1 | /**************************************** |
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2 | * Computer Algebra System SINGULAR * |
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3 | ****************************************/ |
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4 | /* $Id: sparsmat.cc,v 1.18 1999-11-15 17:20:50 obachman 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 "structs.h" |
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12 | #include "tok.h" |
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13 | #include "febase.h" |
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14 | #include "structs.h" |
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15 | #include "intvec.h" |
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16 | #include "lists.h" |
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17 | #include "ring.h" |
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18 | #include "polys.h" |
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19 | #include "ipid.h" |
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20 | #include "ideals.h" |
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21 | #include "numbers.h" |
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22 | #include "longrat.h" |
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23 | #include "sparsmat.h" |
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24 | #include "prCopy.h" |
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25 | |
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26 | /* ----------------- macros ------------------ */ |
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27 | /* #define OLD_DIV */ |
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28 | #ifdef OLD_DIV |
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29 | #define SM_MULT(A,B,C) smMult(A,B) |
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30 | #define SM_DIV smPolyDiv |
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31 | #else |
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32 | #define SM_MULT smMultDiv |
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33 | #define SM_DIV smSpecialPolyDiv |
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34 | #endif |
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35 | /* ----------------- general definitions ------------------ */ |
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36 | /* in structs.h |
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37 | typedef struct smprec sm_prec; |
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38 | typedef sm_prec * smpoly; |
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39 | struct smprec{ |
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40 | smpoly n; // the next element |
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41 | int pos; // position |
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42 | int e; // level |
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43 | poly m; // the element |
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44 | float f; // complexity of the element |
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45 | }; |
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46 | */ |
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47 | /* declare internal 'C' stuff */ |
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48 | static void smExactPolyDiv(poly, poly); |
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49 | static BOOLEAN smIsScalar(const poly); |
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50 | static BOOLEAN smIsNegQuot(poly, const poly, const poly); |
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51 | static poly smEMult(poly, const poly); |
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52 | static BOOLEAN smCheckLead(const poly, const poly); |
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53 | static poly smDMult(poly, const poly); |
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54 | static void smPolyDivN(poly a, const number); |
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55 | static BOOLEAN smSmaller(poly, poly); |
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56 | static void smCombineChain(poly *, poly); |
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57 | static void smFindRef(poly *, poly *, poly); |
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58 | |
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59 | static void smElemDelete(smpoly *); |
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60 | static smpoly smElemCopy(smpoly); |
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61 | static float smPolyWeight(smpoly); |
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62 | static smpoly smPoly2Smpoly(poly); |
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63 | static poly smSmpoly2Poly(smpoly); |
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64 | static BOOLEAN smHaveDenom(poly); |
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65 | static number smCleardenom(ideal); |
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66 | |
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67 | /* class for sparse matrix: |
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68 | * 3 parts of matrix during the algorithm |
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69 | * m_act[cols][pos(rows)] => m_row[rows][pos(cols)] => m_res[cols][pos(rows)] |
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70 | * input pivotcols as rows result |
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71 | * pivot like a stack from pivot and pivotcols |
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72 | * elimination rows reordered according |
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73 | * to pivot choise |
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74 | * stored in perm |
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75 | * a step is as follows |
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76 | * - search of pivot (smPivot) |
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77 | * - swap pivot column and last column (smSwapC) |
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78 | * select pivotrow to piv and red (smSelectPR) |
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79 | * consider sign |
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80 | * - elimination (smInitElim, sm0Elim, sm1Elim) |
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81 | * clear zero column as result of elimination (smZeroElim) |
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82 | * - tranfer from |
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83 | * piv and m_row to m_res (smRowToCol) |
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84 | * m_act to m_row (smColToRow) |
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85 | */ |
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86 | class sparse_mat{ |
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87 | private: |
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88 | int nrows, ncols; // dimension of the problem |
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89 | int sign; // for determinant (start: 1) |
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90 | int act; // number of unreduced columns (start: ncols) |
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91 | int crd; // number of reduced columns (start: 0) |
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92 | int tored; // border for rows to reduce |
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93 | int inred; // unreducable part |
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94 | int rpiv, cpiv; // position of the pivot |
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95 | int normalize; // Normalization flag |
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96 | Exponent_t *perm; // permutation of rows |
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97 | float wpoints; // weight of all points |
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98 | float *wrw, *wcl; // weights of rows and columns |
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99 | smpoly * m_act; // unreduced columns |
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100 | smpoly * m_res; // reduced columns (result) |
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101 | smpoly * m_row; // reduced part of rows |
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102 | smpoly red; // row to reduce |
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103 | smpoly piv, oldpiv; // pivot and previous pivot |
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104 | smpoly dumm; // allocated dummy |
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105 | void smColToRow(); |
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106 | void smRowToCol(); |
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107 | void smFinalMult(); |
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108 | void smSparseHomog(); |
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109 | void smWeights(); |
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110 | void smPivot(); |
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111 | void smNewWeights(); |
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112 | void smNewPivot(); |
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113 | void smZeroElim(); |
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114 | void smToredElim(); |
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115 | void smCopToRes(); |
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116 | void smSelectPR(); |
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117 | void smElim(); |
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118 | void sm1Elim(); |
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119 | void smHElim(); |
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120 | void smMultCol(); |
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121 | poly smMultPoly(smpoly); |
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122 | void smActDel(); |
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123 | void smColDel(); |
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124 | void smPivDel(); |
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125 | void smSign(); |
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126 | void smInitPerm(); |
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127 | int smCheckNormalize(); |
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128 | void smNormalize(); |
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129 | public: |
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130 | sparse_mat(ideal); |
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131 | ~sparse_mat(); |
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132 | int smGetSign() { return sign; } |
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133 | smpoly * smGetAct() { return m_act; } |
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134 | int smGetRed() { return tored; } |
