1 | /**************************************** |
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2 | * Computer Algebra System SINGULAR * |
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3 | ****************************************/ |
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4 | /* $Id: sparsmat.cc,v 1.4 1999-03-03 16:58:52 Singular Exp $ */ |
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5 | |
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6 | /* |
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7 | * ABSTRACT: operations with sparse matrices (bareiss, ...) |
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8 | */ |
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9 | |
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10 | #include "mod2.h" |
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11 | #include "tok.h" |
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12 | #include "febase.h" |
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13 | #include "structs.h" |
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14 | #include "intvec.h" |
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15 | #include "lists.h" |
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16 | #include "ring.h" |
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17 | #include "polys.h" |
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18 | #include "ipid.h" |
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19 | #include "ideals.h" |
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20 | #include "numbers.h" |
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21 | #include "sparsmat.h" |
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22 | |
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23 | /* ----------------- macros ------------------ */ |
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24 | /* #define OLD_DIV */ |
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25 | #ifdef OLD_DIV |
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26 | #define SM_MULT(A,B,C) smMult(A,B) |
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27 | #define SM_DIV smPolyDiv |
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28 | #else |
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29 | #define SM_MULT smMultDiv |
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30 | #define SM_DIV smSpecialPolyDiv |
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31 | #endif |
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32 | /* ----------------- general definitions ------------------ */ |
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33 | |
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34 | /* elements of a 'sparse' matrix in SINGULAR */ |
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35 | typedef struct smprec sm_prec; |
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36 | typedef sm_prec * smpoly; |
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37 | struct smprec{ |
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38 | smpoly n; // the next element |
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39 | int pos; // position |
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40 | int e; // level |
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41 | poly m; // the element |
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42 | float f; // complexity of the element |
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43 | }; |
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44 | |
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45 | /* declare internal 'C' stuff */ |
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46 | static void smDebug() { int k=0; } |
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47 | static void smExactPolyDiv(poly, poly); |
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48 | static BOOLEAN smIsScalar(const poly); |
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49 | static BOOLEAN smIsNegQuot(poly, const poly, const poly); |
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50 | static poly smEMult(poly, const poly); |
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51 | static BOOLEAN smCheckLead(const poly, const poly); |
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52 | static poly smDMult(poly, const poly); |
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53 | static void smPolyDivN(poly a, const number); |
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54 | static BOOLEAN smSmaller(poly, poly); |
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55 | static void smCombineChain(poly *, poly); |
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56 | static void smFindRef(poly *, poly *, poly); |
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57 | |
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58 | static void smElemDelete(smpoly *); |
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59 | static smpoly smElemCopy(smpoly); |
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60 | static float smPolyWeight(smpoly); |
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61 | static smpoly smPoly2Smpoly(poly p); |
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62 | static poly smSmpoly2Poly(smpoly a); |
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63 | |
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64 | /* class for sparse matrix: |
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65 | * 3 parts of matrix during the algorithm |
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66 | * m_act[cols][pos(rows)] => m_row[rows][pos(cols)] => m_res[cols][pos(rows)] |
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67 | * input pivotcols as rows result |
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68 | * pivot like a stack from pivot and pivotcols |
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69 | * elimination rows reordered according |
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70 | * to pivot choise |
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71 | * stored in perm |
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72 | * a step is as follows |
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73 | * - search of pivot (smPivot) |
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74 | * - swap pivot column and last column (smSwapC) |
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75 | * select pivotrow to piv and red (smSelectPR) |
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76 | * consider sign |
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77 | * - elimination (smInitElim, sm0Elim, sm1Elim) |
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78 | * clear zero column as result of elimination (smZeroElim) |
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79 | * - tranfer from |
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80 | * piv and m_row to m_res (smRowToCol) |
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81 | * m_act to m_row (smColToRow) |
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82 | */ |
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83 | class sparse_mat{ |
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84 | private: |
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85 | int nrows, ncols; // dimension of the problem |
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86 | int sign; // for determinant (start: 1) |
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87 | int act; // number of unreduced columns (start: ncols) |
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88 | int crd; // number of reduced columns (start: 0) |
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89 | int tored; // border for rows to reduce |
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90 | int rpiv, cpiv; // position of the pivot |
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91 | unsigned short *perm;// permutation of rows |
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92 | float wpoints; // weight of all points |
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93 | float *wrw, *wcl; // weights of rows and columns |
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94 | smpoly * m_act; // unreduced columns |
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95 | smpoly * m_res; // reduced columns (result) |
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96 | smpoly * m_row; // reduced part of rows |
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97 | smpoly red; // row to reduce |
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98 | smpoly piv, oldpiv; // pivot and previous pivot |
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99 | smpoly dumm; // allocated dummy |
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100 | void smColToRow(); |
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101 | void smRowToCol(); |
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102 | void smFinalMult(); |
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103 | void smSparseHomog(); |
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104 | void smWeights(); |
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105 | void smPivot(); |
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106 | void smNewWeights(); |
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107 | void smNewPivot(); |
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108 | void smZeroElim(); |
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109 | void smToredElim(); |
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110 | void smCopToRes(); |
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111 | void smSelectPR(); |
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112 | void smElim(); |
