1 | typedef int perm[100]; |
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2 | static void mpReplace(int j, int n, int &sign, int *perm); |
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3 | static int mpNextperm(perm * z, int max); |
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4 | static poly mp_Leibnitz(matrix a, const ring); |
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5 | static poly minuscopy (poly p, const ring); |
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6 | static poly p_Insert(poly p1, poly p2, const ring); |
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7 | |
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8 | static void mp_PartClean(matrix, int, int, const ring); |
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9 | static void mp_FinalClean(matrix, const ring); |
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10 | static int mp_PrepareRow (matrix, int, int, const ring); |
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11 | static int mp_PreparePiv (matrix, int, int, const ring); |
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12 | static int mp_PivBar(matrix, int, int, const ring); |
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13 | static int mp_PivRow(matrix, int, int, const ring); |
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14 | static float mp_PolyWeight(poly, const ring); |
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15 | static void mp_SwapRow(matrix, int, int, int, const ring); |
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16 | static void mp_SwapCol(matrix, int, int, int, const ring); |
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17 | static void mp_ElimBar(matrix, matrix, poly, int, int, const ring); |
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18 | |
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19 | /*2 |
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20 | * prepare one step of 'Bareiss' algorithm |
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21 | * for application in minor |
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22 | */ |
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23 | static int mp_PrepareRow (matrix a, int lr, int lc, const ring R) |
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24 | { |
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25 | int r; |
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26 | |
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27 | r = mp_PivBar(a,lr,lc, R); |
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28 | if(r==0) return 0; |
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29 | if(r<lr) mp_SwapRow(a, r, lr, lc, R); |
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30 | return 1; |
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31 | } |
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32 | |
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33 | /*2 |
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34 | * prepare one step of 'Bareiss' algorithm |
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35 | * for application in minor |
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36 | */ |
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37 | static int mp_PreparePiv (matrix a, int lr, int lc, const ring R) |
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38 | { |
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39 | int c; |
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40 | |
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41 | c = mp_PivRow(a, lr, lc, R); |
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42 | if(c==0) return 0; |
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43 | if(c<lc) mp_SwapCol(a, c, lr, lc, R); |
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44 | return 1; |
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45 | } |
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46 | |
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47 | /* |
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48 | * find best row |
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49 | */ |
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50 | static int mp_PivBar(matrix a, int lr, int lc, const ring R) |
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51 | { |
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52 | float f1, f2; |
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53 | poly *q1; |
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54 | int i,j,io; |
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55 | |
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56 | io = -1; |
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57 | f1 = 1.0e30; |
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58 | for (i=lr-1;i>=0;i--) |
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59 | { |
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60 | q1 = &(a->m)[i*a->ncols]; |
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61 | f2 = 0.0; |
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62 | for (j=lc-1;j>=0;j--) |
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63 | { |
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64 | if (q1[j]!=NULL) |
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65 | f2 += mp_PolyWeight(q1[j], R); |
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66 | } |
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67 | if ((f2!=0.0) && (f2<f1)) |
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68 | { |
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69 | f1 = f2; |
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70 | io = i; |
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71 | } |
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72 | } |
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73 | if (io<0) return 0; |
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74 | else return io+1; |
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75 | } |
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76 | |
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77 | /* |
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78 | * find pivot in the last row |
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79 | */ |
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80 | static int mp_PivRow(matrix a, int lr, int lc, const ring R) |
