real* xj=xj0; k=n; while(k--) { sum += *xi++ * *xj++; } |
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82 | xi=xi0; k=n; while(k--) { *xj0++ -= sum * *xi++; } |
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83 | M.element(j,i) = sum; |
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84 | } |
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85 | } |
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86 | } |
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87 | |
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88 | /* |
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89 | void QRZ(Matrix& X, UpperTriangularMatrix& U) |
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90 | { |
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91 | Tracer et("QRZ(1)"); |
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92 | int n = X.Nrows(); int s = X.Ncols(); U.resize(s); |
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93 | Real* xi0 = X.Store(); int k; |
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94 | for (int i=0; i<s; i++) |
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95 | { |
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96 | Real sum = 0.0; |
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97 | Real* xi = xi0; k=n; while(k--) { sum += square(*xi); xi+=s; } |
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98 | sum = sqrt(sum); |
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99 | U.element(i,i) = sum; |
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100 | if (sum==0.0) Throw(SingularException(U)); |
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101 | Real* xj0=xi0; k=n; while(k--) { *xj0 /= sum; xj0+=s; } |
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102 | xj0 = xi0; |
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103 | for (int j=i+1; j<s; j++) |
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104 | { |
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105 | sum=0.0; |
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106 | xi=xi0; k=n; xj0++; Real* xj=xj0; |
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107 | while(k--) { sum += *xi * *xj; xi+=s; xj+=s; } |
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108 | xi=xi0; k=n; xj=xj0; |
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109 | while(k--) { *xj -= sum * *xi; xj+=s; xi+=s; } |
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110 | U.element(i,j) = sum; |
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111 | } |
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112 | xi0++; |
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113 | } |
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114 | } |
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115 | */ |
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116 | |
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117 | void QRZ(Matrix& X, UpperTriangularMatrix& U) |
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118 | { |
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119 | REPORT |
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120 | Tracer et("QRZ(1)"); |
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121 | int n = X.Nrows(); int s = X.Ncols(); U.resize(s); U = 0.0; |
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122 | if (n == 0 || s == 0) return; |
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123 | Real* xi0 = X.Store(); Real* u0 = U.Store(); Real* u; |
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124 | int j, k; int J = s; int i = s; |
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125 | while (i--) |
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126 | { |
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127 | Real* xj0 = xi0; Real* xi = xi0; k = n; |
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128 | if (k) for (;;) |
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129 | { |
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130 | u = u0; Real Xi = *xi; Real* xj = xj0; |
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131 | j = J; while(j--) *u++ += Xi * *xj++; |
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132 | if (!(--k)) break; |
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133 | xi += s; xj0 += s; |
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134 | } |
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135 | |
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136 | Real sum = sqrt(*u0); *u0 = sum; u = u0+1; |
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137 | if (sum == 0.0) |
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138 | { |
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139 | REPORT |
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140 | j = J - 1; while(j--) *u++ = 0.0; |
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141 | |
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142 | xj0 = xi0++; k = n; |
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143 | if (k) for (;;) |
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144 | { |
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145 | *xj0 = 0.0; |
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146 | if (!(--k)) break; |
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147 | xj0 += s; |
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148 | } |
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149 | u0 += J--; |
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150 | } |
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151 | else |
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152 | { |
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153 | int J1 = J-1; j = J1; while(j--) *u++ /= sum; |
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154 | |
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155 | xj0 = xi0; xi = xi0++; k = n; |
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156 | if (k) for (;;) |
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157 | { |
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158 | u = u0+1; Real Xi = *xi; Real* xj = xj0; |
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159 | Xi /= sum; *xj++ = Xi; |
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160 | j = J1; while(j--) *xj++ -= *u++ * Xi; |
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161 | if (!(--k)) break; |
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162 | xi += s; xj0 += s; |
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163 | } |
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164 | u0 += J--; |
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165 | } |
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166 | } |
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167 | } |
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168 | |
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169 | void QRZ(const Matrix& X, Matrix& Y, Matrix& M) |
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170 | { |
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171 | REPORT |
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172 | Tracer et("QRZ(2)"); |
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173 | int n = X.Nrows(); int s = X.Ncols(); int t = Y.Ncols(); |
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174 | if (Y.Nrows() != n) |
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175 | { Throw(ProgramException("Unequal column lengths",X,Y)); } |
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176 | M.resize(s,t); M = 0;Real* m0 = M.Store(); Real* m; |
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177 | Real* xi0 = X.Store(); |
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178 | int j, k; int i = s; |
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179 | while (i--) |