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113 | void sm1Elim(); |
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114 | void smHElim(); |
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115 | void smMultCol(); |
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116 | poly smMultPoly(smpoly); |
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117 | public: |
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118 | sparse_mat(ideal); |
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119 | ~sparse_mat(); |
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120 | smpoly * smGetAct() { return m_act; } |
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121 | int smGetRed() { return tored; } |
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122 | ideal smRes2Mod(); |
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123 | void smBareiss(int, int); |
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124 | void smNewBareiss(int, int); |
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125 | void smToIntvec(intvec *); |
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126 | }; |
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127 | |
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128 | /* ----------------- basics (used from 'C') ------------------ */ |
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129 | |
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130 | lists smCallBareiss(ideal I, int x, int y) |
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131 | { |
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132 | lists res=(lists)Alloc(sizeof(slists)); |
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133 | ideal II = idCopy(I); |
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134 | sparse_mat *bareiss = new sparse_mat(II); |
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135 | intvec *v; |
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136 | ideal m; |
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137 | |
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138 | idDelete(&II); |
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139 | if (bareiss->smGetAct() == NULL) |
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140 | { |
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141 | Free((ADDRESS)res, sizeof(slists)); |
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142 | return NULL; |
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143 | } |
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144 | bareiss->smBareiss(x, y); |
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145 | m = bareiss->smRes2Mod(); |
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146 | v = new intvec(bareiss->smGetRed()); |
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147 | bareiss->smToIntvec(v); |
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148 | delete bareiss; |
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149 | res->Init(2); |
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150 | res->m[0].rtyp=MODUL_CMD; |
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151 | res->m[0].data=(void *)m; |
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152 | res->m[1].rtyp=INTVEC_CMD; |
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153 | res->m[1].data=(void *)v; |
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154 | return res; |
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155 | } |
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156 | |
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157 | lists smCallNewBareiss(ideal I, int x, int y) |
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158 | { |
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159 | lists res=(lists)Alloc(sizeof(slists)); |
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160 | ring origR =NULL; |
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161 | sip_sring tmpR; |
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162 | ideal II; |
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163 | if (currRing->order[0]!=ringorder_c) |
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164 | { |
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165 | origR =currRing; |
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166 | tmpR=*origR; |
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167 | int *ord=(int*)Alloc0(3*sizeof(int)); |
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168 | int *block0=(int*)Alloc(3*sizeof(int)); |
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169 | int *block1=(int*)Alloc(3*sizeof(int)); |
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170 | ord[0]=ringorder_c; |
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171 | ord[1]=ringorder_dp; |
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172 | tmpR.order=ord; |
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173 | block0[1]=1; |
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174 | tmpR.block0=block0; |
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175 | block1[1]=tmpR.N; |
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176 | tmpR.block1=block1; |
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177 | rComplete(&tmpR,1); |
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178 | rChangeCurrRing(&tmpR,TRUE); |
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179 | // fetch data from the old ring |
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180 | II=idInit(IDELEMS(I),I->rank); |
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181 | int k; |
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182 | for (k=0;k<IDELEMS(I);k++) II->m[k] = pFetchCopy(origR, I->m[k]); |
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183 | } |
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184 | else |
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185 | { |
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186 | II=idCopy(I); |
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187 | } |
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188 | sparse_mat *bareiss = new sparse_mat(II); |
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189 | ideal mm=II; |
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190 | intvec *v; |
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191 | ideal m; |
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192 | |
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193 | if (bareiss->smGetAct() == NULL) |
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194 | { |
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195 | delete bareiss; |
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196 | if (origR!=NULL) |
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197 | { |
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198 | rChangeCurrRing(origR,TRUE); |
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199 | rUnComplete(&tmpR); |
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200 | Free((ADDRESS)tmpR.order,3*sizeof(int)); |
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201 | Free((ADDRESS)tmpR.block0,3*sizeof(int)); |
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202 | Free((ADDRESS)tmpR.block1,3*sizeof(int)); |
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203 | } |
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204 | v=new intvec(1,pVariables); |
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205 | } |
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206 | else |
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207 | { |
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208 | idDelete(&II); |
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209 | bareiss->smNewBareiss(x, y); |
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210 | m = bareiss->smRes2Mod(); |
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211 | v = new intvec(bareiss->smGetRed()); |
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212 | bareiss->smToIntvec(v); |
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213 | delete bareiss; |
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214 | if (origR!=NULL) |
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215 | { |
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216 | rChangeCurrRing(origR,TRUE); |
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217 | mm=idInit(IDELEMS(m),m->rank); |
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218 | int k; |
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219 | for (k=0;k<IDELEMS(m);k++) mm->m[k] = pFetchCopy(origR, m->m[k]); |
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220 | rChangeCurrRing(&tmpR,FALSE); |
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221 | idDelete(&m); |
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222 | rChangeCurrRing(origR,TRUE); |
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223 | rUnComplete(&tmpR); |
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224 | Free((ADDRESS)tmpR.order,3*sizeof(int)); |
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225 | Free((ADDRESS)tmpR.block0,3*sizeof(int)); |
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226 | Free((ADDRESS)tmpR.block1,3*sizeof(int)); |
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227 | } |
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228 | else |
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229 | { |
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230 | mm=m; |
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231 | } |
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232 | } |
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233 | res->Init(2); |