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81 | { |
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82 | float f1, f2; |
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83 | poly *q1; |
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84 | int j,jo; |
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85 | |
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86 | jo = -1; |
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87 | f1 = 1.0e30; |
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88 | q1 = &(a->m)[(lr-1)*a->ncols]; |
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89 | for (j=lc-1;j>=0;j--) |
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90 | { |
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91 | if (q1[j]!=NULL) |
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92 | { |
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93 | f2 = mp_PolyWeight(q1[j], R); |
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94 | if (f2<f1) |
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95 | { |
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96 | f1 = f2; |
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97 | jo = j; |
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98 | } |
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99 | } |
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100 | } |
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101 | if (jo<0) return 0; |
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102 | else return jo+1; |
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103 | } |
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104 | |
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105 | /* |
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106 | * weigth of a polynomial, for pivot strategy |
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107 | */ |
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108 | static float mp_PolyWeight(poly p, const ring R) |
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109 | { |
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110 | int i; |
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111 | float res; |
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112 | |
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113 | if (pNext(p) == NULL) |
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114 | { |
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115 | res = (float)n_Size(p_GetCoeff(p, R), R); |
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116 | for (i=rVar(R);i>0;i--) |
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117 | { |
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118 | if(p_GetExp(p,i, R)!=0) |
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119 | { |
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120 | res += 2.0; |
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121 | break; |
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122 | } |
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123 | } |
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124 | } |
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125 | else |
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126 | { |
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127 | res = 0.0; |
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128 | do |
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129 | { |
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130 | res += (float)n_Size(p_GetCoeff(p, R), R) + 2.0; |
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131 | pIter(p); |
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132 | } |
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133 | while (p); |
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134 | } |
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135 | return res; |
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136 | } |
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137 | |
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138 | static void mpSwapRow(matrix a, int pos, int lr, int lc) |
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139 | { |
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140 | poly sw; |
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141 | int j; |
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142 | poly* a2 = a->m; |
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143 | poly* a1 = &a2[a->ncols*(pos-1)]; |
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144 | |
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145 | a2 = &a2[a->ncols*(lr-1)]; |
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146 | for (j=lc-1; j>=0; j--) |
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147 | { |
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148 | sw = a1[j]; |
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149 | a1[j] = a2[j]; |
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150 | a2[j] = sw; |
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151 | } |
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152 | } |
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153 | |
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154 | static void mpSwapCol(matrix a, int pos, int lr, int lc) |
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155 | { |
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156 | poly sw; |
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157 | int j; |
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158 | poly* a2 = a->m; |
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159 | poly* a1 = &a2[pos-1]; |
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160 | |
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161 | a2 = &a2[lc-1]; |
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162 | for (j=a->ncols*(lr-1); j>=0; j-=a->ncols) |
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163 | { |
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164 | sw = a1[j]; |
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165 | a1[j] = a2[j]; |
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166 | a2[j] = sw; |
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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 | * C++ classes for Bareiss algorithm |
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172 | */ |
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173 | class row_col_weight |
