1 | /**************************************** |
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2 | * Computer Algebra System SINGULAR * |
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3 | ****************************************/ |
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4 | /* $Id: sparsmat.cc,v 1.47 2000-12-31 15:14:45 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 "sparsmat.h" |
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23 | #include "prCopy.h" |
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24 | #include "p_Procs.h" |
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25 | #include "kbuckets.h" |
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26 | #include "p_Mult_q.h" |
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27 | |
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28 | // define SM_NO_BUCKETS, if sparsemat stuff should not use buckets |
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29 | // #define SM_NO_BUCKETS |
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30 | |
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31 | // this is also influenced by TEST_OPT_NOTBUCKETS |
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32 | #ifndef SM_NO_BUCKETS |
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33 | // buckets do carry a small additional overhead: only use them if |
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34 | // min-length of polys is >= SM_MIN_LENGTH_BUCKET |
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35 | #define SM_MIN_LENGTH_BUCKET MIN_LENGTH_BUCKET - 5 |
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36 | #else |
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37 | #define SM_MIN_LENGTH_BUCKET INT_MAX |
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38 | #endif |
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39 | |
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40 | |
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41 | /* declare internal 'C' stuff */ |
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42 | static void smExactPolyDiv(poly, poly); |
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43 | static BOOLEAN smIsNegQuot(poly, const poly, const poly); |
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44 | static void smExpMultDiv(poly, const poly, const poly); |
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45 | static void smPolyDivN(poly, const number); |
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46 | static BOOLEAN smSmaller(poly, poly); |
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47 | static void smCombineChain(poly *, poly); |
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48 | static void smFindRef(poly *, poly *, poly); |
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49 | |
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50 | static void smElemDelete(smpoly *); |
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51 | static smpoly smElemCopy(smpoly); |
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52 | static float smPolyWeight(smpoly); |
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53 | static smpoly smPoly2Smpoly(poly); |
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54 | static poly smSmpoly2Poly(smpoly); |
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55 | static BOOLEAN smHaveDenom(poly); |
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56 | static number smCleardenom(ideal); |
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57 | |
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58 | static poly pp_Mult_Coeff_mm_DivSelect_MultDiv(poly p, int &lp, poly m, |
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59 | poly a, poly b) |
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60 | { |
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61 | if (rOrd_is_c_dp(currRing)) |
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62 | { |
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63 | int shorter; |
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64 | p = currRing->p_Procs->pp_Mult_Coeff_mm_DivSelectMult(p, m, a, b, |
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65 | shorter, currRing); |
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66 | lp -= shorter; |
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67 | } |
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68 | else |
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69 | { |
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70 | p = pp_Mult_Coeff_mm_DivSelect(p, lp, m, currRing); |
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71 | smExpMultDiv(p, a, b); |
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72 | } |
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73 | return p; |
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74 | } |
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75 | |
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76 | static poly smSelectCopy_ExpMultDiv(poly p, poly m, poly a, poly b) |
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77 | { |
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78 | int lp = 0; |
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79 | return pp_Mult_Coeff_mm_DivSelect_MultDiv(p, lp, m, a, b); |
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80 | } |
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81 | |
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82 | |
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83 | /* class for sparse matrix: |
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84 | * 3 parts of matrix during the algorithm |
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85 | * m_act[cols][pos(rows)] => m_row[rows][pos(cols)] => m_res[cols][pos(rows)] |
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86 | * input pivotcols as rows result |
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87 | * pivot like a stack from pivot and pivotcols |
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88 | * elimination rows reordered according |
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89 | * to pivot choise |
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90 | * stored in perm |
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91 | * a step is as follows |
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92 | * - search of pivot (smPivot) |
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93 | * - swap pivot column and last column (smSwapC) |
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94 | * select pivotrow to piv and red (smSelectPR) |
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95 | * consider sign |
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96 | * - elimination (smInitElim, sm0Elim, sm1Elim) |
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97 | * clear zero column as result of elimination (smZeroElim) |
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98 | * - tranfer from |
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99 | * piv and m_row to m_res (smRowToCol) |
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100 | * m_act to m_row (smColToRow) |
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101 | */ |
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102 | class sparse_mat{ |
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103 | private: |
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104 | int nrows, ncols; // dimension of the problem |
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105 | int sign; // for determinant (start: 1) |
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106 | int act; // number of unreduced columns (start: ncols) |
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107 | int crd; // number of reduced columns (start: 0) |
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108 | int tored; // border for rows to reduce |
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109 | int inred; // unreducable part |
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110 | int rpiv, cpiv; // position of the pivot |
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111 | int normalize; // Normalization flag |
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112 | int *perm; // permutation of rows |
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113 | float wpoints; // weight of all points |
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114 | float *wrw, *wcl; // weights of rows and columns |
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115 | smpoly * m_act; // unreduced columns |
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116 | smpoly * m_res; // reduced columns (result) |
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117 | smpoly * m_row; // reduced part of rows |
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118 | smpoly red; // row to reduce |
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119 | smpoly piv, oldpiv; // pivot and previous pivot |
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120 | smpoly dumm; // allocated dummy |
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121 | void smColToRow(); |
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122 | void smRowToCol(); |
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123 | void smFinalMult(); |
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124 | void smSparseHomog(); |
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125 | void smWeights(); |
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126 | void smPivot(); |
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127 | void smNewWeights(); |
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128 | void smNewPivot(); |
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129 | void smZeroElim(); |
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130 | void smToredElim(); |
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131 | void smCopToRes(); |
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132 | void smSelectPR(); |
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133 | void smElim(); |
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134 | void sm1Elim(); |
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135 | void smHElim(); |
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136 | void smMultCol(); |
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137 | poly smMultPoly(smpoly); |
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138 | void smActDel(); |
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139 | void smColDel(); |
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140 | void smPivDel(); |
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141 | void smSign(); |
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142 | void smInitPerm(); |
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143 | int smCheckNormalize(); |
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144 | void smNormalize(); |
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145 | public: |
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146 | sparse_mat(ideal); |
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147 | ~sparse_mat(); |
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148 | int smGetSign() { return sign; } |
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149 | smpoly * smGetAct() { return m_act; } |
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150 | int smGetRed() { return tored; } |
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151 | ideal smRes2Mod(); |
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152 | poly smDet(); |
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153 | void smBareiss(int, int); |
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154 | void smNewBareiss(int, int); |
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155 | void smToIntvec(intvec *); |
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156 | }; |
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157 | |
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158 | Exponent_t smExpBound(ideal Id) |
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159 | { |
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160 | Exponent_t max = 0; |
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161 | long ldeg; |
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162 | int dummy, i, n = IDELEMS(Id); |
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163 | |
