1 | /**************************************** |
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2 | * Computer Algebra System SINGULAR * |
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3 | ****************************************/ |
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4 | /* $Id: weight.cc,v 1.7 1998-04-27 09:11:56 pohl Exp $ */ |
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5 | |
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6 | /* |
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7 | * ABSTRACT: |
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8 | */ |
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9 | |
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10 | #include <math.h> |
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11 | #include "mod2.h" |
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12 | #include "tok.h" |
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13 | #include "mmemory.h" |
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14 | #include "polys.h" |
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15 | #include "intvec.h" |
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16 | #include "febase.h" |
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17 | #include "ipid.h" |
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18 | #include "ipshell.h" |
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19 | #include "subexpr.h" |
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20 | #include "ideals.h" |
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21 | #include "weight.h" |
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22 | |
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23 | /*0 implementation*/ |
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24 | |
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25 | pFDegProc pFDegOld; |
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26 | pLDegProc pLDegOld; |
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27 | #ifndef __MWERKS__ |
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28 | extern "C" double (*wFunctional)(int *degw, int *lpol, int npol, |
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29 | double *rel, double wx); |
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30 | extern "C" double wFunctionalMora(int *degw, int *lpol, int npol, |
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31 | double *rel, double wx); |
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32 | extern "C" double wFunctionalBuch(int *degw, int *lpol, int npol, |
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33 | double *rel, double wx); |
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34 | extern "C" double * wDouble(void *adr); |
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35 | extern "C" void wAdd(int *A, int mons, int kn, int xx); |
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36 | extern "C" void wNorm(int *degw, int *lpol, int npol, double *rel); |
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37 | extern "C" void wFirstSearch(int *A, int *x, int mons, |
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38 | int *lpol, int npol, double *rel, double *fopt); |
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39 | extern "C" void wSecondSearch(int *A, int *x, int *lpol, |
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40 | int npol, int mons, double *rel, double *fk); |
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41 | extern "C" void wGcd(int *x, int n); |
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42 | extern double nsqr; |
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43 | #else |
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44 | short * ecartWeights=NULL; |
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45 | extern int pVariables; |
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46 | |
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47 | static double * wDouble(void *adr) |
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48 | { |
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49 | long i = (long)adr; |
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50 | return (double *)((i+7)&(~7)); |
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51 | } |
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52 | |
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53 | double nsqr; |
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54 | double (*wFunctional)(int *degw, int *lpol, int npol, |
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55 | double *rel, double wx); |
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56 | |
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57 | |
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58 | static double wFunctionalMora(int *degw, int *lpol, int npol, |
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59 | double *rel, double wx) |
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60 | { |
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61 | int i, j, e1, ecu, ecl, ec; |
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62 | int *ex; |
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63 | double gfmax, gecart, ghom, pfmax; |
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64 | double *r; |
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65 | |
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66 | ex = degw; |
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67 | r = rel; |
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68 | gfmax = (double)0.0; |
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69 | gecart = (double)0.4 + (double)npol; |
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70 | ghom = (double)1.0; |
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71 | for (i = 0; i < npol; i++) |
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72 | { |
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73 | ecl = ecu = e1 = *ex++; |
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74 | for (j = lpol[i] - 1; j; j--) |
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75 | { |
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76 | ec = *ex++; |
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77 | if (ec > ecu) |
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78 | ecu = ec; |
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79 | else if (ec < ecl) |
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80 | ecl = ec; |
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81 | } |
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82 | pfmax = (double)ecl / (double)ecu; |
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83 | if (pfmax < ghom) |
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84 | ghom = pfmax; |