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174 | { |
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175 | private: |
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176 | int ym, yn; |
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177 | public: |
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178 | float *wrow, *wcol; |
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179 | row_col_weight() : ym(0) {} |
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180 | row_col_weight(int, int); |
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181 | ~row_col_weight(); |
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182 | }; |
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183 | |
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184 | /*2 |
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185 | * a submatrix M of a matrix X[m,n]: |
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186 | * 0 <= i < s_m <= a_m |
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187 | * 0 <= j < s_n <= a_n |
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188 | * M = ( Xarray[qrow[i],qcol[j]] ) |
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189 | * if a_m = a_n and s_m = s_n |
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190 | * det(X) = sign*div^(s_m-1)*det(M) |
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191 | * resticted pivot for elimination |
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192 | * 0 <= j < piv_s |
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193 | */ |
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194 | class mp_permmatrix |
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195 | { |
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196 | private: |
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197 | int a_m, a_n, s_m, s_n, sign, piv_s; |
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198 | int *qrow, *qcol; |
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199 | poly *Xarray; |
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200 | ring R; |
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201 | |
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202 | void mpInitMat(); |
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203 | poly * mpRowAdr(int); |
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204 | poly * mpColAdr(int); |
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205 | void mpRowWeight(float *); |
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206 | void mpColWeight(float *); |
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207 | void mpRowSwap(int, int); |
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208 | void mpColSwap(int, int); |
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209 | public: |
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210 | mp_permmatrix() : a_m(0), R(NULL) {} |
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211 | mp_permmatrix(matrix, const ring); |
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212 | mp_permmatrix(mp_permmatrix *); |
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213 | ~mp_permmatrix(); |
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214 | int mpGetRow(); |
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215 | int mpGetCol(); |
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216 | int mpGetRdim(); |
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217 | int mpGetCdim(); |
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218 | int mpGetSign(); |
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219 | void mpSetSearch(int s); |
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220 | void mpSaveArray(); |
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221 | poly mpGetElem(int, int); |
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222 | void mpSetElem(poly, int, int); |
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223 | void mpDelElem(int, int); |
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224 | void mpElimBareiss(poly); |
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225 | int mpPivotBareiss(row_col_weight *); |
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226 | int mpPivotRow(row_col_weight *, int); |
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227 | void mpToIntvec(intvec *); |
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228 | void mpRowReorder(); |
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229 | void mpColReorder(); |
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230 | }; |
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231 | |
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232 | |
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233 | |
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234 | /*2 |
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235 | *returns the determinant of the matrix m; |
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236 | *uses Newtons formulea for symmetric functions |
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237 | */ |
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238 | poly mp_Det (matrix m, const ring R) |
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239 | { |
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240 | int i,j,k,n; |
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241 | poly p,q; |
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242 | matrix a, s; |
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243 | matrix ma[100]; |
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244 | number c=NULL, d=NULL, ONE=NULL; |
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245 | |
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246 | n = MATROWS(m); |
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247 | if (n != MATCOLS(m)) |
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248 | { |
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249 | Werror("det of %d x %d matrix",n,MATCOLS(m)); |
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250 | return NULL; |
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251 | } |
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252 | k=rChar(R); |
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253 | if ((k > 0) && (k <= n)) |
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254 | return mp_Leibnitz(m, R); |
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255 | ONE = n_Init(1, R); |