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135 | ideal smRes2Mod(); |
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136 | poly smDet(); |
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137 | void smBareiss(int, int); |
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138 | void smNewBareiss(int, int); |
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139 | void smToIntvec(intvec *); |
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140 | }; |
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141 | |
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142 | /* ----------------- ops with rings ------------------ */ |
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143 | ideal smRingCopy(ideal I, ring *ri, sip_sring &tmpR) |
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144 | { |
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145 | ring origR =NULL; |
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146 | ideal II; |
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147 | if (currRing->order[0]!=ringorder_c) |
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148 | { |
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149 | origR =currRing; |
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150 | tmpR=*origR; |
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151 | int *ord=(int*)Alloc0(3*sizeof(int)); |
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152 | int *block0=(int*)Alloc(3*sizeof(int)); |
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153 | int *block1=(int*)Alloc(3*sizeof(int)); |
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154 | ord[0]=ringorder_c; |
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155 | ord[1]=ringorder_dp; |
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156 | tmpR.order=ord; |
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157 | block0[1]=1; |
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158 | tmpR.block0=block0; |
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159 | block1[1]=tmpR.N; |
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160 | tmpR.block1=block1; |
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161 | rComplete(&tmpR,1); |
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162 | rChangeCurrRing(&tmpR,TRUE); |
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163 | // fetch data from the old ring |
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164 | II=idInit(IDELEMS(I),I->rank); |
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165 | int k; |
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166 | for (k=0;k<IDELEMS(I);k++) II->m[k] = prCopyR( I->m[k], origR); |
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167 | } |
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168 | else |
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169 | { |
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170 | II=idCopy(I); |
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171 | } |
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172 | *ri = origR; |
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173 | return II; |
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174 | } |
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175 | |
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176 | void smRingClean(ring origR, ip_sring &tmpR) |
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177 | { |
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178 | rChangeCurrRing(origR,TRUE); |
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179 | rUnComplete(&tmpR); |
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180 | Free((ADDRESS)tmpR.order,3*sizeof(int)); |
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181 | Free((ADDRESS)tmpR.block0,3*sizeof(int)); |
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182 | Free((ADDRESS)tmpR.block1,3*sizeof(int)); |
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183 | } |
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184 | |
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185 | /* ----------------- basics (used from 'C') ------------------ */ |
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186 | /*2 |
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187 | *returns the determinant of the module I; |
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188 | *uses Bareiss algorithm |
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189 | */ |
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190 | poly smCallDet(ideal I) |
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191 | { |
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192 | int r=idRankFreeModule(I); |
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193 | if (I->ncols != r) |
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194 | { |
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195 | Werror("det of %d x %d module (matrix)",r,I->ncols); |
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196 | return NULL; |
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197 | } |
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198 | number diag,h=nInit(1); |
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199 | poly res,save; |
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200 | ring origR; |
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201 | sip_sring tmpR; |
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202 | sparse_mat *det; |
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203 | ideal II=smRingCopy(I,&origR,tmpR); |
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204 | |
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205 | diag = smCleardenom(II); |
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206 | det = new sparse_mat(II); |
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207 | idDelete(&II); |
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208 | if (det->smGetAct() == NULL) |
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209 | { |
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210 | delete det; |
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211 | if (origR!=NULL) smRingClean(origR,tmpR); |
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212 | return NULL; |
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213 | } |
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214 | res=det->smDet(); |
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215 | if(det->smGetSign()<0) res=pNeg(res); |
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216 | delete det; |
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217 | if (origR!=NULL) |
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218 | { |
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219 | rChangeCurrRing(origR,TRUE); |
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220 | save = res; |
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221 | res = prCopyR( save, &tmpR); |
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222 | rChangeCurrRing(&tmpR,FALSE); |
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223 | pDelete(&save); |
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224 | smRingClean(origR,tmpR); |
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225 | } |
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226 | if (nEqual(diag,h) == FALSE) |
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227 | { |
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228 | pMultN(res,diag); |
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229 | pNormalize(res); |
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230 | } |
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231 | nDelete(&diag); |
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232 | nDelete(&h); |
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233 | return res; |
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234 | } |
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235 | |
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236 | lists smCallBareiss(ideal I, int x, int y) |
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237 | { |
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238 | ring origR; |
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239 | sip_sring tmpR; |
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240 | lists res=(lists)AllocSizeOf(slists); |
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241 | ideal II = smRingCopy(I,&origR,tmpR); |
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242 | sparse_mat *bareiss = new sparse_mat(II); |
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243 | ideal mm=II; |
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244 | intvec *v; |
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245 | ideal m; |
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246 | |
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247 | if (bareiss->smGetAct() == NULL) |
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248 | { |
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249 | delete bareiss; |
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250 | if (origR!=NULL) smRingClean(origR,tmpR); |
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251 | v=NewIntvec2(1,pVariables); |
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252 | } |
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253 | else |
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254 | { |
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255 | idDelete(&II); |
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256 | bareiss->smBareiss(x, y); |
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257 | m = bareiss->smRes2Mod(); |
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258 | v = NewIntvec1(bareiss->smGetRed()); |
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259 | bareiss->smToIntvec(v); |
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260 | delete bareiss; |
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261 | if (origR!=NULL) |
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262 | { |
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263 | rChangeCurrRing(origR,TRUE); |
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264 | mm=idInit(IDELEMS(m),m->rank); |
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265 | int k; |
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266 | for (k=0;k<IDELEMS(m);k++) mm->m[k] = prCopyR( m->m[k], &tmpR); |
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267 | rChangeCurrRing(&tmpR,FALSE); |
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268 | idDelete(&m); |
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269 | smRingClean(origR,tmpR); |
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270 | } |
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271 | else |
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272 | { |
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273 | mm=m; |
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274 | } |