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234 | res->m[0].rtyp=MODUL_CMD; |
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235 | res->m[0].data=(void *)mm; |
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236 | res->m[1].rtyp=INTVEC_CMD; |
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237 | res->m[1].data=(void *)v; |
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238 | return res; |
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239 | } |
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240 | |
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241 | /* |
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242 | * constructor |
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243 | */ |
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244 | sparse_mat::sparse_mat(ideal smat) |
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245 | { |
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246 | int i; |
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247 | polyset pmat; |
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248 | |
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249 | ncols = smat->ncols; |
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250 | nrows = idRankFreeModule(smat); |
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251 | if (nrows <= 0) |
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252 | { |
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253 | m_act = NULL; |
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254 | return; |
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255 | } |
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256 | sign = 1; |
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257 | act = ncols; |
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258 | crd = 0; |
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259 | tored = nrows; // without border |
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260 | i = tored+1; |
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261 | perm = (unsigned short *)Alloc(sizeof(unsigned short)*i); |
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262 | m_row = (smpoly *)Alloc0(sizeof(smpoly)*i); |
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263 | wrw = (float *)Alloc(sizeof(float)*i); |
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264 | i = ncols+1; |
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265 | wcl = (float *)Alloc(sizeof(float)*i); |
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266 | m_act = (smpoly *)Alloc(sizeof(smpoly)*i); |
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267 | m_res = (smpoly *)Alloc0(sizeof(smpoly)*i); |
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268 | dumm = (smpoly)Alloc(sizeof(smprec)); |
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269 | m_res[0] = (smpoly)Alloc(sizeof(smprec)); |
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270 | m_res[0]->m = NULL; |
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271 | pmat = smat->m; |
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272 | for(i=ncols; i; i--) |
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273 | { |
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274 | m_act[i] = smPoly2Smpoly(pmat[i-1]); |
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275 | pmat[i-1] = NULL; |
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276 | } |
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277 | this->smZeroElim(); |
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278 | oldpiv = NULL; |
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279 | } |
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280 | |
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281 | /* |
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282 | * destructor |
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283 | */ |
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284 | sparse_mat::~sparse_mat() |
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285 | { |
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286 | int i; |
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287 | if (m_act == NULL) return; |
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288 | Free((ADDRESS)m_res[0], sizeof(smprec)); |
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289 | Free((ADDRESS)dumm, sizeof(smprec)); |
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290 | i = ncols+1; |
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291 | Free((ADDRESS)m_res, sizeof(smpoly)*i); |
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292 | Free((ADDRESS)m_act, sizeof(smpoly)*i); |
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293 | Free((ADDRESS)wcl, sizeof(float)*i); |
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294 | i = nrows+1; |
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295 | Free((ADDRESS)wrw, sizeof(float)*i); |
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296 | Free((ADDRESS)m_row, sizeof(smpoly)*i); |
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297 | Free((ADDRESS)perm, sizeof(unsigned short)*i); |
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298 | } |
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299 | |
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300 | /* |
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301 | * transform the result to a module |
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302 | */ |
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303 | ideal sparse_mat::smRes2Mod() |
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304 | { |
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305 | ideal res = idInit(crd, crd); |
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306 | int i; |
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307 | |
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308 | for (i=crd; i; i--) res->m[i-1] = smSmpoly2Poly(m_res[i]); |
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309 | res->rank = idRankFreeModule(res); |
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310 | return res; |
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311 | } |
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312 | |
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313 | /* |
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314 | * permutation of rows |
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315 | */ |
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316 | void sparse_mat::smToIntvec(intvec *v) |
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317 | { |
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318 | int i; |
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319 | |
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320 | for (i=v->rows()-1; i>=0; i--) |
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321 | (*v)[i] = perm[i+1]; |
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322 | } |
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323 | |
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324 | /* |
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325 | * the Bareiss elimination: |
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326 | * - with x unreduced last rows, pivots from here are not allowed |
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327 | * - the method will finish for number of unreduced columns < y |
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328 | */ |
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329 | void sparse_mat::smBareiss(int x, int y) |
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330 | { |
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331 | if ((x > 0) && (x < nrows)) |
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332 | { |
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333 | tored -= x; |
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334 | this->smToredElim(); |
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335 | } |
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336 | if (y < 2) y = 2; |
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337 | if (act < y) |
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338 | { |
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339 | if (act != 0) |
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340 | { |
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341 | oldpiv = NULL; |
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342 | this->smCopToRes(); |
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343 | } |
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344 | return; |
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345 | } |
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346 | this->smPivot(); |
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347 | this->smSelectPR(); |
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348 | this->smElim(); |
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349 | crd++; |
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350 | this->smColToRow(); |
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351 | act--; |
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352 | this->smRowToCol(); |
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353 | this->smZeroElim(); |
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354 | if (tored != nrows) |
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355 | this->smToredElim(); |
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356 | if (act < y) |
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357 | { |
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358 | this->smCopToRes(); |
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359 | return; |