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85 | pfmax = (double)e1 / (double)ecu; |
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86 | if (pfmax > (double)0.5) |
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87 | gecart -= (pfmax * pfmax); |
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88 | else |
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89 | gecart -= (double)0.25; |
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90 | ecu = 2 * ecu - ecl; |
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91 | gfmax += (double)(ecu * ecu) * (*r++); |
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92 | } |
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93 | if (ghom > (double)0.8) |
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94 | { |
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95 | ghom *= (double)5.0; |
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96 | gecart *= ((double)5.0 - ghom); |
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97 | } |
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98 | return (gfmax * gecart) / pow(wx, nsqr); |
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99 | } |
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100 | |
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101 | |
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102 | static double wFunctionalBuch(int *degw, int *lpol, int npol, |
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103 | double *rel, double wx) |
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104 | { |
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105 | int i, j, ecl, ecu, ec; |
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106 | int *ex; |
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107 | double gfmax, ghom, pfmax; |
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108 | double *r; |
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109 | |
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110 | ex = degw; |
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111 | r = rel; |
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112 | gfmax = (double)0.0; |
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113 | ghom = (double)1.0; |
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114 | for (i = 0; i < npol; i++) |
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115 | { |
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116 | ecu = ecl = *ex++; |
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117 | for (j = lpol[i] - 1; j; j--) |
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118 | { |
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119 | ec = *ex++; |
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120 | if (ec < ecl) |
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121 | ecl = ec; |
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122 | else if (ec > ecu) |
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123 | ecu = ec; |
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124 | } |
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125 | pfmax = (double)ecl / (double)ecu; |
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126 | if (pfmax < ghom) |
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127 | ghom = pfmax; |
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128 | gfmax += (double)(ecu * ecu) * (*r++); |
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129 | } |
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130 | if (ghom > (double)0.5) |
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131 | gfmax *= ((double)1.0 - (ghom * ghom)) / (double)0.75; |
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132 | return gfmax / pow(wx, nsqr); |
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133 | } |
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134 | |
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135 | |
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136 | static void wSub(int *A, int mons, int kn, int xx) |
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137 | { |
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138 | int i, *B, *ex; |
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139 | |
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140 | B = A + ((kn - 1) * mons); |
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141 | ex = A + (pVariables * mons); |
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142 | if (xx == 1) |
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143 | { |
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144 | for (i = mons; i; i--) |
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145 | *ex++ -= *B++; |
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146 | } |
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147 | else |
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148 | { |
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149 | for (i = mons; i; i--) |
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150 | *ex++ -= (*B++) * xx; |
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151 | } |
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152 | } |
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153 | |
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154 | |
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155 | static void wAdd(int *A, int mons, int kn, int xx) |
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156 | { |
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157 | int i, *B, *ex; |
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158 | |
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159 | B = A + ((kn - 1) * mons); |
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160 | ex = A + (pVariables * mons); |
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161 | if (xx == 1) |
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162 | { |
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163 | for (i = mons; i; i--) |
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164 | *ex++ += *B++; |
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165 | } |
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166 | else |
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167 | { |
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168 | for (i = mons; i; i--) |
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169 | *ex++ += (*B++) * xx; |
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170 | } |
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171 | } |
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172 | |
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173 | |
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174 | static void wFirstSearch(int *A, int *x, int mons, |
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175 | int *lpol, int npol, double *rel, double *fopt) |