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275 | } |
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276 | res->Init(2); |
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277 | res->m[0].rtyp=MODUL_CMD; |
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278 | res->m[0].data=(void *)mm; |
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279 | res->m[1].rtyp=INTVEC_CMD; |
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280 | res->m[1].data=(void *)v; |
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281 | return res; |
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282 | } |
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283 | |
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284 | lists smCallNewBareiss(ideal I, int x, int y) |
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285 | { |
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286 | ring origR; |
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287 | sip_sring tmpR; |
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288 | lists res=(lists)AllocSizeOf(slists); |
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289 | ideal II=smRingCopy(I,&origR,tmpR); |
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290 | sparse_mat *bareiss = new sparse_mat(II); |
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291 | ideal mm=II; |
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292 | intvec *v; |
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293 | ideal m; |
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294 | |
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295 | if (bareiss->smGetAct() == NULL) |
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296 | { |
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297 | delete bareiss; |
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298 | if (origR!=NULL) smRingClean(origR,tmpR); |
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299 | v=NewIntvec2(1,pVariables); |
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300 | } |
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301 | else |
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302 | { |
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303 | idDelete(&II); |
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304 | bareiss->smNewBareiss(x, y); |
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305 | m = bareiss->smRes2Mod(); |
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306 | v = NewIntvec1(bareiss->smGetRed()); |
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307 | bareiss->smToIntvec(v); |
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308 | delete bareiss; |
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309 | if (origR!=NULL) |
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310 | { |
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311 | rChangeCurrRing(origR,TRUE); |
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312 | mm=idInit(IDELEMS(m),m->rank); |
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313 | int k; |
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314 | for (k=0;k<IDELEMS(m);k++) mm->m[k] = prCopyR( m->m[k], &tmpR); |
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315 | rChangeCurrRing(&tmpR,FALSE); |
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316 | idDelete(&m); |
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317 | smRingClean(origR,tmpR); |
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318 | } |
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319 | else |
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320 | { |
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321 | mm=m; |
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322 | } |
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323 | } |
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324 | res->Init(2); |
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325 | res->m[0].rtyp=MODUL_CMD; |
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326 | res->m[0].data=(void *)mm; |
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327 | res->m[1].rtyp=INTVEC_CMD; |
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328 | res->m[1].data=(void *)v; |
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329 | return res; |
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330 | } |
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331 | |
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332 | /* |
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333 | * constructor |
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334 | */ |
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335 | sparse_mat::sparse_mat(ideal smat) |
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336 | { |
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337 | int i; |
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338 | polyset pmat; |
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339 | |
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340 | ncols = smat->ncols; |
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341 | nrows = idRankFreeModule(smat); |
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342 | if (nrows <= 0) |
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343 | { |
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344 | m_act = NULL; |
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345 | return; |
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346 | } |
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347 | sign = 1; |
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348 | inred = act = ncols; |
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349 | crd = 0; |
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350 | tored = nrows; // without border |
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351 | i = tored+1; |
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352 | perm = (Exponent_t *)Alloc(sizeof(Exponent_t)*(i+1)); |
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353 | perm[i] = 0; |
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354 | m_row = (smpoly *)Alloc0(sizeof(smpoly)*i); |
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355 | wrw = (float *)Alloc(sizeof(float)*i); |
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356 | i = ncols+1; |
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357 | wcl = (float *)Alloc(sizeof(float)*i); |
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358 | m_act = (smpoly *)Alloc(sizeof(smpoly)*i); |
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359 | m_res = (smpoly *)Alloc0(sizeof(smpoly)*i); |
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360 | dumm = (smpoly)AllocSizeOf(smprec); |
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361 | m_res[0] = (smpoly)AllocSizeOf(smprec); |
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362 | m_res[0]->m = NULL; |
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363 | pmat = smat->m; |
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364 | for(i=ncols; i; i--) |
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365 | { |
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366 | m_act[i] = smPoly2Smpoly(pmat[i-1]); |
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367 | pmat[i-1] = NULL; |
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368 | } |
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369 | this->smZeroElim(); |
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370 | oldpiv = NULL; |
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371 | } |
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372 | |
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373 | /* |
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374 | * destructor |
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375 | */ |
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376 | sparse_mat::~sparse_mat() |
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377 | { |
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378 | int i; |
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379 | if (m_act == NULL) return; |
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380 | FreeSizeOf((ADDRESS)m_res[0], smprec); |
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381 | FreeSizeOf((ADDRESS)dumm, smprec); |
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382 | i = ncols+1; |
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383 | Free((ADDRESS)m_res, sizeof(smpoly)*i); |
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384 | Free((ADDRESS)m_act, sizeof(smpoly)*i); |
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385 | Free((ADDRESS)wcl, sizeof(float)*i); |
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386 | i = nrows+1; |
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387 | Free((ADDRESS)wrw, sizeof(float)*i); |
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388 | Free((ADDRESS)m_row, sizeof(smpoly)*i); |
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389 | Free((ADDRESS)perm, sizeof(Exponent_t)*(i+1)); |
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390 | } |
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391 | |
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392 | /* |
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393 | * transform the result to a module |
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394 | */ |
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395 | ideal sparse_mat::smRes2Mod() |
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396 | { |
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397 | ideal res = idInit(crd, crd); |
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398 | int i; |
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399 | |
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400 | for (i=crd; i; i--) res->m[i-1] = smSmpoly2Poly(m_res[i]); |
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401 | res->rank = idRankFreeModule(res); |
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402 | return res; |
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403 | } |
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404 | |
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405 | /* |
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406 | * permutation of rows |
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407 | */ |
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408 | void sparse_mat::smToIntvec(intvec *v) |
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409 | { |
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410 | int i; |
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411 | |
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412 | for (i=v->rows()-1; i>=0; i--) |
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413 | (*v)[i] = perm[i+1]; |
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414 | } |
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415 | |
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416 | /* ---------------- the algorithm's ------------------ */ |
