1 | /************************************ |
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2 | Extended Kalman Filter |
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3 | Matrix operations |
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4 | |
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5 | V. Smidl, Z. Peroutka |
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6 | |
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7 | Rev. 28.10.2010 (ZP) |
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8 | |
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9 | 26.10.2010 Prvni verze (VS) |
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10 | |
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11 | 26.10.2010 Upravena chyba v Thorton_fast - spatne shiftovani o vypoctu SIGMA. |
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12 | 27.10.2010 Pokus o odstraneni problemu v Thorton_fast - potize dela omezovani (orezavani) varianci. |
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13 | 28.10.2010 Drobne upravy v kodu. |
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14 | |
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15 | *************************************/ |
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16 | |
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17 | #include "matrix_vs.h" |
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18 | |
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19 | /* Matrix multiply Full matrix by upper diagonal matrix; */ |
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20 | void mmultAU(int16 *m1, int16 *up, int16 *result, unsigned int16 rows, unsigned int16 columns) { |
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21 | unsigned int16 i, j, k; |
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22 | int32 tmp_sum=0L; //in 15+qAU |
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23 | int16 *m2pom; |
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24 | int16 *m1pom=m1; |
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25 | int16 *respom=result; |
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26 | |
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27 | for (i=0; i<rows; i++) //rows of result |
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28 | { |
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29 | for (j=0; j<columns; j++) //columns of result |
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30 | { |
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31 | m2pom=up+j;//?? |
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32 | |
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33 | for (k=0; k<j; k++) //inner loop up to "j" - U(j,j)==1; |
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34 | { |
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35 | tmp_sum+=((int32)(*(m1pom++))**m2pom)>>(15-qAU); |
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36 | m2pom+=columns; |
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37 | } |
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38 | // add the missing A(i,j) |
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39 | tmp_sum +=(int32)(*m1pom)<<qAU; // no need to shift |
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40 | m1pom-=(j); // shift back to first element |
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41 | |
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42 | *respom++=tmp_sum>>15; |
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43 | |
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44 | tmp_sum=0; |
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45 | } |
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46 | m1pom+=(columns); |
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47 | } |
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48 | }; |
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49 | |
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50 | |
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51 | void bierman_fast(int16 *difz, int16 *xp, int16 *U, int16 *D, int16 *R, unsigned int16 dimy, unsigned int16 dimx ) |
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52 | { |
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53 | int16 alpha; |
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54 | int16 beta,lambda; |
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55 | int16 b[5]; // ok even for 4-dim state |
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56 | int16 *a; // in [0,1] -> q15 |
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57 | unsigned int16 iy,j,i; |
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58 | |
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59 | int16 *b_j,*b_i; |
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60 | int16 *a_j; |
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61 | int16 *D_j; |
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62 | int16 *U_ij; |
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63 | int16 *x_i; |
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64 | |
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65 | int32 z_pom; |
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66 | int16 z_pom_int16; |
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67 | |
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68 | a = U; // iyth row of U |
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69 | for (iy=0; iy<dimy; iy++, a+=dimx) { |
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70 | // a is a row |
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71 | for (j=0,a_j=a,b_j=b,D_j=D; j<dimx; j++,b_j++,D_j++,a_j++) |
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72 | *b_j=((int32)(*D_j)*(*a_j))>>15; |
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73 | |
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74 | alpha = R[iy]; //\alpha = R+vDv = R+a*b |
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75 | // R in q15, a in q15, b=q15 |
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76 | // gamma = (1<<15)/alpha; //(in q15) |
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77 | //min alpha = R[iy] = 164 |
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78 | //max gamma = 0.0061 => gamma_ref = q7 |
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79 | for (j=0,a_j=a,b_j=b,D_j=D; j<dimx; j++,a_j++,b_j++,D_j++) { |
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80 | /* beta=alpha; |
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81 | lambda = -((int32)(*a_j)<<15)/beta; |
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82 | alpha += ((int32)(*a_j)*(*b_j))>>15; |
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83 | D[j] = ((int32)beta**D_j)/alpha;*/ |
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84 | /*xx*/ |
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85 | lambda=alpha; |
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86 | alpha += ((int32)(*a_j)*(*b_j))>>15; |
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87 | D[j] = ((int32)lambda**D_j)/alpha; |
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88 | z_pom_int16 = -((int32)(*a_j)<<15)/lambda; |
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89 | /*xx*/ |
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90 | |
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91 | if (*D_j==0) *D_j=1; |
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92 | |
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93 | for (i=0,b_i=b,U_ij=U+j; i<j; i++, b_i++,U_ij+=dimx) { |