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164 | for (i=0; i<n; i++) |
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165 | { |
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166 | if (Id->m[i] != NULL) |
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167 | { |
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168 | ldeg = pLDeg(Id->m[i], &dummy); |
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169 | if (ldeg > max) max = ldeg; |
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170 | } |
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171 | } |
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172 | return max*2*n; |
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173 | } |
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174 | |
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175 | // #define HOMOG_LP |
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176 | /* ----------------- ops with rings ------------------ */ |
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177 | ideal smRingCopy(ideal I, ring *ri, sip_sring &tmpR) |
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178 | { |
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179 | ring origR =NULL; |
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180 | ideal II; |
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181 | origR =currRing; |
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182 | tmpR=*origR; |
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183 | int *ord=(int*)omAlloc0(3*sizeof(int)); |
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184 | int *block0=(int*)omAlloc(3*sizeof(int)); |
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185 | int *block1=(int*)omAlloc(3*sizeof(int)); |
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186 | ord[0]=ringorder_c; |
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187 | #ifdef HOMOG_LP |
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188 | if (idHomIdeal(I)) |
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189 | ord[1] = ringorder_lp; |
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190 | else |
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191 | #endif |
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192 | ord[1]=ringorder_dp; |
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193 | tmpR.order=ord; |
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194 | tmpR.OrdSgn=1; |
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195 | block0[1]=1; |
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196 | tmpR.block0=block0; |
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197 | block1[1]=tmpR.N; |
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198 | tmpR.block1=block1; |
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199 | |
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200 | tmpR.bitmask = smExpBound(I); |
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201 | |
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202 | // unfortunately, we can not work (yet) with r->N == 0 |
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203 | if (tmpR.bitmask < 1) tmpR.bitmask = 1; |
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204 | if (tmpR.bitmask > currRing->bitmask) tmpR.bitmask = currRing->bitmask; |
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205 | |
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206 | rComplete(&tmpR,1); |
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207 | rChangeCurrRing(&tmpR); |
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208 | if (TEST_OPT_PROT) |
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209 | Print("[%d:%d]", (long) tmpR.bitmask, tmpR.ExpL_Size); |
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210 | // fetch data from the old ring |
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211 | II = idrCopyR(I, origR); |
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212 | idTest(II); |
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213 | *ri = origR; |
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214 | return II; |
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215 | } |
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216 | |
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217 | void smRingClean(ring origR, ip_sring &tmpR) |
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218 | { |
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219 | rChangeCurrRing(origR); |
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220 | rUnComplete(&tmpR); |
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221 | omFreeSize((ADDRESS)tmpR.order,3*sizeof(int)); |
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222 | omFreeSize((ADDRESS)tmpR.block0,3*sizeof(int)); |
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223 | omFreeSize((ADDRESS)tmpR.block1,3*sizeof(int)); |
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224 | } |
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225 | |
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226 | /* ----------------- basics (used from 'C') ------------------ */ |
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227 | /*2 |
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228 | *returns the determinant of the module I; |
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229 | *uses Bareiss algorithm |
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230 | */ |
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231 | poly smCallDet(ideal I) |
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232 | { |
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233 | if (I->ncols != I->rank) |
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234 | { |
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235 | Werror("det of %d x %d module (matrix)",I->rank,I->ncols); |
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236 | return NULL; |
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237 | } |
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238 | int r=idRankFreeModule(I); |
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239 | if (I->ncols != r) // some 0-lines at the end |
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240 | { |
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241 | return NULL; |
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242 | } |
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243 | number diag,h=nInit(1); |
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244 | poly res,save; |
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245 | ring origR; |
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246 | sip_sring tmpR; |
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247 | sparse_mat *det; |
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248 | ideal II=smRingCopy(I,&origR,tmpR); |
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249 | |
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250 | diag = smCleardenom(II); |
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251 | det = new sparse_mat(II); |
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252 | idDelete(&II); |
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253 | if (det->smGetAct() == NULL) |
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254 | { |
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255 | delete det; |
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256 | if (origR!=NULL) smRingClean(origR,tmpR); |
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257 | return NULL; |
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258 | } |
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259 | res=det->smDet(); |
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260 | if(det->smGetSign()<0) res=pNeg(res); |
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261 | delete det; |
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262 | if (origR!=NULL) |
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263 | { |
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264 | rChangeCurrRing(origR); |
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265 | save = res; |
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266 | res = prCopyR( save, &tmpR); |
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267 | rChangeCurrRing(&tmpR); |
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268 | pDelete(&save); |
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269 | smRingClean(origR,tmpR); |
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270 | } |
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271 | if (nEqual(diag,h) == FALSE) |
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272 | { |
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273 | pMult_nn(res,diag); |
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274 | pNormalize(res); |
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275 | } |
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276 | nDelete(&diag); |
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277 | nDelete(&h); |
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278 | return res; |
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279 | } |
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280 | |
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281 | lists smCallBareiss(ideal I, int x, int y) |
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282 | { |
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283 | ring origR; |
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284 | sip_sring tmpR; |
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285 | lists res=(lists)omAllocBin(slists_bin); |
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286 | ideal II = smRingCopy(I,&origR,tmpR); |
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287 | sparse_mat *bareiss = new sparse_mat(II); |
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288 | ideal mm=II; |
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289 | intvec *v; |
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290 | ideal m; |
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291 | |
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292 | if (bareiss->smGetAct() == NULL) |
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293 | { |
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294 | delete bareiss; |
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295 | if (origR!=NULL) smRingClean(origR,tmpR); |
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296 | v=new intvec(1,pVariables); |
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297 | } |
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298 | else |
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299 | { |
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300 | idDelete(&II); |
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301 | bareiss->smBareiss(x, y); |
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302 | m = bareiss->smRes2Mod(); |
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303 | v = new intvec(bareiss->smGetRed()); |
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304 | bareiss->smToIntvec(v); |
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305 | delete bareiss; |
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306 | if (origR!=NULL) |
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307 | { |
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308 | rChangeCurrRing(origR); |
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309 | mm=idInit(IDELEMS(m),m->rank); |
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310 | int k; |
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311 | for (k=0;k<IDELEMS(m);k++) mm->m[k] = prCopyR( m->m[k], &tmpR); |
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312 | rChangeCurrRing(&tmpR); |
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313 | idDelete(&m); |
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314 | smRingClean(origR,tmpR); |
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315 | } |
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316 | else |
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317 | { |
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318 | mm=m; |
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319 | } |
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320 | } |