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417 | /* |
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418 | * the determinant (up to sign), uses new Bareiss elimination |
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419 | */ |
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420 | poly sparse_mat::smDet() |
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421 | { |
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422 | int y; |
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423 | poly res = NULL; |
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424 | |
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425 | if (sign == 0) |
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426 | { |
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427 | this->smActDel(); |
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428 | return NULL; |
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429 | } |
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430 | if (act < 2) |
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431 | { |
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432 | if (act != 0) res = m_act[1]->m; |
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433 | FreeSizeOf((void *)m_act[1], smprec); |
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434 | return res; |
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435 | } |
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436 | normalize = 0; |
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437 | this->smInitPerm(); |
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438 | this->smPivot(); |
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439 | this->smSign(); |
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440 | this->smSelectPR(); |
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441 | this->sm1Elim(); |
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442 | crd++; |
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443 | m_res[crd] = piv; |
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444 | this->smColDel(); |
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445 | act--; |
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446 | this->smZeroElim(); |
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447 | if (sign == 0) |
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448 | { |
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449 | this->smActDel(); |
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450 | return NULL; |
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451 | } |
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452 | if (act < 2) |
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453 | { |
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454 | this->smFinalMult(); |
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455 | this->smPivDel(); |
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456 | if (act != 0) res = m_act[1]->m; |
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457 | FreeSizeOf((void *)m_act[1], smprec); |
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458 | return res; |
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459 | } |
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460 | loop |
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461 | { |
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462 | this->smNewPivot(); |
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463 | this->smSign(); |
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464 | this->smSelectPR(); |
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465 | this->smMultCol(); |
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466 | this->smHElim(); |
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467 | crd++; |
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468 | m_res[crd] = piv; |
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469 | this->smColDel(); |
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470 | act--; |
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471 | this->smZeroElim(); |
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472 | if (sign == 0) |
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473 | { |
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474 | this->smPivDel(); |
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475 | this->smActDel(); |
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476 | return NULL; |
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477 | } |
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478 | if (act < 2) |
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479 | { |
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480 | this->smFinalMult(); |
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481 | this->smPivDel(); |
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482 | if (act != 0) res = m_act[1]->m; |
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483 | FreeSizeOf((void *)m_act[1], smprec); |
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484 | return res; |
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485 | } |
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486 | } |
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487 | } |
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488 | |
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489 | /* |
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490 | * the Bareiss elimination: |
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491 | * - with x unreduced last rows, pivots from here are not allowed |
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492 | * - the method will finish for number of unreduced columns < y |
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493 | */ |
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494 | void sparse_mat::smBareiss(int x, int y) |
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495 | { |
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496 | if ((x > 0) && (x < nrows)) |
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497 | { |
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498 | tored -= x; |
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499 | this->smToredElim(); |
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500 | } |
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501 | if (y < 1) y = 1; |
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502 | if (act <= y) |
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503 | { |
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504 | this->smCopToRes(); |
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505 | return; |
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506 | } |
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507 | normalize = this->smCheckNormalize(); |
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508 | if (normalize) this->smNormalize(); |
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509 | this->smPivot(); |
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510 | this->smSelectPR(); |
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511 | this->smElim(); |
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512 | crd++; |
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513 | this->smColToRow(); |
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514 | act--; |
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515 | this->smRowToCol(); |
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516 | this->smZeroElim(); |
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517 | if (tored != nrows) |
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518 | this->smToredElim(); |
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519 | if (act < y) |
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520 | { |
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521 | this->smCopToRes(); |
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522 | return; |
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523 | } |
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524 | loop |
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525 | { |
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526 | if (normalize) this->smNormalize(); |
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527 | this->smPivot(); |
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528 | oldpiv = piv; |
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529 | this->smSelectPR(); |
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530 | this->smElim(); |
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531 | crd++; |
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532 | this->smColToRow(); |
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533 | act--; |
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534 | this->smRowToCol(); |
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535 | this->smZeroElim(); |
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536 | if (tored != nrows) |
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537 | this->smToredElim(); |
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538 | if (act < y) |
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539 | { |
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540 | this->smCopToRes(); |
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541 | return; |
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542 | } |
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543 | } |
---|
544 | } |
---|
545 | |
---|
546 | /* |
---|
547 | * the new Bareiss elimination: |
---|
548 | * - with x unreduced last rows, pivots from here are not allowed |
---|
549 | * - the method will finish for number of unreduced columns < y |
---|
550 | */ |
---|
551 | void sparse_mat::smNewBareiss(int x, int y) |
---|
552 | { |
---|
553 | if ((x > 0) && (x < nrows)) |
---|
554 | { |
---|
555 | tored -= x; |
---|
556 | this->smToredElim(); |
---|
557 | } |
---|
558 | if (y < 1) y = 1; |
---|
559 | if (act <= y) |
---|
560 | { |
---|
561 | this->smCopToRes(); |
---|
562 | return; |
---|
563 | } |
---|
564 | normalize = this->smCheckNormalize(); |
---|
565 | if (normalize) this->smNormalize(); |
---|
566 | this->smPivot(); |
---|
567 | this->smSelectPR(); |
---|
568 | this->sm1Elim(); |
---|
569 | crd++; |
---|
570 | this->smColToRow(); |
---|
571 | act--; |
---|
572 | this->smRowToCol(); |
---|
573 | this->smZeroElim(); |
---|
574 | if (tored != nrows) |
---|
575 | this->smToredElim(); |
---|
576 | if (act < y) |
---|
577 | { |
---|
578 | this->smFinalMult(); |
---|
579 | this->smCopToRes(); |
---|
580 | return; |
---|
581 | } |
---|
582 | loop |
---|
583 | { |
---|
584 | if (normalize) this->smNormalize(); |
---|
585 | this->smNewPivot(); |
---|
586 | this->smSelectPR(); |
---|
587 | this->smMultCol(); |
---|
588 | this->smHElim(); |
---|
589 | crd++; |
---|
590 | this->smColToRow(); |
---|
591 | act--; |
---|
592 | this->smRowToCol(); |
---|
593 | this->smZeroElim(); |
---|
594 | if (tored != nrows) |
---|
595 | this->smToredElim(); |
