1 | /* generated code, do not edit. */ |
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2 | |
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3 | #include "ode/matrix.h" |
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4 | |
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5 | /* solve L*X=B, with B containing 1 right hand sides. |
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6 | * L is an n*n lower triangular matrix with ones on the diagonal. |
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7 | * L is stored by rows and its leading dimension is lskip. |
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8 | * B is an n*1 matrix that contains the right hand sides. |
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9 | * B is stored by columns and its leading dimension is also lskip. |
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10 | * B is overwritten with X. |
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11 | * this processes blocks of 2*2. |
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12 | * if this is in the factorizer source file, n must be a multiple of 2. |
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13 | */ |
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14 | |
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15 | static void dSolveL1_1 (const dReal *L, dReal *B, int n, int lskip1) |
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16 | { |
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17 | /* declare variables - Z matrix, p and q vectors, etc */ |
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18 | dReal Z11,m11,Z21,m21,p1,q1,p2,*ex; |
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19 | const dReal *ell; |
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20 | int i,j; |
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21 | /* compute all 2 x 1 blocks of X */ |
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22 | for (i=0; i < n; i+=2) { |
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23 | /* compute all 2 x 1 block of X, from rows i..i+2-1 */ |
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24 | /* set the Z matrix to 0 */ |
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25 | Z11=0; |
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26 | Z21=0; |
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27 | ell = L + i*lskip1; |
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28 | ex = B; |
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29 | /* the inner loop that computes outer products and adds them to Z */ |
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30 | for (j=i-2; j >= 0; j -= 2) { |
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31 | /* compute outer product and add it to the Z matrix */ |
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32 | p1=ell[0]; |
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33 | q1=ex[0]; |
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34 | m11 = p1 * q1; |
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35 | p2=ell[lskip1]; |
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36 | m21 = p2 * q1; |
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37 | Z11 += m11; |
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38 | Z21 += m21; |
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39 | /* compute outer product and add it to the Z matrix */ |
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40 | p1=ell[1]; |
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41 | q1=ex[1]; |
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42 | m11 = p1 * q1; |
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43 | p2=ell[1+lskip1]; |
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44 | m21 = p2 * q1; |
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45 | /* advance pointers */ |
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46 | ell += 2; |
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47 | ex += 2; |
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48 | Z11 += m11; |
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49 | Z21 += m21; |
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50 | /* end of inner loop */ |
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51 | } |
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52 | /* compute left-over iterations */ |
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53 | j += 2; |
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54 | for (; j > 0; j--) { |
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55 | /* compute outer product and add it to the Z matrix */ |
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56 | p1=ell[0]; |
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57 | q1=ex[0]; |
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58 | m11 = p1 * q1; |
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59 | p2=ell[lskip1]; |
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60 | m21 = p2 * q1; |
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61 | /* advance pointers */ |
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62 | ell += 1; |
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63 | ex += 1; |
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64 | Z11 += m11; |
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65 | Z21 += m21; |
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66 | } |
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67 | /* finish computing the X(i) block */ |
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68 | Z11 = ex[0] - Z11; |
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69 | ex[0] = Z11; |
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70 | p1 = ell[lskip1]; |
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71 | Z21 = ex[1] - Z21 - p1*Z11; |
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72 | ex[1] = Z21; |
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73 | /* end of outer loop */ |
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74 | } |
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75 | } |
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76 | |
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77 | /* solve L*X=B, with B containing 2 right hand sides. |
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78 | * L is an n*n lower triangular matrix with ones on the diagonal. |
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79 | * L is stored by rows and its leading dimension is lskip. |
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80 | * B is an n*2 matrix that contains the right hand sides. |
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81 | * B is stored by columns and its leading dimension is also lskip. |
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82 | * B is overwritten with X. |
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83 | * this processes blocks of 2*2. |
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84 | * if this is in the factorizer source file, n must be a multiple of 2. |
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85 | */ |
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86 | |
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87 | static void dSolveL1_2 (const dReal *L, dReal *B, int n, int lskip1) |
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88 | { |
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89 | /* declare variables - Z matrix, p and q vectors, etc */ |