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360 | } |
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361 | loop |
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362 | { |
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363 | this->smPivot(); |
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364 | oldpiv = piv; |
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365 | this->smSelectPR(); |
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366 | this->smElim(); |
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367 | crd++; |
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368 | this->smColToRow(); |
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369 | act--; |
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370 | this->smRowToCol(); |
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371 | this->smZeroElim(); |
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372 | if (tored != nrows) |
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373 | this->smToredElim(); |
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374 | if (act < y) |
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375 | { |
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376 | if (act != 0) |
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377 | { |
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378 | this->smCopToRes(); |
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379 | } |
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380 | else |
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381 | tored = crd; |
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382 | return; |
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383 | } |
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384 | } |
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385 | } |
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386 | |
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387 | /* |
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388 | * the new Bareiss elimination: |
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389 | * - with x unreduced last rows, pivots from here are not allowed |
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390 | * - the method will finish for number of unreduced columns < y |
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391 | */ |
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392 | void sparse_mat::smNewBareiss(int x, int y) |
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393 | { |
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394 | if ((x > 0) && (x < nrows)) |
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395 | { |
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396 | tored -= x; |
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397 | this->smToredElim(); |
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398 | } |
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399 | if (y < 2) y = 2; |
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400 | if (act < y) |
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401 | { |
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402 | if (act != 0) |
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403 | { |
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404 | oldpiv = NULL; |
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405 | this->smCopToRes(); |
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406 | } |
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407 | return; |
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408 | } |
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409 | this->smPivot(); |
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410 | this->smSelectPR(); |
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411 | this->sm1Elim(); |
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412 | crd++; |
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413 | this->smColToRow(); |
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414 | act--; |
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415 | this->smRowToCol(); |
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416 | this->smZeroElim(); |
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417 | if (tored != nrows) |
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418 | this->smToredElim(); |
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419 | if (act < y) |
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420 | { |
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421 | this->smFinalMult(); |
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422 | this->smCopToRes(); |
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423 | return; |
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424 | } |
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425 | loop |
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426 | { |
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427 | this->smNewPivot(); |
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428 | this->smSelectPR(); |
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429 | this->smMultCol(); |
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430 | this->smHElim(); |
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431 | crd++; |
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432 | this->smColToRow(); |
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433 | act--; |
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434 | this->smRowToCol(); |
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435 | this->smZeroElim(); |
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436 | if (tored != nrows) |
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437 | this->smToredElim(); |
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438 | if (act < y) |
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439 | { |
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440 | if (act != 0) |
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441 | { |
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442 | this->smFinalMult(); |
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443 | this->smCopToRes(); |
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444 | } |
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445 | else |
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446 | tored = crd; |
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447 | return; |
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448 | } |
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449 | } |
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450 | } |
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451 | |
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452 | /* ----------------- pivot method ------------------ */ |
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453 | |
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454 | /* |
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455 | * prepare smPivot, compute weights for rows and columns |
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456 | * and the weight for all points |
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457 | */ |
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458 | void sparse_mat::smWeights() |
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459 | { |
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460 | float wc, wp, w; |
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461 | smpoly a; |
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462 | int i; |
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463 | |
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464 | wp = 0.0; |
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465 | for (i=tored; i; i--) wrw[i] = 0.0; // ??? |
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466 | for (i=act; i; i--) |
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467 | { |
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468 | wc = 0.0; |
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469 | a = m_act[i]; |
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470 | loop |
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471 | { |
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472 | if (a->pos > tored) |
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473 | break; |
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474 | w = a->f = smPolyWeight(a); |
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475 | wc += w; |
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476 | wrw[a->pos] += w; |
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477 | a = a->n; |
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478 | if (a == NULL) |
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479 | break; |
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480 | } |
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481 | wp += wc; |
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482 | wcl[i] = wc; |
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483 | } |
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484 | wpoints = wp; |
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485 | } |
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486 | |
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487 | /* |
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488 | * compute pivot |
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489 | */ |
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490 | void sparse_mat::smPivot() |
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491 | { |
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492 | float wopt = 1.0e30; |
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493 | float wc, wr, wp, w; |