---|
596 | if (act <= y) |
---|
597 | { |
---|
598 | this->smFinalMult(); |
---|
599 | this->smCopToRes(); |
---|
600 | return; |
---|
601 | } |
---|
602 | } |
---|
603 | } |
---|
604 | |
---|
605 | /* ----------------- pivot method ------------------ */ |
---|
606 | |
---|
607 | /* |
---|
608 | * prepare smPivot, compute weights for rows and columns |
---|
609 | * and the weight for all points |
---|
610 | */ |
---|
611 | void sparse_mat::smWeights() |
---|
612 | { |
---|
613 | float wc, wp, w; |
---|
614 | smpoly a; |
---|
615 | int i; |
---|
616 | |
---|
617 | wp = 0.0; |
---|
618 | for (i=tored; i; i--) wrw[i] = 0.0; // ??? |
---|
619 | for (i=act; i; i--) |
---|
620 | { |
---|
621 | wc = 0.0; |
---|
622 | a = m_act[i]; |
---|
623 | loop |
---|
624 | { |
---|
625 | if (a->pos > tored) |
---|
626 | break; |
---|
627 | w = a->f = smPolyWeight(a); |
---|
628 | wc += w; |
---|
629 | wrw[a->pos] += w; |
---|
630 | a = a->n; |
---|
631 | if (a == NULL) |
---|
632 | break; |
---|
633 | } |
---|
634 | wp += wc; |
---|
635 | wcl[i] = wc; |
---|
636 | } |
---|
637 | wpoints = wp; |
---|
638 | } |
---|
639 | |
---|
640 | /* |
---|
641 | * compute pivot |
---|
642 | */ |
---|
643 | void sparse_mat::smPivot() |
---|
644 | { |
---|
645 | float wopt = 1.0e30; |
---|
646 | float wc, wr, wp, w; |
---|
647 | smpoly a; |
---|
648 | int i, copt, ropt; |
---|
649 | |
---|
650 | this->smWeights(); |
---|
651 | for (i=act; i; i--) |
---|
652 | { |
---|
653 | a = m_act[i]; |
---|
654 | loop |
---|
655 | { |
---|
656 | if (a->pos > tored) |
---|
657 | break; |
---|
658 | w = a->f; |
---|
659 | wc = wcl[i]-w; |
---|
660 | wr = wrw[a->pos]-w; |
---|
661 | if ((wr<0.25) || (wc<0.25)) // row or column with only one point |
---|
662 | { |
---|
663 | if (w<wopt) |
---|
664 | { |
---|
665 | wopt = w; |
---|
666 | copt = i; |
---|
667 | ropt = a->pos; |
---|
668 | } |
---|
669 | } |
---|
670 | else // elimination |
---|
671 | { |
---|
672 | wp = w*(wpoints-wcl[i]-wr); |
---|
673 | wp += wr*wc; |
---|
674 | if (wp < wopt) |
---|
675 | { |
---|
676 | wopt = wp; |
---|
677 | copt = i; |
---|
678 | ropt = a->pos; |
---|
679 | } |
---|
680 | } |
---|
681 | a = a->n; |
---|
682 | if (a == NULL) |
---|
683 | break; |
---|
684 | } |
---|
685 | } |
---|
686 | rpiv = ropt; |
---|
687 | cpiv = copt; |
---|
688 | if (cpiv != act) |
---|
689 | { |
---|
690 | a = m_act[act]; |
---|
691 | m_act[act] = m_act[cpiv]; |
---|
692 | m_act[cpiv] = a; |
---|
693 | } |
---|
694 | } |
---|
695 | |
---|
696 | /* |
---|
697 | * prepare smPivot, compute weights for rows and columns |
---|
698 | * and the weight for all points |
---|
699 | */ |
---|
700 | void sparse_mat::smNewWeights() |
---|
701 | { |
---|
702 | float wc, wp, w, hp = piv->f; |
---|
703 | smpoly a; |
---|
704 | int i, f, e = crd; |
---|
705 | |
---|
706 | wp = 0.0; |
---|
707 | for (i=tored; i; i--) wrw[i] = 0.0; // ??? |
---|
708 | for (i=act; i; i--) |
---|
709 | { |
---|
710 | wc = 0.0; |
---|
711 | a = m_act[i]; |
---|
712 | loop |
---|
713 | { |
---|
714 | if (a->pos > tored) |
---|
715 | break; |
---|
716 | w = a->f; |
---|
717 | f = a->e; |
---|
718 | if (f < e) |
---|
719 | { |
---|
720 | w *= hp; |
---|
721 | if (f) w /= m_res[f]->f; |
---|
722 | } |
---|
723 | wc += w; |
---|
724 | wrw[a->pos] += w; |
---|
725 | a = a->n; |
---|
726 | if (a == NULL) |
---|
727 | break; |
---|
728 | } |
---|
729 | wp += wc; |
---|
730 | wcl[i] = wc; |
---|
731 | } |
---|
732 | wpoints = wp; |
---|
733 | } |
---|
734 | |
---|
735 | /* |
---|
736 | * compute pivot |
---|
737 | */ |
---|
738 | void sparse_mat::smNewPivot() |
---|
739 | { |
---|
740 | float wopt = 1.0e30, hp = piv->f; |
---|
741 | float wc, wr, wp, w; |
---|
742 | smpoly a; |
---|
743 | int i, copt, ropt, f, e = crd; |
---|
744 | |
---|
745 | this->smNewWeights(); |
---|
746 | for (i=act; i; i--) |
---|
747 | { |
---|
748 | a = m_act[i]; |
---|
749 | loop |
---|
750 | { |
---|
751 | if (a->pos > tored) |
---|
752 | break; |
---|
753 | w = a->f; |
---|
754 | f = a->e; |
---|
755 | if (f < e) |
---|
756 | { |
---|
757 | w *= hp; |
---|
758 | if (f) w /= m_res[f]->f; |
---|
759 | } |
---|
760 | wc = wcl[i]-w; |
---|
761 | wr = wrw[a->pos]-w; |
---|
762 | if ((wr<0.25) || (wc<0.25)) // row or column with only one point |
---|
763 | { |
---|
764 | if (w<wopt) |
---|
765 | { |
---|
766 | wopt = w; |
---|
767 | copt = i; |
---|
768 | ropt = a->pos; |
---|
769 | } |
---|
770 | } |
---|
771 | else // elimination |
---|
772 | { |
---|
773 | wp = w*(wpoints-wcl[i]-wr); |
---|
774 | wp += wr*wc; |
---|
775 | if (wp < wopt) |
---|
776 | { |
---|
777 | wopt = wp; |
---|
778 | copt = i; |
---|
779 | ropt = a->pos; |
---|
780 | } |
---|
781 | } |
---|
782 | a = a->n; |
---|
783 | if (a == NULL) |
---|
784 | break; |
---|
785 | } |
---|
786 | } |
---|
787 | rpiv = ropt; |
---|
788 | cpiv = copt; |
---|
789 | if (cpiv != act) |
---|
790 | { |
---|
791 | a = m_act[act]; |
---|
792 | m_act[act] = m_act[cpiv]; |
---|
793 | m_act[cpiv] = a; |
---|
794 | } |
---|
795 | } |
---|
796 | |
---|
797 | /* ----------------- elimination ------------------ */ |
---|
798 | |
---|
799 | /* steps of elimination */ |
---|
800 | void sparse_mat::smElim() |
---|
801 | { |
---|
802 | poly p = piv->m; // pivotelement |
---|
803 | smpoly c = m_act[act]; // pivotcolumn |
---|
804 | smpoly r = red; // row to reduce |
---|
805 | poly q; |
---|
806 | smpoly res, a, b; |
---|
807 | poly w, ha, hb; |
---|
808 | int i; |
---|
809 | |
---|
810 | if (oldpiv != NULL) q = oldpiv->m; // previous pivot |
---|
811 | else q = NULL; |
---|
812 | if ((c == NULL) || (r == NULL)) |
---|
813 | { |
---|
814 | while (r) smElemDelete(&r); |
---|
815 | for (i=1; i<act; i++) |
---|
816 | { |
---|
817 | a = m_act[i]; |
---|
818 | while (a != NULL) |
---|
819 | { |
---|
820 | ha = SM_MULT(a->m, p, q); |
---|
821 | pDelete(&a->m); |
---|
822 | if (q) SM_DIV(ha, q); |
---|
823 | a->m = ha; |
---|
824 | a = a->n; |
---|
825 | } |
---|
826 | } |
---|
827 | return; |
---|
828 | } |
---|
829 | for (i=1; i<act; i++) |
---|
830 | { |
---|
831 | a = m_act[i]; |
---|
832 | if ((r == NULL) || (i != r->pos)) // cols without elimination |
---|
833 | { |
---|
834 | while (a != NULL) |
---|
835 | { |
---|
836 | ha = SM_MULT(a->m, p, q); |
---|
837 | pDelete(&a->m); |
---|
838 | if (q) SM_DIV(ha, q); |
---|
839 | a->m = ha; |
---|
840 | a = a->n; |
---|
841 | } |
---|
842 | } |
---|
843 | else // cols with elimination |
---|
844 | { |
---|
845 | res = dumm; |
---|
846 | res->n = NULL; |
---|
847 | b = c; |
---|
848 | w = r->m; |
---|
849 | loop // combine the chains a and b: p*a + w*b |
---|
850 | { |
---|
851 | if (a == NULL) |
---|
852 | { |
---|
853 | if (b != NULL) |
---|
854 | { |
---|
855 | do |
---|
856 | { |
---|
857 | res = res->n = smElemCopy(b); |
---|
858 | hb = SM_MULT(b->m, w, q); |
---|
859 | if (q) SM_DIV(hb, q); |
---|
860 | res->m = hb; |
---|
861 | b = b->n; |
---|
862 | } while (b != NULL); |
---|
863 | } |
---|
864 | else |
---|
865 | res->n = NULL; |
---|
866 | break; |
---|
867 | } |
---|
868 | if (b == NULL) |
---|
869 | { |
---|
870 | do |
---|
871 | { |
---|
872 | ha = SM_MULT(a->m, p, q); |
---|
873 | pDelete(&a->m); |
---|
874 | if (q) SM_DIV(ha, q); |
---|
875 | a->m = ha; |
---|
876 | res = res->n = a; |
---|
877 | a = a->n; |
---|
878 | } while (a != NULL); |
---|
879 | break; |
---|
880 | } |
---|
881 | if (a->pos < b->pos) |
---|
882 | { |
---|
883 | ha = SM_MULT(a->m, p, q); |
---|
884 | pDelete(&a->m); |
---|
885 | if (q) SM_DIV(ha, q); |
---|
886 | a->m = ha; |
---|
887 | res = res->n = a; |
---|
888 | a = a->n; |
---|
889 | } |
---|
890 | else if (a->pos > b->pos) |
---|
891 | { |
---|
892 | res = res->n = smElemCopy(b); |
---|
893 | hb = SM_MULT(b->m, w, q); |
---|
894 | b = b->n; |
---|
895 | if (q) SM_DIV(hb, q); |
---|
896 | res->m = hb; |
---|
897 | } |
---|
898 | else |
---|
899 | { |
---|
900 | ha = SM_MULT(a->m, p, q); |
---|
901 | pDelete(&a->m); |
---|
902 | hb = SM_MULT(b->m, w, q); |
---|
903 | ha = pAdd(ha, hb); |
---|
904 | if (ha != NULL) |
---|
905 | { |
---|
906 | if (q) SM_DIV(ha, q); |
---|
907 | a->m = ha; |
---|
908 | res = res->n = a; |
---|
909 | a = a->n; |
---|
910 | } |
---|
911 | else |
---|
912 | { |
---|
913 | smElemDelete(&a); |
---|
914 | } |
---|
915 | b = b->n; |
---|
916 | } |
---|
917 | } |
---|
918 | m_act[i] = dumm->n; |
---|
919 | if (r) smElemDelete(&r); |
---|
920 | } |
---|
921 | } |
---|
922 | } |
---|
923 | |
---|
924 | /* first step of elimination */ |
---|
925 | void sparse_mat::sm1Elim() |
---|
926 | { |
---|
927 | poly p = piv->m; // pivotelement |
---|
928 | smpoly c = m_act[act]; // pivotcolumn |
---|
929 | smpoly r = red; // row to reduce |
---|
930 | smpoly res, a, b; |
---|
931 | poly w, ha, hb; |
---|
932 | |
---|
933 | if ((c == NULL) || (r == NULL)) |
---|
934 | { |
---|
935 | while (r!=NULL) smElemDelete(&r); |
---|
936 | return; |
---|
937 | } |
---|
938 | do |
---|
939 | { |
---|
940 | a = m_act[r->pos]; |
---|
941 | res = dumm; |
---|
942 | res->n = NULL; |
---|
943 | b = c; |
---|
944 | w = r->m; |
---|
945 | loop // combine the chains a and b: p*a + w*b |
---|
946 | { |
---|
947 | if (a->pos < b->pos) |
---|
948 | { |
---|
949 | res = res->n = a; |
---|
950 | a = a->n; |
---|
951 | } |
---|
952 | else if (a->pos > b->pos) |
---|
953 | { |
---|
954 | res = res->n = smElemCopy(b); |
---|
955 | res->m = smMult(b->m, w); |
---|
956 | res->e = 1; |
---|
957 | res->f = smPolyWeight(res); |
---|
958 | b = b->n; |
---|
959 | } |
---|
960 | else |
---|
961 | { |
---|
962 | ha = smMult(a->m, p); |
---|
963 | pDelete(&a->m); |
---|
964 | hb = smMult(b->m, w); |
---|
965 | ha = pAdd(ha, hb); |
---|
966 | if (ha != NULL) |
---|
967 | { |
---|
968 | a->m = ha; |
---|
969 | a->e = 1; |
---|
970 | a->f = smPolyWeight(a); |
---|
971 | res = res->n = a; |
---|
972 | a = a->n; |
---|
973 | } |
---|
974 | else |
---|
975 | { |
---|
976 | smElemDelete(&a); |
---|
977 | } |
---|
978 | b = b->n; |
---|
979 | } |
---|
980 | if (b == NULL) |
---|
981 | { |
---|
982 | res->n = a; |
---|
983 | break; |
---|
984 | } |
---|
985 | if (a == NULL) |
---|
986 | { |
---|
987 | do |
---|
988 | { |
---|
989 | res = res->n = smElemCopy(b); |
---|
990 | res->m = smMult(b->m, w); |
---|
991 | res->e = 1; |
---|
992 | res->f = smPolyWeight(res); |
---|
993 | b = b->n; |
---|
994 | } while (b != NULL); |
---|
995 | break; |
---|
996 | } |
---|
997 | } |
---|
998 | m_act[r->pos] = dumm->n; |
---|
999 | smElemDelete(&r); |
---|
1000 | } while (r != NULL); |
---|
1001 | } |
---|
1002 | |
---|
1003 | /* higher steps of elimination */ |
---|
1004 | void sparse_mat::smHElim() |
---|
1005 | { |
---|
1006 | poly hp = this->smMultPoly(piv); |
---|
1007 | poly gp = piv->m; // pivotelement |
---|
1008 | smpoly c = m_act[act]; // pivotcolumn |
---|
1009 | smpoly r = red; // row to reduce |
---|
1010 | smpoly res, a, b; |
---|
1011 | poly ha, hr, x, y; |
---|
1012 | int e, ip, ir, ia, lev; |
---|
1013 | |
---|
1014 | if ((c == NULL) || (r == NULL)) |
---|
1015 | { |
---|
1016 | while(r!=NULL) smElemDelete(&r); |
---|
1017 | pDelete(&hp); |
---|
1018 | return; |
---|
1019 | } |
---|
1020 | e = crd+1; |
---|
1021 | ip = piv->e; |
---|
1022 | do |
---|
1023 | { |
---|
1024 | a = m_act[r->pos]; |
---|