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90 | dReal Z11,m11,Z12,m12,Z21,m21,Z22,m22,p1,q1,p2,q2,*ex; |
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91 | const dReal *ell; |
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92 | int i,j; |
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93 | /* compute all 2 x 2 blocks of X */ |
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94 | for (i=0; i < n; i+=2) { |
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95 | /* compute all 2 x 2 block of X, from rows i..i+2-1 */ |
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96 | /* set the Z matrix to 0 */ |
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97 | Z11=0; |
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98 | Z12=0; |
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99 | Z21=0; |
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100 | Z22=0; |
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101 | ell = L + i*lskip1; |
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102 | ex = B; |
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103 | /* the inner loop that computes outer products and adds them to Z */ |
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104 | for (j=i-2; j >= 0; j -= 2) { |
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105 | /* compute outer product and add it to the Z matrix */ |
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106 | p1=ell[0]; |
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107 | q1=ex[0]; |
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108 | m11 = p1 * q1; |
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109 | q2=ex[lskip1]; |
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110 | m12 = p1 * q2; |
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111 | p2=ell[lskip1]; |
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112 | m21 = p2 * q1; |
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113 | m22 = p2 * q2; |
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114 | Z11 += m11; |
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115 | Z12 += m12; |
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116 | Z21 += m21; |
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117 | Z22 += m22; |
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118 | /* compute outer product and add it to the Z matrix */ |
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119 | p1=ell[1]; |
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120 | q1=ex[1]; |
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121 | m11 = p1 * q1; |
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122 | q2=ex[1+lskip1]; |
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123 | m12 = p1 * q2; |
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124 | p2=ell[1+lskip1]; |
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125 | m21 = p2 * q1; |
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126 | m22 = p2 * q2; |
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127 | /* advance pointers */ |
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128 | ell += 2; |
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129 | ex += 2; |
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130 | Z11 += m11; |
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131 | Z12 += m12; |
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132 | Z21 += m21; |
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133 | Z22 += m22; |
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134 | /* end of inner loop */ |
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135 | } |
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136 | /* compute left-over iterations */ |
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137 | j += 2; |
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138 | for (; j > 0; j--) { |
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139 | /* compute outer product and add it to the Z matrix */ |
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140 | p1=ell[0]; |
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141 | q1=ex[0]; |
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142 | m11 = p1 * q1; |
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143 | q2=ex[lskip1]; |
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144 | m12 = p1 * q2; |
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145 | p2=ell[lskip1]; |
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146 | m21 = p2 * q1; |
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147 | m22 = p2 * q2; |
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148 | /* advance pointers */ |
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149 | ell += 1; |
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150 | ex += 1; |
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151 | Z11 += m11; |
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152 | Z12 += m12; |
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153 | Z21 += m21; |
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154 | Z22 += m22; |
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155 | } |
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156 | /* finish computing the X(i) block */ |
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157 | Z11 = ex[0] - Z11; |
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158 | ex[0] = Z11; |
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159 | Z12 = ex[lskip1] - Z12; |
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160 | ex[lskip1] = Z12; |
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161 | p1 = ell[lskip1]; |
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162 | Z21 = ex[1] - Z21 - p1*Z11; |
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163 | ex[1] = Z21; |
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164 | Z22 = ex[1+lskip1] - Z22 - p1*Z12; |
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165 | ex[1+lskip1] = Z22; |
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166 | /* end of outer loop */ |
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167 | } |
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168 | } |
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169 | |
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170 | |
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171 | void dFactorLDLT (dReal *A, dReal *d, int n, int nskip1) |
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172 | { |
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173 | int i,j; |
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174 | dReal sum,*ell,*dee,dd,p1,p2,q1,q2,Z11,m11,Z21,m21,Z22,m22; |
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175 | if (n < 1) return; |
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176 | |
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177 | for (i=0; i<=n-2; i += 2) { |
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178 | /* solve L*(D*l)=a, l is scaled elements in 2 x i block at A(i,0) */ |
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179 | dSolveL1_2 (A,A+i*nskip1,i,nskip1); |
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180 | /* scale the elements in a 2 x i block at A(i,0), and also */ |
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181 | /* compute Z = the outer product matrix that we'll need. */ |
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182 | Z11 = 0; |
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183 | Z21 = 0; |