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494 | smpoly a; |
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495 | int i, copt, ropt; |
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496 | |
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497 | this->smWeights(); |
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498 | for (i=act; i; i--) |
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499 | { |
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500 | a = m_act[i]; |
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501 | loop |
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502 | { |
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503 | if (a->pos > tored) |
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504 | break; |
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505 | w = a->f; |
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506 | wc = wcl[i]-w; |
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507 | wr = wrw[a->pos]-w; |
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508 | if ((wr<0.25) || (wc<0.25)) // row or column with only one point |
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509 | { |
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510 | if (w<wopt) |
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511 | { |
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512 | wopt = w; |
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513 | copt = i; |
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514 | ropt = a->pos; |
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515 | } |
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516 | } |
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517 | else // elimination |
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518 | { |
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519 | wp = w*(wpoints-wcl[i]-wr); |
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520 | wp += wr*wc; |
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521 | if (wp < wopt) |
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522 | { |
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523 | wopt = wp; |
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524 | copt = i; |
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525 | ropt = a->pos; |
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526 | } |
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527 | } |
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528 | a = a->n; |
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529 | if (a == NULL) |
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530 | break; |
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531 | } |
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532 | } |
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533 | rpiv = ropt; |
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534 | cpiv = copt; |
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535 | if (cpiv != act) |
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536 | { |
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537 | a = m_act[act]; |
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538 | m_act[act] = m_act[cpiv]; |
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539 | m_act[cpiv] = a; |
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540 | } |
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541 | } |
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542 | |
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543 | /* |
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544 | * prepare smPivot, compute weights for rows and columns |
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545 | * and the weight for all points |
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546 | */ |
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547 | void sparse_mat::smNewWeights() |
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548 | { |
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549 | float wc, wp, w, hp = piv->f; |
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550 | smpoly a; |
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551 | int i, f, e = crd; |
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552 | |
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553 | wp = 0.0; |
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554 | for (i=tored; i; i--) wrw[i] = 0.0; // ??? |
---|
555 | for (i=act; i; i--) |
---|
556 | { |
---|
557 | wc = 0.0; |
---|
558 | a = m_act[i]; |
---|
559 | loop |
---|
560 | { |
---|
561 | if (a->pos > tored) |
---|
562 | break; |
---|
563 | w = a->f; |
---|
564 | f = a->e; |
---|
565 | if (f < e) |
---|
566 | { |
---|
567 | w *= hp; |
---|
568 | if (f) w /= m_res[f]->f; |
---|
569 | } |
---|
570 | wc += w; |
---|
571 | wrw[a->pos] += w; |
---|
572 | a = a->n; |
---|
573 | if (a == NULL) |
---|
574 | break; |
---|
575 | } |
---|
576 | wp += wc; |
---|
577 | wcl[i] = wc; |
---|
578 | } |
---|
579 | wpoints = wp; |
---|
580 | } |
---|
581 | |
---|
582 | /* |
---|
583 | * compute pivot |
---|
584 | */ |
---|
585 | void sparse_mat::smNewPivot() |
---|
586 | { |
---|
587 | float wopt = 1.0e30, hp = piv->f; |
---|
588 | float wc, wr, wp, w; |
---|
589 | smpoly a; |
---|
590 | int i, copt, ropt, f, e = crd; |
---|
591 | |
---|
592 | this->smNewWeights(); |
---|
593 | for (i=act; i; i--) |
---|
594 | { |
---|
595 | a = m_act[i]; |
---|
596 | loop |
---|
597 | { |
---|
598 | if (a->pos > tored) |
---|
599 | break; |
---|
600 | w = a->f; |
---|
601 | f = a->e; |
---|
602 | if (f < e) |
---|
603 | { |
---|
604 | w *= hp; |
---|
605 | if (f) w /= m_res[f]->f; |
---|
606 | } |
---|
607 | wc = wcl[i]-w; |
---|
608 | wr = wrw[a->pos]-w; |
---|
609 | if ((wr<0.25) || (wc<0.25)) // row or column with only one point |
---|
610 | { |
---|
611 | if (w<wopt) |
---|
612 | { |
---|
613 | wopt = w; |
---|
614 | copt = i; |
---|
615 | ropt = a->pos; |
---|
616 | } |
---|
617 | } |
---|
618 | else // elimination |
---|
619 | { |
---|
620 | wp = w*(wpoints-wcl[i]-wr); |
---|
621 | wp += wr*wc; |
---|
622 | if (wp < wopt) |
---|
623 | { |
---|
624 | wopt = wp; |
---|
625 | copt = i; |
---|
626 | ropt = a->pos; |
---|
627 | } |
---|
628 | } |
---|
629 | a = a->n; |
---|
630 | if (a == NULL) |
---|
631 | break; |
---|
632 | } |
---|
633 | } |
---|
634 | rpiv = ropt; |
---|
635 | cpiv = copt; |
---|
636 | if (cpiv != act) |
---|
637 | { |
---|
638 | a = m_act[act]; |
---|
639 | m_act[act] = m_act[cpiv]; |
---|
640 | m_act[cpiv] = a; |
---|
641 | } |
---|
642 | } |
---|
643 | |
---|
644 | /* ----------------- elimination ------------------ */ |
---|
645 | |
---|
646 | /* steps of elimination */ |
---|
647 | void sparse_mat::smElim() |
---|
648 | { |
---|
649 | poly p = piv->m; // pivotelement |
---|
650 | smpoly c = m_act[act]; // pivotcolumn |
---|
651 | smpoly r = red; // row to reduce |
---|
652 | poly q; |
---|
653 | smpoly res, a, b; |
---|
654 | poly w, ha, hb; |
---|
655 | int i; |
---|
656 | |
---|
657 | if (oldpiv != NULL) q = oldpiv->m; // previous pivot |
---|
658 | else q = NULL; |
---|
659 | if ((c == NULL) || (r == NULL)) |
---|
660 | { |
---|
661 | while (r) smElemDelete(&r); |
---|
662 | for (i=1; i<act; i++) |
---|
663 | { |
---|
664 | a = m_act[i]; |
---|
665 | do |
---|
666 | { |
---|
667 | ha = SM_MULT(a->m, p, q); |
---|
668 | pDelete(&a->m); |
---|
669 | if (q) SM_DIV(ha, q); |
---|
670 | a->m = ha; |
---|
671 | a = a->n; |
---|
672 | } while (a != NULL); |
---|
673 | } |
---|
674 | return; |
---|
675 | } |
---|
676 | for (i=1; i<act; i++) |
---|
677 | { |
---|
678 | a = m_act[i]; |
---|
679 | if ((r == NULL) || (i != r->pos)) // cols without elimination |
---|
680 | { |
---|
681 | do |
---|
682 | { |
---|
683 | ha = SM_MULT(a->m, p, q); |
---|
684 | pDelete(&a->m); |
---|
685 | if (q) SM_DIV(ha, q); |
---|
686 | a->m = ha; |
---|
687 | a = a->n; |
---|
688 | } while (a != NULL); |
---|
689 | } |
---|
690 | else // cols with elimination |
---|
691 | { |
---|
692 | res = dumm; |
---|
693 | res->n = NULL; |
---|
694 | b = c; |
---|
695 | w = r->m; |
---|
696 | loop // combine the chains a and b: p*a + w*b |
---|
697 | { |
---|
698 | if (a->pos < b->pos) |
---|
699 | { |
---|
700 | ha = SM_MULT(a->m, p, q); |
---|
701 | pDelete(&a->m); |
---|
702 | if (q) SM_DIV(ha, q); |
---|
703 | a->m = ha; |
---|
704 | res = res->n = a; |
---|
705 | a = a->n; |
---|
706 | } |
---|
707 | else if (a->pos > b->pos) |
---|
708 | { |
---|
709 | res = res->n = smElemCopy(b); |
---|
710 | hb = SM_MULT(b->m, w, q); |
---|
711 | b = b->n; |
---|
712 | if (q) SM_DIV(hb, q); |
---|
713 | res->m = hb; |
---|
714 | } |
---|
715 | else |
---|
716 | { |
---|
717 | ha = SM_MULT(a->m, p, q); |
---|
718 | pDelete(&a->m); |
---|
719 | hb = SM_MULT(b->m, w, q); |
---|
720 | ha = pAdd(ha, hb); |
---|
721 | if (ha != NULL) |
---|
722 | { |
---|
723 | if (q) SM_DIV(ha, q); |
---|
724 | a->m = ha; |
---|
725 | res = res->n = a; |
---|
726 | a = a->n; |
---|
727 | } |
---|
728 | else |
---|
729 | { |
---|
730 | smElemDelete(&a); |
---|
731 | } |
---|
732 | b = b->n; |
---|
733 | } |
---|
734 | if (a == NULL) |
---|
735 | { |
---|
736 | if (b != NULL) |
---|
737 | { |
---|
738 | do |
---|
739 | { |
---|
740 | res = res->n = smElemCopy(b); |
---|
741 | hb = SM_MULT(b->m, w, q); |
---|
742 | if (q) SM_DIV(hb, q); |
---|
743 | res->m = hb; |
---|
744 | b = b->n; |
---|
745 | } while (b != NULL); |
---|
746 | } |
---|
747 | else |
---|
748 | res->n = NULL; |
---|
749 | break; |
---|
750 | } |
---|
751 | if (b == NULL) |
---|
752 | { |
---|
753 | do |
---|
754 | { |
---|
755 | ha = SM_MULT(a->m, p, q); |
---|
756 | pDelete(&a->m); |
---|
757 | if (q) SM_DIV(ha, q); |
---|
758 | a->m = ha; |
---|
759 | res = res->n = a; |
---|
760 | a = a->n; |
---|
761 | } while (a != NULL); |