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321 | res->Init(2); |
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322 | res->m[0].rtyp=MODUL_CMD; |
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323 | res->m[0].data=(void *)mm; |
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324 | res->m[1].rtyp=INTVEC_CMD; |
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325 | res->m[1].data=(void *)v; |
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326 | return res; |
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327 | } |
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328 | |
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329 | lists smCallNewBareiss(ideal I, int x, int y) |
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330 | { |
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331 | ring origR; |
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332 | sip_sring tmpR; |
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333 | lists res=(lists)omAllocBin(slists_bin); |
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334 | ideal II=smRingCopy(I,&origR,tmpR); |
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335 | sparse_mat *bareiss = new sparse_mat(II); |
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336 | ideal mm=II; |
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337 | intvec *v; |
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338 | ideal m; |
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339 | |
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340 | if (bareiss->smGetAct() == NULL) |
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341 | { |
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342 | delete bareiss; |
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343 | if (origR!=NULL) smRingClean(origR,tmpR); |
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344 | v=new intvec(1,pVariables); |
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345 | } |
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346 | else |
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347 | { |
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348 | idDelete(&II); |
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349 | bareiss->smNewBareiss(x, y); |
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350 | m = bareiss->smRes2Mod(); |
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351 | v = new intvec(bareiss->smGetRed()); |
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352 | bareiss->smToIntvec(v); |
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353 | delete bareiss; |
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354 | if (origR!=NULL) |
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355 | { |
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356 | rChangeCurrRing(origR); |
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357 | mm=idInit(IDELEMS(m),m->rank); |
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358 | int k; |
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359 | for (k=0;k<IDELEMS(m);k++) mm->m[k] = prCopyR( m->m[k], &tmpR); |
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360 | rChangeCurrRing(&tmpR); |
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361 | idDelete(&m); |
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362 | smRingClean(origR,tmpR); |
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363 | } |
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364 | else |
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365 | { |
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366 | mm=m; |
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367 | } |
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368 | } |
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369 | res->Init(2); |
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370 | res->m[0].rtyp=MODUL_CMD; |
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371 | res->m[0].data=(void *)mm; |
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372 | res->m[1].rtyp=INTVEC_CMD; |
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373 | res->m[1].data=(void *)v; |
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374 | return res; |
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375 | } |
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376 | |
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377 | /* |
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378 | * constructor |
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379 | */ |
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380 | sparse_mat::sparse_mat(ideal smat) |
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381 | { |
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382 | int i; |
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383 | polyset pmat; |
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384 | |
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385 | ncols = smat->ncols; |
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386 | nrows = idRankFreeModule(smat); |
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387 | if (nrows <= 0) |
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388 | { |
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389 | m_act = NULL; |
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390 | return; |
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391 | } |
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392 | sign = 1; |
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393 | inred = act = ncols; |
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394 | crd = 0; |
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395 | tored = nrows; // without border |
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396 | i = tored+1; |
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397 | perm = (int *)omAlloc(sizeof(int)*(i+1)); |
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398 | perm[i] = 0; |
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399 | m_row = (smpoly *)omAlloc0(sizeof(smpoly)*i); |
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400 | wrw = (float *)omAlloc(sizeof(float)*i); |
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401 | i = ncols+1; |
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402 | wcl = (float *)omAlloc(sizeof(float)*i); |
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403 | m_act = (smpoly *)omAlloc(sizeof(smpoly)*i); |
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404 | m_res = (smpoly *)omAlloc0(sizeof(smpoly)*i); |
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405 | dumm = (smpoly)omAllocBin(smprec_bin); |
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406 | m_res[0] = (smpoly)omAllocBin(smprec_bin); |
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407 | m_res[0]->m = NULL; |
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408 | pmat = smat->m; |
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409 | for(i=ncols; i; i--) |
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410 | { |
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411 | m_act[i] = smPoly2Smpoly(pmat[i-1]); |
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412 | pmat[i-1] = NULL; |
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413 | } |
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414 | this->smZeroElim(); |
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415 | oldpiv = NULL; |
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416 | } |
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417 | |
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418 | /* |
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419 | * destructor |
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420 | */ |
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421 | sparse_mat::~sparse_mat() |
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422 | { |
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423 | int i; |
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424 | if (m_act == NULL) return; |
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425 | omFreeBin((ADDRESS)m_res[0], smprec_bin); |
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426 | omFreeBin((ADDRESS)dumm, smprec_bin); |
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427 | i = ncols+1; |
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428 | omFreeSize((ADDRESS)m_res, sizeof(smpoly)*i); |
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429 | omFreeSize((ADDRESS)m_act, sizeof(smpoly)*i); |
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430 | omFreeSize((ADDRESS)wcl, sizeof(float)*i); |
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431 | i = nrows+1; |
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432 | omFreeSize((ADDRESS)wrw, sizeof(float)*i); |
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433 | omFreeSize((ADDRESS)m_row, sizeof(smpoly)*i); |
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434 | omFreeSize((ADDRESS)perm, sizeof(int)*(i+1)); |
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435 | } |
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436 | |
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437 | /* |
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438 | * transform the result to a module |
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439 | */ |
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440 | ideal sparse_mat::smRes2Mod() |
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441 | { |
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442 | ideal res = idInit(crd, crd); |
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443 | int i; |
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444 | |
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445 | for (i=crd; i; i--) res->m[i-1] = smSmpoly2Poly(m_res[i]); |
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446 | res->rank = idRankFreeModule(res); |
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447 | return res; |
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448 | } |
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449 | |
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450 | /* |
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451 | * permutation of rows |
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452 | */ |
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453 | void sparse_mat::smToIntvec(intvec *v) |
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454 | { |
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455 | int i; |
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456 | |
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457 | for (i=v->rows()-1; i>=0; i--) |
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458 | (*v)[i] = perm[i+1]; |
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459 | } |
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460 | /* ---------------- the algorithm's ------------------ */ |
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461 | /* |
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462 | * the determinant (up to sign), uses new Bareiss elimination |
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463 | */ |
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464 | poly sparse_mat::smDet() |
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465 | { |
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466 | int y; |
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467 | poly res = NULL; |
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468 | |
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469 | if (sign == 0) |
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470 | { |
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471 | this->smActDel(); |
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472 | return NULL; |
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473 | } |
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474 | if (act < 2) |
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475 | { |
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476 | if (act != 0) res = m_act[1]->m; |
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477 | omFreeBin((void *)m_act[1], smprec_bin); |
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478 | return res; |
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479 | } |
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480 | normalize = 0; |