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180 | { |
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181 | Real* xj0 = Y.Store(); Real* xi = xi0; k = n; |
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182 | if (k) for (;;) |
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183 | { |
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184 | m = m0; Real Xi = *xi; Real* xj = xj0; |
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185 | j = t; while(j--) *m++ += Xi * *xj++; |
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186 | if (!(--k)) break; |
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187 | xi += s; xj0 += t; |
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188 | } |
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189 | |
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190 | xj0 = Y.Store(); xi = xi0++; k = n; |
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191 | if (k) for (;;) |
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192 | { |
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193 | m = m0; Real Xi = *xi; Real* xj = xj0; |
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194 | j = t; while(j--) *xj++ -= *m++ * Xi; |
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195 | if (!(--k)) break; |
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196 | xi += s; xj0 += t; |
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197 | } |
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198 | m0 += t; |
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199 | } |
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200 | } |
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201 | |
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202 | /* |
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203 | |
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204 | void QRZ(const Matrix& X, Matrix& Y, Matrix& M) |
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205 | { |
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206 | Tracer et("QRZ(2)"); |
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207 | int n = X.Nrows(); int s = X.Ncols(); int t = Y.Ncols(); |
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208 | if (Y.Nrows() != n) |
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209 | { Throw(ProgramException("Unequal column lengths",X,Y)); } |
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210 | M.resize(s,t); |
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211 | Real* xi0 = X.Store(); int k; |
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212 | for (int i=0; i<s; i++) |
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213 | { |
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214 | Real* xj0 = Y.Store(); |
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215 | for (int j=0; j<t; j++) |
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216 | { |
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217 | Real sum=0.0; |
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218 | Real* xi=xi0; Real* xj=xj0; k=n; |
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219 | while(k--) { sum += *xi * *xj; xi+=s; xj+=t; } |
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220 | xi=xi0; k=n; xj=xj0++; |
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221 | while(k--) { *xj -= sum * *xi; xj+=t; xi+=s; } |
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222 | M.element(i,j) = sum; |
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223 | } |
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224 | xi0++; |
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225 | } |
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226 | } |
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227 | */ |
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228 | |
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229 | void updateQRZT(Matrix& X, LowerTriangularMatrix& L) |
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230 | { |
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231 | REPORT |
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232 | Tracer et("updateQRZT"); |
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233 | int n = X.Ncols(); int s = X.Nrows(); |
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234 | if (s != L.Nrows()) |
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235 | Throw(ProgramException("Incompatible dimensions",X,L)); |
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236 | if (n == 0 || s == 0) return; |
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237 | Real* xi = X.Store(); int k; |
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238 | for (int i=0; i<s; i++) |
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239 | { |
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240 | Real r = L.element(i,i); |
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241 | Real sum = 0.0; |
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242 | Real* xi0=xi; k=n; while(k--) { sum += square(*xi++); } |
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243 | sum = sqrt(sum + square(r)); |
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244 | if (sum == 0.0) |
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245 | { |
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246 | REPORT |
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247 | k=n; while(k--) { *xi0++ = 0.0; } |
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248 | for (int j=i; j<s; j++) L.element(j,i) = 0.0; |
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249 | } |
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250 | else |
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251 | { |
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252 | Real frs = fabs(r) + sum; |
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253 | Real a0 = sqrt(frs / sum); Real alpha = a0 / frs; |
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254 | if (r <= 0) { REPORT L.element(i,i) = sum; alpha = -alpha; } |
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255 | else { REPORT L.element(i,i) = -sum; } |
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256 | Real* xj0=xi0; k=n; while(k--) { *xj0++ *= alpha; } |
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257 | for (int j=i+1; j<s; j++) |
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258 | { |
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259 | sum = 0.0; |
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260 | xi=xi0; Real* xj=xj0; k=n; while(k--) { sum += *xi++ * *xj++; } |
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261 | sum += a0 * L.element(j,i); |
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262 | xi=xi0; k=n; while(k--) { *xj0++ -= sum * *xi++; } |
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263 | L.element(j,i) -= sum * a0; |
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264 | } |
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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 | void updateQRZ(Matrix& X, UpperTriangularMatrix& U) |
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270 | { |
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271 | REPORT |
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272 | Tracer et("updateQRZ"); |
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273 | int n = X.Nrows(); int s = X.Ncols(); |
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274 | if (s != U.Ncols()) |
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275 | Throw(ProgramException("Incompatible dimensions",X,U)); |
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276 | if (n == 0 || s == 0) return; |
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277 | Real* xi0 = X.Store(); Real* u0 = U.Store(); Real* u; |