---|
762 | break; |
---|
763 | } |
---|
764 | } |
---|
765 | m_act[i] = dumm->n; |
---|
766 | if (r) smElemDelete(&r); |
---|
767 | } |
---|
768 | } |
---|
769 | } |
---|
770 | |
---|
771 | /* first step of elimination */ |
---|
772 | void sparse_mat::sm1Elim() |
---|
773 | { |
---|
774 | poly p = piv->m; // pivotelement |
---|
775 | smpoly c = m_act[act]; // pivotcolumn |
---|
776 | smpoly r = red; // row to reduce |
---|
777 | smpoly res, a, b; |
---|
778 | poly w, ha, hb; |
---|
779 | |
---|
780 | if ((c == NULL) || (r == NULL)) |
---|
781 | return; |
---|
782 | do |
---|
783 | { |
---|
784 | a = m_act[r->pos]; |
---|
785 | res = dumm; |
---|
786 | res->n = NULL; |
---|
787 | b = c; |
---|
788 | w = r->m; |
---|
789 | loop // combine the chains a and b: p*a + w*b |
---|
790 | { |
---|
791 | if (a->pos < b->pos) |
---|
792 | { |
---|
793 | res = res->n = a; |
---|
794 | a = a->n; |
---|
795 | } |
---|
796 | else if (a->pos > b->pos) |
---|
797 | { |
---|
798 | res = res->n = smElemCopy(b); |
---|
799 | res->m = smMult(b->m, w); |
---|
800 | res->e = 1; |
---|
801 | res->f = smPolyWeight(res); |
---|
802 | b = b->n; |
---|
803 | } |
---|
804 | else |
---|
805 | { |
---|
806 | ha = smMult(a->m, p); |
---|
807 | pDelete(&a->m); |
---|
808 | hb = smMult(b->m, w); |
---|
809 | ha = pAdd(ha, hb); |
---|
810 | if (ha != NULL) |
---|
811 | { |
---|
812 | a->m = ha; |
---|
813 | a->e = 1; |
---|
814 | a->f = smPolyWeight(a); |
---|
815 | res = res->n = a; |
---|
816 | a = a->n; |
---|
817 | } |
---|
818 | else |
---|
819 | { |
---|
820 | smElemDelete(&a); |
---|
821 | } |
---|
822 | b = b->n; |
---|
823 | } |
---|
824 | if (b == NULL) |
---|
825 | { |
---|
826 | res->n = a; |
---|
827 | break; |
---|
828 | } |
---|
829 | if (a == NULL) |
---|
830 | { |
---|
831 | do |
---|
832 | { |
---|
833 | res = res->n = smElemCopy(b); |
---|
834 | res->m = smMult(b->m, w); |
---|
835 | res->e = 1; |
---|
836 | res->f = smPolyWeight(res); |
---|
837 | b = b->n; |
---|
838 | } while (b != NULL); |
---|
839 | break; |
---|
840 | } |
---|
841 | } |
---|
842 | m_act[r->pos] = dumm->n; |
---|
843 | smElemDelete(&r); |
---|
844 | } while (r != NULL); |
---|
845 | } |
---|
846 | |
---|
847 | /* higher steps of elimination */ |
---|
848 | void sparse_mat::smHElim() |
---|
849 | { |
---|
850 | poly hp = this->smMultPoly(piv); |
---|
851 | poly gp = piv->m; // pivotelement |
---|
852 | smpoly c = m_act[act]; // pivotcolumn |
---|
853 | smpoly r = red; // row to reduce |
---|
854 | smpoly res, a, b; |
---|
855 | poly ha, hr, gc, x, y; |
---|
856 | int e, ip, ir, ia, lev; |
---|
857 | |
---|
858 | if ((c == NULL) || (r == NULL)) |
---|
859 | { |
---|
860 | pDelete(&hp); |
---|
861 | return; |
---|
862 | } |
---|
863 | e = crd+1; |
---|
864 | ip = piv->e; |
---|
865 | do |
---|
866 | { |
---|
867 | a = m_act[r->pos]; |
---|
868 | res = dumm; |
---|
869 | res->n = NULL; |
---|
870 | b = c; |
---|
871 | hr = r->m; |
---|
872 | ir = r->e; |
---|
873 | loop // combine the chains a and b: (hp,gp)*a(l) + hr*b(h) |
---|
874 | { |
---|
875 | if (a->pos < b->pos) |
---|
876 | { |
---|
877 | res = res->n = a; |
---|
878 | a = a->n; |
---|
879 | } |
---|
880 | else if (a->pos > b->pos) |
---|
881 | { |
---|
882 | res = res->n = smElemCopy(b); |
---|
883 | x = SM_MULT(b->m, hr, m_res[ir]->m); |
---|
884 | b = b->n; |
---|
885 | if(ir) SM_DIV(x, m_res[ir]->m); |
---|
886 | res->m = x; |
---|
887 | res->e = e; |
---|
888 | res->f = smPolyWeight(res); |
---|
889 | } |
---|
890 | else |
---|
891 | { |
---|
892 | y = NULL; |
---|
893 | x = hr; |
---|
894 | ha = a->m; |
---|
895 | ia = a->e; |
---|
896 | if (ir > ia) |
---|
897 | { |
---|
898 | gc = SM_MULT(ha, m_res[ir]->m, m_res[ia]->m); |
---|
899 | pDelete(&ha); |
---|
900 | ha = gc; |
---|
901 | if (ia) SM_DIV(ha, m_res[ia]->m); |
---|
902 | ia = ir; |
---|
903 | } |
---|
904 | else if (ir < ia) |
---|
905 | { |
---|
906 | if (ip < ia) |
---|
907 | { |
---|
908 | gc = SM_MULT(ha, m_res[crd]->m, m_res[ia]->m); |
---|
909 | pDelete(&ha); |
---|
910 | ha = gc; |
---|
911 | if (ia) SM_DIV(ha, m_res[ia]->m); |
---|
912 | y = hp; |
---|
913 | ia = ip; |
---|
914 | if (ir > ia) |
---|
915 | { |
---|
916 | y = SM_MULT(y, m_res[ir]->m, m_res[ia]->m); |
---|
917 | if (ia) SM_DIV(y, m_res[ia]->m); |
---|
918 | ia = ir; |
---|
919 | } |
---|
920 | else if (ir < ia) |
---|
921 | { |
---|
922 | x = SM_MULT(x, m_res[ia]->m, m_res[ir]->m); |
---|
923 | if (ir) SM_DIV(x, m_res[ir]->m); |
---|
924 | } |
---|
925 | } |
---|
926 | else |
---|
927 | { |
---|
928 | x = SM_MULT(x, m_res[ia]->m, m_res[ir]->m); |
---|
929 | if (ir) SM_DIV(x, m_res[ir]->m); |
---|
930 | } |
---|
931 | } |
---|
932 | if (y == NULL) y = gp; |
---|
933 | gc = SM_MULT(ha, y, m_res[ia]->m); |
---|
934 | pDelete(&ha); |
---|
935 | x = SM_MULT(x, b->m, m_res[ia]->m); |
---|
936 | x = pAdd(x, gc); |
---|
937 | if (x != NULL) |
---|
938 | { |
---|
939 | if (ia) SM_DIV(x, m_res[ia]->m); |
---|
940 | a->m = x; |
---|
941 | a->e = e; |
---|
942 | a->f = smPolyWeight(a); |
---|
943 | res = res->n = a; |
---|
944 | a = a->n; |
---|
945 | } |
---|
946 | else |
---|
947 | { |
---|
948 | a->m = NULL; |
---|
949 | smElemDelete(&a); |
---|
950 | } |
---|
951 | b = b->n; |
---|
952 | } |
---|
953 | if (b == NULL) |
---|
954 | { |
---|
955 | res->n = a; |
---|
956 | break; |
---|
957 | } |
---|
958 | if (a == NULL) |
---|
959 | { |
---|
960 | do |
---|
961 | { |
---|
962 | res = res->n = smElemCopy(b); |
---|
963 | x = SM_MULT(b->m, hr, m_res[ir]->m); |
---|
964 | b = b->n; |
---|
965 | if(ir) SM_DIV(x, m_res[ir]->m); |
---|
966 | res->m = x; |
---|
967 | res->e = e; |
---|
968 | res->f = smPolyWeight(res); |
---|
969 | } while (b != NULL); |
---|
970 | break; |
---|
971 | } |
---|
972 | } |
---|
973 | m_act[r->pos] = dumm->n; |
---|
974 | smElemDelete(&r); |
---|
975 | } while (r != NULL); |
---|
976 | pDelete(&hp); |
---|
977 | } |
---|
978 | |
---|
979 | /* ----------------- transfer ------------------ */ |
---|
980 | |
---|
981 | /* |
---|
982 | * select the pivotrow and store it to red and piv |
---|
983 | */ |
---|
984 | void sparse_mat::smSelectPR() |
---|
985 | { |
---|
986 | smpoly b = dumm; |
---|
987 | smpoly a, ap; |
---|
988 | int i; |
---|
989 | |
---|
990 | a = m_act[act]; |
---|
991 | if (a->pos < rpiv) |
---|
992 | { |
---|
993 | do |
---|
994 | { |
---|
995 | ap = a; |
---|
996 | a = a->n; |
---|
997 | } while (a->pos < rpiv); |
---|
998 | ap->n = a->n; |
---|
999 | } |
---|
1000 | else |
---|
1001 | m_act[act] = a->n; |
---|
1002 | piv = a; |
---|
1003 | a->n = NULL; |
---|
1004 | for (i=1; i<act; i++) |
---|
1005 | { |
---|
1006 | a = m_act[i]; |
---|
1007 | if (a->pos < rpiv) |
---|
1008 | { |
---|
1009 | loop |
---|
1010 | { |
---|
1011 | ap = a; |
---|
1012 | a = a->n; |
---|
1013 | if ((a == NULL) || (a->pos > rpiv)) |
---|
1014 | break; |
---|
1015 | if (a->pos == rpiv) |
---|
1016 | { |
---|
1017 | ap->n = a->n; |
---|
1018 | a->m = pNeg(a->m); |
---|
1019 | b = b->n = a; |
---|
1020 | b->pos = i; |
---|
1021 | break; |
---|
1022 | } |
---|
1023 | } |
---|
1024 | } |
---|
1025 | else if (a->pos == rpiv) |
---|
1026 | { |
---|
1027 | m_act[i] = a->n; |
---|
1028 | a->m = pNeg(a->m); |
---|
1029 | b = b->n = a; |
---|
1030 | b->pos = i; |
---|
1031 | } |
---|
1032 | } |
---|
1033 | b->n = NULL; |
---|
1034 | red = dumm->n; |
---|
1035 | } |
---|
1036 | |
---|
1037 | /* |
---|
1038 | * store the pivotcol in m_row |
---|
1039 | * m_act[cols][pos(rows)] => m_row[rows][pos(cols)] |
---|
1040 | */ |
---|
1041 | void sparse_mat::smColToRow() |
---|
1042 | { |
---|
1043 | smpoly c = m_act[act]; |
---|
1044 | smpoly h; |
---|
1045 | |
---|
1046 | while (c != NULL) |
---|
1047 | { |
---|
1048 | h = c; |
---|
1049 | c = c->n; |
---|
1050 | h->n = m_row[h->pos]; |
---|
1051 | m_row[h->pos] = h; |
---|
1052 | h->pos = crd; |
---|
1053 | } |
---|
1054 | } |
---|
1055 | |
---|
1056 | /* |
---|
1057 | * store the pivot and the assosiated row in m_row |
---|
1058 | * to m_res (result): |
---|
1059 | * piv + m_row[rows][pos(cols)] => m_res[cols][pos(rows)] |
---|
1060 | */ |
---|
1061 | void sparse_mat::smRowToCol() |
---|
1062 | { |
---|
1063 | smpoly r = m_row[rpiv]; |
---|
1064 | smpoly a, ap, h; |
---|
1065 | |
---|
1066 | m_row[rpiv] = NULL; |
---|
1067 | perm[crd] = rpiv; |
---|
1068 | piv->pos = crd; |
---|
1069 | m_res[crd] = piv; |
---|
1070 | while (r != NULL) |
---|
1071 | { |
---|
1072 | ap = m_res[r->pos]; |
---|
1073 | loop |
---|
1074 | { |
---|
1075 | a = ap->n; |
---|
1076 | if (a == NULL) |
---|
1077 | { |
---|
1078 | ap->n = h = r; |
---|
1079 | r = r->n; |
---|
1080 | h->n = a; |
---|
1081 | h->pos = crd; |
---|
1082 | break; |
---|
1083 | } |
---|
1084 | ap = a; |
---|
1085 | } |
---|
1086 | } |
---|
1087 | } |
---|
1088 | |
---|
1089 | /* ----------------- C++ stuff ------------------ */ |
---|
1090 | |
---|
1091 | /* |
---|
1092 | * clean m_act from zeros (after elim) |
---|
1093 | */ |
---|
1094 | void sparse_mat::smZeroElim() |
---|
1095 | { |
---|
1096 | int i = 0; |
---|
1097 | int j; |
---|
1098 | |
---|
1099 | loop |
---|
1100 | { |
---|
1101 | i++; |
---|
1102 | if (i > act) return; |
---|
1103 | if (m_act[i] == NULL) break; |
---|
1104 | } |
---|
1105 | j = i; |
---|
1106 | loop |
---|
1107 | { |
---|
1108 | j++; |
---|
1109 | if (j > act) break; |
---|
1110 | if (m_act[j] != NULL) |
---|
1111 | { |
---|
1112 | m_act[i] = m_act[j]; |
---|
1113 | i++; |
---|
1114 | } |
---|
1115 | } |
---|
1116 | act -= (j-i); |
---|
1117 | sign = 0; |
---|
1118 | } |
---|
1119 | |
---|
1120 | /* |
---|
1121 | * clean m_act from cols not to reduced (after elim) |
---|
1122 | * put them to m_res |
---|
1123 | */ |
---|
1124 | void sparse_mat::smToredElim() |
---|
1125 | { |
---|
1126 | int i = 0; |
---|
1127 | int j; |
---|
1128 | |
---|
1129 | loop |
---|
1130 | { |
---|
1131 | i++; |
---|
1132 | if (i > act) return; |
---|
1133 | if (m_act[i]->pos > tored) |