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94 | beta = *U_ij; |
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95 | // *U_ij += ((int32)lambda*(*b_i))>>15; // puvodni reseni |
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96 | *U_ij -= ((int32)(*a_j)*(*b_i))/lambda; // pozadovane optimalni reseni |
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97 | // *U_ij -= ((int32)((int16)((int32)(*a_j)<<15)/lambda)**b_i)>>15; // tohle funguje - problem je s tim pretypovanim na (int16) |
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98 | // *U_ij -= (int16)((int32)(*a_j)*(*b_i))/lambda; |
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99 | // z_pom = (((int32)(*a_j)*(*b_i))/lambda); |
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100 | /* z_pom = (int32)(*U_ij)-(int16)((int32)(*a_j)*(*b_i))/lambda; |
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101 | if (z_pom > 32767) z_pom = 32767; |
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102 | if (z_pom < - 32768) z_pom = -32768; |
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103 | *U_ij = z_pom; /**/ |
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104 | // *U_ij += ((int32)z_pom_int16*(*b_i))>>15; // puvodni reseni - jen jina konstanta |
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105 | *b_i += ((int32)beta*(*b_j))>>15; |
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106 | } |
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107 | } |
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108 | // no shift due to gamma |
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109 | for (i=0,x_i=xp,b_i=b; i<dimx; i++,x_i++,b_i++) { |
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110 | *x_i += ((int32)difz[iy]*(*b_i))/alpha; // multiply by unscaled Kalman gain |
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111 | } |
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112 | } |
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113 | } |
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114 | |
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115 | |
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116 | // Thorton procedure - Kalman predictive variance in UD |
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117 | void thorton_fast(int16 *U, int16 *D, int16 *PSIU, int16 *Q, int16 *G, int16 *Dold, unsigned int16 rows) { |
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118 | unsigned int16 i,j,k; |
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119 | // copy D to Dold |
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120 | int16 *Dold_i,*Dold_k; |
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121 | int16 *D_i; |
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122 | int16 *PSIU_ij,*PSIU_ik,*PSIU_jk; |
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123 | int16 *Q_jj,*Q_ii,*Q_kk; |
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124 | int16 *U_ji; |
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125 | int16 *G_ik,*G_jk; |
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126 | int16 irows,jrows; |
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127 | int32 sigma; // in qAU+15!! |
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128 | int32 z; |
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129 | |
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130 | for (i=0,Dold_i=Dold,D_i=D;i<rows;i++,Dold_i++,D_i++) { |
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131 | *Dold_i=*D_i; |
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132 | } |
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133 | |
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134 | // initialize G = eye() |
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135 | G_ik= G; |
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136 | *G_ik++=32767; |
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137 | for (i=0;i<rows-1;i++) { |
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138 | // clean elem before diag |
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139 | for (k=0; k<rows; k++) { |
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140 | *G_ik++=0; |
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141 | } |
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142 | *G_ik++=32767; |
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143 | } |
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144 | // eye created |
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145 | |
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146 | for (i=rows-1, Dold_i=Dold+i, D_i=D+i; |
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147 | 1; i--, Dold_i--,D_i--) { // stop if i==0 at the END! |
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148 | irows=i*rows; |
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149 | sigma = 0; |
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150 | for (k=0, PSIU_ik=PSIU+irows,Dold_k=Dold; |
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151 | k<rows; k++, PSIU_ik++,Dold_k++) { |
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152 | sigma += (((int32)(*PSIU_ik)**PSIU_ik)>>(qAU))*(*Dold_k); |
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153 | } |
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154 | sigma += (int32)(*(Q+i+irows))<<qAU; |
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155 | for (j=i+1, G_ik=G+irows+i+1; j<rows; j++,G_ik++) { |
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156 | sigma += (((int32)(*G_ik)**G_ik)>>16)**(Q+j+j*rows); |
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157 | } |
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158 | |
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159 | if (sigma>((int32)1<<(qAU+15))) { |
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160 | *D_i = 32767; |
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161 | // *(Dold+i)-=*(Q+i+irows); |
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162 | } else { |
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163 | *D_i=sigma>>qAU; |
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164 | } |
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165 | if (*D_i==0) *D_i=1; |
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166 | |
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167 | for (j=0;j<i;j++) { |
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168 | jrows = j*rows; |
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169 | |
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170 | sigma =0; |
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171 | for (k=0, PSIU_ik=PSIU+irows, PSIU_jk=PSIU+jrows, Dold_k=Dold; |
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172 | k<rows; k++, PSIU_ik++, PSIU_jk++, Dold_k++) { |
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173 | |
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174 | sigma += ((((int32)(*PSIU_ik)**PSIU_jk)>>qAU)**Dold_k); |
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175 | } |
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176 | |
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177 | for (k=i,G_ik=G+irows+i,G_jk=G+jrows+i,Q_kk=Q+k*rows+k; |
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178 | k<rows;k++,G_ik++,G_jk++,Q_kk+=rows+1) { |
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179 | sigma += ((((int32)*G_ik)**G_jk)>>16)**Q_kk; |
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180 | } |
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181 | |