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256 | ma[1]=mp_Copy(m, R); |
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257 | k = (n+1) / 2; |
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258 | s = mpNew(1, n); |
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259 | MATELEM(s,1,1) = mp_Trace(m, R); |
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260 | for (i=2; i<=k; i++) |
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261 | { |
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262 | //ma[i] = mpNew(n,n); |
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263 | ma[i]=mp_Mult(ma[i-1], ma[1], R); |
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264 | MATELEM(s,1,i) = mp_Trace(ma[i], R); |
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265 | p_Test(MATELEM(s,1,i), R); |
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266 | } |
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267 | for (i=k+1; i<=n; i++) |
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268 | { |
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269 | MATELEM(s,1,i) = TraceOfProd(ma[i / 2], ma[(i+1) / 2], n, R); |
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270 | p_Test(MATELEM(s,1,i), R); |
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271 | } |
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272 | for (i=1; i<=k; i++) |
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273 | id_Delete((ideal *)&(ma[i]), R); |
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274 | /* the array s contains the traces of the powers of the matrix m, |
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275 | * these are the power sums of the eigenvalues of m */ |
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276 | a = mpNew(1,n); |
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277 | MATELEM(a,1,1) = minuscopy(MATELEM(s,1,1), R); |
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278 | for (i=2; i<=n; i++) |
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279 | { |
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280 | p = p_Copy(MATELEM(s,1,i), R); |
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281 | for (j=i-1; j>=1; j--) |
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282 | { |
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283 | q = pp_Mult_qq(MATELEM(s,1,j), MATELEM(a,1,i-j), R); |
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284 | p_Test(q, R); |
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285 | p = p_Add_q(p,q, R); |
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286 | } |
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287 | // c= -1/i |
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288 | d = n_Init(-(int)i, R); |
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289 | c = n_Div(ONE, d, R); |
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290 | n_Delete(&d, R); |
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291 | |
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292 | p_Mult_nn(p, c, R); |
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293 | p_Test(p, R); |
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294 | MATELEM(a,1,i) = p; |
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295 | n_Delete(&c, R); |
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296 | } |
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297 | /* the array a contains the elementary symmetric functions of the |
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298 | * eigenvalues of m */ |
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299 | for (i=1; i<=n-1; i++) |
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300 | { |
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301 | //p_Delete(&(MATELEM(a,1,i)), R); |
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302 | p_Delete(&(MATELEM(s,1,i)), R); |
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303 | } |
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304 | p_Delete(&(MATELEM(s,1,n)), R); |
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305 | /* up to a sign, the determinant is the n-th elementary symmetric function */ |
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306 | if ((n/2)*2 < n) |
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307 | { |
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308 | d = n_Init(-1, R); |
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309 | p_Mult_nn(MATELEM(a,1,n), d, R); |
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310 | n_Delete(&d, R); |
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311 | } |
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312 | n_Delete(&ONE, R); |
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313 | id_Delete((ideal *)&s, R); |
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314 | poly result=MATELEM(a,1,n); |
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315 | MATELEM(a,1,n)=NULL; |
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316 | id_Delete((ideal *)&a, R); |
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317 | return result; |
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318 | } |
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319 | |
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320 | |
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321 | ///*2 |
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322 | //*homogenize all elements of matrix (not the matrix itself) |
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323 | //*/ |
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324 | //matrix mpHomogen(matrix a, int v) |
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325 | //{ |
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326 | // int i,j; |
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327 | // poly p; |
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328 | // |
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329 | // for (i=1;i<=MATROWS(a);i++) |
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330 | // { |
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331 | // for (j=1;j<=MATCOLS(a);j++) |
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332 | // { |
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333 | // p=pHomogen(MATELEM(a,i,j),v); |
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334 | // p_Delete(&(MATELEM(a,i,j)), ?); |