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184 | Z22 = 0; |
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185 | ell = A+i*nskip1; |
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186 | dee = d; |
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187 | for (j=i-6; j >= 0; j -= 6) { |
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188 | p1 = ell[0]; |
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189 | p2 = ell[nskip1]; |
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190 | dd = dee[0]; |
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191 | q1 = p1*dd; |
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192 | q2 = p2*dd; |
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193 | ell[0] = q1; |
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194 | ell[nskip1] = q2; |
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195 | m11 = p1*q1; |
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196 | m21 = p2*q1; |
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197 | m22 = p2*q2; |
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198 | Z11 += m11; |
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199 | Z21 += m21; |
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200 | Z22 += m22; |
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201 | p1 = ell[1]; |
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202 | p2 = ell[1+nskip1]; |
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203 | dd = dee[1]; |
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204 | q1 = p1*dd; |
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205 | q2 = p2*dd; |
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206 | ell[1] = q1; |
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207 | ell[1+nskip1] = q2; |
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208 | m11 = p1*q1; |
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209 | m21 = p2*q1; |
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210 | m22 = p2*q2; |
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211 | Z11 += m11; |
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212 | Z21 += m21; |
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213 | Z22 += m22; |
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214 | p1 = ell[2]; |
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215 | p2 = ell[2+nskip1]; |
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216 | dd = dee[2]; |
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217 | q1 = p1*dd; |
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218 | q2 = p2*dd; |
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219 | ell[2] = q1; |
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220 | ell[2+nskip1] = q2; |
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221 | m11 = p1*q1; |
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222 | m21 = p2*q1; |
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223 | m22 = p2*q2; |
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224 | Z11 += m11; |
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225 | Z21 += m21; |
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226 | Z22 += m22; |
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227 | p1 = ell[3]; |
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228 | p2 = ell[3+nskip1]; |
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229 | dd = dee[3]; |
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230 | q1 = p1*dd; |
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231 | q2 = p2*dd; |
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232 | ell[3] = q1; |
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233 | ell[3+nskip1] = q2; |
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234 | m11 = p1*q1; |
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235 | m21 = p2*q1; |
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236 | m22 = p2*q2; |
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237 | Z11 += m11; |
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238 | Z21 += m21; |
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239 | Z22 += m22; |
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240 | p1 = ell[4]; |
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241 | p2 = ell[4+nskip1]; |
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242 | dd = dee[4]; |
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243 | q1 = p1*dd; |
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244 | q2 = p2*dd; |
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245 | ell[4] = q1; |
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246 | ell[4+nskip1] = q2; |
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247 | m11 = p1*q1; |
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248 | m21 = p2*q1; |
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249 | m22 = p2*q2; |
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250 | Z11 += m11; |
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251 | Z21 += m21; |
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252 | Z22 += m22; |
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253 | p1 = ell[5]; |
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254 | p2 = ell[5+nskip1]; |
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255 | dd = dee[5]; |
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256 | q1 = p1*dd; |
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257 | q2 = p2*dd; |
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258 | ell[5] = q1; |
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259 | ell[5+nskip1] = q2; |
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260 | m11 = p1*q1; |
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261 | m21 = p2*q1; |
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262 | m22 = p2*q2; |
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263 | Z11 += m11; |
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264 | Z21 += m21; |
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265 | Z22 += m22; |
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266 | ell += 6; |
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267 | dee += 6; |
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268 | } |
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269 | /* compute left-over iterations */ |
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270 | j += 6; |
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271 | for (; j > 0; j--) { |
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272 | p1 = ell[0]; |
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273 | p2 = ell[nskip1]; |
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274 | dd = dee[0]; |
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275 | q1 = p1*dd; |
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276 | q2 = p2*dd; |
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277 | ell[0] = q1; |
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278 | ell[nskip1] = q2; |
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279 | m11 = p1*q1; |
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280 | m21 = p2*q1; |
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281 | m22 = p2*q2; |
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282 | Z11 += m11; |
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283 | Z21 += m21; |
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284 | Z22 += m22; |