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176 | { |
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177 | int a0, a, n, xn, t, xx, y1; |
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178 | int *y, *degw, *xopt; |
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179 | double fy, fmax, wx; |
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180 | double *pr; |
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181 | void *adr; |
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182 | |
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183 | fy = *fopt; |
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184 | n = pVariables; |
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185 | xn = n + 6 + (21 / n); |
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186 | a0 = n * sizeof(double) + 8; |
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187 | a = n * sizeof(int); |
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188 | y = (int * )Alloc(a); |
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189 | adr = (void * )Alloc(a0); |
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190 | pr = wDouble(adr); |
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191 | *pr = (double)1.0; |
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192 | *y = 0; |
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193 | degw = A + (n * mons); |
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194 | xopt = x + (n + 2); |
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195 | t = 1; |
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196 | loop |
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197 | { |
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198 | while (t < n) |
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199 | { |
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200 | xx = x[t] + 1; |
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201 | wx = pr[t-1] * (double)xx; |
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202 | y1 = y[t-1] + xx; |
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203 | if ((y1 + n - t) <= xn) |
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204 | { |
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205 | pr[t] = wx; |
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206 | y[t] = y1; |
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207 | x[t] = xx; |
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208 | if (xx > 1) |
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209 | wAdd(A, mons, t, 1); |
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210 | t++; |
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211 | } |
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212 | else |
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213 | { |
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214 | xx = x[t] - 1; |
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215 | x[t] = 0; |
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216 | if (xx!=0) |
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217 | wSub(A, mons, t, xx); |
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218 | t--; |
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219 | if (t==0) |
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220 | { |
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221 | *fopt = fy; |
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222 | Free((ADDRESS)y, a); |
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223 | Free((ADDRESS)adr, a0); |
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224 | return; |
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225 | } |
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226 | } |
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227 | } |
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228 | xx = xn - y[t-1]; |
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229 | wx = pr[t-1] * (double)xx; |
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230 | x[t] = xx; |
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231 | xx--; |
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232 | if (xx!=0) |
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233 | wAdd(A, mons, t, xx); |
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234 | fmax = (*wFunctional)(degw, lpol, npol, rel, wx); |
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235 | if (xx!=0) |
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236 | wSub(A, mons, t, xx); |
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237 | if (fmax < fy) |
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238 | { |
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239 | fy = fmax; |
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240 | memcpy(xopt, x + 1, a); |
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241 | } |
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242 | t--; |
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243 | } /* end loop */ |
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244 | } |
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245 | |
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246 | |
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247 | static double wPrWeight(int *x, int n) |
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248 | { |
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249 | int i; |
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250 | double y; |
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251 | |
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252 | y = (double)x[n]; |
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253 | for (i = n - 1; i; i--) |
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254 | y *= (double)x[i]; |
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255 | return y; |
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256 | } |
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257 | |
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258 | |
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259 | static void wEstimate(int *A, int *x, int *lpol, int npol, int mons, |
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260 | double wx, double *rel, double *fopt, int *s0, int *s1, int *s2) |
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261 | { |
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262 | int n, i1, i2, k0 = 0, k1 = 0, k2 = 0; |
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263 | int *degw; |
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264 | double fo1, fo2, fmax, wx1, wx2; |
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265 | |
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266 | n = pVariables; |
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267 | degw = A + (n * mons); |