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335 | // MATELEM(a,i,j)=p; |
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336 | // } |
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337 | // } |
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338 | // return a; |
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339 | //} |
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340 | |
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341 | |
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342 | |
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343 | /* --------------- internal stuff ------------------- */ |
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344 | |
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345 | row_col_weight::row_col_weight(int i, int j) |
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346 | { |
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347 | ym = i; |
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348 | yn = j; |
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349 | wrow = (float *)omAlloc(i*sizeof(float)); |
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350 | wcol = (float *)omAlloc(j*sizeof(float)); |
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351 | } |
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352 | |
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353 | row_col_weight::~row_col_weight() |
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354 | { |
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355 | if (ym!=0) |
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356 | { |
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357 | omFreeSize((ADDRESS)wcol, yn*sizeof(float)); |
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358 | omFreeSize((ADDRESS)wrow, ym*sizeof(float)); |
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359 | } |
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360 | } |
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361 | |
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362 | mp_permmatrix::mp_permmatrix(matrix A, const ring r) : sign(1), R(r) |
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363 | { |
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364 | a_m = A->nrows; |
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365 | a_n = A->ncols; |
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366 | this->mpInitMat(); |
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367 | Xarray = A->m; |
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368 | } |
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369 | |
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370 | mp_permmatrix::mp_permmatrix(mp_permmatrix *M) |
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371 | { |
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372 | poly p, *athis, *aM; |
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373 | int i, j; |
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374 | |
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375 | a_m = M->s_m; |
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376 | a_n = M->s_n; |
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377 | sign = M->sign; |
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378 | R = M->R; |
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379 | |
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380 | this->mpInitMat(); |
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381 | Xarray = (poly *)omAlloc0(a_m*a_n*sizeof(poly)); |
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382 | for (i=a_m-1; i>=0; i--) |
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383 | { |
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384 | athis = this->mpRowAdr(i); |
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385 | aM = M->mpRowAdr(i); |
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386 | for (j=a_n-1; j>=0; j--) |
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387 | { |
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388 | p = aM[M->qcol[j]]; |
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389 | if (p) |
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390 | { |
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391 | athis[j] = p_Copy(p, R); |
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392 | } |
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393 | } |
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394 | } |
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395 | } |
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396 | |
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397 | mp_permmatrix::~mp_permmatrix() |
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398 | { |
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399 | int k; |
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400 | |
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401 | if (a_m != 0) |
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402 | { |
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403 | omFreeSize((ADDRESS)qrow,a_m*sizeof(int)); |
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404 | omFreeSize((ADDRESS)qcol,a_n*sizeof(int)); |
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405 | if (Xarray != NULL) |
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406 | { |
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407 | for (k=a_m*a_n-1; k>=0; k--) |
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408 | p_Delete(&Xarray[k], R); |
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409 | omFreeSize((ADDRESS)Xarray,a_m*a_n*sizeof(poly)); |
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410 | } |
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411 | } |
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412 | } |
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413 | |
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414 | int mp_permmatrix::mpGetRdim() { return s_m; } |
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415 | |
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416 | int mp_permmatrix::mpGetCdim() { return s_n; } |
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417 | |
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418 | int mp_permmatrix::mpGetSign() { return sign; } |
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419 | |