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481 | this->smInitPerm(); |
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482 | this->smPivot(); |
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483 | this->smSign(); |
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484 | this->smSelectPR(); |
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485 | this->sm1Elim(); |
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486 | crd++; |
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487 | m_res[crd] = piv; |
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488 | this->smColDel(); |
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489 | act--; |
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490 | this->smZeroElim(); |
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491 | if (sign == 0) |
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492 | { |
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493 | this->smActDel(); |
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494 | return NULL; |
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495 | } |
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496 | if (act < 2) |
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497 | { |
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498 | this->smFinalMult(); |
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499 | this->smPivDel(); |
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500 | if (act != 0) res = m_act[1]->m; |
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501 | omFreeBin((void *)m_act[1], smprec_bin); |
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502 | return res; |
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503 | } |
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504 | loop |
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505 | { |
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506 | this->smNewPivot(); |
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507 | this->smSign(); |
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508 | this->smSelectPR(); |
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509 | this->smMultCol(); |
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510 | this->smHElim(); |
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511 | crd++; |
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512 | m_res[crd] = piv; |
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513 | this->smColDel(); |
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514 | act--; |
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515 | this->smZeroElim(); |
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516 | if (sign == 0) |
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517 | { |
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518 | this->smPivDel(); |
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519 | this->smActDel(); |
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520 | return NULL; |
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521 | } |
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522 | if (act < 2) |
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523 | { |
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524 | if (TEST_OPT_PROT) PrintS(".\n"); |
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525 | this->smFinalMult(); |
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526 | this->smPivDel(); |
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527 | if (act != 0) res = m_act[1]->m; |
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528 | omFreeBin((void *)m_act[1], smprec_bin); |
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529 | return res; |
---|
530 | } |
---|
531 | } |
---|
532 | } |
---|
533 | |
---|
534 | /* |
---|
535 | * the Bareiss elimination: |
---|
536 | * - with x unreduced last rows, pivots from here are not allowed |
---|
537 | * - the method will finish for number of unreduced columns < y |
---|
538 | */ |
---|
539 | void sparse_mat::smBareiss(int x, int y) |
---|
540 | { |
---|
541 | if ((x > 0) && (x < nrows)) |
---|
542 | { |
---|
543 | tored -= x; |
---|
544 | this->smToredElim(); |
---|
545 | } |
---|
546 | if (y < 1) y = 1; |
---|
547 | if (act <= y) |
---|
548 | { |
---|
549 | this->smCopToRes(); |
---|
550 | return; |
---|
551 | } |
---|
552 | normalize = this->smCheckNormalize(); |
---|
553 | if (normalize) this->smNormalize(); |
---|
554 | this->smPivot(); |
---|
555 | this->smSelectPR(); |
---|
556 | this->smElim(); |
---|
557 | crd++; |
---|
558 | this->smColToRow(); |
---|
559 | act--; |
---|
560 | this->smRowToCol(); |
---|
561 | this->smZeroElim(); |
---|
562 | if (tored != nrows) |
---|
563 | this->smToredElim(); |
---|
564 | if (act < y) |
---|
565 | { |
---|
566 | this->smCopToRes(); |
---|
567 | return; |
---|
568 | } |
---|
569 | loop |
---|
570 | { |
---|
571 | if (normalize) this->smNormalize(); |
---|
572 | this->smPivot(); |
---|
573 | oldpiv = piv; |
---|
574 | this->smSelectPR(); |
---|
575 | this->smElim(); |
---|
576 | crd++; |
---|
577 | this->smColToRow(); |
---|
578 | act--; |
---|
579 | this->smRowToCol(); |
---|
580 | this->smZeroElim(); |
---|
581 | if (tored != nrows) |
---|
582 | this->smToredElim(); |
---|
583 | if (act < y) |
---|
584 | { |
---|
585 | if (TEST_OPT_PROT) PrintS(".\n"); |
---|
586 | this->smCopToRes(); |
---|
587 | return; |
---|
588 | } |
---|
589 | } |
---|
590 | } |
---|
591 | |
---|
592 | /* |
---|
593 | * the new Bareiss elimination: |
---|
594 | * - with x unreduced last rows, pivots from here are not allowed |
---|
595 | * - the method will finish for number of unreduced columns < y |
---|
596 | */ |
---|
597 | void sparse_mat::smNewBareiss(int x, int y) |
---|
598 | { |
---|
599 | if ((x > 0) && (x < nrows)) |
---|
600 | { |
---|
601 | tored -= x; |
---|
602 | this->smToredElim(); |
---|
603 | } |
---|
604 | if (y < 1) y = 1; |
---|
605 | if (act <= y) |
---|
606 | { |
---|
607 | this->smCopToRes(); |
---|
608 | return; |
---|
609 | } |
---|
610 | normalize = this->smCheckNormalize(); |
---|
611 | if (normalize) this->smNormalize(); |
---|
612 | this->smPivot(); |
---|
613 | this->smSelectPR(); |
---|
614 | this->sm1Elim(); |
---|
615 | crd++; |
---|
616 | this->smColToRow(); |
---|
617 | act--; |
---|
618 | this->smRowToCol(); |
---|
619 | this->smZeroElim(); |
---|
620 | if (tored != nrows) |
---|
621 | this->smToredElim(); |
---|
622 | if (act <= y) |
---|
623 | { |
---|
624 | this->smFinalMult(); |
---|
625 | this->smCopToRes(); |
---|
626 | return; |
---|
627 | } |
---|
628 | loop |
---|
629 | { |
---|
630 | if (normalize) this->smNormalize(); |
---|
631 | this->smNewPivot(); |
---|
632 | this->smSelectPR(); |
---|
633 | this->smMultCol(); |
---|
634 | this->smHElim(); |
---|
635 | crd++; |
---|
636 | this->smColToRow(); |
---|
637 | act--; |
---|
638 | this->smRowToCol(); |
---|
639 | this->smZeroElim(); |
---|
640 | if (tored != nrows) |
---|
641 | this->smToredElim(); |
---|
642 | if (act <= y) |
---|
643 | { |
---|
644 | if (TEST_OPT_PROT) PrintS(".\n"); |
---|
645 | this->smFinalMult(); |
---|
646 | this->smCopToRes(); |
---|
647 | return; |
---|
648 | } |
---|
649 | } |
---|
650 | } |
---|
651 | |
---|
652 | /* ----------------- pivot method ------------------ */ |
---|
653 | |
---|
654 | /* |
---|
655 | * prepare smPivot, compute weights for rows and columns |
---|
656 | * and the weight for all points |
---|
657 | */ |
---|
658 | void sparse_mat::smWeights() |
---|
659 | { |
---|
660 | float wc, wp, w; |
---|
661 | smpoly a; |
---|
662 | int i; |
---|
663 | |
---|
664 | wp = 0.0; |
---|
665 | for (i=tored; i; i--) wrw[i] = 0.0; // ??? |
---|
666 | for (i=act; i; i--) |
---|
667 | { |
---|
668 | wc = 0.0; |
---|
669 | a = m_act[i]; |
---|
670 | loop |
---|
671 | { |
---|
672 | if (a->pos > tored) |
---|
673 | break; |
---|
674 | w = a->f = smPolyWeight(a); |
---|
675 | wc += w; |
---|
676 | wrw[a->pos] += w; |
---|
677 | a = a->n; |
---|
678 | if (a == NULL) |
---|
679 | break; |
---|
680 | } |
---|
681 | wp += wc; |
---|
682 | wcl[i] = wc; |
---|
683 | } |
---|
684 | wpoints = wp; |
---|
685 | } |
---|
686 | |
---|
687 | /* |
---|
688 | * compute pivot |
---|
689 | */ |
---|
690 | void sparse_mat::smPivot() |
---|
691 | { |
---|
692 | float wopt = 1.0e30; |
---|
693 | float wc, wr, wp, w; |
---|
694 | smpoly a; |
---|
695 | int i, copt, ropt; |
---|
696 | |
---|
697 | this->smWeights(); |
---|
698 | for (i=act; i; i--) |
---|
699 | { |
---|
700 | a = m_act[i]; |
---|
701 | loop |
---|
702 | { |
---|
703 | if (a->pos > tored) |
---|
704 | break; |
---|
705 | w = a->f; |
---|
706 | wc = wcl[i]-w; |
---|
707 | wr = wrw[a->pos]-w; |
---|
708 | if ((wr<0.25) || (wc<0.25)) // row or column with only one point |
---|
709 | { |
---|
710 | if (w<wopt) |
---|
711 | { |
---|
712 | wopt = w; |
---|
713 | copt = i; |
---|
714 | ropt = a->pos; |
---|
715 | } |
---|
716 | } |
---|
717 | else // elimination |
---|
718 | { |
---|
719 | wp = w*(wpoints-wcl[i]-wr); |
---|
720 | wp += wr*wc; |
---|
721 | if (wp < wopt) |
---|
722 | { |
---|
723 | wopt = wp; |
---|
724 | copt = i; |
---|
725 | ropt = a->pos; |
---|
726 | } |
---|
727 | } |
---|
728 | a = a->n; |
---|
729 | if (a == NULL) |
---|
730 | break; |
---|
731 | } |
---|
732 | } |
---|
733 | rpiv = ropt; |
---|
734 | cpiv = copt; |
---|
735 | if (cpiv != act) |
---|
736 | { |
---|
737 | a = m_act[act]; |
---|
738 | m_act[act] = m_act[cpiv]; |
---|
739 | m_act[cpiv] = a; |
---|
740 | } |
---|
741 | } |
---|
742 | |
---|
743 | /* |
---|
744 | * prepare smPivot, compute weights for rows and columns |
---|
745 | * and the weight for all points |
---|
746 | */ |
---|
747 | void sparse_mat::smNewWeights() |
---|
748 | { |
---|
749 | float wc, wp, w, hp = piv->f; |
---|
750 | smpoly a; |
---|
751 | int i, f, e = crd; |
---|
752 | |
---|
753 | wp = 0.0; |
---|
754 | for (i=tored; i; i--) wrw[i] = 0.0; // ??? |
---|
755 | for (i=act; i; i--) |
---|
756 | { |
---|
757 | wc = 0.0; |
---|
758 | a = m_act[i]; |
---|
759 | loop |
---|
760 | { |
---|
761 | if (a->pos > tored) |
---|
762 | break; |
---|
763 | w = a->f; |
---|
764 | f = a->e; |
---|
765 | if (f < e) |
---|
766 | { |
---|
767 | w *= hp; |
---|
768 | if (f) w /= m_res[f]->f; |
---|
769 | } |
---|
770 | wc += w; |
---|
771 | wrw[a->pos] += w; |
---|
772 | a = a->n; |
---|
773 | if (a == NULL) |
---|
774 | break; |
---|
775 | } |
---|
776 | wp += wc; |
---|
777 | wcl[i] = wc; |
---|
778 | } |
---|
779 | wpoints = wp; |
---|
780 | } |
---|
781 | |
---|
782 | /* |
---|
783 | * compute pivot |
---|
784 | */ |
---|
785 | void sparse_mat::smNewPivot() |
---|
786 | { |
---|
787 | float wopt = 1.0e30, hp = piv->f; |
---|
788 | float wc, wr, wp, w; |
---|
789 | smpoly a; |
---|
790 | int i, copt, ropt, f, e = crd; |
---|
791 | |
---|
792 | this->smNewWeights(); |
---|
793 | for (i=act; i; i--) |
---|
794 | { |
---|
795 | a = m_act[i]; |
---|
796 | loop |
---|
797 | { |
---|
798 | if (a->pos > tored) |
---|
799 | break; |
---|
800 | w = a->f; |
---|
801 | f = a->e; |
---|
802 | if (f < e) |
---|
803 | { |
---|
804 | w *= hp; |
---|
805 | if (f) w /= m_res[f]->f; |
---|
806 | } |
---|
807 | wc = wcl[i]-w; |
---|
808 | wr = wrw[a->pos]-w; |
---|
809 | if ((wr<0.25) || (wc<0.25)) // row or column with only one point |
---|
810 | { |
---|
811 | if (w<wopt) |
---|
812 | { |
---|
813 | wopt = w; |
---|
814 | copt = i; |
---|
815 | ropt = a->pos; |
---|
816 | } |
---|
817 | } |
---|
818 | else // elimination |
---|
819 | { |
---|
820 | wp = w*(wpoints-wcl[i]-wr); |
---|
821 | wp += wr*wc; |
---|
822 | if (wp < wopt) |
---|
823 | { |
---|
824 | wopt = wp; |
---|
825 | copt = i; |
---|
826 | ropt = a->pos; |
---|
827 | } |
---|
828 | } |
---|
829 | a = a->n; |
---|
830 | if (a == NULL) |
---|
831 | break; |
---|
832 | } |
---|
833 | } |
---|
834 | rpiv = ropt; |
---|
835 | cpiv = copt; |
---|
836 | if (cpiv != act) |
---|
837 | { |
---|
838 | a = m_act[act]; |
---|
839 | m_act[act] = m_act[cpiv]; |
---|
840 | m_act[cpiv] = a; |
---|
841 | } |
---|
842 | } |
---|
843 | |
---|
844 | /* ----------------- elimination ------------------ */ |
---|
845 | |
---|
846 | /* steps of elimination */ |
---|
847 | void sparse_mat::smElim() |
---|
848 | { |
---|
849 | poly p = piv->m; // pivotelement |
---|
850 | smpoly c = m_act[act]; // pivotcolumn |
---|
851 | smpoly r = red; // row to reduce |
---|
852 | poly q; |
---|
853 | smpoly res, a, b; |
---|
854 | poly w, ha, hb; |
---|
855 | int i; |
---|
856 | |
---|
857 | if (oldpiv != NULL) q = oldpiv->m; // previous pivot |
---|
858 | else q = NULL; |