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268 | fo2 = fo1 = (double)1.0e10; |
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269 | for (i1 = n; i1; i1--) |
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270 | { |
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271 | if (x[i1] > 1) |
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272 | { |
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273 | wSub(A, mons, i1, 1); |
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274 | wx1 = wx - wx / (double)x[i1]; |
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275 | x[i1]--; |
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276 | fmax = (*wFunctional)(degw, lpol, npol, rel, wx1); |
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277 | if (fmax < fo1) |
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278 | { |
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279 | fo1 = fmax; |
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280 | k0 = i1; |
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281 | } |
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282 | for (i2 = i1; i2; i2--) |
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283 | { |
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284 | if (x[i2] > 1) |
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285 | { |
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286 | wSub(A, mons, i2, 1); |
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287 | wx2 = wx1 - wx1 / (double)x[i2]; |
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288 | fmax = (*wFunctional)(degw, lpol, npol, rel, wx2); |
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289 | if (fmax < fo2) |
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290 | { |
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291 | fo2 = fmax; |
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292 | k1 = i1; |
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293 | k2 = i2; |
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294 | } |
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295 | wAdd(A, mons, i2, 1); |
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296 | } |
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297 | } |
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298 | wAdd(A, mons, i1, 1); |
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299 | x[i1]++; |
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300 | } |
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301 | } |
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302 | if (fo1 < fo2) |
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303 | { |
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304 | *fopt = fo1; |
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305 | *s0 = k0; |
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306 | } |
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307 | else |
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308 | { |
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309 | *fopt = fo2; |
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310 | *s0 = 0; |
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311 | } |
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312 | *s1 = k1; |
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313 | *s2 = k2; |
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314 | } |
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315 | |
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316 | |
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317 | static void wSecondSearch(int *A, int *x, int *lpol, |
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318 | int npol, int mons, double *rel, double *fk) |
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319 | { |
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320 | int n, s0, s1, s2, *xopt; |
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321 | double one, fx, fopt, wx; |
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322 | |
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323 | n = pVariables; |
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324 | xopt = x + (n + 2); |
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325 | fopt = *fk * (double)0.999999999999; |
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326 | wx = wPrWeight(x, n); |
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327 | one = (double)1.0; |
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328 | loop |
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329 | { |
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330 | wEstimate(A, x, lpol, npol, mons, wx, rel, &fx, &s0, &s1, &s2); |
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331 | if (fx > fopt) |
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332 | { |
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333 | if (s0!=0) |
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334 | x[s0]--; |
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335 | else if (s1!=0) |
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336 | { |
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337 | x[s1]--; |
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338 | x[s2]--; |
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339 | } |
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340 | else |
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341 | break; |
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342 | } |
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343 | else |
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344 | { |
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345 | fopt = fx; |
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346 | if (s0!=0) |
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347 | { |
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348 | x[s0]--; |
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349 | memcpy(xopt, x + 1, n * sizeof(int)); |
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350 | if (s1==0) |
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351 | break; |
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352 | } |
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353 | else if (s1!=0) |
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354 | { |
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355 | x[s1]--; |
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356 | x[s2]--; |
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357 | memcpy(xopt, x + 1, n * sizeof(int)); |
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358 | } |
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359 | else |
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360 | break; |
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361 | } |