1025 | res = dumm; |
---|
1026 | res->n = NULL; |
---|
1027 | b = c; |
---|
1028 | hr = r->m; |
---|
1029 | ir = r->e; |
---|
1030 | loop // combine the chains a and b: (hp,gp)*a(l) + hr*b(h) |
---|
1031 | { |
---|
1032 | if (a->pos < b->pos) |
---|
1033 | { |
---|
1034 | res = res->n = a; |
---|
1035 | a = a->n; |
---|
1036 | } |
---|
1037 | else if (a->pos > b->pos) |
---|
1038 | { |
---|
1039 | res = res->n = smElemCopy(b); |
---|
1040 | x = SM_MULT(b->m, hr, m_res[ir]->m); |
---|
1041 | b = b->n; |
---|
1042 | if(ir) SM_DIV(x, m_res[ir]->m); |
---|
1043 | res->m = x; |
---|
1044 | res->e = e; |
---|
1045 | res->f = smPolyWeight(res); |
---|
1046 | } |
---|
1047 | else |
---|
1048 | { |
---|
1049 | ha = a->m; |
---|
1050 | ia = a->e; |
---|
1051 | if (ir >= ia) |
---|
1052 | { |
---|
1053 | if (ir > ia) |
---|
1054 | { |
---|
1055 | x = SM_MULT(ha, m_res[ir]->m, m_res[ia]->m); |
---|
1056 | pDelete(&ha); |
---|
1057 | ha = x; |
---|
1058 | if (ia) SM_DIV(ha, m_res[ia]->m); |
---|
1059 | ia = ir; |
---|
1060 | } |
---|
1061 | x = SM_MULT(ha, gp, m_res[ia]->m); |
---|
1062 | pDelete(&ha); |
---|
1063 | y = SM_MULT(b->m, hr, m_res[ia]->m); |
---|
1064 | } |
---|
1065 | else if (ir >= ip) |
---|
1066 | { |
---|
1067 | if (ia < crd) |
---|
1068 | { |
---|
1069 | x = SM_MULT(ha, m_res[crd]->m, m_res[ia]->m); |
---|
1070 | pDelete(&ha); |
---|
1071 | ha = x; |
---|
1072 | SM_DIV(ha, m_res[ia]->m); |
---|
1073 | } |
---|
1074 | y = hp; |
---|
1075 | if(ir > ip) |
---|
1076 | { |
---|
1077 | y = SM_MULT(y, m_res[ir]->m, m_res[ip]->m); |
---|
1078 | if (ip) SM_DIV(y, m_res[ip]->m); |
---|
1079 | } |
---|
1080 | ia = ir; |
---|
1081 | x = SM_MULT(ha, y, m_res[ia]->m); |
---|
1082 | if (y != hp) pDelete(&y); |
---|
1083 | pDelete(&ha); |
---|
1084 | y = SM_MULT(b->m, hr, m_res[ia]->m); |
---|
1085 | } |
---|
1086 | else |
---|
1087 | { |
---|
1088 | x = SM_MULT(hr, m_res[ia]->m, m_res[ir]->m); |
---|
1089 | if (ir) SM_DIV(x, m_res[ir]->m); |
---|
1090 | y = SM_MULT(b->m, x, m_res[ia]->m); |
---|
1091 | pDelete(&x); |
---|
1092 | x = SM_MULT(ha, gp, m_res[ia]->m); |
---|
1093 | pDelete(&ha); |
---|
1094 | } |
---|
1095 | ha = pAdd(x, y); |
---|
1096 | if (ha != NULL) |
---|
1097 | { |
---|
1098 | if (ia) SM_DIV(ha, m_res[ia]->m); |
---|
1099 | a->m = ha; |
---|
1100 | a->e = e; |
---|
1101 | a->f = smPolyWeight(a); |
---|
1102 | res = res->n = a; |
---|
1103 | a = a->n; |
---|
1104 | } |
---|
1105 | else |
---|
1106 | { |
---|
1107 | a->m = NULL; |
---|
1108 | smElemDelete(&a); |
---|
1109 | } |
---|
1110 | b = b->n; |
---|
1111 | } |
---|
1112 | if (b == NULL) |
---|
1113 | { |
---|
1114 | res->n = a; |
---|
1115 | break; |
---|
1116 | } |
---|
1117 | if (a == NULL) |
---|
1118 | { |
---|
1119 | do |
---|
1120 | { |
---|
1121 | res = res->n = smElemCopy(b); |
---|
1122 | x = SM_MULT(b->m, hr, m_res[ir]->m); |
---|
1123 | b = b->n; |
---|
1124 | if(ir) SM_DIV(x, m_res[ir]->m); |
---|
1125 | res->m = x; |
---|
1126 | res->e = e; |
---|
1127 | res->f = smPolyWeight(res); |
---|
1128 | } while (b != NULL); |
---|
1129 | break; |
---|
1130 | } |
---|
1131 | } |
---|
1132 | m_act[r->pos] = dumm->n; |
---|
1133 | smElemDelete(&r); |
---|
1134 | } while (r != NULL); |
---|
1135 | pDelete(&hp); |
---|
1136 | } |
---|
1137 | |
---|
1138 | /* ----------------- transfer ------------------ */ |
---|
1139 | |
---|
1140 | /* |
---|
1141 | * select the pivotrow and store it to red and piv |
---|
1142 | */ |
---|
1143 | void sparse_mat::smSelectPR() |
---|
1144 | { |
---|
1145 | smpoly b = dumm; |
---|
1146 | smpoly a, ap; |
---|
1147 | int i; |
---|
1148 | |
---|
1149 | a = m_act[act]; |
---|
1150 | if (a->pos < rpiv) |
---|
1151 | { |
---|
1152 | do |
---|
1153 | { |
---|
1154 | ap = a; |
---|
1155 | a = a->n; |
---|
1156 | } while (a->pos < rpiv); |
---|
1157 | ap->n = a->n; |
---|
1158 | } |
---|
1159 | else |
---|
1160 | m_act[act] = a->n; |
---|
1161 | piv = a; |
---|
1162 | a->n = NULL; |
---|
1163 | for (i=1; i<act; i++) |
---|
1164 | { |
---|
1165 | a = m_act[i]; |
---|
1166 | if (a->pos < rpiv) |
---|
1167 | { |
---|
1168 | loop |
---|
1169 | { |
---|
1170 | ap = a; |
---|
1171 | a = a->n; |
---|
1172 | if ((a == NULL) || (a->pos > rpiv)) |
---|
1173 | break; |
---|
1174 | if (a->pos == rpiv) |
---|
1175 | { |
---|
1176 | ap->n = a->n; |
---|
1177 | a->m = pNeg(a->m); |
---|
1178 | b = b->n = a; |
---|
1179 | b->pos = i; |
---|
1180 | break; |
---|
1181 | } |
---|
1182 | } |
---|
1183 | } |
---|
1184 | else if (a->pos == rpiv) |
---|
1185 | { |
---|
1186 | m_act[i] = a->n; |
---|
1187 | a->m = pNeg(a->m); |
---|
1188 | b = b->n = a; |
---|
1189 | b->pos = i; |
---|
1190 | } |
---|
1191 | } |
---|
1192 | b->n = NULL; |
---|
1193 | red = dumm->n; |
---|
1194 | } |
---|
1195 | |
---|
1196 | /* |
---|
1197 | * store the pivotcol in m_row |
---|
1198 | * m_act[cols][pos(rows)] => m_row[rows][pos(cols)] |
---|
1199 | */ |
---|
1200 | void sparse_mat::smColToRow() |
---|
1201 | { |
---|
1202 | smpoly c = m_act[act]; |
---|
1203 | smpoly h; |
---|
1204 | |
---|
1205 | while (c != NULL) |
---|
1206 | { |
---|
1207 | h = c; |
---|
1208 | c = c->n; |
---|
1209 | h->n = m_row[h->pos]; |
---|
1210 | m_row[h->pos] = h; |
---|
1211 | h->pos = crd; |
---|
1212 | } |
---|
1213 | } |
---|
1214 | |
---|
1215 | /* |
---|
1216 | * store the pivot and the assosiated row in m_row |
---|
1217 | * to m_res (result): |
---|
1218 | * piv + m_row[rows][pos(cols)] => m_res[cols][pos(rows)] |
---|
1219 | */ |
---|
1220 | void sparse_mat::smRowToCol() |
---|
1221 | { |
---|
1222 | smpoly r = m_row[rpiv]; |
---|
1223 | smpoly a, ap, h; |
---|
1224 | |
---|
1225 | m_row[rpiv] = NULL; |
---|
1226 | perm[crd] = rpiv; |
---|
1227 | piv->pos = crd; |
---|
1228 | m_res[crd] = piv; |
---|
1229 | while (r != NULL) |
---|
1230 | { |
---|
1231 | ap = m_res[r->pos]; |
---|
1232 | loop |
---|
1233 | { |
---|
1234 | a = ap->n; |
---|
1235 | if (a == NULL) |
---|
1236 | { |
---|
1237 | ap->n = h = r; |
---|
1238 | r = r->n; |
---|
1239 | h->n = a; |
---|
1240 | h->pos = crd; |
---|
1241 | break; |
---|
1242 | } |
---|
1243 | ap = a; |
---|
1244 | } |
---|
1245 | } |
---|
1246 | } |
---|
1247 | |
---|
1248 | /* ----------------- C++ stuff ------------------ */ |
---|
1249 | |
---|
1250 | /* |
---|
1251 | * clean m_act from zeros (after elim) |
---|
1252 | */ |
---|
1253 | void sparse_mat::smZeroElim() |
---|
1254 | { |
---|
1255 | int i = 0; |
---|
1256 | int j; |
---|
1257 | |
---|
1258 | loop |
---|
1259 | { |
---|
1260 | i++; |
---|
1261 | if (i > act) return; |
---|
1262 | if (m_act[i] == NULL) break; |
---|
1263 | } |
---|
1264 | j = i; |
---|
1265 | loop |
---|
1266 | { |
---|
1267 | j++; |
---|
1268 | if (j > act) break; |
---|
1269 | if (m_act[j] != NULL) |
---|
1270 | { |
---|
1271 | m_act[i] = m_act[j]; |
---|
1272 | i++; |
---|
1273 | } |
---|
1274 | } |
---|
1275 | act -= (j-i); |
---|
1276 | sign = 0; |
---|
1277 | } |
---|
1278 | |
---|
1279 | /* |
---|
1280 | * clean m_act from cols not to reduced (after elim) |
---|
1281 | * put them to m_res |
---|
1282 | */ |
---|
1283 | void sparse_mat::smToredElim() |
---|
1284 | { |
---|
1285 | int i = 0; |
---|
1286 | int j; |
---|
1287 | |
---|
1288 | loop |
---|
1289 | { |
---|
1290 | i++; |
---|
1291 | if (i > act) return; |
---|
1292 | if (m_act[i]->pos > tored) |
---|
1293 | { |
---|
1294 | m_res[inred] = m_act[i]; |
---|
1295 | inred--; |
---|
1296 | break; |
---|
1297 | } |
---|
1298 | } |
---|
1299 | j = i; |
---|
1300 | loop |
---|
1301 | { |
---|
1302 | j++; |
---|
1303 | if (j > act) break; |
---|
1304 | if (m_act[j]->pos > tored) |
---|
1305 | { |
---|
1306 | m_res[inred] = m_act[j]; |
---|
1307 | inred--; |
---|
1308 | } |
---|
1309 | else |
---|
1310 | { |
---|
1311 | m_act[i] = m_act[j]; |
---|
1312 | i++; |
---|
1313 | } |
---|
1314 | } |
---|
1315 | act -= (j-i); |
---|
1316 | sign = 0; |
---|
1317 | } |
---|
1318 | |
---|
1319 | /* |
---|
1320 | * copy m_act to m_res |
---|
1321 | */ |
---|
1322 | void sparse_mat::smCopToRes() |
---|
1323 | { |
---|
1324 | smpoly a,ap,r,h; |
---|
1325 | int i,j,k,l; |
---|
1326 | |
---|
1327 | i = 0; |
---|
1328 | if (act) |
---|
1329 | { |
---|
1330 | a = m_act[act]; // init perm |
---|
1331 | do |
---|
1332 | { |
---|
1333 | i++; |
---|
1334 | perm[crd+i] = a->pos; |
---|
1335 | a = a->n; |
---|
1336 | } while ((a != NULL) && (a->pos <= tored)); |
---|
1337 | for (j=act-1;j;j--) // load all positions of perm |
---|
1338 | { |
---|
1339 | a = m_act[j]; |
---|
1340 | k = 1; |
---|
1341 | loop |
---|
1342 | { |
---|
1343 | if (perm[crd+k] >= a->pos) |
---|
1344 | { |
---|
1345 | if (perm[crd+k] > a->pos) |
---|
1346 | { |
---|
1347 | for (l=i;l>=k;l--) perm[crd+l+1] = perm[crd+l]; |
---|
1348 | perm[crd+k] = a->pos; |
---|
1349 | i++; |
---|
1350 | } |
---|
1351 | a = a->n; |
---|
1352 | if ((a == NULL) || (a->pos > tored)) break; |
---|
1353 | } |
---|
1354 | k++; |
---|
1355 | if ((k > i) && (a->pos <= tored)) |
---|
1356 | { |
---|
1357 | do |
---|
1358 | { |
---|
1359 | i++; |
---|
1360 | perm[crd+i] = a->pos; |
---|
1361 | a = a->n; |
---|
1362 | } while ((a != NULL) && (a->pos <= tored)); |
---|
1363 | break; |
---|
1364 | } |
---|
1365 | } |
---|
1366 | } |
---|
1367 | } |
---|
1368 | for (j=act;j;j--) // renumber m_act |
---|
1369 | { |
---|
1370 | k = 1; |
---|
1371 | a = m_act[j]; |
---|
1372 | while ((a != NULL) && (a->pos <= tored)) |
---|
1373 | { |
---|
1374 | if (perm[crd+k] == a->pos) |
---|
1375 | { |
---|
1376 | a->pos = crd+k; |
---|
1377 | a = a->n; |
---|
1378 | } |
---|
1379 | k++; |
---|
1380 | } |
---|
1381 | } |
---|
1382 | tored = crd+i; |
---|
1383 | for(k=1;k<=i;k++) // clean this from m_row |
---|
1384 | { |
---|
1385 | j = perm[crd+k]; |
---|
1386 | if (m_row[j] != NULL) |
---|
1387 | { |
---|
1388 | r = m_row[j]; |
---|
1389 | m_row[j] = NULL; |
---|
1390 | do |
---|
1391 | { |
---|
1392 | ap = m_res[r->pos]; |
---|
1393 | loop |
---|
1394 | { |
---|
1395 | a = ap->n; |
---|
1396 | if (a == NULL) |
---|
1397 | { |
---|
1398 | h = ap->n = r; |
---|
1399 | r = r->n; |
---|
1400 | h->n = NULL; |
---|
1401 | h->pos = crd+k; |
---|
1402 | break; |
---|
1403 | } |
---|
1404 | ap = a; |
---|
1405 | } |
---|
1406 | } while (r!=NULL); |
---|
1407 | } |
---|
1408 | } |
---|
1409 | while(act) // clean m_act |
---|
1410 | { |
---|
1411 | crd++; |
---|
1412 | m_res[crd] = m_act[act]; |
---|
1413 | act--; |
---|
1414 | } |
---|
1415 | for (i=1;i<=tored;i++) // take the rest of m_row |
---|
1416 | { |
---|
1417 | if(m_row[i] != NULL) |
---|
1418 | { |
---|
1419 | tored++; |
---|
1420 | r = m_row[i]; |
---|
1421 | m_row[i] = NULL; |
---|
1422 | perm[tored] = i; |
---|
1423 | do |
---|
1424 | { |
---|
1425 | ap = m_res[r->pos]; |
---|
1426 | loop |
---|
1427 | { |
---|
1428 | a = ap->n; |
---|
1429 | if (a == NULL) |
---|
1430 | { |
---|
1431 | h = ap->n = r; |
---|
1432 | r = r->n; |
---|
1433 | h->n = NULL; |
---|
1434 | h->pos = tored; |
---|
1435 | break; |
---|
1436 | } |
---|
1437 | ap = a; |
---|
1438 | } |
---|
1439 | } while (r!=NULL); |
---|
1440 | } |
---|
1441 | } |
---|
1442 | for (i=tored+1;i<=nrows;i++) // take the rest of m_row |
---|
1443 | { |
---|
1444 | if(m_row[i] != NULL) |
---|
1445 | { |
---|
1446 | r = m_row[i]; |
---|
1447 | m_row[i] = NULL; |
---|