---|
859 | if ((c == NULL) || (r == NULL)) |
---|
860 | { |
---|
861 | while (r) smElemDelete(&r); |
---|
862 | for (i=1; i<act; i++) |
---|
863 | { |
---|
864 | a = m_act[i]; |
---|
865 | while (a != NULL) |
---|
866 | { |
---|
867 | ha = SM_MULT(a->m, p, q); |
---|
868 | pDelete(&a->m); |
---|
869 | if (q) SM_DIV(ha, q); |
---|
870 | a->m = ha; |
---|
871 | a = a->n; |
---|
872 | } |
---|
873 | } |
---|
874 | return; |
---|
875 | } |
---|
876 | for (i=1; i<act; i++) |
---|
877 | { |
---|
878 | a = m_act[i]; |
---|
879 | if ((r == NULL) || (i != r->pos)) // cols without elimination |
---|
880 | { |
---|
881 | while (a != NULL) |
---|
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 | a = a->n; |
---|
888 | } |
---|
889 | } |
---|
890 | else // cols with elimination |
---|
891 | { |
---|
892 | res = dumm; |
---|
893 | res->n = NULL; |
---|
894 | b = c; |
---|
895 | w = r->m; |
---|
896 | loop // combine the chains a and b: p*a + w*b |
---|
897 | { |
---|
898 | if (a == NULL) |
---|
899 | { |
---|
900 | if (b != NULL) |
---|
901 | { |
---|
902 | do |
---|
903 | { |
---|
904 | res = res->n = smElemCopy(b); |
---|
905 | hb = SM_MULT(b->m, w, q); |
---|
906 | if (q) SM_DIV(hb, q); |
---|
907 | res->m = hb; |
---|
908 | b = b->n; |
---|
909 | } while (b != NULL); |
---|
910 | } |
---|
911 | else |
---|
912 | res->n = NULL; |
---|
913 | break; |
---|
914 | } |
---|
915 | if (b == NULL) |
---|
916 | { |
---|
917 | do |
---|
918 | { |
---|
919 | ha = SM_MULT(a->m, p, q); |
---|
920 | pDelete(&a->m); |
---|
921 | if (q) SM_DIV(ha, q); |
---|
922 | a->m = ha; |
---|
923 | res = res->n = a; |
---|
924 | a = a->n; |
---|
925 | } while (a != NULL); |
---|
926 | break; |
---|
927 | } |
---|
928 | if (a->pos < b->pos) |
---|
929 | { |
---|
930 | ha = SM_MULT(a->m, p, q); |
---|
931 | pDelete(&a->m); |
---|
932 | if (q) SM_DIV(ha, q); |
---|
933 | a->m = ha; |
---|
934 | res = res->n = a; |
---|
935 | a = a->n; |
---|
936 | } |
---|
937 | else if (a->pos > b->pos) |
---|
938 | { |
---|
939 | res = res->n = smElemCopy(b); |
---|
940 | hb = SM_MULT(b->m, w, q); |
---|
941 | b = b->n; |
---|
942 | if (q) SM_DIV(hb, q); |
---|
943 | res->m = hb; |
---|
944 | } |
---|
945 | else |
---|
946 | { |
---|
947 | ha = SM_MULT(a->m, p, q); |
---|
948 | pDelete(&a->m); |
---|
949 | hb = SM_MULT(b->m, w, q); |
---|
950 | ha = pAdd(ha, hb); |
---|
951 | if (ha != NULL) |
---|
952 | { |
---|
953 | if (q) SM_DIV(ha, q); |
---|
954 | a->m = ha; |
---|
955 | res = res->n = a; |
---|
956 | a = a->n; |
---|
957 | } |
---|
958 | else |
---|
959 | { |
---|
960 | smElemDelete(&a); |
---|
961 | } |
---|
962 | b = b->n; |
---|
963 | } |
---|
964 | } |
---|
965 | m_act[i] = dumm->n; |
---|
966 | if (r) smElemDelete(&r); |
---|
967 | } |
---|
968 | } |
---|
969 | } |
---|
970 | |
---|
971 | /* first step of elimination */ |
---|
972 | void sparse_mat::sm1Elim() |
---|
973 | { |
---|
974 | poly p = piv->m; // pivotelement |
---|
975 | smpoly c = m_act[act]; // pivotcolumn |
---|
976 | smpoly r = red; // row to reduce |
---|
977 | smpoly res, a, b; |
---|
978 | poly w, ha, hb; |
---|
979 | |
---|
980 | if ((c == NULL) || (r == NULL)) |
---|
981 | { |
---|
982 | while (r!=NULL) smElemDelete(&r); |
---|
983 | return; |
---|
984 | } |
---|
985 | do |
---|
986 | { |
---|
987 | a = m_act[r->pos]; |
---|
988 | res = dumm; |
---|
989 | res->n = NULL; |
---|
990 | b = c; |
---|
991 | w = r->m; |
---|
992 | loop // combine the chains a and b: p*a + w*b |
---|
993 | { |
---|
994 | if (a == NULL) |
---|
995 | { |
---|
996 | do |
---|
997 | { |
---|
998 | res = res->n = smElemCopy(b); |
---|
999 | res->m = ppMult_qq(b->m, w); |
---|
1000 | res->e = 1; |
---|
1001 | res->f = smPolyWeight(res); |
---|
1002 | b = b->n; |
---|
1003 | } while (b != NULL); |
---|
1004 | break; |
---|
1005 | } |
---|
1006 | if (a->pos < b->pos) |
---|
1007 | { |
---|
1008 | res = res->n = a; |
---|
1009 | a = a->n; |
---|
1010 | } |
---|
1011 | else if (a->pos > b->pos) |
---|
1012 | { |
---|
1013 | res = res->n = smElemCopy(b); |
---|
1014 | res->m = ppMult_qq(b->m, w); |
---|
1015 | res->e = 1; |
---|
1016 | res->f = smPolyWeight(res); |
---|
1017 | b = b->n; |
---|
1018 | } |
---|
1019 | else |
---|
1020 | { |
---|
1021 | ha = ppMult_qq(a->m, p); |
---|
1022 | pDelete(&a->m); |
---|
1023 | hb = ppMult_qq(b->m, w); |
---|
1024 | ha = pAdd(ha, hb); |
---|
1025 | if (ha != NULL) |
---|
1026 | { |
---|
1027 | a->m = ha; |
---|
1028 | a->e = 1; |
---|
1029 | a->f = smPolyWeight(a); |
---|
1030 | res = res->n = a; |
---|
1031 | a = a->n; |
---|
1032 | } |
---|
1033 | else |
---|
1034 | { |
---|
1035 | smElemDelete(&a); |
---|
1036 | } |
---|
1037 | b = b->n; |
---|
1038 | } |
---|
1039 | if (b == NULL) |
---|
1040 | { |
---|
1041 | res->n = a; |
---|
1042 | break; |
---|
1043 | } |
---|
1044 | } |
---|
1045 | m_act[r->pos] = dumm->n; |
---|
1046 | smElemDelete(&r); |
---|
1047 | } while (r != NULL); |
---|
1048 | } |
---|
1049 | |
---|
1050 | /* higher steps of elimination */ |
---|
1051 | void sparse_mat::smHElim() |
---|
1052 | { |
---|
1053 | poly hp = this->smMultPoly(piv); |
---|
1054 | poly gp = piv->m; // pivotelement |
---|
1055 | smpoly c = m_act[act]; // pivotcolumn |
---|
1056 | smpoly r = red; // row to reduce |
---|
1057 | smpoly res, a, b; |
---|
1058 | poly ha, hr, x, y; |
---|
1059 | int e, ip, ir, ia, lev; |
---|
1060 | |
---|
1061 | if ((c == NULL) || (r == NULL)) |
---|
1062 | { |
---|
1063 | while(r!=NULL) smElemDelete(&r); |
---|
1064 | pDelete(&hp); |
---|
1065 | return; |
---|
1066 | } |
---|
1067 | e = crd+1; |
---|
1068 | ip = piv->e; |
---|
1069 | do |
---|
1070 | { |
---|
1071 | a = m_act[r->pos]; |
---|
1072 | res = dumm; |
---|
1073 | res->n = NULL; |
---|
1074 | b = c; |
---|
1075 | hr = r->m; |
---|
1076 | ir = r->e; |
---|
1077 | loop // combine the chains a and b: (hp,gp)*a(l) + hr*b(h) |
---|
1078 | { |
---|
1079 | if (a == NULL) |
---|
1080 | { |
---|
1081 | do |
---|
1082 | { |
---|
1083 | res = res->n = smElemCopy(b); |
---|
1084 | x = SM_MULT(b->m, hr, m_res[ir]->m); |
---|
1085 | b = b->n; |
---|
1086 | if(ir) SM_DIV(x, m_res[ir]->m); |
---|
1087 | res->m = x; |
---|
1088 | res->e = e; |
---|
1089 | res->f = smPolyWeight(res); |
---|
1090 | } while (b != NULL); |
---|
1091 | break; |
---|
1092 | } |
---|
1093 | if (a->pos < b->pos) |
---|
1094 | { |
---|
1095 | res = res->n = a; |
---|
1096 | a = a->n; |
---|
1097 | } |
---|
1098 | else if (a->pos > b->pos) |
---|
1099 | { |
---|
1100 | res = res->n = smElemCopy(b); |
---|
1101 | x = SM_MULT(b->m, hr, m_res[ir]->m); |
---|
1102 | b = b->n; |
---|
1103 | if(ir) SM_DIV(x, m_res[ir]->m); |
---|
1104 | res->m = x; |
---|
1105 | res->e = e; |
---|
1106 | res->f = smPolyWeight(res); |
---|
1107 | } |
---|
1108 | else |
---|
1109 | { |
---|
1110 | ha = a->m; |
---|
1111 | ia = a->e; |
---|
1112 | if (ir >= ia) |
---|
1113 | { |
---|
1114 | if (ir > ia) |
---|
1115 | { |
---|
1116 | x = SM_MULT(ha, m_res[ir]->m, m_res[ia]->m); |
---|
1117 | pDelete(&ha); |
---|
1118 | ha = x; |
---|
1119 | if (ia) SM_DIV(ha, m_res[ia]->m); |
---|
1120 | ia = ir; |
---|
1121 | } |
---|
1122 | x = SM_MULT(ha, gp, m_res[ia]->m); |
---|
1123 | pDelete(&ha); |
---|
1124 | y = SM_MULT(b->m, hr, m_res[ia]->m); |
---|
1125 | } |
---|
1126 | else if (ir >= ip) |
---|
1127 | { |
---|
1128 | if (ia < crd) |
---|
1129 | { |
---|
1130 | x = SM_MULT(ha, m_res[crd]->m, m_res[ia]->m); |
---|
1131 | pDelete(&ha); |
---|
1132 | ha = x; |
---|
1133 | SM_DIV(ha, m_res[ia]->m); |
---|
1134 | } |
---|
1135 | y = hp; |
---|
1136 | if(ir > ip) |
---|
1137 | { |
---|
1138 | y = SM_MULT(y, m_res[ir]->m, m_res[ip]->m); |
---|
1139 | if (ip) SM_DIV(y, m_res[ip]->m); |
---|
1140 | } |
---|
1141 | ia = ir; |
---|
1142 | x = SM_MULT(ha, y, m_res[ia]->m); |
---|
1143 | if (y != hp) pDelete(&y); |
---|
1144 | pDelete(&ha); |
---|
1145 | y = SM_MULT(b->m, hr, m_res[ia]->m); |
---|
1146 | } |
---|
1147 | else |
---|
1148 | { |
---|
1149 | x = SM_MULT(hr, m_res[ia]->m, m_res[ir]->m); |
---|
1150 | if (ir) SM_DIV(x, m_res[ir]->m); |
---|
1151 | y = SM_MULT(b->m, x, m_res[ia]->m); |
---|
1152 | pDelete(&x); |
---|
1153 | x = SM_MULT(ha, gp, m_res[ia]->m); |
---|
1154 | pDelete(&ha); |
---|
1155 | } |
---|
1156 | ha = pAdd(x, y); |
---|
1157 | if (ha != NULL) |
---|
1158 | { |
---|
1159 | if (ia) SM_DIV(ha, m_res[ia]->m); |
---|
1160 | a->m = ha; |
---|
1161 | a->e = e; |
---|
1162 | a->f = smPolyWeight(a); |
---|
1163 | res = res->n = a; |
---|
1164 | a = a->n; |
---|
1165 | } |
---|
1166 | else |
---|
1167 | { |
---|
1168 | a->m = NULL; |
---|
1169 | smElemDelete(&a); |
---|
1170 | } |
---|
1171 | b = b->n; |
---|
1172 | } |
---|
1173 | if (b == NULL) |
---|
1174 | { |
---|
1175 | res->n = a; |
---|
1176 | break; |
---|
1177 | } |
---|
1178 | } |
---|
1179 | m_act[r->pos] = dumm->n; |
---|
1180 | smElemDelete(&r); |
---|
1181 | } while (r != NULL); |
---|
1182 | pDelete(&hp); |
---|
1183 | } |
---|
1184 | |
---|
1185 | /* ----------------- transfer ------------------ */ |
---|
1186 | |
---|
1187 | /* |
---|
1188 | * select the pivotrow and store it to red and piv |
---|
1189 | */ |
---|
1190 | void sparse_mat::smSelectPR() |
---|
1191 | { |
---|
1192 | smpoly b = dumm; |
---|
1193 | smpoly a, ap; |
---|
1194 | int i; |
---|
1195 | |
---|
1196 | if (TEST_OPT_PROT) |
---|
1197 | { |
---|
1198 | if ((crd+1)%10) |
---|
1199 | PrintS("."); |
---|
1200 | else |
---|
1201 | PrintS(".\n"); |
---|
1202 | } |
---|
1203 | a = m_act[act]; |
---|
1204 | if (a->pos < rpiv) |
---|
1205 | { |
---|
1206 | do |
---|
1207 | { |
---|
1208 | ap = a; |
---|
1209 | a = a->n; |
---|
1210 | } while (a->pos < rpiv); |
---|
1211 | ap->n = a->n; |
---|
1212 | } |
---|
1213 | else |
---|
1214 | m_act[act] = a->n; |
---|
1215 | piv = a; |
---|
1216 | a->n = NULL; |
---|
1217 | for (i=1; i<act; i++) |
---|
1218 | { |
---|
1219 | a = m_act[i]; |
---|
1220 | if (a->pos < rpiv) |
---|
1221 | { |
---|
1222 | loop |
---|
1223 | { |
---|
1224 | ap = a; |
---|
1225 | a = a->n; |
---|
1226 | if ((a == NULL) || (a->pos > rpiv)) |
---|
1227 | break; |
---|
1228 | if (a->pos == rpiv) |
---|
1229 | { |
---|
1230 | ap->n = a->n; |
---|
1231 | a->m = pNeg(a->m); |
---|
1232 | b = b->n = a; |
---|
1233 | b->pos = i; |
---|
1234 | break; |
---|
1235 | } |
---|
1236 | } |
---|
1237 | } |
---|
1238 | else if (a->pos == rpiv) |
---|
1239 | { |
---|
1240 | m_act[i] = a->n; |
---|
1241 | a->m = pNeg(a->m); |
---|
1242 | b = b->n = a; |
---|
1243 | b->pos = i; |
---|
1244 | } |
---|
1245 | } |
---|
1246 | b->n = NULL; |
---|
1247 | red = dumm->n; |
---|
1248 | } |
---|
1249 | |
---|
1250 | /* |
---|
1251 | * store the pivotcol in m_row |
---|
1252 | * m_act[cols][pos(rows)] => m_row[rows][pos(cols)] |
---|
1253 | */ |
---|
1254 | void sparse_mat::smColToRow() |
---|
1255 | { |
---|
1256 | smpoly c = m_act[act]; |
---|
1257 | smpoly h; |
---|
1258 | |
---|
1259 | while (c != NULL) |
---|
1260 | { |
---|
1261 | h = c; |
---|
1262 | c = c->n; |
---|
1263 | h->n = m_row[h->pos]; |
---|
1264 | m_row[h->pos] = h; |
---|
1265 | h->pos = crd; |
---|
1266 | } |
---|
1267 | } |
---|
1268 | |
---|
1269 | /* |
---|
1270 | * store the pivot and the assosiated row in m_row |
---|
1271 | * to m_res (result): |
---|
1272 | * piv + m_row[rows][pos(cols)] => m_res[cols][pos(rows)] |
---|
1273 | */ |
---|
1274 | void sparse_mat::smRowToCol() |
---|
1275 | { |
---|
1276 | smpoly r = m_row[rpiv]; |
---|
1277 | smpoly a, ap, h; |
---|
1278 | |
---|
1279 | m_row[rpiv] = NULL; |
---|
1280 | perm[crd] = rpiv; |
---|
1281 | piv->pos = crd; |
---|
1282 | m_res[crd] = piv; |
---|
1283 | while (r != NULL) |
---|
1284 | { |
---|
1285 | ap = m_res[r->pos]; |
---|
1286 | loop |
---|
1287 | { |
---|
1288 | a = ap->n; |
---|
1289 | if (a == NULL) |
---|
1290 | { |
---|
1291 | ap->n = h = r; |
---|
1292 | r = r->n; |
---|
1293 | h->n = a; |
---|
1294 | h->pos = crd; |
---|
1295 | break; |
---|
1296 | } |
---|
1297 | ap = a; |
---|
1298 | } |
---|
1299 | } |
---|
1300 | } |
---|
1301 | |
---|
1302 | /* ----------------- C++ stuff ------------------ */ |
---|
1303 | |
---|
1304 | /* |
---|
1305 | * clean m_act from zeros (after elim) |
---|
1306 | */ |
---|
1307 | void sparse_mat::smZeroElim() |
---|
1308 | { |
---|
1309 | int i = 0; |
---|
1310 | int j; |
---|
1311 | |
---|
1312 | loop |
---|
1313 | { |
---|
1314 | i++; |
---|
1315 | if (i > act) return; |
---|
1316 | if (m_act[i] == NULL) break; |
---|
1317 | } |
---|
1318 | j = i; |
---|
1319 | loop |
---|
1320 | { |
---|
1321 | j++; |
---|
1322 | if (j > act) break; |
---|
1323 | if (m_act[j] != NULL) |
---|
1324 | { |
---|
1325 | m_act[i] = m_act[j]; |
---|
1326 | i++; |
---|