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362 | if (s0!=0) |
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363 | wSub(A, mons, s0, 1); |
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364 | else |
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365 | { |
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366 | wSub(A, mons, s1, 1); |
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367 | wSub(A, mons, s2, 1); |
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368 | } |
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369 | wx = wPrWeight(x, n); |
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370 | } |
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371 | *fk = fopt; |
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372 | } |
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373 | |
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374 | |
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375 | static void wGcd(int *x, int n) |
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376 | { |
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377 | int i, b, a, h; |
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378 | |
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379 | i = n; |
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380 | b = x[i]; |
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381 | loop |
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382 | { |
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383 | i--; |
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384 | if (i==0) |
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385 | break; |
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386 | a = x[i]; |
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387 | if (a < b) |
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388 | { |
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389 | h = a; |
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390 | a = b; |
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391 | b = h; |
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392 | } |
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393 | do |
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394 | { |
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395 | h = a % b; |
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396 | a = b; |
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397 | b = h; |
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398 | } |
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399 | while (b!=0); |
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400 | b = a; |
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401 | if (b == 1) |
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402 | return; |
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403 | } |
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404 | for (i = n; i; i--) |
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405 | x[i] /= b; |
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406 | } |
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407 | |
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408 | |
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409 | static void wSimple(int *x, int n) |
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410 | { |
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411 | int g, min, c, d, f, kopt, k, i; |
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412 | int *xopt; |
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413 | double sopt, s1, s2; |
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414 | |
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415 | xopt = x + (n + 1); |
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416 | kopt = k = g = 0; |
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417 | min = 1000000; |
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418 | for (i = n; i; i--) |
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419 | { |
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420 | c = xopt[i]; |
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421 | if (c > 1) |
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422 | { |
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423 | if (c < min) |
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424 | min = c; |
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425 | if (c > k) |
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426 | k = c; |
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427 | } |
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428 | else |
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429 | g = 1; |
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430 | } |
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431 | k -= min; |
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432 | if ((g==0) && (k < 4)) |
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433 | return; |
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434 | if (k < min) |
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435 | min = k+1; |
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436 | sopt = (double)1.0e10; |
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437 | for (k = min; k > 1; k--) |
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438 | { |
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439 | s2 = s1 = (double)0.0; |
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440 | for(i = n; i; i--) |
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441 | { |
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442 | c = xopt[i]; |
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443 | if (c > 1) |
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444 | { |
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445 | d = c / k; |
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446 | d *= k; |
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447 | f = d = c - d; |
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448 | if (f!=0) |
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449 | { |
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450 | f = k - f; |
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451 | if (f < d) |
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452 | s2 += (double)f / (double)c; |
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453 | else |
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454 | s1 += (double)d / (double)c; |
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455 | } |
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456 | } |
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457 | } |
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458 | s1 += s2 + sqrt(s1 * s2); |