1448 | do |
---|
1449 | { |
---|
1450 | ap = m_res[r->pos]; |
---|
1451 | loop |
---|
1452 | { |
---|
1453 | a = ap->n; |
---|
1454 | if (a == NULL) |
---|
1455 | { |
---|
1456 | h = ap->n = r; |
---|
1457 | r = r->n; |
---|
1458 | h->n = NULL; |
---|
1459 | h->pos = i; |
---|
1460 | break; |
---|
1461 | } |
---|
1462 | ap = a; |
---|
1463 | } |
---|
1464 | } while (r!=NULL); |
---|
1465 | } |
---|
1466 | } |
---|
1467 | while (inred < ncols) // take unreducable |
---|
1468 | { |
---|
1469 | crd++; |
---|
1470 | inred++; |
---|
1471 | m_res[crd] = m_res[inred]; |
---|
1472 | } |
---|
1473 | } |
---|
1474 | |
---|
1475 | /* |
---|
1476 | * multiply and divide the column, that goes to result |
---|
1477 | */ |
---|
1478 | void sparse_mat::smMultCol() |
---|
1479 | { |
---|
1480 | smpoly a = m_act[act]; |
---|
1481 | int e = crd; |
---|
1482 | poly ha; |
---|
1483 | int f; |
---|
1484 | |
---|
1485 | while (a != NULL) |
---|
1486 | { |
---|
1487 | f = a->e; |
---|
1488 | if (f < e) |
---|
1489 | { |
---|
1490 | ha = SM_MULT(a->m, m_res[e]->m, m_res[f]->m); |
---|
1491 | pDelete(&a->m); |
---|
1492 | if (f) SM_DIV(ha, m_res[f]->m); |
---|
1493 | a->m = ha; |
---|
1494 | if (normalize) pNormalize(a->m); |
---|
1495 | } |
---|
1496 | a = a->n; |
---|
1497 | } |
---|
1498 | } |
---|
1499 | |
---|
1500 | /* |
---|
1501 | * multiply and divide the m_act finaly |
---|
1502 | */ |
---|
1503 | void sparse_mat::smFinalMult() |
---|
1504 | { |
---|
1505 | smpoly a; |
---|
1506 | poly ha; |
---|
1507 | int i, f; |
---|
1508 | int e = crd; |
---|
1509 | |
---|
1510 | for (i=act; i; i--) |
---|
1511 | { |
---|
1512 | a = m_act[i]; |
---|
1513 | do |
---|
1514 | { |
---|
1515 | f = a->e; |
---|
1516 | if (f < e) |
---|
1517 | { |
---|
1518 | ha = SM_MULT(a->m, m_res[e]->m, m_res[f]->m); |
---|
1519 | pDelete(&a->m); |
---|
1520 | if (f) SM_DIV(ha, m_res[f]->m); |
---|
1521 | a->m = ha; |
---|
1522 | } |
---|
1523 | if (normalize) pNormalize(a->m); |
---|
1524 | a = a->n; |
---|
1525 | } while (a != NULL); |
---|
1526 | } |
---|
1527 | } |
---|
1528 | |
---|
1529 | /* |
---|
1530 | * check for denominators |
---|
1531 | */ |
---|
1532 | int sparse_mat::smCheckNormalize() |
---|
1533 | { |
---|
1534 | int i; |
---|
1535 | smpoly a; |
---|
1536 | |
---|
1537 | for (i=act; i; i--) |
---|
1538 | { |
---|
1539 | a = m_act[i]; |
---|
1540 | do |
---|
1541 | { |
---|
1542 | if(smHaveDenom(a->m)) return 1; |
---|
1543 | a = a->n; |
---|
1544 | } while (a != NULL); |
---|
1545 | } |
---|
1546 | return 0; |
---|
1547 | } |
---|
1548 | |
---|
1549 | /* |
---|
1550 | * normalize |
---|
1551 | */ |
---|
1552 | void sparse_mat::smNormalize() |
---|
1553 | { |
---|
1554 | smpoly a; |
---|
1555 | int i; |
---|
1556 | int e = crd; |
---|
1557 | |
---|
1558 | for (i=act; i; i--) |
---|
1559 | { |
---|
1560 | a = m_act[i]; |
---|
1561 | do |
---|
1562 | { |
---|
1563 | if (e == a->e) pNormalize(a->m); |
---|
1564 | a = a->n; |
---|
1565 | } while (a != NULL); |
---|
1566 | } |
---|
1567 | } |
---|
1568 | |
---|
1569 | /* |
---|
1570 | * multiply and divide the element, save poly |
---|
1571 | */ |
---|
1572 | poly sparse_mat::smMultPoly(smpoly a) |
---|
1573 | { |
---|
1574 | int f = a->e; |
---|
1575 | poly r, h; |
---|
1576 | |
---|
1577 | if (f < crd) |
---|
1578 | { |
---|
1579 | h = r = a->m; |
---|
1580 | h = SM_MULT(h, m_res[crd]->m, m_res[f]->m); |
---|
1581 | if (f) SM_DIV(h, m_res[f]->m); |
---|
1582 | a->m = h; |
---|
1583 | if (normalize) pNormalize(a->m); |
---|
1584 | a->f = smPolyWeight(a); |
---|
1585 | return r; |
---|
1586 | } |
---|
1587 | else |
---|
1588 | return NULL; |
---|
1589 | } |
---|
1590 | |
---|
1591 | /* |
---|
1592 | * delete the m_act finaly |
---|
1593 | */ |
---|
1594 | void sparse_mat::smActDel() |
---|
1595 | { |
---|
1596 | smpoly a; |
---|
1597 | int i; |
---|
1598 | |
---|
1599 | for (i=act; i; i--) |
---|
1600 | { |
---|
1601 | a = m_act[i]; |
---|
1602 | do |
---|
1603 | { |
---|
1604 | smElemDelete(&a); |
---|
1605 | } while (a != NULL); |
---|
1606 | } |
---|
1607 | } |
---|
1608 | |
---|
1609 | /* |
---|
1610 | * delete the pivotcol |
---|
1611 | */ |
---|
1612 | void sparse_mat::smColDel() |
---|
1613 | { |
---|
1614 | smpoly a = m_act[act]; |
---|
1615 | |
---|
1616 | while (a != NULL) |
---|
1617 | { |
---|
1618 | smElemDelete(&a); |
---|
1619 | } |
---|
1620 | } |
---|
1621 | |
---|
1622 | /* |
---|
1623 | * delete pivot elements |
---|
1624 | */ |
---|
1625 | void sparse_mat::smPivDel() |
---|
1626 | { |
---|
1627 | int i=crd; |
---|
1628 | |
---|
1629 | while (i != 0) |
---|
1630 | { |
---|
1631 | smElemDelete(&m_res[i]); |
---|
1632 | i--; |
---|
1633 | } |
---|
1634 | } |
---|
1635 | |
---|
1636 | /* |
---|
1637 | * the sign of the determinant |
---|
1638 | */ |
---|
1639 | void sparse_mat::smSign() |
---|
1640 | { |
---|
1641 | int j,i; |
---|
1642 | if (act > 2) |
---|
1643 | { |
---|
1644 | if (cpiv!=act) sign=-sign; |
---|
1645 | if ((act%2)==0) sign=-sign; |
---|
1646 | i=1; |
---|
1647 | j=perm[1]; |
---|
1648 | while(j<rpiv) |
---|
1649 | { |
---|
1650 | sign=-sign; |
---|
1651 | i++; |
---|
1652 | j=perm[i]; |
---|
1653 | } |
---|
1654 | while(perm[i]!=0) |
---|
1655 | { |
---|
1656 | perm[i]=perm[i+1]; |
---|
1657 | i++; |
---|
1658 | } |
---|
1659 | } |
---|
1660 | else |
---|
1661 | { |
---|
1662 | if (cpiv!=1) sign=-sign; |
---|
1663 | if (rpiv!=perm[1]) sign=-sign; |
---|
1664 | } |
---|
1665 | } |
---|
1666 | |
---|
1667 | void sparse_mat::smInitPerm() |
---|
1668 | { |
---|
1669 | int i; |
---|
1670 | for (i=act;i;i--) perm[i]=i; |
---|
1671 | } |
---|
1672 | |
---|
1673 | /* ----------------- arithmetic ------------------ */ |
---|
1674 | |
---|
1675 | /* |
---|
1676 | * returns a*b |
---|
1677 | * a,b NOT destroyed |
---|
1678 | */ |
---|
1679 | poly smMult(poly a, poly b) |
---|
1680 | { |
---|
1681 | poly pa, res, r; |
---|
1682 | |
---|
1683 | if (smSmaller(a, b)) |
---|
1684 | { |
---|
1685 | r = a; |
---|
1686 | a = b; |
---|
1687 | b = r; |
---|
1688 | } |
---|
1689 | if (pNext(b) == NULL) |
---|
1690 | { |
---|
1691 | if (smIsScalar(b)) |
---|
1692 | return pMultCopyN(a, pGetCoeff(b)); |
---|
1693 | else |
---|
1694 | return smEMult(a, b); |
---|
1695 | } |
---|
1696 | pa = res = smEMult(a, b); |
---|
1697 | pIter(b); |
---|
1698 | do |
---|
1699 | { |
---|
1700 | r = smEMult(a, b); |
---|
1701 | smCombineChain(&pa, r); |
---|
1702 | pIter(b); |
---|
1703 | } while (b != NULL); |
---|
1704 | return res; |
---|
1705 | } |
---|
1706 | |
---|
1707 | /*2 |
---|
1708 | * exact division a/b |
---|
1709 | * a destroyed, b NOT destroyed |
---|
1710 | */ |
---|
1711 | void smPolyDiv(poly a, poly b) |
---|
1712 | { |
---|
1713 | const number x = pGetCoeff(b); |
---|
1714 | number y, yn; |
---|
1715 | poly t, h, dummy; |
---|
1716 | int i; |
---|
1717 | |
---|
1718 | if (pNext(b) == NULL) |
---|
1719 | { |
---|
1720 | do |
---|
1721 | { |
---|
1722 | if (!smIsScalar(b)) |
---|
1723 | { |
---|
1724 | for (i=pVariables; i; i--) |
---|
1725 | pSubExp(a,i,pGetExp(b,i)); |
---|
1726 | pSetm(a); |
---|
1727 | } |
---|
1728 | y = nDiv(pGetCoeff(a),x); |
---|
1729 | nNormalize(y); |
---|
1730 | pSetCoeff(a,y); |
---|
1731 | pIter(a); |
---|
1732 | } while (a != NULL); |
---|
1733 | return; |
---|
1734 | } |
---|
1735 | dummy = pInit(); |
---|
1736 | do |
---|
1737 | { |
---|
1738 | for (i=pVariables; i; i--) |
---|
1739 | pSubExp(a,i,pGetExp(b,i)); |
---|
1740 | pSetm(a); |
---|
1741 | y = nDiv(pGetCoeff(a),x); |
---|
1742 | nNormalize(y); |
---|
1743 | pSetCoeff(a,y); |
---|
1744 | yn = nNeg(nCopy(y)); |
---|
1745 | t = pNext(b); |
---|
1746 | h = dummy; |
---|
1747 | do |
---|
1748 | { |
---|
1749 | h = pNext(h) = pInit(); |
---|
1750 | //pSetComp(h,0); |
---|
1751 | for (i=pVariables; i; i--) |
---|
1752 | pSetExp(h,i,pGetExp(a,i)+pGetExp(t,i)); |
---|
1753 | pSetm(h); |
---|
1754 | pSetCoeff0(h,nMult(yn, pGetCoeff(t))); |
---|
1755 | pIter(t); |
---|
1756 | } while (t != NULL); |
---|
1757 | nDelete(&yn); |
---|
1758 | pNext(h) = NULL; |
---|
1759 | a = pNext(a) = pAdd(pNext(a), pNext(dummy)); |
---|
1760 | } while (a!=NULL); |
---|
1761 | pFree1(dummy); |
---|
1762 | } |
---|
1763 | |
---|
1764 | /* |
---|
1765 | * returns the part of (a*b)/exp(lead(c)) with nonegative exponents |
---|
1766 | */ |
---|
1767 | poly smMultDiv(poly a, poly b, const poly c) |
---|
1768 | { |
---|
1769 | poly pa, e, res, r; |
---|
1770 | BOOLEAN lead; |
---|
1771 | |
---|
1772 | if (smSmaller(a, b)) |
---|
1773 | { |
---|
1774 | r = a; |
---|
1775 | a = b; |
---|
1776 | b = r; |
---|
1777 | } |
---|
1778 | if ((c == NULL) || smIsScalar(c)) |
---|
1779 | { |
---|
1780 | if (pNext(b) == NULL) |
---|
1781 | { |
---|
1782 | if (smIsScalar(b)) |
---|
1783 | return pMultCopyN(a, pGetCoeff(b)); |
---|
1784 | else |
---|
1785 | return smEMult(a, b); |
---|
1786 | } |
---|
1787 | pa = res = smEMult(a, b); |
---|
1788 | pIter(b); |
---|
1789 | do |
---|
1790 | { |
---|
1791 | r = smEMult(a, b); |
---|
1792 | smCombineChain(&pa, r); |
---|
1793 | pIter(b); |
---|
1794 | } while (b != NULL); |
---|
1795 | return res; |
---|
1796 | } |
---|
1797 | res = NULL; |
---|
1798 | e = pInit(); |
---|
1799 | lead = FALSE; |
---|
1800 | while (!lead) |
---|
1801 | { |
---|
1802 | pSetCoeff0(e,pGetCoeff(b)); |
---|
1803 | if (smIsNegQuot(e, b, c)) |
---|
1804 | { |
---|
1805 | lead = smCheckLead(a, e); |
---|
1806 | r = smDMult(a, e); |
---|
1807 | } |
---|
1808 | else |
---|
1809 | { |
---|
1810 | lead = TRUE; |
---|
1811 | r = smEMult(a, e); |
---|
1812 | } |
---|
1813 | if (lead) |
---|
1814 | { |
---|
1815 | if (res != NULL) |
---|
1816 | { |
---|
1817 | smFindRef(&pa, &res, r); |
---|
1818 | if (pa == NULL) |
---|
1819 | lead = FALSE; |
---|
1820 | } |
---|
1821 | else |
---|
1822 | { |
---|
1823 | pa = res = r; |
---|
1824 | } |
---|
1825 | } |
---|
1826 | else |
---|
1827 | res = pAdd(res, r); |
---|
1828 | pIter(b); |
---|
1829 | if (b == NULL) |
---|
1830 | { |
---|
1831 | pFree1(e); |
---|
1832 | return res; |
---|
1833 | } |
---|
1834 | } |
---|
1835 | do |
---|
1836 | { |
---|
1837 | pSetCoeff0(e,pGetCoeff(b)); |
---|
1838 | if (smIsNegQuot(e, b, c)) |
---|
1839 | { |
---|
1840 | r = smDMult(a, e); |
---|
1841 | if (smCheckLead(a, e)) |
---|
1842 | smCombineChain(&pa, r); |
---|
1843 | else |
---|
1844 | pa = pAdd(pa,r); |
---|
1845 | } |
---|
1846 | else |
---|
1847 | { |
---|
1848 | r = smEMult(a, e); |
---|
1849 | smCombineChain(&pa, r); |
---|
1850 | } |
---|
1851 | pIter(b); |
---|
1852 | } while (b != NULL); |
---|
1853 | pFree1(e); |
---|
1854 | return res; |
---|
1855 | } |
---|
1856 | |
---|
1857 | /*n |
---|
1858 | * exact division a/b |
---|
1859 | * a is a result of smMultDiv |
---|
1860 | * a destroyed, b NOT destroyed |
---|
1861 | */ |
---|
1862 | void smSpecialPolyDiv(poly a, poly b) |
---|
1863 | { |
---|
1864 | if (pNext(b) == NULL) |
---|
1865 | { |
---|
1866 | smPolyDivN(a, pGetCoeff(b)); |
---|
1867 | return; |
---|
1868 | } |
---|
1869 | smExactPolyDiv(a, b); |
---|
1870 | } |
---|
1871 | |
---|
1872 | /* ------------ internals arithmetic ------------- */ |
---|
1873 | static void smExactPolyDiv(poly a, poly b) |
---|
1874 | { |
---|
1875 | const number x = pGetCoeff(b); |
---|
1876 | poly tail = pNext(b), e = pInit(); |