1327 | } |
---|
1328 | } |
---|
1329 | act -= (j-i); |
---|
1330 | sign = 0; |
---|
1331 | } |
---|
1332 | |
---|
1333 | /* |
---|
1334 | * clean m_act from cols not to reduced (after elim) |
---|
1335 | * put them to m_res |
---|
1336 | */ |
---|
1337 | void sparse_mat::smToredElim() |
---|
1338 | { |
---|
1339 | int i = 0; |
---|
1340 | int j; |
---|
1341 | |
---|
1342 | loop |
---|
1343 | { |
---|
1344 | i++; |
---|
1345 | if (i > act) return; |
---|
1346 | if (m_act[i]->pos > tored) |
---|
1347 | { |
---|
1348 | m_res[inred] = m_act[i]; |
---|
1349 | inred--; |
---|
1350 | break; |
---|
1351 | } |
---|
1352 | } |
---|
1353 | j = i; |
---|
1354 | loop |
---|
1355 | { |
---|
1356 | j++; |
---|
1357 | if (j > act) break; |
---|
1358 | if (m_act[j]->pos > tored) |
---|
1359 | { |
---|
1360 | m_res[inred] = m_act[j]; |
---|
1361 | inred--; |
---|
1362 | } |
---|
1363 | else |
---|
1364 | { |
---|
1365 | m_act[i] = m_act[j]; |
---|
1366 | i++; |
---|
1367 | } |
---|
1368 | } |
---|
1369 | act -= (j-i); |
---|
1370 | sign = 0; |
---|
1371 | } |
---|
1372 | |
---|
1373 | /* |
---|
1374 | * copy m_act to m_res |
---|
1375 | */ |
---|
1376 | void sparse_mat::smCopToRes() |
---|
1377 | { |
---|
1378 | smpoly a,ap,r,h; |
---|
1379 | int i,j,k,l; |
---|
1380 | |
---|
1381 | i = 0; |
---|
1382 | if (act) |
---|
1383 | { |
---|
1384 | a = m_act[act]; // init perm |
---|
1385 | do |
---|
1386 | { |
---|
1387 | i++; |
---|
1388 | perm[crd+i] = a->pos; |
---|
1389 | a = a->n; |
---|
1390 | } while ((a != NULL) && (a->pos <= tored)); |
---|
1391 | for (j=act-1;j;j--) // load all positions of perm |
---|
1392 | { |
---|
1393 | a = m_act[j]; |
---|
1394 | k = 1; |
---|
1395 | loop |
---|
1396 | { |
---|
1397 | if (perm[crd+k] >= a->pos) |
---|
1398 | { |
---|
1399 | if (perm[crd+k] > a->pos) |
---|
1400 | { |
---|
1401 | for (l=i;l>=k;l--) perm[crd+l+1] = perm[crd+l]; |
---|
1402 | perm[crd+k] = a->pos; |
---|
1403 | i++; |
---|
1404 | } |
---|
1405 | a = a->n; |
---|
1406 | if ((a == NULL) || (a->pos > tored)) break; |
---|
1407 | } |
---|
1408 | k++; |
---|
1409 | if ((k > i) && (a->pos <= tored)) |
---|
1410 | { |
---|
1411 | do |
---|
1412 | { |
---|
1413 | i++; |
---|
1414 | perm[crd+i] = a->pos; |
---|
1415 | a = a->n; |
---|
1416 | } while ((a != NULL) && (a->pos <= tored)); |
---|
1417 | break; |
---|
1418 | } |
---|
1419 | } |
---|
1420 | } |
---|
1421 | } |
---|
1422 | for (j=act;j;j--) // renumber m_act |
---|
1423 | { |
---|
1424 | k = 1; |
---|
1425 | a = m_act[j]; |
---|
1426 | while ((a != NULL) && (a->pos <= tored)) |
---|
1427 | { |
---|
1428 | if (perm[crd+k] == a->pos) |
---|
1429 | { |
---|
1430 | a->pos = crd+k; |
---|
1431 | a = a->n; |
---|
1432 | } |
---|
1433 | k++; |
---|
1434 | } |
---|
1435 | } |
---|
1436 | tored = crd+i; |
---|
1437 | for(k=1;k<=i;k++) // clean this from m_row |
---|
1438 | { |
---|
1439 | j = perm[crd+k]; |
---|
1440 | if (m_row[j] != NULL) |
---|
1441 | { |
---|
1442 | r = m_row[j]; |
---|
1443 | m_row[j] = NULL; |
---|
1444 | do |
---|
1445 | { |
---|
1446 | ap = m_res[r->pos]; |
---|
1447 | loop |
---|
1448 | { |
---|
1449 | a = ap->n; |
---|
1450 | if (a == NULL) |
---|
1451 | { |
---|
1452 | h = ap->n = r; |
---|
1453 | r = r->n; |
---|
1454 | h->n = NULL; |
---|
1455 | h->pos = crd+k; |
---|
1456 | break; |
---|
1457 | } |
---|
1458 | ap = a; |
---|
1459 | } |
---|
1460 | } while (r!=NULL); |
---|
1461 | } |
---|
1462 | } |
---|
1463 | while(act) // clean m_act |
---|
1464 | { |
---|
1465 | crd++; |
---|
1466 | m_res[crd] = m_act[act]; |
---|
1467 | act--; |
---|
1468 | } |
---|
1469 | for (i=1;i<=tored;i++) // take the rest of m_row |
---|
1470 | { |
---|
1471 | if(m_row[i] != NULL) |
---|
1472 | { |
---|
1473 | tored++; |
---|
1474 | r = m_row[i]; |
---|
1475 | m_row[i] = NULL; |
---|
1476 | perm[tored] = i; |
---|
1477 | do |
---|
1478 | { |
---|
1479 | ap = m_res[r->pos]; |
---|
1480 | loop |
---|
1481 | { |
---|
1482 | a = ap->n; |
---|
1483 | if (a == NULL) |
---|
1484 | { |
---|
1485 | h = ap->n = r; |
---|
1486 | r = r->n; |
---|
1487 | h->n = NULL; |
---|
1488 | h->pos = tored; |
---|
1489 | break; |
---|
1490 | } |
---|
1491 | ap = a; |
---|
1492 | } |
---|
1493 | } while (r!=NULL); |
---|
1494 | } |
---|
1495 | } |
---|
1496 | for (i=tored+1;i<=nrows;i++) // take the rest of m_row |
---|
1497 | { |
---|
1498 | if(m_row[i] != NULL) |
---|
1499 | { |
---|
1500 | r = m_row[i]; |
---|
1501 | m_row[i] = NULL; |
---|
1502 | do |
---|
1503 | { |
---|
1504 | ap = m_res[r->pos]; |
---|
1505 | loop |
---|
1506 | { |
---|
1507 | a = ap->n; |
---|
1508 | if (a == NULL) |
---|
1509 | { |
---|
1510 | h = ap->n = r; |
---|
1511 | r = r->n; |
---|
1512 | h->n = NULL; |
---|
1513 | h->pos = i; |
---|
1514 | break; |
---|
1515 | } |
---|
1516 | ap = a; |
---|
1517 | } |
---|
1518 | } while (r!=NULL); |
---|
1519 | } |
---|
1520 | } |
---|
1521 | while (inred < ncols) // take unreducable |
---|
1522 | { |
---|
1523 | crd++; |
---|
1524 | inred++; |
---|
1525 | m_res[crd] = m_res[inred]; |
---|
1526 | } |
---|
1527 | } |
---|
1528 | |
---|
1529 | /* |
---|
1530 | * multiply and divide the column, that goes to result |
---|
1531 | */ |
---|
1532 | void sparse_mat::smMultCol() |
---|
1533 | { |
---|
1534 | smpoly a = m_act[act]; |
---|
1535 | int e = crd; |
---|
1536 | poly ha; |
---|
1537 | int f; |
---|
1538 | |
---|
1539 | while (a != NULL) |
---|
1540 | { |
---|
1541 | f = a->e; |
---|
1542 | if (f < e) |
---|
1543 | { |
---|
1544 | ha = SM_MULT(a->m, m_res[e]->m, m_res[f]->m); |
---|
1545 | pDelete(&a->m); |
---|
1546 | if (f) SM_DIV(ha, m_res[f]->m); |
---|
1547 | a->m = ha; |
---|
1548 | if (normalize) pNormalize(a->m); |
---|
1549 | } |
---|
1550 | a = a->n; |
---|
1551 | } |
---|
1552 | } |
---|
1553 | |
---|
1554 | /* |
---|
1555 | * multiply and divide the m_act finaly |
---|
1556 | */ |
---|
1557 | void sparse_mat::smFinalMult() |
---|
1558 | { |
---|
1559 | smpoly a; |
---|
1560 | poly ha; |
---|
1561 | int i, f; |
---|
1562 | int e = crd; |
---|
1563 | |
---|
1564 | for (i=act; i; i--) |
---|
1565 | { |
---|
1566 | a = m_act[i]; |
---|
1567 | do |
---|
1568 | { |
---|
1569 | f = a->e; |
---|
1570 | if (f < e) |
---|
1571 | { |
---|
1572 | ha = SM_MULT(a->m, m_res[e]->m, m_res[f]->m); |
---|
1573 | pDelete(&a->m); |
---|
1574 | if (f) SM_DIV(ha, m_res[f]->m); |
---|
1575 | a->m = ha; |
---|
1576 | } |
---|
1577 | if (normalize) pNormalize(a->m); |
---|
1578 | a = a->n; |
---|
1579 | } while (a != NULL); |
---|
1580 | } |
---|
1581 | } |
---|
1582 | |
---|
1583 | /* |
---|
1584 | * check for denominators |
---|
1585 | */ |
---|
1586 | int sparse_mat::smCheckNormalize() |
---|
1587 | { |
---|
1588 | int i; |
---|
1589 | smpoly a; |
---|
1590 | |
---|
1591 | for (i=act; i; i--) |
---|
1592 | { |
---|
1593 | a = m_act[i]; |
---|
1594 | do |
---|
1595 | { |
---|
1596 | if(smHaveDenom(a->m)) return 1; |
---|
1597 | a = a->n; |
---|
1598 | } while (a != NULL); |
---|
1599 | } |
---|
1600 | return 0; |
---|
1601 | } |
---|
1602 | |
---|
1603 | /* |
---|
1604 | * normalize |
---|
1605 | */ |
---|
1606 | void sparse_mat::smNormalize() |
---|
1607 | { |
---|
1608 | smpoly a; |
---|
1609 | int i; |
---|
1610 | int e = crd; |
---|
1611 | |
---|
1612 | for (i=act; i; i--) |
---|
1613 | { |
---|
1614 | a = m_act[i]; |
---|
1615 | do |
---|
1616 | { |
---|
1617 | if (e == a->e) pNormalize(a->m); |
---|
1618 | a = a->n; |
---|
1619 | } while (a != NULL); |
---|
1620 | } |
---|
1621 | } |
---|
1622 | |
---|
1623 | /* |
---|
1624 | * multiply and divide the element, save poly |
---|
1625 | */ |
---|
1626 | poly sparse_mat::smMultPoly(smpoly a) |
---|
1627 | { |
---|
1628 | int f = a->e; |
---|
1629 | poly r, h; |
---|
1630 | |
---|
1631 | if (f < crd) |
---|
1632 | { |
---|
1633 | h = r = a->m; |
---|
1634 | h = SM_MULT(h, m_res[crd]->m, m_res[f]->m); |
---|
1635 | if (f) SM_DIV(h, m_res[f]->m); |
---|
1636 | a->m = h; |
---|
1637 | if (normalize) pNormalize(a->m); |
---|
1638 | a->f = smPolyWeight(a); |
---|
1639 | return r; |
---|
1640 | } |
---|
1641 | else |
---|
1642 | return NULL; |
---|
1643 | } |
---|
1644 | |
---|
1645 | /* |
---|
1646 | * delete the m_act finaly |
---|
1647 | */ |
---|
1648 | void sparse_mat::smActDel() |
---|
1649 | { |
---|
1650 | smpoly a; |
---|
1651 | int i; |
---|
1652 | |
---|
1653 | for (i=act; i; i--) |
---|
1654 | { |
---|
1655 | a = m_act[i]; |
---|
1656 | do |
---|
1657 | { |
---|
1658 | smElemDelete(&a); |
---|
1659 | } while (a != NULL); |
---|
1660 | } |
---|
1661 | } |
---|
1662 | |
---|
1663 | /* |
---|
1664 | * delete the pivotcol |
---|
1665 | */ |
---|
1666 | void sparse_mat::smColDel() |
---|
1667 | { |
---|
1668 | smpoly a = m_act[act]; |
---|
1669 | |
---|
1670 | while (a != NULL) |
---|
1671 | { |
---|
1672 | smElemDelete(&a); |
---|
1673 | } |
---|
1674 | } |
---|
1675 | |
---|
1676 | /* |
---|
1677 | * delete pivot elements |
---|
1678 | */ |
---|
1679 | void sparse_mat::smPivDel() |
---|
1680 | { |
---|
1681 | int i=crd; |
---|
1682 | |
---|
1683 | while (i != 0) |
---|
1684 | { |
---|
1685 | smElemDelete(&m_res[i]); |
---|
1686 | i--; |
---|
1687 | } |
---|
1688 | } |
---|
1689 | |
---|
1690 | /* |
---|
1691 | * the sign of the determinant |
---|
1692 | */ |
---|
1693 | void sparse_mat::smSign() |
---|
1694 | { |
---|
1695 | int j,i; |
---|
1696 | if (act > 2) |
---|
1697 | { |
---|
1698 | if (cpiv!=act) sign=-sign; |
---|
1699 | if ((act%2)==0) sign=-sign; |
---|
1700 | i=1; |
---|
1701 | j=perm[1]; |
---|
1702 | while(j<rpiv) |
---|
1703 | { |
---|
1704 | sign=-sign; |
---|
1705 | i++; |
---|
1706 | j=perm[i]; |
---|
1707 | } |
---|
1708 | while(perm[i]!=0) |
---|
1709 | { |
---|
1710 | perm[i]=perm[i+1]; |
---|
1711 | i++; |
---|
1712 | } |
---|
1713 | } |
---|
1714 | else |
---|
1715 | { |
---|
1716 | if (cpiv!=1) sign=-sign; |
---|
1717 | if (rpiv!=perm[1]) sign=-sign; |
---|
1718 | } |
---|
1719 | } |
---|
1720 | |
---|
1721 | void sparse_mat::smInitPerm() |
---|
1722 | { |
---|
1723 | int i; |
---|
1724 | for (i=act;i;i--) perm[i]=i; |
---|
1725 | } |
---|
1726 | |
---|
1727 | /* ----------------- arithmetic ------------------ */ |
---|
1728 | /*2 |
---|
1729 | * exact division a/b |
---|
1730 | * a destroyed, b NOT destroyed |
---|
1731 | */ |
---|
1732 | void smPolyDiv(poly a, poly b) |
---|
1733 | { |
---|
1734 | const number x = pGetCoeff(b); |
---|
1735 | number y, yn; |
---|
1736 | poly t, h, dummy; |
---|
1737 | int i; |
---|
1738 | |
---|
1739 | if (pNext(b) == NULL) |
---|
1740 | { |
---|
1741 | do |
---|
1742 | { |
---|
1743 | if (!pLmIsConstantComp(b)) |
---|
1744 | { |
---|
1745 | for (i=pVariables; i; i--) |
---|
1746 | pSubExp(a,i,pGetExp(b,i)); |
---|
1747 | pSetm(a); |
---|
1748 | } |
---|
1749 | y = nDiv(pGetCoeff(a),x); |
---|
1750 | nNormalize(y); |
---|
1751 | pSetCoeff(a,y); |
---|
1752 | pIter(a); |
---|
1753 | } while (a != NULL); |
---|
1754 | return; |
---|
1755 | } |
---|
1756 | dummy = pInit(); |
---|
1757 | do |
---|
1758 | { |
---|
1759 | for (i=pVariables; i; i--) |
---|
1760 | pSubExp(a,i,pGetExp(b,i)); |
---|
1761 | pSetm(a); |
---|
1762 | y = nDiv(pGetCoeff(a),x); |
---|
1763 | nNormalize(y); |
---|
1764 | pSetCoeff(a,y); |
---|
1765 | yn = nNeg(nCopy(y)); |
---|
1766 | t = pNext(b); |
---|
1767 | h = dummy; |
---|
1768 | do |
---|
1769 | { |
---|
1770 | h = pNext(h) = pInit(); |
---|
1771 | //pSetComp(h,0); |
---|
1772 | for (i=pVariables; i; i--) |
---|
1773 | pSetExp(h,i,pGetExp(a,i)+pGetExp(t,i)); |
---|
1774 | pSetm(h); |
---|
1775 | pSetCoeff0(h,nMult(yn, pGetCoeff(t))); |
---|
1776 | pIter(t); |
---|
1777 | } while (t != NULL); |
---|
1778 | nDelete(&yn); |
---|
1779 | pNext(h) = NULL; |
---|
1780 | a = pNext(a) = pAdd(pNext(a), pNext(dummy)); |
---|
1781 | } while (a!=NULL); |
---|
1782 | pLmFree(dummy); |
---|
1783 | } |
---|
1784 | |
---|
1785 | #define X_MAS |
---|
1786 | #ifdef X_MAS |
---|
1787 | |
---|
1788 | /* |
---|
1789 | * returns the part of (a*b)/exp(lead(c)) with nonegative exponents |
---|
1790 | */ |
---|
1791 | poly smMultDiv(poly a, poly b, const poly c) |
---|
1792 | { |
---|
1793 | poly pa, e, res, r; |
---|
1794 | BOOLEAN lead;\ |
---|
1795 | int la, lb, lr; |
---|
1796 | |
---|
1797 | if ((c == NULL) || pLmIsConstantComp(c)) |
---|
1798 | { |
---|
1799 | return ppMult_qq(a, b); |
---|
1800 | } |
---|
1801 | |
---|
1802 | pqLength(a, b, la, lb, SM_MIN_LENGTH_BUCKET); |
---|
1803 | |
---|
1804 | // we iter over b, so, make sure b is the shortest |
---|
1805 | // such that we minimize our iterations |
---|
1806 | if (lb > la) |
---|
1807 | { |
---|
1808 | r = a; |
---|
1809 | a = b; |
---|
1810 | b = r; |
---|
1811 | lr = la; |
---|
1812 | la = lb; |
---|