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459 | s1 -= (double)0.01 * sqrt((double)k); |
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460 | if (s1 < sopt) |
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461 | { |
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462 | sopt = s1; |
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463 | kopt = k; |
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464 | } |
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465 | } |
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466 | for(i = n; i; i--) |
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467 | { |
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468 | x[i] = 1; |
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469 | c = xopt[i]; |
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470 | if (c > 1) |
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471 | { |
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472 | d = c / kopt; |
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473 | d *= kopt; |
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474 | x[i] = d; |
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475 | d = c - d; |
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476 | if ((d!=0) && (kopt < 2 * d)) |
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477 | x[i] += kopt; |
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478 | } |
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479 | } |
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480 | if (g==0) |
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481 | wGcd(x, n); |
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482 | } |
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483 | |
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484 | |
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485 | static void wNorm(int *degw, int *lpol, int npol, double *rel) |
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486 | { |
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487 | int i, j, ecu, ec; |
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488 | int *ex; |
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489 | double *r; |
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490 | |
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491 | ex = degw; |
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492 | r = rel; |
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493 | for (i = 0; i < npol; i++) |
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494 | { |
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495 | ecu = *ex++; |
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496 | for (j = lpol[i] - 1; j; j--) |
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497 | { |
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498 | ec = *ex++; |
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499 | if (ec > ecu) |
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500 | ecu = ec; |
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501 | } |
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502 | *r = (double)1.0 / (double)(ecu * ecu); |
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503 | r++; |
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504 | } |
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505 | } |
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506 | #endif /* __MWERKS */ |
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507 | |
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508 | |
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509 | static void wDimensions(polyset s, int sl, int *lpol, int *npol, int *mons) |
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510 | { |
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511 | int i, i1, j, k; |
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512 | poly p, q; |
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513 | |
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514 | i1 = j = 0; |
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515 | for (i = 0; i <= sl; i++) |
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516 | { |
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517 | p = s[i]; |
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518 | if (p!=NULL) |
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519 | { |
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520 | k = 1; |
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521 | q = pNext(p); |
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522 | while (q!=NULL) |
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523 | { |
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524 | k++; |
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525 | q = pNext(q); |
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526 | } |
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527 | if (k > 1) |
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528 | { |
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529 | lpol[i1++] = k; |
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530 | j += k; |
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531 | } |
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532 | } |
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533 | } |
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534 | *npol = i1; |
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535 | *mons = j; |
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536 | } |
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537 | |
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538 | |
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539 | static void wInit(polyset s, int sl, int mons, int *A) |
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540 | { |
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541 | int n, a, i, j, *B, *C; |
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542 | poly p, q; |
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543 | Exponent_t *pl; |
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544 | |
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545 | B = A; |
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546 | n = pVariables; |
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547 | a = (n + 1) * sizeof(Exponent_t); |
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548 | pl = (Exponent_t * )Alloc(a); |
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549 | for (i = 0; i <= sl; i++) |
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550 | { |
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551 | p = s[i]; |
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552 | if (p!=NULL) |
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553 | { |
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554 | q = pNext(p); |