---|
1134 | { |
---|
1135 | m_res[crd] = m_act[i]; |
---|
1136 | crd++; |
---|
1137 | break; |
---|
1138 | } |
---|
1139 | } |
---|
1140 | j = i; |
---|
1141 | loop |
---|
1142 | { |
---|
1143 | j++; |
---|
1144 | if (j > act) break; |
---|
1145 | if (m_act[i]->pos > tored) |
---|
1146 | { |
---|
1147 | m_res[crd] = m_act[i]; |
---|
1148 | crd++; |
---|
1149 | } |
---|
1150 | else |
---|
1151 | { |
---|
1152 | m_act[i] = m_act[j]; |
---|
1153 | i++; |
---|
1154 | } |
---|
1155 | } |
---|
1156 | act -= (j-i); |
---|
1157 | sign = 0; |
---|
1158 | } |
---|
1159 | |
---|
1160 | /* |
---|
1161 | * copy m_act to m_res |
---|
1162 | */ |
---|
1163 | void sparse_mat::smCopToRes() |
---|
1164 | { |
---|
1165 | smpoly p, r, ap, a, h; |
---|
1166 | int c, i; |
---|
1167 | |
---|
1168 | if (act == 0) return; |
---|
1169 | if (act > 1) |
---|
1170 | { |
---|
1171 | Werror("Not implemented"); |
---|
1172 | } |
---|
1173 | crd++; |
---|
1174 | c = crd; |
---|
1175 | p = m_res[c] = m_act[act]; |
---|
1176 | do |
---|
1177 | { |
---|
1178 | r = m_row[p->pos]; |
---|
1179 | m_row[p->pos] = NULL; |
---|
1180 | perm[c] = p->pos; |
---|
1181 | p->pos = c; |
---|
1182 | while (r != NULL) |
---|
1183 | { |
---|
1184 | ap = m_res[r->pos]; |
---|
1185 | loop |
---|
1186 | { |
---|
1187 | a = ap->n; |
---|
1188 | if (a == NULL) |
---|
1189 | { |
---|
1190 | ap->n = h = r; |
---|
1191 | r = r->n; |
---|
1192 | h->n = a; |
---|
1193 | h->pos = c; |
---|
1194 | break; |
---|
1195 | } |
---|
1196 | ap = a; |
---|
1197 | } |
---|
1198 | } |
---|
1199 | c++; |
---|
1200 | p = p->n; |
---|
1201 | } while (p != NULL); |
---|
1202 | for (i=1;i<=nrows;i++) |
---|
1203 | { |
---|
1204 | if(m_row[i] != NULL) |
---|
1205 | { |
---|
1206 | r = m_row[i]; |
---|
1207 | m_row[i] = NULL; |
---|
1208 | do |
---|
1209 | { |
---|
1210 | ap = m_res[r->pos]; |
---|
1211 | loop |
---|
1212 | { |
---|
1213 | a = ap->n; |
---|
1214 | if (a == NULL) |
---|
1215 | { |
---|
1216 | ap->n = h = r; |
---|
1217 | r = r->n; |
---|
1218 | h->n = a; |
---|
1219 | h->pos = c; |
---|
1220 | break; |
---|
1221 | } |
---|
1222 | ap = a; |
---|
1223 | } |
---|
1224 | } while (r!=NULL); |
---|
1225 | c++; |
---|
1226 | } |
---|
1227 | } |
---|
1228 | tored = c-1; |
---|
1229 | } |
---|
1230 | |
---|
1231 | /* |
---|
1232 | * multiply and divide the column, that goes to result |
---|
1233 | */ |
---|
1234 | void sparse_mat::smMultCol() |
---|
1235 | { |
---|
1236 | smpoly a = m_act[act]; |
---|
1237 | int e = crd; |
---|
1238 | poly ha; |
---|
1239 | int f; |
---|
1240 | |
---|
1241 | while (a != NULL) |
---|
1242 | { |
---|
1243 | f = a->e; |
---|
1244 | if (f < e) |
---|
1245 | { |
---|
1246 | ha = SM_MULT(a->m, m_res[e]->m, m_res[f]->m); |
---|
1247 | pDelete(&a->m); |
---|
1248 | if (f) SM_DIV(ha, m_res[f]->m); |
---|
1249 | a->m = ha; |
---|
1250 | } |
---|
1251 | a = a->n; |
---|
1252 | } |
---|
1253 | } |
---|
1254 | |
---|
1255 | /* |
---|
1256 | * multiply and divide the m_act finaly |
---|
1257 | */ |
---|
1258 | void sparse_mat::smFinalMult() |
---|
1259 | { |
---|
1260 | smpoly a = m_act[act]; |
---|
1261 | int e = crd; |
---|
1262 | poly ha; |
---|
1263 | int i, f; |
---|
1264 | |
---|
1265 | for (i=act; i; i--) |
---|
1266 | { |
---|
1267 | a = m_act[i]; |
---|
1268 | do |
---|
1269 | { |
---|
1270 | f = a->e; |
---|
1271 | if (f < e) |
---|
1272 | { |
---|
1273 | ha = SM_MULT(a->m, m_res[e]->m, m_res[f]->m); |
---|
1274 | pDelete(&a->m); |
---|
1275 | if (f) SM_DIV(ha, m_res[f]->m); |
---|
1276 | a->m = ha; |
---|
1277 | } |
---|
1278 | a = a->n; |
---|
1279 | } while (a != NULL); |
---|
1280 | } |
---|
1281 | } |
---|
1282 | |
---|
1283 | /* |
---|
1284 | * multiply and divide the element, save poly |
---|
1285 | */ |
---|
1286 | poly sparse_mat::smMultPoly(smpoly a) |
---|
1287 | { |
---|
1288 | int f = a->e; |
---|
1289 | poly r, h; |
---|
1290 | |
---|
1291 | if (f < crd) |
---|
1292 | { |
---|
1293 | h = r = a->m; |
---|
1294 | h = SM_MULT(h, m_res[crd]->m, m_res[f]->m); |
---|
1295 | if (f) SM_DIV(h, m_res[f]->m); |
---|
1296 | a->m = h; |
---|
1297 | a->f = smPolyWeight(a); |
---|
1298 | return r; |
---|
1299 | } |
---|
1300 | else |
---|
1301 | return NULL; |
---|
1302 | } |
---|
1303 | |
---|
1304 | /* ----------------- arithmetic ------------------ */ |
---|
1305 | |
---|
1306 | /* |
---|
1307 | * returns a*b |
---|
1308 | * a,b NOT destroyed |
---|
1309 | */ |
---|
1310 | poly smMult(poly a, poly b) |
---|
1311 | { |
---|
1312 | poly pa, res, r; |
---|
1313 | |
---|
1314 | if (smSmaller(a, b)) |
---|
1315 | { |
---|
1316 | r = a; |
---|
1317 | a = b; |
---|
1318 | b = r; |
---|
1319 | } |
---|
1320 | if (pNext(b) == NULL) |
---|
1321 | { |
---|
1322 | if (smIsScalar(b)) |
---|
1323 | return pMultCopyN(a, pGetCoeff(b)); |
---|
1324 | else |
---|
1325 | return smEMult(a, b); |
---|
1326 | } |
---|
1327 | pa = res = smEMult(a, b); |
---|
1328 | pIter(b); |
---|
1329 | do |
---|
1330 | { |
---|
1331 | r = smEMult(a, b); |
---|
1332 | smCombineChain(&pa, r); |
---|
1333 | pIter(b); |
---|
1334 | } while (b != NULL); |
---|
1335 | return res; |
---|
1336 | } |
---|
1337 | |
---|
1338 | /*2 |
---|
1339 | * exact division a/b |
---|
1340 | * a destroyed, b NOT destroyed |
---|
1341 | */ |
---|
1342 | void smPolyDiv(poly a, poly b) |
---|
1343 | { |
---|
1344 | const number x = pGetCoeff(b); |
---|
1345 | number y, yn; |
---|
1346 | poly t, h, dummy; |
---|
1347 | int i; |
---|
1348 | |
---|
1349 | if (pNext(b) == NULL) |
---|
1350 | { |
---|
1351 | do |
---|
1352 | { |
---|
1353 | if (!smIsScalar(b)) |
---|
1354 | { |
---|
1355 | for (i=pVariables; i; i--) |
---|
1356 | pSubExp(a,i,pGetExp(b,i)); |
---|
1357 | pSetm(a); |
---|
1358 | } |
---|
1359 | y = nDiv(pGetCoeff(a),x); |
---|
1360 | nNormalize(y); |
---|
1361 | pSetCoeff(a,y); |
---|
1362 | pIter(a); |
---|
1363 | } while (a != NULL); |
---|
1364 | return; |
---|
1365 | } |
---|
1366 | dummy = pNew(); |
---|
1367 | do |
---|
1368 | { |
---|
1369 | for (i=pVariables; i; i--) |
---|
1370 | pSubExp(a,i,pGetExp(b,i)); |
---|
1371 | pSetm(a); |
---|
1372 | y = nDiv(pGetCoeff(a),x); |
---|
1373 | nNormalize(y); |
---|
1374 | pSetCoeff(a,y); |
---|
1375 | yn = nNeg(nCopy(y)); |
---|
1376 | t = pNext(b); |
---|
1377 | h = dummy; |
---|
1378 | do |
---|
1379 | { |
---|
1380 | h = pNext(h) = pNew(); |
---|
1381 | pSetComp(h,0); |
---|
1382 | for (i=pVariables; i; i--) |
---|
1383 | pSetExp(h,i,pGetExp(a,i)+pGetExp(t,i)); |
---|
1384 | pSetm(h); |
---|
1385 | pSetCoeff0(h,nMult(yn, pGetCoeff(t))); |
---|
1386 | pIter(t); |
---|
1387 | } while (t != NULL); |
---|
1388 | nDelete(&yn); |
---|
1389 | pNext(h) = NULL; |
---|
1390 | a = pNext(a) = pAdd(pNext(a), pNext(dummy)); |
---|
1391 | } while (a!=NULL); |
---|
1392 | pFree1(dummy); |
---|
1393 | } |
---|
1394 | |
---|
1395 | /* |
---|
1396 | * returns the part of (a*b)/exp(lead(c)) with nonegative exponents |
---|
1397 | */ |
---|
1398 | poly smMultDiv(poly a, poly b, const poly c) |
---|
1399 | { |
---|
1400 | poly pa, e, res, r; |
---|
1401 | BOOLEAN lead; |
---|
1402 | |
---|
1403 | if (smSmaller(a, b)) |
---|
1404 | { |
---|
1405 | r = a; |
---|
1406 | a = b; |
---|
1407 | b = r; |
---|
1408 | } |
---|
1409 | if ((c == NULL) || smIsScalar(c)) |
---|
1410 | { |
---|
1411 | if (pNext(b) == NULL) |
---|
1412 | { |
---|
1413 | if (smIsScalar(b)) |
---|
1414 | return pMultCopyN(a, pGetCoeff(b)); |
---|
1415 | else |
---|
1416 | return smEMult(a, b); |
---|
1417 | } |
---|
1418 | pa = res = smEMult(a, b); |
---|
1419 | pIter(b); |
---|
1420 | do |
---|
1421 | { |
---|
1422 | r = smEMult(a, b); |
---|
1423 | smCombineChain(&pa, r); |
---|
1424 | pIter(b); |
---|
1425 | } while (b != NULL); |
---|
1426 | return res; |
---|
1427 | } |
---|
1428 | res = NULL; |
---|
1429 | e = pNew(); |
---|
1430 | lead = FALSE; |
---|
1431 | while (!lead) |
---|
1432 | { |
---|
1433 | pSetCoeff0(e,pGetCoeff(b)); |
---|
1434 | if (smIsNegQuot(e, b, c)) |
---|
1435 | { |
---|
1436 | lead = smCheckLead(a, e); |
---|
1437 | r = smDMult(a, e); |
---|
1438 | } |
---|
1439 | else |
---|
1440 | { |
---|
1441 | lead = TRUE; |
---|
1442 | r = smEMult(a, e); |
---|
1443 | } |
---|
1444 | if (lead) |
---|
1445 | { |
---|
1446 | if (res != NULL) |
---|
1447 | { |
---|
1448 | smFindRef(&pa, &res, r); |
---|
1449 | if (pa == NULL) |
---|
1450 | lead = FALSE; |
---|
1451 | } |
---|
1452 | else |
---|
1453 | { |
---|
1454 | pa = res = r; |
---|
1455 | } |
---|
1456 | } |
---|
1457 | else |
---|
1458 | res = pAdd(res, r); |
---|
1459 | pIter(b); |
---|
1460 | if (b == NULL) |
---|
1461 | { |
---|
1462 | pFree1(e); |
---|
1463 | return res; |
---|
1464 | } |
---|
1465 | } |
---|
1466 | do |
---|
1467 | { |
---|
1468 | pSetCoeff0(e,pGetCoeff(b)); |
---|
1469 | if (smIsNegQuot(e, b, c)) |
---|
1470 | { |
---|
1471 | r = smDMult(a, e); |
---|
1472 | if (smCheckLead(a, e)) |
---|
1473 | smCombineChain(&pa, r); |
---|
1474 | else |
---|
1475 | pa = pAdd(pa,r); |
---|
1476 | } |
---|
1477 | else |
---|
1478 | { |
---|
1479 | r = smEMult(a, e); |
---|
1480 | smCombineChain(&pa, r); |
---|
1481 | } |
---|
1482 | pIter(b); |
---|
1483 | } while (b != NULL); |
---|
1484 | pFree1(e); |
---|
1485 | return res; |
---|
1486 | } |
---|
1487 | |
---|
1488 | /*2 |
---|
1489 | * exact division a/b |
---|
1490 | * a is a result of smMultDiv |
---|
1491 | * a destroyed, b NOT destroyed |
---|
1492 | */ |
---|
1493 | void smSpecialPolyDiv(poly a, poly b) |
---|
1494 | { |
---|
1495 | if (pNext(b) == NULL) |
---|
1496 | { |
---|
1497 | smPolyDivN(a, pGetCoeff(b)); |
---|
1498 | return; |
---|
1499 | } |
---|
1500 | smExactPolyDiv(a, b); |
---|
1501 | } |
---|
1502 | |
---|
1503 | /* ------------ internals arithmetic ------------- */ |
---|
1504 | static void smExactPolyDiv(poly a, poly b) |
---|
1505 | { |
---|
1506 | const number x = pGetCoeff(b); |
---|
1507 | poly tail = pNext(b), e = pNew(); |
---|
1508 | poly h; |