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420 | void mp_permmatrix::mpSetSearch(int s) { piv_s = s; } |
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421 | |
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422 | void mp_permmatrix::mpSaveArray() { Xarray = NULL; } |
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423 | |
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424 | poly mp_permmatrix::mpGetElem(int r, int c) |
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425 | { |
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426 | return Xarray[a_n*qrow[r]+qcol[c]]; |
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427 | } |
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428 | |
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429 | void mp_permmatrix::mpSetElem(poly p, int r, int c) |
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430 | { |
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431 | Xarray[a_n*qrow[r]+qcol[c]] = p; |
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432 | } |
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433 | |
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434 | void mp_permmatrix::mpDelElem(int r, int c) |
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435 | { |
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436 | p_Delete(&Xarray[a_n*qrow[r]+qcol[c]], R); |
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437 | } |
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438 | |
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439 | /* |
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440 | * the Bareiss-type elimination with division by div (div != NULL) |
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441 | */ |
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442 | void mp_permmatrix::mpElimBareiss(poly div) |
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443 | { |
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444 | poly piv, elim, q1, q2, *ap, *a; |
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445 | int i, j, jj; |
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446 | |
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447 | ap = this->mpRowAdr(s_m); |
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448 | piv = ap[qcol[s_n]]; |
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449 | for(i=s_m-1; i>=0; i--) |
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450 | { |
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451 | a = this->mpRowAdr(i); |
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452 | elim = a[qcol[s_n]]; |
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453 | if (elim != NULL) |
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454 | { |
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455 | elim = p_Neg(elim, R); |
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456 | for (j=s_n-1; j>=0; j--) |
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457 | { |
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458 | q2 = NULL; |
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459 | jj = qcol[j]; |
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460 | if (ap[jj] != NULL) |
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461 | { |
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462 | q2 = SM_MULT(ap[jj], elim, div, R); |
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463 | if (a[jj] != NULL) |
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464 | { |
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465 | q1 = SM_MULT(a[jj], piv, div, R); |
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466 | p_Delete(&a[jj], R); |
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467 | q2 = p_Add_q(q2, q1, R); |
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468 | } |
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469 | } |
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470 | else if (a[jj] != NULL) |
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471 | { |
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472 | q2 = SM_MULT(a[jj], piv, div, R); |
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473 | } |
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474 | if ((q2!=NULL) && div) |
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475 | SM_DIV(q2, div, R); |
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476 | a[jj] = q2; |
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477 | } |
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478 | p_Delete(&a[qcol[s_n]], R); |
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479 | } |
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480 | else |
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481 | { |
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482 | for (j=s_n-1; j>=0; j--) |
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483 | { |
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484 | jj = qcol[j]; |
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485 | if (a[jj] != NULL) |
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486 | { |
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487 | q2 = SM_MULT(a[jj], piv, div, R); |
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488 | p_Delete(&a[jj], R); |
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489 | if (div) |
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490 | SM_DIV(q2, div, R); |
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491 | a[jj] = q2; |
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492 | } |
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493 | } |
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494 | } |
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495 | } |
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496 | } |
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497 | |
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498 | /*2 |
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499 | * pivot strategy for Bareiss algorithm |
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500 | */ |
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501 | int mp_permmatrix::mpPivotBareiss(row_col_weight *C) |
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502 | { |
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503 | poly p, *a; |
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504 | int i, j, iopt, jopt; |