---|
1877 | poly h; |
---|
1878 | number y, yn; |
---|
1879 | |
---|
1880 | do |
---|
1881 | { |
---|
1882 | y = nDiv(pGetCoeff(a), x); |
---|
1883 | nNormalize(y); |
---|
1884 | pSetCoeff(a,y); |
---|
1885 | yn = nNeg(nCopy(y)); |
---|
1886 | pSetCoeff0(e,yn); |
---|
1887 | if (smIsNegQuot(e, a, b)) |
---|
1888 | h = smDMult(tail, e); |
---|
1889 | else |
---|
1890 | h = smEMult(tail, e); |
---|
1891 | nDelete(&yn); |
---|
1892 | a = pNext(a) = pAdd(pNext(a), h); |
---|
1893 | } while (a!=NULL); |
---|
1894 | pFree1(e); |
---|
1895 | } |
---|
1896 | |
---|
1897 | static BOOLEAN smIsScalar(const poly Term) |
---|
1898 | { |
---|
1899 | int i; |
---|
1900 | |
---|
1901 | for (i=pVariables; i; i--) |
---|
1902 | { |
---|
1903 | if (pGetExp(Term,i)) return FALSE; |
---|
1904 | } |
---|
1905 | return TRUE; |
---|
1906 | } |
---|
1907 | |
---|
1908 | static BOOLEAN smIsNegQuot(poly a, const poly b, const poly c) |
---|
1909 | { |
---|
1910 | int i; |
---|
1911 | |
---|
1912 | for (i=pVariables; i; i--) |
---|
1913 | { |
---|
1914 | pSetExp(a,i,pGetExp(b,i)-pGetExp(c,i)); |
---|
1915 | if (pGetExp(a,i) < 0) |
---|
1916 | { |
---|
1917 | while(--i) pSetExp(a,i,pGetExp(b,i)-pGetExp(c,i)); |
---|
1918 | return TRUE; |
---|
1919 | } |
---|
1920 | } |
---|
1921 | return FALSE; |
---|
1922 | } |
---|
1923 | |
---|
1924 | static poly smEMult(poly t, const poly e) |
---|
1925 | { |
---|
1926 | const number y = pGetCoeff(e); |
---|
1927 | poly res, h; |
---|
1928 | int i; |
---|
1929 | |
---|
1930 | h = res = pInit(); |
---|
1931 | loop |
---|
1932 | { |
---|
1933 | //pSetComp(h,0); |
---|
1934 | for (i=pVariables; i; i--) |
---|
1935 | pSetExp(h,i,pGetExp(e,i)+pGetExp(t,i)); |
---|
1936 | pSetm(h); |
---|
1937 | pSetCoeff0(h,nMult(y,pGetCoeff(t))); |
---|
1938 | pIter(t); |
---|
1939 | if (t == NULL) |
---|
1940 | { |
---|
1941 | pNext(h) = NULL; |
---|
1942 | return res; |
---|
1943 | } |
---|
1944 | h = pNext(h) = pInit(); |
---|
1945 | } |
---|
1946 | } |
---|
1947 | |
---|
1948 | static BOOLEAN smCheckLead(const poly t, const poly e) |
---|
1949 | { |
---|
1950 | int i; |
---|
1951 | for (i=pVariables; i; i--) |
---|
1952 | { |
---|
1953 | if ((pGetExp(e,i)+pGetExp(t,i)) < 0) |
---|
1954 | return FALSE; |
---|
1955 | } |
---|
1956 | return TRUE; |
---|
1957 | } |
---|
1958 | |
---|
1959 | static poly smDMult(poly t, const poly e) |
---|
1960 | { |
---|
1961 | const number y = pGetCoeff(e); |
---|
1962 | poly r = NULL; |
---|
1963 | poly res, h; |
---|
1964 | int i; |
---|
1965 | Exponent_t w; |
---|
1966 | |
---|
1967 | h = res = pInit(); |
---|
1968 | loop |
---|
1969 | { |
---|
1970 | i=pVariables; |
---|
1971 | loop |
---|
1972 | { |
---|
1973 | w = pGetExp(e,i)+pGetExp(t,i); |
---|
1974 | if (w < 0) break; |
---|
1975 | pSetExp(h,i,w); |
---|
1976 | i--; |
---|
1977 | if (i == 0) |
---|
1978 | { |
---|
1979 | pSetm(h); |
---|
1980 | pSetCoeff0(h,nMult(y,pGetCoeff(t))); |
---|
1981 | pIter(t); |
---|
1982 | if (t == NULL) |
---|
1983 | { |
---|
1984 | pNext(h) = NULL; |
---|
1985 | return res; |
---|
1986 | } |
---|
1987 | r = h; |
---|
1988 | h = pNext(h) = pInit(); |
---|
1989 | i=pVariables; |
---|
1990 | } |
---|
1991 | } |
---|
1992 | pIter(t); |
---|
1993 | if (t == NULL) |
---|
1994 | { |
---|
1995 | if (r != NULL) |
---|
1996 | pNext(r) = NULL; |
---|
1997 | else |
---|
1998 | res = NULL; |
---|
1999 | pFree1(h); |
---|
2000 | return res; |
---|
2001 | } |
---|
2002 | } |
---|
2003 | } |
---|
2004 | |
---|
2005 | static void smPolyDivN(poly a, const number x) |
---|
2006 | { |
---|
2007 | number y; |
---|
2008 | |
---|
2009 | do |
---|
2010 | { |
---|
2011 | y = nDiv(pGetCoeff(a),x); |
---|
2012 | nNormalize(y); |
---|
2013 | pSetCoeff(a,y); |
---|
2014 | pIter(a); |
---|
2015 | } while (a != NULL); |
---|
2016 | } |
---|
2017 | |
---|
2018 | static BOOLEAN smSmaller(poly a, poly b) |
---|
2019 | { |
---|
2020 | loop |
---|
2021 | { |
---|
2022 | pIter(b); |
---|
2023 | if (b == NULL) return TRUE; |
---|
2024 | pIter(a); |
---|
2025 | if (a == NULL) return FALSE; |
---|
2026 | } |
---|
2027 | } |
---|
2028 | |
---|
2029 | static void smCombineChain(poly *px, poly r) |
---|
2030 | { |
---|
2031 | poly pa = *px, pb; |
---|
2032 | number x; |
---|
2033 | int i; |
---|
2034 | |
---|
2035 | loop |
---|
2036 | { |
---|
2037 | pb = pNext(pa); |
---|
2038 | if (pb == NULL) |
---|
2039 | { |
---|
2040 | pa = pNext(pa) = r; |
---|
2041 | break; |
---|
2042 | } |
---|
2043 | i = pComp0(pb, r); |
---|
2044 | if (i > 0) |
---|
2045 | pa = pb; |
---|
2046 | else |
---|
2047 | { |
---|
2048 | if (i == 0) |
---|
2049 | { |
---|
2050 | x = nAdd(pGetCoeff(pb), pGetCoeff(r)); |
---|
2051 | pDelete1(&r); |
---|
2052 | if (nIsZero(x)) |
---|
2053 | { |
---|
2054 | pDelete1(&pb); |
---|
2055 | pNext(pa) = pAdd(pb,r); |
---|
2056 | } |
---|
2057 | else |
---|
2058 | { |
---|
2059 | pa = pb; |
---|
2060 | pSetCoeff(pa,x); |
---|
2061 | pNext(pa) = pAdd(pNext(pa), r); |
---|
2062 | } |
---|
2063 | } |
---|
2064 | else |
---|
2065 | { |
---|
2066 | pa = pNext(pa) = r; |
---|
2067 | pNext(pa) = pAdd(pb, pNext(pa)); |
---|
2068 | } |
---|
2069 | break; |
---|
2070 | } |
---|
2071 | } |
---|
2072 | *px = pa; |
---|
2073 | } |
---|
2074 | |
---|
2075 | static void smFindRef(poly *ref, poly *px, poly r) |
---|
2076 | { |
---|
2077 | number x; |
---|
2078 | int i; |
---|
2079 | poly pa = *px, pp = NULL; |
---|
2080 | |
---|
2081 | loop |
---|
2082 | { |
---|
2083 | i = pComp0(pa, r); |
---|
2084 | if (i > 0) |
---|
2085 | { |
---|
2086 | pp = pa; |
---|
2087 | pIter(pa); |
---|
2088 | if (pa==NULL) |
---|
2089 | { |
---|
2090 | pNext(pp) = r; |
---|
2091 | break; |
---|
2092 | } |
---|
2093 | } |
---|
2094 | else |
---|
2095 | { |
---|
2096 | if (i == 0) |
---|
2097 | { |
---|
2098 | x = nAdd(pGetCoeff(pa), pGetCoeff(r)); |
---|
2099 | pDelete1(&r); |
---|
2100 | if (nIsZero(x)) |
---|
2101 | { |
---|
2102 | pDelete1(&pa); |
---|
2103 | if (pp!=NULL) |
---|
2104 | pNext(pp) = pAdd(pa,r); |
---|
2105 | else |
---|
2106 | *px = pAdd(pa,r); |
---|
2107 | } |
---|
2108 | else |
---|
2109 | { |
---|
2110 | pp = pa; |
---|
2111 | pSetCoeff(pp,x); |
---|
2112 | pNext(pp) = pAdd(pNext(pp), r); |
---|
2113 | } |
---|
2114 | } |
---|
2115 | else |
---|
2116 | { |
---|
2117 | if (pp!=NULL) |
---|
2118 | pp = pNext(pp) = r; |
---|
2119 | else |
---|
2120 | *px = pp = r; |
---|
2121 | pNext(pp) = pAdd(pa, pNext(r)); |
---|
2122 | } |
---|
2123 | break; |
---|
2124 | } |
---|
2125 | } |
---|
2126 | *ref = pp; |
---|
2127 | } |
---|
2128 | |
---|
2129 | /* ----------------- internal 'C' stuff ------------------ */ |
---|
2130 | |
---|
2131 | static void smElemDelete(smpoly *r) |
---|
2132 | { |
---|
2133 | smpoly a = *r, b = a->n; |
---|
2134 | |
---|
2135 | pDelete(&a->m); |
---|
2136 | FreeSizeOf((void *)a, smprec); |
---|
2137 | *r = b; |
---|
2138 | } |
---|
2139 | |
---|
2140 | static smpoly smElemCopy(smpoly a) |
---|
2141 | { |
---|
2142 | smpoly r = (smpoly)AllocSizeOf(smprec); |
---|
2143 | memcpy(r, a, sizeof(smprec)); |
---|
2144 | /* r->m = pCopy(r->m); */ |
---|
2145 | return r; |
---|
2146 | } |
---|
2147 | |
---|
2148 | /* |
---|
2149 | * from poly to smpoly |
---|
2150 | * do not destroy p |
---|
2151 | */ |
---|
2152 | static smpoly smPoly2Smpoly(poly q) |
---|
2153 | { |
---|
2154 | poly pp; |
---|
2155 | smpoly res, a; |
---|
2156 | Exponent_t x; |
---|
2157 | |
---|
2158 | if (q == NULL) |
---|
2159 | return NULL; |
---|
2160 | a = res = (smpoly)AllocSizeOf(smprec); |
---|
2161 | a->pos = x = pGetComp(q); |
---|
2162 | a->m = q; |
---|
2163 | a->e = 0; |
---|
2164 | loop |
---|
2165 | { |
---|
2166 | pSetComp(q,0); |
---|
2167 | pp = q; |
---|
2168 | pIter(q); |
---|
2169 | if (q == NULL) |
---|
2170 | { |
---|
2171 | a->n = NULL; |
---|
2172 | return res; |
---|
2173 | } |
---|
2174 | if (pGetComp(q) != x) |
---|
2175 | { |
---|
2176 | a = a->n = (smpoly)AllocSizeOf(smprec); |
---|
2177 | pNext(pp) = NULL; |
---|
2178 | a->pos = x = pGetComp(q); |
---|
2179 | a->m = q; |
---|
2180 | a->e = 0; |
---|
2181 | } |
---|
2182 | } |
---|
2183 | } |
---|
2184 | |
---|
2185 | /* |
---|
2186 | * from smpoly to poly |
---|
2187 | * destroy a |
---|
2188 | */ |
---|
2189 | static poly smSmpoly2Poly(smpoly a) |
---|
2190 | { |
---|
2191 | smpoly b; |
---|
2192 | poly res, pp, q; |
---|
2193 | Exponent_t x; |
---|
2194 | |
---|
2195 | if (a == NULL) |
---|
2196 | return NULL; |
---|
2197 | x = a->pos; |
---|
2198 | q = res = a->m; |
---|
2199 | loop |
---|
2200 | { |
---|
2201 | pSetComp(q,x); |
---|
2202 | pp = q; |
---|
2203 | pIter(q); |
---|
2204 | if (q == NULL) |
---|
2205 | break; |
---|
2206 | } |
---|
2207 | loop |
---|
2208 | { |
---|
2209 | b = a; |
---|
2210 | a = a->n; |
---|
2211 | FreeSizeOf((void *)b, smprec); |
---|
2212 | if (a == NULL) |
---|
2213 | return res; |
---|
2214 | x = a->pos; |
---|
2215 | q = pNext(pp) = a->m; |
---|
2216 | loop |
---|
2217 | { |
---|
2218 | pSetComp(q,x); |
---|
2219 | pp = q; |
---|
2220 | pIter(q); |
---|
2221 | if (q == NULL) |
---|
2222 | break; |
---|
2223 | } |
---|
2224 | } |
---|
2225 | } |
---|
2226 | |
---|
2227 | /* |
---|
2228 | * weigth of a polynomial, for pivot strategy |
---|
2229 | */ |
---|
2230 | static float smPolyWeight(smpoly a) |
---|
2231 | { |
---|
2232 | poly p = a->m; |
---|
2233 | int i; |
---|
2234 | float res = (float)nSize(pGetCoeff(p)); |
---|
2235 | |
---|
2236 | if (pNext(p) == NULL) |
---|
2237 | { |
---|
2238 | for(i=pVariables; i>0; i--) |
---|
2239 | { |
---|
2240 | if (pGetExp(p,i) != 0) return res+1.0; |
---|
2241 | } |
---|
2242 | return res; |
---|
2243 | } |
---|
2244 | else |
---|
2245 | { |
---|
2246 | i = 0; |
---|
2247 | res = 0.0; |
---|
2248 | do |
---|
2249 | { |
---|
2250 | i++; |
---|
2251 | res += (float)nSize(pGetCoeff(p)); |
---|
2252 | pIter(p); |
---|
2253 | } |
---|
2254 | while (p); |
---|
2255 | return res+(float)i; |
---|
2256 | } |
---|
2257 | } |
---|
2258 | |
---|
2259 | static BOOLEAN smHaveDenom(poly a) |
---|
2260 | { |
---|
2261 | BOOLEAN sw; |
---|
2262 | number x,o=nInit(1); |
---|
2263 | |
---|
2264 | while (a != NULL) |
---|
2265 | { |
---|
2266 | x = nGetDenom(pGetCoeff(a)); |
---|
2267 | sw = nEqual(x,o); |
---|
2268 | nDelete(&x); |
---|
2269 | if (!sw) |
---|
2270 | { |
---|
2271 | nDelete(&o); |
---|
2272 | return TRUE; |
---|
2273 | } |
---|
2274 | pIter(a); |
---|
2275 | } |
---|
2276 | nDelete(&o); |
---|
2277 | return FALSE; |
---|
2278 | } |
---|
2279 | |
---|
2280 | static number smCleardenom(ideal id) |
---|
2281 | { |
---|
2282 | poly a; |
---|
2283 | number x,y,res=nInit(1); |
---|
2284 | BOOLEAN sw=FALSE; |
---|
2285 | |
---|
2286 | for (int i=0; i<IDELEMS(id); i++) |
---|
2287 | { |
---|
2288 | a = id->m[i]; |
---|
2289 | sw = smHaveDenom(a); |
---|
2290 | if (sw) break; |
---|
2291 | } |
---|
2292 | if (!sw) return res; |
---|
2293 | for (int i=0; i<IDELEMS(id); i++) |
---|
2294 | { |
---|
2295 | a = id->m[i]; |
---|
2296 | x = nCopy(pGetCoeff(a)); |
---|
2297 | pCleardenom(a); |
---|
2298 | y = nDiv(x,pGetCoeff(a)); |
---|
2299 | nDelete(&x); |
---|
2300 | x = nMult(res,y); |
---|
2301 | nNormalize(x); |
---|
2302 | nDelete(&res); |
---|
2303 | res = x; |
---|
2304 | } |
---|
2305 | return res; |
---|
2306 | } |
---|
2307 | |
---|