---|
1509 | number y, yn; |
---|
1510 | |
---|
1511 | do |
---|
1512 | { |
---|
1513 | y = nDiv(pGetCoeff(a), x); |
---|
1514 | nNormalize(y); |
---|
1515 | pSetCoeff(a,y); |
---|
1516 | yn = nNeg(nCopy(y)); |
---|
1517 | pSetCoeff0(e,yn); |
---|
1518 | if (smIsNegQuot(e, a, b)) |
---|
1519 | h = smDMult(tail, e); |
---|
1520 | else |
---|
1521 | h = smEMult(tail, e); |
---|
1522 | nDelete(&yn); |
---|
1523 | a = pNext(a) = pAdd(pNext(a), h); |
---|
1524 | } while (a!=NULL); |
---|
1525 | pFree1(e); |
---|
1526 | } |
---|
1527 | |
---|
1528 | static BOOLEAN smIsScalar(const poly Term) |
---|
1529 | { |
---|
1530 | int i; |
---|
1531 | |
---|
1532 | for (i=pVariables; i; i--) |
---|
1533 | { |
---|
1534 | if (pGetExp(Term,i)) return FALSE; |
---|
1535 | } |
---|
1536 | return TRUE; |
---|
1537 | } |
---|
1538 | |
---|
1539 | static BOOLEAN smIsNegQuot(poly a, const poly b, const poly c) |
---|
1540 | { |
---|
1541 | int i; |
---|
1542 | |
---|
1543 | for (i=pVariables; i; i--) |
---|
1544 | { |
---|
1545 | pSetExp(a,i,pGetExp(b,i)-pGetExp(c,i)); |
---|
1546 | if (pGetExp(a,i) < 0) |
---|
1547 | { |
---|
1548 | while(--i) pSetExp(a,i,pGetExp(b,i)-pGetExp(c,i)); |
---|
1549 | return TRUE; |
---|
1550 | } |
---|
1551 | } |
---|
1552 | return FALSE; |
---|
1553 | } |
---|
1554 | |
---|
1555 | static poly smEMult(poly t, const poly e) |
---|
1556 | { |
---|
1557 | const number y = pGetCoeff(e); |
---|
1558 | poly res, h; |
---|
1559 | int i; |
---|
1560 | |
---|
1561 | h = res = pNew(); |
---|
1562 | loop |
---|
1563 | { |
---|
1564 | pSetComp(h,0); |
---|
1565 | for (i=pVariables; i; i--) |
---|
1566 | pSetExp(h,i,pGetExp(e,i)+pGetExp(t,i)); |
---|
1567 | pSetm(h); |
---|
1568 | pSetCoeff0(h,nMult(y,pGetCoeff(t))); |
---|
1569 | pIter(t); |
---|
1570 | if (t == NULL) |
---|
1571 | { |
---|
1572 | pNext(h) = NULL; |
---|
1573 | return res; |
---|
1574 | } |
---|
1575 | h = pNext(h) = pNew(); |
---|
1576 | } |
---|
1577 | } |
---|
1578 | |
---|
1579 | static BOOLEAN smCheckLead(const poly t, const poly e) |
---|
1580 | { |
---|
1581 | int i; |
---|
1582 | for (i=pVariables; i; i--) |
---|
1583 | { |
---|
1584 | if ((pGetExp(e,i)+pGetExp(t,i)) < 0) |
---|
1585 | return FALSE; |
---|
1586 | } |
---|
1587 | return TRUE; |
---|
1588 | } |
---|
1589 | |
---|
1590 | static poly smDMult(poly t, const poly e) |
---|
1591 | { |
---|
1592 | const number y = pGetCoeff(e); |
---|
1593 | number x; |
---|
1594 | poly res, h, r; |
---|
1595 | int i; |
---|
1596 | EXPONENT_TYPE w; |
---|
1597 | |
---|
1598 | r = h = res = pNew(); |
---|
1599 | loop |
---|
1600 | { |
---|
1601 | x = pGetCoeff(t); |
---|
1602 | for (i=pVariables; i; i--) |
---|
1603 | { |
---|
1604 | w = pGetExp(e,i)+pGetExp(t,i); |
---|
1605 | if (w < 0) break; |
---|
1606 | pSetExp(h,i,w); |
---|
1607 | } |
---|
1608 | pIter(t); |
---|
1609 | if (i == 0) |
---|
1610 | { |
---|
1611 | pSetComp(h,0); |
---|
1612 | pSetm(h); |
---|
1613 | pSetCoeff0(h,nMult(y,x)); |
---|
1614 | if (t == NULL) |
---|
1615 | { |
---|
1616 | pNext(h) = NULL; |
---|
1617 | return res; |
---|
1618 | } |
---|
1619 | r = h; |
---|
1620 | h = pNext(h) = pNew(); |
---|
1621 | } |
---|
1622 | else if (t == NULL) |
---|
1623 | { |
---|
1624 | if (r != h) |
---|
1625 | pNext(r) = NULL; |
---|
1626 | else |
---|
1627 | res = NULL; |
---|
1628 | pFree1(h); |
---|
1629 | return res; |
---|
1630 | } |
---|
1631 | } |
---|
1632 | } |
---|
1633 | |
---|
1634 | static void smPolyDivN(poly a, const number x) |
---|
1635 | { |
---|
1636 | number y; |
---|
1637 | |
---|
1638 | do |
---|
1639 | { |
---|
1640 | y = nDiv(pGetCoeff(a),x); |
---|
1641 | nNormalize(y); |
---|
1642 | pSetCoeff(a,y); |
---|
1643 | pIter(a); |
---|
1644 | } while (a != NULL); |
---|
1645 | } |
---|
1646 | |
---|
1647 | static BOOLEAN smSmaller(poly a, poly b) |
---|
1648 | { |
---|
1649 | loop |
---|
1650 | { |
---|
1651 | pIter(b); |
---|
1652 | if (b == NULL) return TRUE; |
---|
1653 | pIter(a); |
---|
1654 | if (a == NULL) return FALSE; |
---|
1655 | } |
---|
1656 | } |
---|
1657 | |
---|
1658 | static void smCombineChain(poly *px, poly r) |
---|
1659 | { |
---|
1660 | poly pa = *px, pb; |
---|
1661 | number x; |
---|
1662 | int i; |
---|
1663 | |
---|
1664 | loop |
---|
1665 | { |
---|
1666 | pb = pNext(pa); |
---|
1667 | if (pb == NULL) |
---|
1668 | { |
---|
1669 | pa = pNext(pa) = r; |
---|
1670 | break; |
---|
1671 | } |
---|
1672 | i = pComp0(pb, r); |
---|
1673 | if (i > 0) |
---|
1674 | pa = pb; |
---|
1675 | else |
---|
1676 | { |
---|
1677 | if (i == 0) |
---|
1678 | { |
---|
1679 | x = nAdd(pGetCoeff(pb), pGetCoeff(r)); |
---|
1680 | pDelete1(&r); |
---|
1681 | if (nIsZero(x)) |
---|
1682 | { |
---|
1683 | pDelete1(&pb); |
---|
1684 | pNext(pa) = pAdd(pb,r); |
---|
1685 | } |
---|
1686 | else |
---|
1687 | { |
---|
1688 | pa = pb; |
---|
1689 | pSetCoeff(pa,x); |
---|
1690 | pNext(pa) = pAdd(pNext(pa), r); |
---|
1691 | } |
---|
1692 | } |
---|
1693 | else |
---|
1694 | { |
---|
1695 | pa = pNext(pa) = r; |
---|
1696 | pNext(pa) = pAdd(pb, pNext(pa)); |
---|
1697 | } |
---|
1698 | break; |
---|
1699 | } |
---|
1700 | } |
---|
1701 | *px = pa; |
---|
1702 | } |
---|
1703 | |
---|
1704 | static void smFindRef(poly *ref, poly *px, poly r) |
---|
1705 | { |
---|
1706 | number x; |
---|
1707 | int i; |
---|
1708 | poly pa = *px, pp = NULL; |
---|
1709 | |
---|
1710 | loop |
---|
1711 | { |
---|
1712 | i = pComp0(pa, r); |
---|
1713 | if (i > 0) |
---|
1714 | { |
---|
1715 | pp = pa; |
---|
1716 | pIter(pa); |
---|
1717 | if (pa==NULL) |
---|
1718 | { |
---|
1719 | pNext(pp) = r; |
---|
1720 | break; |
---|
1721 | } |
---|
1722 | } |
---|
1723 | else |
---|
1724 | { |
---|
1725 | if (i == 0) |
---|
1726 | { |
---|
1727 | x = nAdd(pGetCoeff(pa), pGetCoeff(r)); |
---|
1728 | pDelete1(&r); |
---|
1729 | if (nIsZero(x)) |
---|
1730 | { |
---|
1731 | pDelete1(&pa); |
---|
1732 | if (pp!=NULL) |
---|
1733 | pNext(pp) = pAdd(pa,r); |
---|
1734 | else |
---|
1735 | *px = pAdd(pa,r); |
---|
1736 | } |
---|
1737 | else |
---|
1738 | { |
---|
1739 | pp = pa; |
---|
1740 | pSetCoeff(pp,x); |
---|
1741 | pNext(pp) = pAdd(pNext(pp), r); |
---|
1742 | } |
---|
1743 | } |
---|
1744 | else |
---|
1745 | { |
---|
1746 | if (pp!=NULL) |
---|
1747 | pp = pNext(pp) = r; |
---|
1748 | else |
---|
1749 | *px = pp = r; |
---|
1750 | pNext(pp) = pAdd(pa, pNext(r)); |
---|
1751 | } |
---|
1752 | break; |
---|
1753 | } |
---|
1754 | } |
---|
1755 | *ref = pp; |
---|
1756 | } |
---|
1757 | |
---|
1758 | /* ----------------- internal 'C' stuff ------------------ */ |
---|
1759 | |
---|
1760 | static void smElemDelete(smpoly *r) |
---|
1761 | { |
---|
1762 | smpoly a = *r, b = a->n; |
---|
1763 | |
---|
1764 | pDelete(&a->m); |
---|
1765 | Free((void *)a, sizeof(smprec)); |
---|
1766 | *r = b; |
---|
1767 | } |
---|
1768 | |
---|
1769 | static smpoly smElemCopy(smpoly a) |
---|
1770 | { |
---|
1771 | smpoly r = (smpoly)Alloc(sizeof(smprec)); |
---|
1772 | |
---|
1773 | memcpy(r, a, sizeof(smprec)); |
---|
1774 | /* r->m = pCopy(r->m); */ |
---|
1775 | return r; |
---|
1776 | } |
---|
1777 | |
---|
1778 | /* |
---|
1779 | * from poly to smpoly |
---|
1780 | * do not destroy p |
---|
1781 | */ |
---|
1782 | static smpoly smPoly2Smpoly(poly q) |
---|
1783 | { |
---|
1784 | poly pp; |
---|
1785 | smpoly res, a; |
---|
1786 | EXPONENT_TYPE x; |
---|
1787 | |
---|
1788 | if (q == NULL) |
---|
1789 | return NULL; |
---|
1790 | a = res = (smpoly)Alloc(sizeof(smprec)); |
---|
1791 | a->pos = x = pGetComp(q); |
---|
1792 | a->m = q; |
---|
1793 | a->e = 0; |
---|
1794 | loop |
---|
1795 | { |
---|
1796 | pSetComp(q,0); |
---|
1797 | pp = q; |
---|
1798 | pIter(q); |
---|
1799 | if (q == NULL) |
---|
1800 | { |
---|
1801 | a->n = NULL; |
---|
1802 | return res; |
---|
1803 | } |
---|
1804 | if (pGetComp(q) != x) |
---|
1805 | { |
---|
1806 | a = a->n = (smpoly)Alloc(sizeof(smprec)); |
---|
1807 | pNext(pp) = NULL; |
---|
1808 | a->pos = x = pGetComp(q); |
---|
1809 | a->m = q; |
---|
1810 | a->e = 0; |
---|
1811 | } |
---|
1812 | } |
---|
1813 | } |
---|
1814 | |
---|
1815 | /* |
---|
1816 | * from smpoly to poly |
---|
1817 | * destroy a |
---|
1818 | */ |
---|
1819 | static poly smSmpoly2Poly(smpoly a) |
---|
1820 | { |
---|
1821 | smpoly b; |
---|
1822 | poly res, pp, q; |
---|
1823 | EXPONENT_TYPE x; |
---|
1824 | |
---|
1825 | if (a == NULL) |
---|
1826 | return NULL; |
---|
1827 | x = a->pos; |
---|
1828 | q = res = a->m; |
---|
1829 | loop |
---|
1830 | { |
---|
1831 | pSetComp(q,x); |
---|
1832 | pp = q; |
---|
1833 | pIter(q); |
---|
1834 | if (q == NULL) |
---|
1835 | break; |
---|
1836 | } |
---|
1837 | loop |
---|
1838 | { |
---|
1839 | b = a; |
---|
1840 | a = a->n; |
---|
1841 | Free((void *)b, sizeof(smprec)); |
---|
1842 | if (a == NULL) |
---|
1843 | return res; |
---|
1844 | x = a->pos; |
---|
1845 | q = pNext(pp) = a->m; |
---|
1846 | loop |
---|
1847 | { |
---|
1848 | pSetComp(q,x); |
---|
1849 | pp = q; |
---|
1850 | pIter(q); |
---|
1851 | if (q == NULL) |
---|
1852 | break; |
---|
1853 | } |
---|
1854 | } |
---|
1855 | } |
---|
1856 | |
---|
1857 | /* |
---|
1858 | * weigth of a polynomial, for pivot strategy |
---|
1859 | */ |
---|
1860 | static float smPolyWeight(smpoly a) |
---|
1861 | { |
---|
1862 | poly p = a->m; |
---|
1863 | int i; |
---|
1864 | float res = (float)nSize(pGetCoeff(p)); |
---|
1865 | |
---|
1866 | if (pNext(p) == NULL) |
---|
1867 | { |
---|
1868 | for(i=pVariables; i>0; i--) |
---|
1869 | { |
---|
1870 | if (pGetExp(p,i) != 0) return res+1.0; |
---|
1871 | } |
---|
1872 | return res; |
---|
1873 | } |
---|
1874 | else |
---|
1875 | { |
---|
1876 | i = 0; |
---|
1877 | res = 0.0; |
---|
1878 | do |
---|
1879 | { |
---|
1880 | i++; |
---|
1881 | res += (float)nSize(pGetCoeff(p)); |
---|
1882 | pIter(p); |
---|
1883 | } |
---|
1884 | while (p); |
---|
1885 | return res+(float)i; |
---|
1886 | } |
---|
1887 | } |
---|