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505 | float sum, f1, f2, fo, r, ro, lp; |
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506 | float *dr = C->wrow, *dc = C->wcol; |
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507 | |
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508 | fo = 1.0e20; |
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509 | ro = 0.0; |
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510 | iopt = jopt = -1; |
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511 | |
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512 | s_n--; |
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513 | s_m--; |
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514 | if (s_m == 0) |
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515 | return 0; |
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516 | if (s_n == 0) |
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517 | { |
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518 | for(i=s_m; i>=0; i--) |
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519 | { |
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520 | p = this->mpRowAdr(i)[qcol[0]]; |
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521 | if (p) |
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522 | { |
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523 | f1 = mp_PolyWeight(p, R); |
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524 | if (f1 < fo) |
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525 | { |
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526 | fo = f1; |
---|
527 | if (iopt >= 0) |
---|
528 | p_Delete(&(this->mpRowAdr(iopt)[qcol[0]]), R); |
---|
529 | iopt = i; |
---|
530 | } |
---|
531 | else |
---|
532 | p_Delete(&(this->mpRowAdr(i)[qcol[0]]), R); |
---|
533 | } |
---|
534 | } |
---|
535 | if (iopt >= 0) |
---|
536 | mpReplace(iopt, s_m, sign, qrow); |
---|
537 | return 0; |
---|
538 | } |
---|
539 | this->mpRowWeight(dr); |
---|
540 | this->mpColWeight(dc); |
---|
541 | sum = 0.0; |
---|
542 | for(i=s_m; i>=0; i--) |
---|
543 | sum += dr[i]; |
---|
544 | for(i=s_m; i>=0; i--) |
---|
545 | { |
---|
546 | r = dr[i]; |
---|
547 | a = this->mpRowAdr(i); |
---|
548 | for(j=s_n; j>=0; j--) |
---|
549 | { |
---|
550 | p = a[qcol[j]]; |
---|
551 | if (p) |
---|
552 | { |
---|
553 | lp = mp_PolyWeight(p, R); |
---|
554 | ro = r - lp; |
---|
555 | f1 = ro * (dc[j]-lp); |
---|
556 | if (f1 != 0.0) |
---|
557 | { |
---|
558 | f2 = lp * (sum - ro - dc[j]); |
---|
559 | f2 += f1; |
---|
560 | } |
---|
561 | else |
---|
562 | f2 = lp-r-dc[j]; |
---|
563 | if (f2 < fo) |
---|
564 | { |
---|
565 | fo = f2; |
---|
566 | iopt = i; |
---|
567 | jopt = j; |
---|
568 | } |
---|
569 | } |
---|
570 | } |
---|
571 | } |
---|
572 | if (iopt < 0) |
---|
573 | return 0; |
---|
574 | mpReplace(iopt, s_m, sign, qrow); |
---|
575 | mpReplace(jopt, s_n, sign, qcol); |
---|
576 | return 1; |
---|
577 | } |
---|
578 | |
---|
579 | /*2 |
---|
580 | * pivot strategy for Bareiss algorithm with defined row |
---|
581 | */ |
---|
582 | int mp_permmatrix::mpPivotRow(row_col_weight *C, int row) |
---|
583 | { |
---|
584 | poly p, *a; |
---|
585 | int j, iopt, jopt; |
---|
586 | float sum, f1, f2, fo, r, ro, lp; |
---|
587 | float *dr = C->wrow, *dc = C->wcol; |
---|
588 | |
---|
589 | fo = 1.0e20; |
---|
590 | ro = 0.0; |
---|
591 | iopt = jopt = -1; |
---|
592 | |
---|
593 | s_n--; |
---|
594 | s_m--; |
---|
595 | if (s_m == 0) |
---|
596 | return 0; |
---|
597 | if (s_n == 0) |
---|
598 | { |
---|
599 | p = this->mpRowAdr(row)[qcol[0]]; |
---|
600 | if (p) |
---|
601 | { |
---|
602 | f1 = mp_PolyWeight(p, R); |
---|
603 | if (f1 < fo) |
---|
604 | { |
---|
605 | fo = f1; |
---|
606 | if (iopt >= 0) |
---|
607 | p_Delete(&(this->mpRowAdr(iopt)[qcol[0]]), R); |
---|
608 | iopt = row; |
---|
609 | } |
---|
610 | else |
---|
611 | p_Delete(&(this->mpRowAdr(row)[qcol[0]]), R); |
---|
612 | } |
---|
613 | if (iopt >= 0) |
---|
614 | mpReplace(iopt, s_m, sign, qrow); |
---|
615 | return 0; |
---|
616 | } |
---|
617 | this->mpRowWeight(dr); |
---|
618 | this->mpColWeight(dc); |
---|
619 | sum = 0.0; |
---|
620 | for(j=s_m; j>=0; j--) |
---|
621 | sum += dr[j]; |
---|
622 | r = dr[row]; |
---|
623 | a = this->mpRowAdr(row); |
---|
624 | for(j=s_n; j>=0; j--) |
---|
625 | { |
---|
626 | p = a[qcol[j]]; |
---|
627 | if (p) |
---|
628 | { |
---|
629 | lp = mp_PolyWeight(p, R); |
---|
630 | ro = r - lp; |
---|
631 | f1 = ro * (dc[j]-lp); |
---|
632 | if (f1 != 0.0) |
---|
633 | { |
---|
634 | f2 = lp * (sum - ro - dc[j]); |
---|
635 | f2 += f1; |
---|
636 | } |
---|
637 | else |
---|
638 | f2 = lp-r-dc[j]; |
---|
639 | if (f2 < fo) |
---|
640 | { |
---|
641 | fo = f2; |
---|
642 | iopt = row; |
---|
643 | jopt = j; |
---|
644 | } |
---|
645 | } |
---|
646 | } |
---|
647 | if (iopt < 0) |
---|
648 | return 0; |
---|
649 | mpReplace(iopt, s_m, sign, qrow); |
---|
650 | mpReplace(jopt, s_n, sign, qcol); |
---|
651 | return 1; |
---|
652 | } |
---|
653 | |
---|
654 | void mp_permmatrix::mpToIntvec(intvec *v) |
---|
655 | { |
---|
656 | int i; |
---|
657 | |
---|
658 | for (i=v->rows()-1; i>=0; i--) |
---|
659 | (*v)[i] = qcol[i]+1; |
---|
660 | } |
---|
661 | |
---|
662 | void mp_permmatrix::mpRowReorder() |
---|
663 | { |
---|
664 | int k, i, i1, i2; |
---|
665 | |
---|
666 | if (a_m > a_n) |
---|
667 | k = a_m - a_n; |
---|
668 | else |
---|
669 | k = 0; |
---|
670 | for (i=a_m-1; i>=k; i--) |
---|
671 | { |
---|
672 | i1 = qrow[i]; |
---|
673 | if (i1 != i) |
---|
674 | { |
---|
675 | this->mpRowSwap(i1, i); |
---|
676 | i2 = 0; |
---|
677 | while (qrow[i2] != i) i2++; |
---|
678 | qrow[i2] = i1; |
---|
679 | } |
---|
680 | } |
---|
681 | } |
---|
682 | |
---|
683 | void mp_permmatrix::mpColReorder() |
---|
684 | { |
---|
685 | int k, j, j1, j2; |
---|
686 | |
---|
687 | if (a_n > a_m) |
---|
688 | k = a_n - a_m; |
---|
689 | else |
---|
690 | k = 0; |
---|
691 | for (j=a_n-1; j>=k; j--) |
---|
692 | { |
---|
693 | j1 = qcol[j]; |
---|
694 | if (j1 != j) |
---|
695 | { |
---|
696 | this->mpColSwap(j1, j); |
---|
697 | j2 = 0; |
---|
698 | while (qcol[j2] != j) j2++; |
---|
699 | qcol[j2] = j1; |
---|
700 | } |
---|
701 | } |
---|
702 | } |
---|
703 | |
---|
704 | // private |
---|
705 | void mp_permmatrix::mpInitMat() |
---|
706 | { |
---|
707 | int k; |
---|
708 | |
---|
709 | s_m = a_m; |
---|
710 | s_n = a_n; |
---|
711 | piv_s = 0; |
---|
712 | qrow = (int *)omAlloc(a_m*sizeof(int)); |
---|
713 | qcol = (int *)omAlloc(a_n*sizeof(int)); |