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278 | RowVector V(s); Real* v0 = V.Store(); Real* v; V = 0.0; |
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279 | int j, k; int J = s; int i = s; |
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280 | while (i--) |
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281 | { |
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282 | Real* xj0 = xi0; Real* xi = xi0; k = n; |
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283 | if (k) for (;;) |
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284 | { |
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285 | v = v0; Real Xi = *xi; Real* xj = xj0; |
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286 | j = J; while(j--) *v++ += Xi * *xj++; |
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287 | if (!(--k)) break; |
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288 | xi += s; xj0 += s; |
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289 | } |
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290 | |
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291 | Real r = *u0; |
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292 | Real sum = sqrt(*v0 + square(r)); |
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293 | |
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294 | if (sum == 0.0) |
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295 | { |
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296 | REPORT |
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297 | u = u0; v = v0; |
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298 | j = J; while(j--) { *u++ = 0.0; *v++ = 0.0; } |
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299 | xj0 = xi0++; k = n; |
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300 | if (k) for (;;) |
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301 | { |
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302 | *xj0 = 0.0; |
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303 | if (!(--k)) break; |
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304 | xj0 += s; |
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305 | } |
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306 | u0 += J--; |
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307 | } |
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308 | else |
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309 | { |
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310 | Real frs = fabs(r) + sum; |
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311 | Real a0 = sqrt(frs / sum); Real alpha = a0 / frs; |
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312 | if (r <= 0) { REPORT alpha = -alpha; *u0 = sum; } |
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313 | else { REPORT *u0 = -sum; } |
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314 | |
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315 | j = J - 1; v = v0 + 1; u = u0 + 1; |
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316 | while (j--) |
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317 | { *v = a0 * *u + alpha * *v; *u -= a0 * *v; ++v; ++u; } |
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318 | |
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319 | xj0 = xi0; xi = xi0++; k = n; |
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320 | if (k) for (;;) |
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321 | { |
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322 | v = v0 + 1; Real Xi = *xi; Real* xj = xj0; |
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323 | Xi *= alpha; *xj++ = Xi; |
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324 | j = J - 1; while(j--) *xj++ -= *v++ * Xi; |
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325 | if (!(--k)) break; |
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326 | xi += s; xj0 += s; |
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327 | } |
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328 | |
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329 | j = J; v = v0; |
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330 | while (j--) *v++ = 0.0; |
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331 | |
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332 | u0 += J--; |
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333 | } |
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334 | } |
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335 | } |
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336 | |
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337 | // Matrix A's first n columns are orthonormal |
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338 | // so A.Columns(1,n).t() * A.Columns(1,n) is the identity matrix. |
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339 | // Fill out the remaining columns of A to make them orthonormal |
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340 | // so A.t() * A is the identity matrix |
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341 | void extend_orthonormal(Matrix& A, int n) |
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342 | { |
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343 | REPORT |
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344 | Tracer et("extend_orthonormal"); |
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345 | int nr = A.nrows(); int nc = A.ncols(); |
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346 | if (nc > nr) Throw(IncompatibleDimensionsException(A)); |
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347 | if (n > nc) Throw(IncompatibleDimensionsException(A)); |
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348 | ColumnVector SSR; |
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349 | { Matrix A1 = A.Columns(1,n); SSR = A1.sum_square_rows(); } |
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350 | for (int i = n; i < nc; ++i) |
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351 | { |
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352 | // pick row with smallest SSQ |
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353 | int k; SSR.minimum1(k); |
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354 | // orthogonalise column with 1 at element k, 0 elsewhere |
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355 | // next line is rather inefficient |
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356 | ColumnVector X = - A.Columns(1, i) * A.SubMatrix(k, k, 1, i).t(); |
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357 | X(k) += 1.0; |
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358 | // normalise |
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359 | X /= sqrt(X.SumSquare()); |
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360 | // update row sums of squares |
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361 | for (k = 1; k <= nr; ++k) SSR(k) += square(X(k)); |
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362 | // load new column into matrix |
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363 | A.Column(i+1) = X; |
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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 | |
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369 | |
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370 | |
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371 | #ifdef use_namespace |
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372 | } |
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373 | #endif |
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374 | |
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375 | |
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376 | ///@} |
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