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555 | if (q!=NULL) |
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556 | { |
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557 | C = B; |
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558 | B++; |
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559 | pGetExpV(p, pl); |
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560 | for (j = 0; j < n; j++) |
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561 | { |
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562 | *C = pl[j+1]; |
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563 | C += mons; |
---|
564 | } |
---|
565 | } |
---|
566 | while (q!=NULL) |
---|
567 | { |
---|
568 | C = B; |
---|
569 | B++; |
---|
570 | pGetExpV(q, pl); |
---|
571 | for (j = 0; j < n; j++) |
---|
572 | { |
---|
573 | *C = pl[j+1]; |
---|
574 | C += mons; |
---|
575 | } |
---|
576 | q = pNext(q); |
---|
577 | } |
---|
578 | } |
---|
579 | } |
---|
580 | Free((ADDRESS)pl, a); |
---|
581 | } |
---|
582 | |
---|
583 | static void wCall(polyset s, int sl, int *x) |
---|
584 | { |
---|
585 | int n, q, npol, mons, i; |
---|
586 | int *A, *xopt, *lpol, *degw; |
---|
587 | double f1, fx, eps, *rel; |
---|
588 | void *adr; |
---|
589 | |
---|
590 | n = pVariables; |
---|
591 | lpol = (int * )Alloc((sl + 1) * sizeof(int)); |
---|
592 | wDimensions(s, sl, lpol, &npol, &mons); |
---|
593 | xopt = x + (n + 1); |
---|
594 | for (i = n; i; i--) |
---|
595 | xopt[i] = 1; |
---|
596 | if (mons==0) |
---|
597 | { |
---|
598 | Free((ADDRESS)lpol, (sl + 1) * sizeof(int)); |
---|
599 | return; |
---|
600 | } |
---|
601 | adr = (void * )Alloc(npol * sizeof(double) + 8); |
---|
602 | rel = wDouble(adr); |
---|
603 | q = (n + 1) * mons * sizeof(int); |
---|
604 | A = (int * )Alloc(q); |
---|
605 | wInit(s, sl, mons, A); |
---|
606 | degw = A + (n * mons); |
---|
607 | memset(degw, 0, mons * sizeof(int)); |
---|
608 | for (i = n; i; i--) |
---|
609 | wAdd(A, mons, i, 1); |
---|
610 | wNorm(degw, lpol, npol, rel); |
---|
611 | f1 = (*wFunctional)(degw, lpol, npol, rel, (double)1.0); |
---|
612 | if (TEST_OPT_PROT) Print("// %e\n",f1); |
---|
613 | eps = f1; |
---|
614 | fx = (double)2.0 * eps; |
---|
615 | memset(x, 0, (n + 1) * sizeof(int)); |
---|
616 | wFirstSearch(A, x, mons, lpol, npol, rel, &fx); |
---|
617 | if (TEST_OPT_PROT) Print("// %e\n",fx); |
---|
618 | memcpy(x + 1, xopt + 1, n * sizeof(int)); |
---|
619 | memset(degw, 0, mons * sizeof(int)); |
---|
620 | for (i = n; i; i--) |
---|
621 | { |
---|
622 | x[i] *= 16; |
---|
623 | wAdd(A, mons, i, x[i]); |
---|
624 | } |
---|
625 | wSecondSearch(A, x, lpol, npol, mons, rel, &fx); |
---|
626 | if (TEST_OPT_PROT) Print("// %e\n",fx); |
---|
627 | if (fx >= eps) |
---|
628 | { |
---|
629 | for (i = n; i; i--) |
---|
630 | xopt[i] = 1; |
---|
631 | } |
---|
632 | else |
---|
633 | { |
---|
634 | wGcd(xopt, n); |
---|
635 | // if (BTEST1(22)) |
---|
636 | // { |
---|
637 | // f1 = fx + (double)0.1 * (f1 - fx); |
---|
638 | // wSimple(x, n); |
---|
639 | // memset(degw, 0, mons * sizeof(int)); |
---|
640 | // for (i = n; i; i--) |
---|
641 | // wAdd(A, mons, i, x[i]); |
---|
642 | // eps = wPrWeight(x, n); |
---|
643 | // fx = (*wFunctional)(degw, lpol, npol, rel, eps); |
---|
644 | // if (fx < f1) |
---|
645 | // { |
---|
646 | // if (TEST_OPT_PROT) Print("// %e\n",fx); |
---|
647 | // memcpy(xopt + 1, x + 1, n * sizeof(int)); |
---|
648 | // } |
---|
649 | // } |
---|
650 | } |
---|
651 | Free((ADDRESS)A, q); |
---|
652 | Free((ADDRESS)lpol, (sl + 1) * sizeof(int)); |
---|
653 | Free((ADDRESS)adr, npol * sizeof(double) + 8); |
---|
654 | } |
---|
655 | |
---|
656 | |
---|
657 | void kEcartWeights(polyset s, int sl, short *eweight) |
---|
658 | { |
---|
659 | int n, i; |
---|
660 | int *x; |
---|
661 | |
---|
662 | *eweight = 0; |
---|
663 | n = pVariables; |
---|
664 | nsqr = (double)2.0 / (double)n; |
---|
665 | if (pOrdSgn == -1) |
---|
666 | wFunctional = wFunctionalMora; |
---|
667 | else |
---|
668 | wFunctional = wFunctionalBuch; |
---|
669 | x = (int * )Alloc(2 * (n + 1) * sizeof(int)); |
---|
670 | wCall(s, sl, x); |
---|
671 | for (i = n; i; i--) |
---|
672 | eweight[i] = x[i + n + 1]; |
---|
673 | Free((ADDRESS)x, 2 * (n + 1) * sizeof(int)); |
---|
674 | } |
---|
675 | |
---|
676 | |
---|
677 | BOOLEAN kWeight(leftv res,leftv id) |
---|
678 | { |
---|
679 | ideal F=(ideal)id->Data(); |
---|
680 | intvec * iv = new intvec(pVariables); |
---|
681 | polyset s; |
---|
682 | int sl, n, i; |
---|
683 | int *x; |
---|
684 | |
---|
685 | res->data=(char *)iv; |
---|
686 | s = F->m; |
---|
687 | sl = IDELEMS(F) - 1; |
---|
688 | n = pVariables; |
---|
689 | nsqr = (double)2.0 / (double)n; |
---|
690 | wFunctional = wFunctionalBuch; |
---|
691 | x = (int * )Alloc(2 * (n + 1) * sizeof(int)); |
---|
692 | wCall(s, sl, x); |
---|
693 | for (i = n; i; i--) |
---|
694 | (*iv)[i-1] = x[i + n + 1]; |
---|
695 | Free((ADDRESS)x, 2 * (n + 1) * sizeof(int)); |
---|
696 | return FALSE; |
---|
697 | } |
---|
698 | |
---|
699 | BOOLEAN kQHWeight(leftv res,leftv v) |
---|
700 | { |
---|
701 | res->data=(char *)idQHomWeights((ideal)v->Data()); |
---|
702 | if (res->data==NULL) |
---|
703 | res->data=(char *)new intvec(pVariables); |
---|
704 | return FALSE; |
---|
705 | } |
---|
706 | |
---|
707 | short * iv2array(intvec * iv) |
---|
708 | { |
---|
709 | short *s=(short *)Alloc((pVariables+1)*sizeof(short)); |
---|
710 | int len=iv->length(); |
---|
711 | int i; |
---|
712 | |
---|
713 | for (i=1;i<=len;i++) |
---|
714 | s[i]= (*iv)[i-1]; |
---|
715 | for (;i<=pVariables;i++) |
---|
716 | s[i]= 1; |
---|
717 | return s; |
---|
718 | } |
---|
719 | |
---|
720 | /*2 |
---|
721 | *computes the degree of the leading term of the polynomial |
---|
722 | *with respect to given ecartWeights |
---|
723 | *used for Graebes method if BTEST1(31) is set |
---|
724 | */ |
---|
725 | int totaldegreeWecart(poly p) |
---|
726 | { |
---|
727 | int i; |
---|
728 | int j =0; |
---|
729 | |
---|
730 | for (i=pVariables; i; i--) |
---|
731 | j += (int)(pGetExp(p,i) * ecartWeights[i]); |
---|
732 | return j; |
---|
733 | } |
---|
734 | |
---|
735 | /*2 |
---|
736 | *computes the maximal degree of all terms of the polynomial |
---|
737 | *with respect to given ecartWeights and |
---|
738 | *computes the length of the polynomial |
---|
739 | *used for Graebes method if BTEST1(31) is set |
---|
740 | */ |
---|
741 | int maxdegreeWecart(poly p,int *l) |
---|
742 | { |
---|
743 | short k=pGetComp(p); |
---|
744 | int ll=1; |
---|
745 | int t,max; |
---|
746 | |
---|
747 | max=totaldegreeWecart(p); |
---|
748 | pIter(p); |
---|
749 | while ((p!=NULL) && (pGetComp(p)==k)) |
---|
750 | { |
---|
751 | t=totaldegreeWecart(p); |
---|
752 | if (t>max) max=t; |
---|
753 | ll++; |
---|
754 | pIter(p); |
---|
755 | } |
---|
756 | *l=ll; |
---|
757 | return max; |
---|
758 | } |
---|