1813 | lb = lr; |
---|
1814 | } |
---|
1815 | res = NULL; |
---|
1816 | e = pInit(); |
---|
1817 | lead = FALSE; |
---|
1818 | while (!lead) |
---|
1819 | { |
---|
1820 | pSetCoeff0(e,pGetCoeff(b)); |
---|
1821 | if (smIsNegQuot(e, b, c)) |
---|
1822 | { |
---|
1823 | lead = pLmDivisibleByNoComp(e, a); |
---|
1824 | r = smSelectCopy_ExpMultDiv(a, e, b, c); |
---|
1825 | } |
---|
1826 | else |
---|
1827 | { |
---|
1828 | lead = TRUE; |
---|
1829 | r = ppMult_mm(a, e); |
---|
1830 | } |
---|
1831 | if (lead) |
---|
1832 | { |
---|
1833 | if (res != NULL) |
---|
1834 | { |
---|
1835 | smFindRef(&pa, &res, r); |
---|
1836 | if (pa == NULL) |
---|
1837 | lead = FALSE; |
---|
1838 | } |
---|
1839 | else |
---|
1840 | { |
---|
1841 | pa = res = r; |
---|
1842 | } |
---|
1843 | } |
---|
1844 | else |
---|
1845 | res = pAdd(res, r); |
---|
1846 | pIter(b); |
---|
1847 | if (b == NULL) |
---|
1848 | { |
---|
1849 | pLmFree(e); |
---|
1850 | return res; |
---|
1851 | } |
---|
1852 | } |
---|
1853 | |
---|
1854 | if (!TEST_OPT_NOT_BUCKETS && lb >= SM_MIN_LENGTH_BUCKET) |
---|
1855 | { |
---|
1856 | // use buckets if minimum length is smaller than threshold |
---|
1857 | spolyrec rp; |
---|
1858 | poly append; |
---|
1859 | // find the last monomial before pa |
---|
1860 | if (res == pa) |
---|
1861 | { |
---|
1862 | append = &rp; |
---|
1863 | pNext(append) = res; |
---|
1864 | } |
---|
1865 | else |
---|
1866 | { |
---|
1867 | append = res; |
---|
1868 | while (pNext(append) != pa) |
---|
1869 | { |
---|
1870 | assume(pNext(append) != NULL); |
---|
1871 | pIter(append); |
---|
1872 | } |
---|
1873 | } |
---|
1874 | kBucket_pt bucket = kBucketCreate(currRing); |
---|
1875 | kBucketInit(bucket, pNext(append), 0); |
---|
1876 | do |
---|
1877 | { |
---|
1878 | pSetCoeff0(e,pGetCoeff(b)); |
---|
1879 | if (smIsNegQuot(e, b, c)) |
---|
1880 | { |
---|
1881 | lr = la; |
---|
1882 | r = pp_Mult_Coeff_mm_DivSelect_MultDiv(a, lr, e, b, c); |
---|
1883 | if (pLmDivisibleByNoComp(e, a)) |
---|
1884 | append = kBucket_ExtractLarger_Add_q(bucket, append, r, &lr); |
---|
1885 | else |
---|
1886 | kBucket_Add_q(bucket, r, &lr); |
---|
1887 | } |
---|
1888 | else |
---|
1889 | { |
---|
1890 | r = ppMult_mm(a, e); |
---|
1891 | append = kBucket_ExtractLarger_Add_q(bucket, append, r, &la); |
---|
1892 | } |
---|
1893 | pIter(b); |
---|
1894 | } while (b != NULL); |
---|
1895 | pNext(append) = kBucketClear(bucket); |
---|
1896 | kBucketDestroy(&bucket); |
---|
1897 | } |
---|
1898 | else |
---|
1899 | { |
---|
1900 | // use old sm stuff |
---|
1901 | do |
---|
1902 | { |
---|
1903 | pSetCoeff0(e,pGetCoeff(b)); |
---|
1904 | if (smIsNegQuot(e, b, c)) |
---|
1905 | { |
---|
1906 | r = smSelectCopy_ExpMultDiv(a, e, b, c); |
---|
1907 | if (pLmDivisibleByNoComp(e, a)) |
---|
1908 | smCombineChain(&pa, r); |
---|
1909 | else |
---|
1910 | pa = pAdd(pa,r); |
---|
1911 | } |
---|
1912 | else |
---|
1913 | { |
---|
1914 | r = ppMult_mm(a, e); |
---|
1915 | smCombineChain(&pa, r); |
---|
1916 | } |
---|
1917 | pIter(b); |
---|
1918 | } while (b != NULL); |
---|
1919 | } |
---|
1920 | pLmFree(e); |
---|
1921 | return res; |
---|
1922 | } |
---|
1923 | |
---|
1924 | #else |
---|
1925 | |
---|
1926 | /* |
---|
1927 | * returns the part of (a*b)/exp(lead(c)) with nonegative exponents |
---|
1928 | */ |
---|
1929 | poly smMultDiv(poly a, poly b, const poly c) |
---|
1930 | { |
---|
1931 | poly pa, e, res, r; |
---|
1932 | BOOLEAN lead; |
---|
1933 | |
---|
1934 | if ((c == NULL) || pLmIsConstantComp(c)) |
---|
1935 | { |
---|
1936 | return ppMult_qq(a, b); |
---|
1937 | } |
---|
1938 | if (smSmaller(a, b)) |
---|
1939 | { |
---|
1940 | r = a; |
---|
1941 | a = b; |
---|
1942 | b = r; |
---|
1943 | } |
---|
1944 | res = NULL; |
---|
1945 | e = pInit(); |
---|
1946 | lead = FALSE; |
---|
1947 | while (!lead) |
---|
1948 | { |
---|
1949 | pSetCoeff0(e,pGetCoeff(b)); |
---|
1950 | if (smIsNegQuot(e, b, c)) |
---|
1951 | { |
---|
1952 | lead = pLmDivisibleByNoComp(e, a); |
---|
1953 | r = smSelectCopy_ExpMultDiv(a, e, b, c); |
---|
1954 | } |
---|
1955 | else |
---|
1956 | { |
---|
1957 | lead = TRUE; |
---|
1958 | r = ppMult_mm(a, e); |
---|
1959 | } |
---|
1960 | if (lead) |
---|
1961 | { |
---|
1962 | if (res != NULL) |
---|
1963 | { |
---|
1964 | smFindRef(&pa, &res, r); |
---|
1965 | if (pa == NULL) |
---|
1966 | lead = FALSE; |
---|
1967 | } |
---|
1968 | else |
---|
1969 | { |
---|
1970 | pa = res = r; |
---|
1971 | } |
---|
1972 | } |
---|
1973 | else |
---|
1974 | res = pAdd(res, r); |
---|
1975 | pIter(b); |
---|
1976 | if (b == NULL) |
---|
1977 | { |
---|
1978 | pLmFree(e); |
---|
1979 | return res; |
---|
1980 | } |
---|
1981 | } |
---|
1982 | do |
---|
1983 | { |
---|
1984 | pSetCoeff0(e,pGetCoeff(b)); |
---|
1985 | if (smIsNegQuot(e, b, c)) |
---|
1986 | { |
---|
1987 | r = smSelectCopy_ExpMultDiv(a, e, b, c); |
---|
1988 | if (pLmDivisibleByNoComp(e, a)) |
---|
1989 | smCombineChain(&pa, r); |
---|
1990 | else |
---|
1991 | pa = pAdd(pa,r); |
---|
1992 | } |
---|
1993 | else |
---|
1994 | { |
---|
1995 | r = ppMult_mm(a, e); |
---|
1996 | smCombineChain(&pa, r); |
---|
1997 | } |
---|
1998 | pIter(b); |
---|
1999 | } while (b != NULL); |
---|
2000 | pLmFree(e); |
---|
2001 | return res; |
---|
2002 | } |
---|
2003 | #endif |
---|
2004 | /*n |
---|
2005 | * exact division a/b |
---|
2006 | * a is a result of smMultDiv |
---|
2007 | * a destroyed, b NOT destroyed |
---|
2008 | */ |
---|
2009 | void smSpecialPolyDiv(poly a, poly b) |
---|
2010 | { |
---|
2011 | if (pNext(b) == NULL) |
---|
2012 | { |
---|
2013 | smPolyDivN(a, pGetCoeff(b)); |
---|
2014 | return; |
---|
2015 | } |
---|
2016 | smExactPolyDiv(a, b); |
---|
2017 | } |
---|
2018 | |
---|
2019 | |
---|
2020 | /* ------------ internals arithmetic ------------- */ |
---|
2021 | static void smExactPolyDiv(poly a, poly b) |
---|
2022 | { |
---|
2023 | const number x = pGetCoeff(b); |
---|
2024 | poly tail = pNext(b), e = pInit(); |
---|
2025 | poly h; |
---|
2026 | number y, yn; |
---|
2027 | int lt = pLength(tail); |
---|
2028 | |
---|
2029 | if (lt + 1 >= SM_MIN_LENGTH_BUCKET && !TEST_OPT_NOT_BUCKETS) |
---|
2030 | { |
---|
2031 | kBucket_pt bucket = kBucketCreate(currRing); |
---|
2032 | kBucketInit(bucket, pNext(a), 0); |
---|
2033 | int lh = 0; |
---|
2034 | do |
---|
2035 | { |
---|
2036 | y = nDiv(pGetCoeff(a), x); |
---|
2037 | nNormalize(y); |
---|
2038 | pSetCoeff(a,y); |
---|
2039 | yn = nNeg(nCopy(y)); |
---|
2040 | pSetCoeff0(e,yn); |
---|
2041 | lh = lt; |
---|
2042 | if (smIsNegQuot(e, a, b)) |
---|
2043 | { |
---|
2044 | h = pp_Mult_Coeff_mm_DivSelect_MultDiv(tail, lh, e, a, b); |
---|
2045 | } |
---|
2046 | else |
---|
2047 | h = ppMult_mm(tail, e); |
---|
2048 | nDelete(&yn); |
---|
2049 | kBucket_Add_q(bucket, h, &lh); |
---|
2050 | |
---|
2051 | a = pNext(a) = kBucketExtractLm(bucket); |
---|
2052 | } while (a!=NULL); |
---|
2053 | kBucketDestroy(&bucket); |
---|
2054 | } |
---|
2055 | else |
---|
2056 | { |
---|
2057 | do |
---|
2058 | { |
---|
2059 | y = nDiv(pGetCoeff(a), x); |
---|
2060 | nNormalize(y); |
---|
2061 | pSetCoeff(a,y); |
---|
2062 | yn = nNeg(nCopy(y)); |
---|
2063 | pSetCoeff0(e,yn); |
---|
2064 | if (smIsNegQuot(e, a, b)) |
---|
2065 | h = smSelectCopy_ExpMultDiv(tail, e, a, b); |
---|
2066 | else |
---|
2067 | h = ppMult_mm(tail, e); |
---|
2068 | nDelete(&yn); |
---|
2069 | a = pNext(a) = pAdd(pNext(a), h); |
---|
2070 | } while (a!=NULL); |
---|
2071 | } |
---|
2072 | pLmFree(e); |
---|
2073 | } |
---|
2074 | |
---|
2075 | // obachman --> Wilfried: check the following |
---|
2076 | static BOOLEAN smIsNegQuot(poly a, const poly b, const poly c) |
---|
2077 | { |
---|
2078 | if (pLmDivisibleByNoComp(c, b)) |
---|
2079 | { |
---|
2080 | pExpVectorDiff(a, b, c); |
---|
2081 | // Hmm: here used to be a pSetm(a): but it is unnecessary, |
---|
2082 | // if b and c are correct |
---|
2083 | return FALSE; |
---|
2084 | } |
---|
2085 | else |
---|
2086 | { |
---|
2087 | int i; |
---|
2088 | for (i=pVariables; i>0; i--) |
---|
2089 | { |
---|
2090 | if(pGetExp(c,i) > pGetExp(b,i)) |
---|
2091 | pSetExp(a,i,pGetExp(c,i)-pGetExp(b,i)); |
---|
2092 | else |
---|
2093 | pSetExp(a,i,0); |
---|
2094 | } |
---|
2095 | // here we actually might need a pSetm, if a is to be used in |
---|
2096 | // comparisons |
---|
2097 | return TRUE; |
---|
2098 | } |
---|
2099 | } |
---|
2100 | |
---|
2101 | static void smExpMultDiv(poly t, const poly b, const poly c) |
---|
2102 | { |
---|
2103 | int i; |
---|
2104 | pTest(t); |
---|
2105 | pLmTest(b); |
---|
2106 | pLmTest(c); |
---|
2107 | poly bc = p_New(currRing); |
---|
2108 | |
---|
2109 | p_ExpVectorDiff(bc, b, c, currRing); |
---|
2110 | |
---|
2111 | while(t!=NULL) |
---|
2112 | { |
---|
2113 | pExpVectorAdd(t, bc); |
---|
2114 | pIter(t); |
---|
2115 | } |
---|
2116 | p_LmFree(bc, currRing); |
---|
2117 | } |
---|
2118 | |
---|
2119 | |
---|
2120 | static void smPolyDivN(poly a, const number x) |
---|
2121 | { |
---|
2122 | number y; |
---|
2123 | |
---|
2124 | do |
---|
2125 | { |
---|
2126 | y = nDiv(pGetCoeff(a),x); |
---|
2127 | nNormalize(y); |
---|
2128 | pSetCoeff(a,y); |
---|
2129 | pIter(a); |
---|
2130 | } while (a != NULL); |
---|
2131 | } |
---|
2132 | |
---|
2133 | static BOOLEAN smSmaller(poly a, poly b) |
---|
2134 | { |
---|
2135 | loop |
---|
2136 | { |
---|
2137 | pIter(b); |
---|
2138 | if (b == NULL) return TRUE; |
---|
2139 | pIter(a); |
---|
2140 | if (a == NULL) return FALSE; |
---|
2141 | } |
---|
2142 | } |
---|
2143 | |
---|
2144 | static void smCombineChain(poly *px, poly r) |
---|
2145 | { |
---|
2146 | poly pa = *px, pb; |
---|
2147 | number x; |
---|
2148 | int i; |
---|
2149 | |
---|
2150 | loop |
---|
2151 | { |
---|
2152 | pb = pNext(pa); |
---|
2153 | if (pb == NULL) |
---|
2154 | { |
---|
2155 | pa = pNext(pa) = r; |
---|
2156 | break; |
---|
2157 | } |
---|
2158 | i = pLmCmp(pb, r); |
---|
2159 | if (i > 0) |
---|
2160 | pa = pb; |
---|
2161 | else |
---|
2162 | { |
---|
2163 | if (i == 0) |
---|
2164 | { |
---|
2165 | x = nAdd(pGetCoeff(pb), pGetCoeff(r)); |
---|
2166 | pDeleteLm(&r); |
---|
2167 | if (nIsZero(x)) |
---|
2168 | { |
---|
2169 | pDeleteLm(&pb); |
---|
2170 | pNext(pa) = pAdd(pb,r); |
---|
2171 | } |
---|
2172 | else |
---|
2173 | { |
---|
2174 | pa = pb; |
---|
2175 | pSetCoeff(pa,x); |
---|
2176 | pNext(pa) = pAdd(pNext(pa), r); |
---|
2177 | } |
---|
2178 | } |
---|
2179 | else |
---|
2180 | { |
---|
2181 | pa = pNext(pa) = r; |
---|
2182 | pNext(pa) = pAdd(pb, pNext(pa)); |
---|
2183 | } |
---|
2184 | break; |
---|
2185 | } |
---|
2186 | } |
---|
2187 | *px = pa; |
---|
2188 | } |
---|
2189 | |
---|
2190 | |
---|
2191 | static void smFindRef(poly *ref, poly *px, poly r) |
---|
2192 | { |
---|
2193 | number x; |
---|
2194 | int i; |
---|
2195 | poly pa = *px, pp = NULL; |
---|
2196 | |
---|
2197 | loop |
---|
2198 | { |
---|
2199 | i = pLmCmp(pa, r); |
---|
2200 | if (i > 0) |
---|
2201 | { |
---|
2202 | pp = pa; |
---|
2203 | pIter(pa); |
---|
2204 | if (pa==NULL) |
---|
2205 | { |
---|
2206 | pNext(pp) = r; |
---|
2207 | break; |
---|
2208 | } |
---|
2209 | } |
---|
2210 | else |
---|
2211 | { |
---|
2212 | if (i == 0) |
---|
2213 | { |
---|
2214 | x = nAdd(pGetCoeff(pa), pGetCoeff(r)); |
---|
2215 | pDeleteLm(&r); |
---|
2216 | if (nIsZero(x)) |
---|
2217 | { |
---|
2218 | pDeleteLm(&pa); |
---|
2219 | if (pp!=NULL) |
---|
2220 | pNext(pp) = pAdd(pa,r); |
---|
2221 | else |
---|
2222 | *px = pAdd(pa,r); |
---|
2223 | } |
---|
2224 | else |
---|
2225 | { |
---|
2226 | pp = pa; |
---|
2227 | pSetCoeff(pp,x); |
---|
2228 | pNext(pp) = pAdd(pNext(pp), r); |
---|
2229 | } |
---|
2230 | } |
---|
2231 | else |
---|
2232 | { |
---|
2233 | if (pp!=NULL) |
---|
2234 | pp = pNext(pp) = r; |
---|
2235 | else |
---|
2236 | *px = pp = r; |
---|
2237 | pNext(pp) = pAdd(pa, pNext(r)); |
---|
2238 | } |
---|
2239 | break; |
---|
2240 | } |
---|
2241 | } |
---|
2242 | *ref = pp; |
---|
2243 | } |
---|
2244 | |
---|
2245 | /* ----------------- internal 'C' stuff ------------------ */ |
---|
2246 | |
---|
2247 | static void smElemDelete(smpoly *r) |
---|
2248 | { |
---|
2249 | smpoly a = *r, b = a->n; |
---|
2250 | |
---|
2251 | pDelete(&a->m); |
---|
2252 | omFreeBin((void *)a, smprec_bin); |
---|
2253 | *r = b; |
---|
2254 | } |
---|
2255 | |
---|
2256 | static smpoly smElemCopy(smpoly a) |
---|
2257 | { |
---|
2258 | smpoly r = (smpoly)omAllocBin(smprec_bin); |
---|
2259 | memcpy(r, a, sizeof(smprec)); |
---|
2260 | /* r->m = pCopy(r->m); */ |
---|
2261 | return r; |
---|
2262 | } |
---|
2263 | |
---|
2264 | /* |
---|
2265 | * from poly to smpoly |
---|
2266 | * do not destroy p |