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182 | z=(sigma/(*D_i))<<(15-qAU); // shift to q15 |
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183 | if (z>32767) z=32767; |
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184 | if (z<-32768) z=-32768; |
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185 | |
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186 | U_ji=U+jrows+i; |
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187 | *U_ji = (int16)z; |
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188 | |
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189 | |
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190 | for (k=0,PSIU_ik=PSIU+irows,PSIU_jk=PSIU+jrows; |
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191 | k<rows;k++,PSIU_ik++,PSIU_jk++) { |
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192 | *PSIU_jk -= ((int32)*U_ji**PSIU_ik)>>15; |
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193 | } |
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194 | |
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195 | for (k=0,G_jk=G+jrows,G_ik=G+irows; |
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196 | k<rows;k++, G_jk++, G_ik++) { |
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197 | *G_jk -= ((int32)*U_ji**G_ik)>>15; |
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198 | } |
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199 | |
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200 | } |
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201 | if (i==0) return; |
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202 | } |
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203 | } |
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204 | |
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205 | /* square root of 0<a<1 using taylor at 0.5 in q15*/ |
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206 | int int_sqrt(int x) { |
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207 | double xd(double(x)/32768.); |
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208 | return round(sqrt(xd)*32768); |
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209 | |
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210 | //sqrt(x) == 1/2*2^(1/2)+1/2*2^(1/2)*(x-1/2)-1/4*2^(1/2)*(x-1/2)^2 |
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211 | // = k1 + k1*(x-0.5) - k2*(x-0.5)(x-0.5); |
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212 | #define k1 23170 //0.5*sqrt(2)*32768 |
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213 | #define k2 11585 //0.25*sqrt(2)*32768 |
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214 | |
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215 | int tmp; |
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216 | if (x>6554) { |
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217 | int xm05=x-16384; |
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218 | tmp = ((long)k1*xm05)>>15; |
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219 | tmp-=(((long(k2)*xm05)>>15)*xm05)>>15; |
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220 | tmp +=k1; |
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221 | } else { |
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222 | tmp = 4*x; |
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223 | tmp-=long(8*x)*x>>15; |
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224 | } |
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225 | return tmp; |
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226 | } |
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227 | |
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228 | void householder(int *Ch /*= int *PSICh*/, int *Q, unsigned int dimx) { |
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229 | int k,j,i; |
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230 | int alpha,beta; |
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231 | long sigma; |
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232 | int B[25];//beware |
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233 | int w[5]; |
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234 | int v[5]; |
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235 | |
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236 | // copy Q to B |
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237 | for (i=0;i<dimx*dimx;i++) |
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238 | { |
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239 | B[i]=Q[i]; |
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240 | } |
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241 | |
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242 | for (k=dimx-1; k>=0; k--) |
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243 | { |
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244 | sigma=0; |
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245 | for (j=0;j<dimx;j++) |
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246 | { |
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247 | sigma+=(long)B[k*dimx+j]*B[k*dimx+j]; |
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248 | } |
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249 | for (j=0;j<=k;j++) |
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250 | { |
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251 | sigma+=(long)Ch[k*dimx+j]*Ch[k*dimx+j]; |
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252 | } |
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253 | /* double sigf=double(sigma)/(1<<15); |
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254 | double alpf = sqrt(sigf);*/ |
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255 | // if (sigma>16384) sigma=16384; |
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256 | // alpha=int_sqrt(sigma); |
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257 | alpha = (int)(sqrt((double)sigma)+0.5); // predelat pro DSP |
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258 | // alpha = alpf*(1<<15); |
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259 | // |
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260 | sigma=0; |
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261 | for (j=0;j<dimx;j++) { |
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262 | w[j]=B[k*dimx+j]; |
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263 | sigma+=(long)w[j])*w[j]; |
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264 | } |
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265 | for (j=0; j<=k;j++) { |
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266 | if (j==k) { |
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267 | v[j]=Ch[k*dimx+j]-alpha; |
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268 | } else { |
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269 | v[j]=Ch[k*dimx+j]; |
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270 | } |
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271 | sigma+=(long)v[j]*v[j]; |
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272 | } |
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273 | |
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274 | alpha=sigma>>16; |
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275 | if (alpha==0) alpha =1; |
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276 | |
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277 | for (i=0;i<=k;i++) { |
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278 | sigma=0; |
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279 | for (j=0;j<dimx;j++) { |