---|
714 | for (k=a_m-1; k>=0; k--) qrow[k] = k; |
---|
715 | for (k=a_n-1; k>=0; k--) qcol[k] = k; |
---|
716 | } |
---|
717 | |
---|
718 | poly * mp_permmatrix::mpRowAdr(int r) |
---|
719 | { |
---|
720 | return &(Xarray[a_n*qrow[r]]); |
---|
721 | } |
---|
722 | |
---|
723 | poly * mp_permmatrix::mpColAdr(int c) |
---|
724 | { |
---|
725 | return &(Xarray[qcol[c]]); |
---|
726 | } |
---|
727 | |
---|
728 | void mp_permmatrix::mpRowWeight(float *wrow) |
---|
729 | { |
---|
730 | poly p, *a; |
---|
731 | int i, j; |
---|
732 | float count; |
---|
733 | |
---|
734 | for (i=s_m; i>=0; i--) |
---|
735 | { |
---|
736 | a = this->mpRowAdr(i); |
---|
737 | count = 0.0; |
---|
738 | for(j=s_n; j>=0; j--) |
---|
739 | { |
---|
740 | p = a[qcol[j]]; |
---|
741 | if (p) |
---|
742 | count += mp_PolyWeight(p, R); |
---|
743 | } |
---|
744 | wrow[i] = count; |
---|
745 | } |
---|
746 | } |
---|
747 | |
---|
748 | void mp_permmatrix::mpColWeight(float *wcol) |
---|
749 | { |
---|
750 | poly p, *a; |
---|
751 | int i, j; |
---|
752 | float count; |
---|
753 | |
---|
754 | for (j=s_n; j>=0; j--) |
---|
755 | { |
---|
756 | a = this->mpColAdr(j); |
---|
757 | count = 0.0; |
---|
758 | for(i=s_m; i>=0; i--) |
---|
759 | { |
---|
760 | p = a[a_n*qrow[i]]; |
---|
761 | if (p) |
---|
762 | count += mp_PolyWeight(p, R); |
---|
763 | } |
---|
764 | wcol[j] = count; |
---|
765 | } |
---|
766 | } |
---|
767 | |
---|
768 | void mp_permmatrix::mpRowSwap(int i1, int i2) |
---|
769 | { |
---|
770 | poly p, *a1, *a2; |
---|
771 | int j; |
---|
772 | |
---|
773 | a1 = &(Xarray[a_n*i1]); |
---|
774 | a2 = &(Xarray[a_n*i2]); |
---|
775 | for (j=a_n-1; j>= 0; j--) |
---|
776 | { |
---|
777 | p = a1[j]; |
---|
778 | a1[j] = a2[j]; |
---|
779 | a2[j] = p; |
---|
780 | } |
---|
781 | } |
---|
782 | |
---|
783 | void mp_permmatrix::mpColSwap(int j1, int j2) |
---|
784 | { |
---|
785 | poly p, *a1, *a2; |
---|
786 | int i, k = a_n*a_m; |
---|
787 | |
---|
788 | a1 = &(Xarray[j1]); |
---|
789 | a2 = &(Xarray[j2]); |
---|
790 | for (i=0; i< k; i+=a_n) |
---|
791 | { |
---|
792 | p = a1[i]; |
---|
793 | a1[i] = a2[i]; |
---|
794 | a2[i] = p; |
---|
795 | } |
---|
796 | } |
---|
797 | |
---|
798 | int mp_permmatrix::mpGetRow() |
---|
799 | { |
---|
800 | return qrow[s_m]; |
---|
801 | } |
---|
802 | |
---|
803 | int mp_permmatrix::mpGetCol() |
---|
804 | { |
---|
805 | return qcol[s_n]; |
---|
806 | } |
---|
807 | |
---|
808 | /// perform replacement for pivot strategy in Bareiss algorithm |
---|
809 | /// change sign of determinant |
---|
810 | static void mpReplace(int j, int n, int &sign, int *perm) |
---|
811 | { |
---|
812 | int k; |
---|
813 | |
---|
814 | if (j != n) |
---|
815 | { |
---|
816 | k = perm[n]; |
---|
817 | perm[n] = perm[j]; |
---|
818 | perm[j] = k; |
---|
819 | sign = -sign; |
---|
820 | } |
---|
821 | } |
---|
822 | |
---|
823 | static int mpNextperm(perm * z, int max) |
---|
824 | { |
---|
825 | int s, i, k, t; |
---|
826 | s = max; |
---|
827 | do |
---|
828 | { |
---|
829 | s--; |
---|
830 | } |
---|
831 | while ((s > 0) && ((*z)[s] >= (*z)[s+1])); |
---|
832 | if (s==0) |
---|
833 | return 0; |
---|
834 | do |
---|
835 | { |
---|
836 | (*z)[s]++; |
---|
837 | k = 0; |
---|
838 | do |
---|
839 | { |
---|
840 | k++; |
---|
841 | } |
---|
842 | while (((*z)[k] != (*z)[s]) && (k!=s)); |
---|
843 | } |
---|
844 | while (k < s); |
---|
845 | for (i=s+1; i <= max; i++) |
---|
846 | { |
---|
847 | (*z)[i]=0; |
---|
848 | do |
---|
849 | { |
---|
850 | (*z)[i]++; |
---|
851 | k=0; |
---|
852 | do |
---|
853 | { |
---|
854 | k++; |
---|
855 | } |
---|
856 | while (((*z)[k] != (*z)[i]) && (k != i)); |
---|
857 | } |
---|
858 | while (k < i); |
---|
859 | } |
---|
860 | s = max+1; |
---|
861 | do |
---|
862 | { |
---|
863 | s--; |
---|
864 | } |
---|
865 | while ((s > 0) && ((*z)[s] > (*z)[s+1])); |
---|
866 | t = 1; |
---|
867 | for (i=1; i<max; i++) |
---|
868 | for (k=i+1; k<=max; k++) |
---|
869 | if ((*z)[k] < (*z)[i]) |
---|
870 | t = -t; |
---|
871 | (*z)[0] = t; |
---|
872 | return s; |
---|
873 | } |
---|
874 | |
---|
875 | static poly mp_Leibnitz(matrix a, const ring R) |
---|
876 | { |
---|
877 | int i, e, n; |
---|
878 | poly p, d; |
---|
879 | perm z; |
---|
880 | |
---|
881 | n = MATROWS(a); |
---|
882 | memset(&z,0,(n+2)*sizeof(int)); |
---|
883 | p = p_One(R); |
---|
884 | for (i=1; i <= n; i++) |
---|
885 | p = p_Mult_q(p, p_Copy(MATELEM(a, i, i), R), R); |
---|
886 | d = p; |
---|
887 | for (i=1; i<= n; i++) |
---|
888 | z[i] = i; |
---|
889 | z[0]=1; |
---|
890 | e = 1; |
---|
891 | if (n!=1) |
---|
892 | { |
---|
893 | while (e) |
---|
894 | { |
---|
895 | e = mpNextperm((perm *)&z, n); |
---|
896 | p = p_One(R); |
---|
897 | for (i = 1; i <= n; i++) |
---|
898 | p = p_Mult_q(p, p_Copy(MATELEM(a, i, z[i]), R), R); |
---|
899 | if (z[0] > 0) |
---|
900 | d = p_Add_q(d, p, R); |
---|
901 | else |
---|
902 | d = p_Sub(d, p, R); |
---|
903 | } |
---|
904 | } |
---|
905 | return d; |
---|
906 | } |
---|
907 | |
---|
908 | static void mp_ElimBar(matrix a0, matrix re, poly div, int lr, int lc, const ring R) |
---|
909 | { |
---|
910 | int r=lr-1, c=lc-1; |
---|
911 | poly *b = a0->m, *x = re->m; |
---|
912 | poly piv, elim, q1, q2, *ap, *a, *q; |
---|
913 | int i, j; |
---|
914 | |
---|
915 | ap = &b[r*a0->ncols]; |
---|
916 | piv = ap[c]; |
---|
917 | for(j=c-1; j>=0; j--) |
---|
918 | if (ap[j] != NULL) ap[j] = p_Neg(ap[j], R); |
---|
919 | for(i=r-1; i>=0; i--) |
---|
920 | { |
---|
921 | a = &b[i*a0->ncols]; |
---|
922 | q = &x[i*re->ncols]; |
---|
923 | if (a[c] != NULL) |
---|
924 | { |
---|
925 | elim = a[c]; |
---|
926 | for (j=c-1; j>=0; j--) |
---|
927 | { |
---|
928 | q1 = NULL; |
---|
929 | if (a[j] != NULL) |
---|
930 | { |
---|
931 | q1 = SM_MULT(a[j], piv, div, R); |
---|
932 | if (ap[j] != NULL) |
---|
933 | { |
---|
934 | q2 = SM_MULT(ap[j], elim, div, R); |
---|
935 | q1 = p_Add_q(q1,q2, R); |
---|
936 | } |
---|
937 | } |
---|
938 | else if (ap[j] != NULL) |
---|
939 | q1 = SM_MULT(ap[j], elim, div, R); |
---|
940 | if (q1 != NULL) |
---|
941 | { |
---|
942 | if (div) |
---|
943 | SM_DIV(q1, div, R); |
---|
944 | q[j] = q1; |
---|
945 | } |
---|
946 | } |
---|
947 | } |
---|
948 | else |
---|
949 | { |
---|
950 | for (j=c-1; j>=0; j--) |
---|
951 | { |
---|
952 | if (a[j] != NULL) |
---|
953 | { |
---|
954 | q1 = SM_MULT(a[j], piv, div, R); |
---|
955 | if (div) |
---|
956 | SM_DIV(q1, div, R); |
---|
957 | q[j] = q1; |
---|
958 | } |
---|
959 | } |
---|
960 | } |
---|
961 | } |
---|
962 | } |
---|
963 | |
---|