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285 | ell++; |
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286 | dee++; |
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287 | } |
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288 | /* solve for diagonal 2 x 2 block at A(i,i) */ |
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289 | Z11 = ell[0] - Z11; |
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290 | Z21 = ell[nskip1] - Z21; |
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291 | Z22 = ell[1+nskip1] - Z22; |
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292 | dee = d + i; |
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293 | /* factorize 2 x 2 block Z,dee */ |
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294 | /* factorize row 1 */ |
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295 | dee[0] = dRecip(Z11); |
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296 | /* factorize row 2 */ |
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297 | sum = 0; |
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298 | q1 = Z21; |
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299 | q2 = q1 * dee[0]; |
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300 | Z21 = q2; |
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301 | sum += q1*q2; |
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302 | dee[1] = dRecip(Z22 - sum); |
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303 | /* done factorizing 2 x 2 block */ |
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304 | ell[nskip1] = Z21; |
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305 | } |
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306 | /* compute the (less than 2) rows at the bottom */ |
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307 | switch (n-i) { |
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308 | case 0: |
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309 | break; |
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310 | |
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311 | case 1: |
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312 | dSolveL1_1 (A,A+i*nskip1,i,nskip1); |
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313 | /* scale the elements in a 1 x i block at A(i,0), and also */ |
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314 | /* compute Z = the outer product matrix that we'll need. */ |
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315 | Z11 = 0; |
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316 | ell = A+i*nskip1; |
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317 | dee = d; |
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318 | for (j=i-6; j >= 0; j -= 6) { |
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319 | p1 = ell[0]; |
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320 | dd = dee[0]; |
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321 | q1 = p1*dd; |
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322 | ell[0] = q1; |
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323 | m11 = p1*q1; |
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324 | Z11 += m11; |
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325 | p1 = ell[1]; |
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326 | dd = dee[1]; |
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327 | q1 = p1*dd; |
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328 | ell[1] = q1; |
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329 | m11 = p1*q1; |
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330 | Z11 += m11; |
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331 | p1 = ell[2]; |
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332 | dd = dee[2]; |
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333 | q1 = p1*dd; |
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334 | ell[2] = q1; |
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335 | m11 = p1*q1; |
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336 | Z11 += m11; |
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337 | p1 = ell[3]; |
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338 | dd = dee[3]; |
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339 | q1 = p1*dd; |
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340 | ell[3] = q1; |
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341 | m11 = p1*q1; |
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342 | Z11 += m11; |
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343 | p1 = ell[4]; |
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344 | dd = dee[4]; |
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345 | q1 = p1*dd; |
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346 | ell[4] = q1; |
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347 | m11 = p1*q1; |
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348 | Z11 += m11; |
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349 | p1 = ell[5]; |
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350 | dd = dee[5]; |
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351 | q1 = p1*dd; |
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352 | ell[5] = q1; |
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353 | m11 = p1*q1; |
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354 | Z11 += m11; |
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355 | ell += 6; |
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356 | dee += 6; |
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357 | } |
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358 | /* compute left-over iterations */ |
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359 | j += 6; |
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360 | for (; j > 0; j--) { |
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361 | p1 = ell[0]; |
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362 | dd = dee[0]; |
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363 | q1 = p1*dd; |
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364 | ell[0] = q1; |
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365 | m11 = p1*q1; |
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366 | Z11 += m11; |
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367 | ell++; |
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368 | dee++; |
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369 | } |
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370 | /* solve for diagonal 1 x 1 block at A(i,i) */ |
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371 | Z11 = ell[0] - Z11; |
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372 | dee = d + i; |
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373 | /* factorize 1 x 1 block Z,dee */ |
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374 | /* factorize row 1 */ |
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375 | dee[0] = dRecip(Z11); |
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376 | /* done factorizing 1 x 1 block */ |
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377 | break; |
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378 | |
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379 | default: *((char*)0)=0; /* this should never happen! */ |
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380 | } |
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381 | } |
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