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280 | sigma+=(long)B[i*dimx+j]*w[j]; |
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281 | } |
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282 | for (j=0;j<=k;j++) { |
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283 | sigma+=(long)Ch[i*dimx+j]*v[j]; |
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284 | } |
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285 | |
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286 | sigma = sigma >> 15; // navrat do Q15 |
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287 | |
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288 | for (j=0;j<dimx;j++) |
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289 | { |
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290 | B[i*dimx+j]-=(sigma*w[j])/alpha; |
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291 | }; |
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292 | |
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293 | for (j=0;j<=k;j++) |
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294 | { |
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295 | Ch[i*dimx+j]-=(sigma*v[j])/alpha; |
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296 | } |
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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 | |
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302 | void carlson(int *difz, int *xp, int *Ch, int *R, unsigned int dimy, unsigned int dimx ) { |
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303 | int alpha,beta,gamma; |
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304 | int delta, eta,epsilon,zeta,sigma,tau; |
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305 | int i,j,iy; |
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306 | int w[5]; |
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307 | |
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308 | for (iy=0; iy<dimy; iy++) |
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309 | { |
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310 | alpha=R[iy]; |
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311 | delta = difz[iy]; |
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312 | |
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313 | for (j=0;j<dimx;j++) |
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314 | { |
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315 | sigma=Ch[iy*dimx+j]; |
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316 | beta=alpha; |
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317 | alpha+=((long)sigma*sigma)>>15; |
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318 | // double ab=(double)alpha*beta/32768./32768.; |
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319 | // double s_ab=sqrt(ab); |
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320 | gamma=(int)(sqrt((double)((long)alpha*beta))+0.5); // predelat v DSP |
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321 | //gamma = round(s_ab*(1<<15)); |
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322 | // eta=((long)beta<<15) / gamma; |
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323 | //zeta=(long(sigma)<<15)/ gamma; |
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324 | w[j]=0; |
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325 | for (i=0;i<=j;i++) { |
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326 | tau=Ch[i*dimx+j]; |
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327 | Ch[i*dimx+j]=((long)beta*Ch[i*dimx+j] -(long)sigma*w[i])/gamma; |
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328 | w[i]+=((long)tau*sigma)>>15; |
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329 | } |
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330 | } |
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331 | |
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332 | //epsilon=(long(difz)<<15) / (alpha); // q15*q13/q13 = q15 |
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333 | for (i=0;i<dimx;i++) { |
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334 | xp[i]+=((long)w[i]*delta)/alpha; |
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335 | } |
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336 | } |
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337 | } |
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338 | |
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339 | /* perform Householder update of Ch matrix using PSI*Ch , Q, */ |
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340 | extern void givens(int *Ch /*= int *PSICh*/, int *Q, unsigned int dimx){ |
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341 | int i,j,k; |
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342 | int rho,s,c,tau; |
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343 | |
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344 | int A[25];//beware |
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345 | // copy Q to A |
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346 | for (i=0;i<dimx*dimx;i++) { |
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347 | A[i]=Q[i]; |
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348 | } |
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349 | |
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350 | |
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351 | for (i=dimx-1; i>=0; i--){ |
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352 | for (j=0; j<dimx; j++) { |
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353 | rho=int_sqrt(((long)Ch[i*dimx+i]*Ch[i*dimx+i]+long(A[i*dimx+j])*A[i*dimx+j])>>15); |
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354 | if (rho==0) break; |
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355 | s=(long(A[i*dimx+j])<<15)/rho; |
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356 | c=(long(Ch[i*dimx+i])<<15)/rho; |
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357 | for (k=0;k<=i; k++){ |
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358 | tau=(long(c)*A[k*dimx+j]-long(s)*Ch[k*dimx+i])>>15; |
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359 | Ch[k*dimx +i]=(long(s)*A[k*dimx+j]+long(c)*Ch[k*dimx+i])>>15; |
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360 | A[k*dimx +j]=tau; |
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361 | } |
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362 | } |
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363 | } |
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364 | for (j=0; j<i; j++){ |
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365 | rho=int_sqrt((long(Ch[i*dimx+i])*Ch[i*dimx+i]+long(Ch[i*dimx+j])*Ch[i*dimx+j])>>15); |
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366 | if (rho==0) break; |
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367 | s=(long(Ch[i*dimx+j])<<15)/rho; |
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368 | c=(long(Ch[i*dimx+i])<<15)/rho; |
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369 | for (k=0; k<=i; k++){ |
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370 | tau=(long(c)*Ch[k*dimx+j]-long(s)*Ch[k*dimx+i])>>15; |
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371 | Ch[k*dimx+i]=(long(s)*Ch[k*dimx+j]+long(c)*Ch[k*dimx+i])>>15; |
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372 | Ch[k*dimx+j]=tau; |
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373 | } |
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374 | } |
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375 | } |
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