---|
2267 | */ |
---|
2268 | static smpoly smPoly2Smpoly(poly q) |
---|
2269 | { |
---|
2270 | poly pp; |
---|
2271 | smpoly res, a; |
---|
2272 | Exponent_t x; |
---|
2273 | |
---|
2274 | if (q == NULL) |
---|
2275 | return NULL; |
---|
2276 | a = res = (smpoly)omAllocBin(smprec_bin); |
---|
2277 | a->pos = x = pGetComp(q); |
---|
2278 | a->m = q; |
---|
2279 | a->e = 0; |
---|
2280 | loop |
---|
2281 | { |
---|
2282 | pSetComp(q,0); |
---|
2283 | pp = q; |
---|
2284 | pIter(q); |
---|
2285 | if (q == NULL) |
---|
2286 | { |
---|
2287 | a->n = NULL; |
---|
2288 | return res; |
---|
2289 | } |
---|
2290 | if (pGetComp(q) != x) |
---|
2291 | { |
---|
2292 | a = a->n = (smpoly)omAllocBin(smprec_bin); |
---|
2293 | pNext(pp) = NULL; |
---|
2294 | a->pos = x = pGetComp(q); |
---|
2295 | a->m = q; |
---|
2296 | a->e = 0; |
---|
2297 | } |
---|
2298 | } |
---|
2299 | } |
---|
2300 | |
---|
2301 | /* |
---|
2302 | * from smpoly to poly |
---|
2303 | * destroy a |
---|
2304 | */ |
---|
2305 | static poly smSmpoly2Poly(smpoly a) |
---|
2306 | { |
---|
2307 | smpoly b; |
---|
2308 | poly res, pp, q; |
---|
2309 | Exponent_t x; |
---|
2310 | |
---|
2311 | if (a == NULL) |
---|
2312 | return NULL; |
---|
2313 | x = a->pos; |
---|
2314 | q = res = a->m; |
---|
2315 | loop |
---|
2316 | { |
---|
2317 | pSetComp(q,x); |
---|
2318 | pp = q; |
---|
2319 | pIter(q); |
---|
2320 | if (q == NULL) |
---|
2321 | break; |
---|
2322 | } |
---|
2323 | loop |
---|
2324 | { |
---|
2325 | b = a; |
---|
2326 | a = a->n; |
---|
2327 | omFreeBin((void *)b, smprec_bin); |
---|
2328 | if (a == NULL) |
---|
2329 | return res; |
---|
2330 | x = a->pos; |
---|
2331 | q = pNext(pp) = a->m; |
---|
2332 | loop |
---|
2333 | { |
---|
2334 | pSetComp(q,x); |
---|
2335 | pp = q; |
---|
2336 | pIter(q); |
---|
2337 | if (q == NULL) |
---|
2338 | break; |
---|
2339 | } |
---|
2340 | } |
---|
2341 | } |
---|
2342 | |
---|
2343 | /* |
---|
2344 | * weigth of a polynomial, for pivot strategy |
---|
2345 | */ |
---|
2346 | static float smPolyWeight(smpoly a) |
---|
2347 | { |
---|
2348 | poly p = a->m; |
---|
2349 | int i; |
---|
2350 | float res = (float)nSize(pGetCoeff(p)); |
---|
2351 | |
---|
2352 | if (pNext(p) == NULL) |
---|
2353 | { |
---|
2354 | for(i=pVariables; i>0; i--) |
---|
2355 | { |
---|
2356 | if (pGetExp(p,i) != 0) return res+1.0; |
---|
2357 | } |
---|
2358 | return res; |
---|
2359 | } |
---|
2360 | else |
---|
2361 | { |
---|
2362 | i = 0; |
---|
2363 | res = 0.0; |
---|
2364 | do |
---|
2365 | { |
---|
2366 | i++; |
---|
2367 | res += (float)nSize(pGetCoeff(p)); |
---|
2368 | pIter(p); |
---|
2369 | } |
---|
2370 | while (p); |
---|
2371 | return res+(float)i; |
---|
2372 | } |
---|
2373 | } |
---|
2374 | |
---|
2375 | static BOOLEAN smHaveDenom(poly a) |
---|
2376 | { |
---|
2377 | BOOLEAN sw; |
---|
2378 | number x,o=nInit(1); |
---|
2379 | |
---|
2380 | while (a != NULL) |
---|
2381 | { |
---|
2382 | x = nGetDenom(pGetCoeff(a)); |
---|
2383 | sw = nEqual(x,o); |
---|
2384 | nDelete(&x); |
---|
2385 | if (!sw) |
---|
2386 | { |
---|
2387 | nDelete(&o); |
---|
2388 | return TRUE; |
---|
2389 | } |
---|
2390 | pIter(a); |
---|
2391 | } |
---|
2392 | nDelete(&o); |
---|
2393 | return FALSE; |
---|
2394 | } |
---|
2395 | |
---|
2396 | static number smCleardenom(ideal id) |
---|
2397 | { |
---|
2398 | poly a; |
---|
2399 | number x,y,res=nInit(1); |
---|
2400 | BOOLEAN sw=FALSE; |
---|
2401 | |
---|
2402 | for (int i=0; i<IDELEMS(id); i++) |
---|
2403 | { |
---|
2404 | a = id->m[i]; |
---|
2405 | sw = smHaveDenom(a); |
---|
2406 | if (sw) break; |
---|
2407 | } |
---|
2408 | if (!sw) return res; |
---|
2409 | for (int i=0; i<IDELEMS(id); i++) |
---|
2410 | { |
---|
2411 | a = id->m[i]; |
---|
2412 | x = nCopy(pGetCoeff(a)); |
---|
2413 | pCleardenom(a); |
---|
2414 | y = nDiv(x,pGetCoeff(a)); |
---|
2415 | nDelete(&x); |
---|
2416 | x = nMult(res,y); |
---|
2417 | nNormalize(x); |
---|
2418 | nDelete(&res); |
---|
2419 | res = x; |
---|
2420 | } |
---|
2421 | return res; |
---|
2422 | } |
---|
2423 | |
---|
2424 | /* ----------------- gauss elimination ------------------ */ |
---|
2425 | /* in structs.h */ |
---|
2426 | typedef struct smnrec sm_nrec; |
---|
2427 | typedef sm_nrec * smnumber; |
---|
2428 | struct smnrec{ |
---|
2429 | smnumber n; // the next element |
---|
2430 | int pos; // position |
---|
2431 | number m; // the element |
---|
2432 | }; |
---|
2433 | |
---|
2434 | static omBin smnrec_bin = omGetSpecBin(sizeof(smnrec)); |
---|
2435 | |
---|
2436 | /* declare internal 'C' stuff */ |
---|
2437 | static void smNumberDelete(smnumber *); |
---|
2438 | static smnumber smNumberCopy(smnumber); |
---|
2439 | static smnumber smPoly2Smnumber(poly); |
---|
2440 | static poly smSmnumber2Poly(number); |
---|
2441 | static BOOLEAN smCheckSolv(ideal); |
---|
2442 | |
---|
2443 | /* class for sparse number matrix: |
---|
2444 | */ |
---|
2445 | class sparse_number_mat{ |
---|
2446 | private: |
---|
2447 | int nrows, ncols; // dimension of the problem |
---|
2448 | int act; // number of unreduced columns (start: ncols) |
---|
2449 | int crd; // number of reduced columns (start: 0) |
---|
2450 | int tored; // border for rows to reduce |
---|
2451 | int sing; // indicator for singular problem |
---|
2452 | int rpiv; // row-position of the pivot |
---|
2453 | int *perm; // permutation of rows |
---|
2454 | number one; // the "1" |
---|
2455 | number *sol; // field for solution |
---|
2456 | int *wrw, *wcl; // weights of rows and columns |
---|
2457 | smnumber * m_act; // unreduced columns |
---|
2458 | smnumber * m_res; // reduced columns (result) |
---|
2459 | smnumber * m_row; // reduced part of rows |
---|
2460 | smnumber red; // row to reduce |
---|
2461 | smnumber piv; // pivot |
---|
2462 | smnumber dumm; // allocated dummy |
---|
2463 | void smColToRow(); |
---|
2464 | void smRowToCol(); |
---|
2465 | void smSelectPR(); |
---|
2466 | void smRealPivot(); |
---|
2467 | void smZeroToredElim(); |
---|
2468 | void smGElim(); |
---|
2469 | void smAllDel(); |
---|
2470 | public: |
---|
2471 | sparse_number_mat(ideal); |
---|
2472 | ~sparse_number_mat(); |
---|
2473 | int smIsSing() { return sing; } |
---|
2474 | void smTriangular(); |
---|
2475 | void smSolv(); |
---|
2476 | ideal smRes2Ideal(); |
---|
2477 | }; |
---|
2478 | |
---|
2479 | /* ----------------- basics (used from 'C') ------------------ */ |
---|
2480 | /*2 |
---|
2481 | * returns the solution of a linear equation |
---|
2482 | * solution of M*x = r (M has dimension nXn) => |
---|
2483 | * I = module(transprose(M)) + r*gen(n+1) |
---|
2484 | * uses Gauss-elimination |
---|
2485 | */ |
---|
2486 | lists smCallSolv(ideal I) |
---|
2487 | { |
---|
2488 | sparse_number_mat *linsolv; |
---|
2489 | int k; |
---|
2490 | ring origR; |
---|
2491 | sip_sring tmpR; |
---|
2492 | ideal rr, ss; |
---|
2493 | lists res; |
---|
2494 | |
---|
2495 | if (idIsConstant(I)==FALSE) |
---|
2496 | { |
---|
2497 | WerrorS("symbol in equation"); |
---|
2498 | return NULL; |
---|
2499 | } |
---|
2500 | I->rank = idRankFreeModule(I); |
---|
2501 | if (smCheckSolv(I)) return NULL; |
---|
2502 | res=(lists)omAllocBin(slists_bin); |
---|
2503 | rr=smRingCopy(I,&origR,tmpR); |
---|
2504 | ss = NULL; |
---|
2505 | linsolv = new sparse_number_mat(rr); |
---|
2506 | linsolv->smTriangular(); |
---|
2507 | if (linsolv->smIsSing() == 0) |
---|
2508 | { |
---|
2509 | linsolv->smSolv(); |
---|
2510 | ss = linsolv->smRes2Ideal(); |
---|
2511 | } |
---|
2512 | else |
---|
2513 | WerrorS("singular problem for linsolv"); |
---|
2514 | delete linsolv; |
---|
2515 | if ((origR!=NULL) && (ss!=NULL)) |
---|
2516 | { |
---|
2517 | rChangeCurrRing(origR); |
---|
2518 | rr = idInit(IDELEMS(ss), 1); |
---|
2519 | for (k=0;k<IDELEMS(ss);k++) |
---|
2520 | rr->m[k] = prCopyR(ss->m[k], &tmpR); |
---|
2521 | rChangeCurrRing(&tmpR); |
---|
2522 | idDelete(&ss); |
---|
2523 | ss = rr; |
---|
2524 | } |
---|
2525 | if(origR!=NULL) |
---|
2526 | smRingClean(origR,tmpR); |
---|
2527 | res->Init(1); |
---|
2528 | res->m[0].rtyp=IDEAL_CMD; |
---|
2529 | res->m[0].data=(void *)ss; |
---|
2530 | return res; |
---|
2531 | } |
---|
2532 | |
---|
2533 | /* |
---|
2534 | * constructor, destroy smat |
---|
2535 | */ |
---|
2536 | sparse_number_mat::sparse_number_mat(ideal smat) |
---|
2537 | { |
---|
2538 | int i; |
---|
2539 | polyset pmat; |
---|
2540 | |
---|
2541 | crd = sing = 0; |
---|
2542 | act = ncols = smat->ncols; |
---|
2543 | tored = nrows = smat->rank; |
---|
2544 | i = tored+1; |
---|
2545 | perm = (int *)omAlloc(sizeof(int)*i); |
---|
2546 | m_row = (smnumber *)omAlloc0(sizeof(smnumber)*i); |
---|
2547 | wrw = (int *)omAlloc(sizeof(int)*i); |
---|
2548 | i = ncols+1; |
---|
2549 | wcl = (int *)omAlloc(sizeof(int)*i); |
---|
2550 | m_act = (smnumber *)omAlloc(sizeof(smnumber)*i); |
---|
2551 | m_res = (smnumber *)omAlloc0(sizeof(smnumber)*i); |
---|
2552 | dumm = (smnumber)omAllocBin(smnrec_bin); |
---|
2553 | pmat = smat->m; |
---|
2554 | for(i=ncols; i; i--) |
---|
2555 | { |
---|
2556 | m_act[i] = smPoly2Smnumber(pmat[i-1]); |
---|
2557 | } |
---|
2558 | omFreeSize((ADDRESS)pmat,smat->ncols*sizeof(poly)); |
---|
2559 | omFreeBin((ADDRESS)smat, sip_sideal_bin); |
---|
2560 | one = nInit(1); |
---|
2561 | } |
---|
2562 | |
---|
2563 | /* |
---|
2564 | * destructor |
---|
2565 | */ |
---|
2566 | sparse_number_mat::~sparse_number_mat() |
---|
2567 | { |
---|
2568 | int i; |
---|
2569 | omFreeBin((ADDRESS)dumm, smnrec_bin); |
---|
2570 | i = ncols+1; |
---|
2571 | omFreeSize((ADDRESS)m_res, sizeof(smnumber)*i); |
---|
2572 | omFreeSize((ADDRESS)m_act, sizeof(smnumber)*i); |
---|
2573 | omFreeSize((ADDRESS)wcl, sizeof(int)*i); |
---|
2574 | i = nrows+1; |
---|
2575 | omFreeSize((ADDRESS)wrw, sizeof(int)*i); |
---|
2576 | omFreeSize((ADDRESS)m_row, sizeof(smnumber)*i); |
---|
2577 | omFreeSize((ADDRESS)perm, sizeof(int)*i); |
---|
2578 | nDelete(&one); |
---|
2579 | } |
---|
2580 | |
---|
2581 | /* |
---|
2582 | * triangularization by Gauss-elimination |
---|
2583 | */ |
---|
2584 | void sparse_number_mat::smTriangular() |
---|
2585 | { |
---|
2586 | tored--; |
---|
2587 | this->smZeroToredElim(); |
---|
2588 | if (sing != 0) return; |
---|
2589 | while (act > 1) |
---|
2590 | { |
---|
2591 | this->smRealPivot(); |
---|
2592 | this->smSelectPR(); |
---|
2593 | this->smGElim(); |
---|
2594 | crd++; |
---|
2595 | this->smColToRow(); |
---|
2596 | act--; |
---|
2597 | this->smRowToCol(); |
---|
2598 | this->smZeroToredElim(); |
---|
2599 | if (sing != 0) return; |
---|
2600 | } |
---|
2601 | if (TEST_OPT_PROT) PrintS(".\n"); |
---|
2602 | piv = m_act[1]; |
---|
2603 | rpiv = piv->pos; |
---|
2604 | m_act[1] = piv->n; |
---|
2605 | piv->n = NULL; |
---|
2606 | crd++; |
---|
2607 | this->smColToRow(); |
---|
2608 | act--; |
---|
2609 | this->smRowToCol(); |
---|
2610 | } |
---|
2611 | |
---|
2612 | /* |
---|
2613 | * solve the triangular system |
---|
2614 | */ |
---|
2615 | void sparse_number_mat::smSolv() |
---|
2616 | { |
---|
2617 | int i, j; |
---|
2618 | number x, y, z; |
---|
2619 | smnumber s, d, r = m_row[nrows]; |
---|
2620 | |
---|
2621 | m_row[nrows] = NULL; |
---|
2622 | sol = (number *)omAlloc0(sizeof(number)*(crd+1)); |
---|
2623 | while (r != NULL) // expand the rigth hand side |
---|
2624 | { |
---|
2625 | sol[r->pos] = r->m; |
---|
2626 | s = r; |
---|
2627 | r = r->n; |
---|
2628 | omFreeBin((ADDRESS)s, smnrec_bin); |
---|
2629 | } |
---|
2630 | i = crd; // solve triangular system |
---|
2631 | if (sol[i] != NULL) |
---|
2632 | { |
---|
2633 | x = sol[i]; |
---|
2634 | sol[i] = nDiv(x, m_res[i]->m); |
---|
2635 | nDelete(&x); |
---|
2636 | } |
---|
2637 | i--; |
---|
2638 | while (i > 0) |
---|
2639 | { |
---|
2640 | x = NULL; |
---|
2641 | d = m_res[i]; |
---|
2642 | s = d->n; |
---|
2643 | while (s != NULL) |
---|
2644 | { |
---|
2645 | j = s->pos; |
---|
2646 | if (sol[j] != NULL) |
---|
2647 | { |
---|
2648 | z = nMult(sol[j], s->m); |
---|
2649 | if (x != NULL) |
---|
2650 | { |
---|
2651 | y = x; |
---|
2652 | x = nSub(y, z); |
---|
2653 | nDelete(&y); |
---|
2654 | nDelete(&z); |
---|
2655 | } |
---|
2656 | else |
---|
2657 | x = nNeg(z); |
---|
2658 | } |
---|
2659 | s = s->n; |
---|
2660 | } |
---|
2661 | if (sol[i] != NULL) |
---|
2662 | { |
---|
2663 | if (x != NULL) |
---|
2664 | { |
---|
2665 | y = nAdd(x, sol[i]); |
---|
2666 | nDelete(&x); |
---|
2667 | if (nIsZero(y)) |
---|
2668 | { |
---|
2669 | nDelete(&sol[i]); |
---|
2670 | sol[i] = NULL; |
---|
2671 | } |
---|
2672 | else |
---|
2673 | sol[i] = y; |
---|
2674 | } |
---|
2675 | } |
---|
2676 | else |
---|
2677 | sol[i] = x; |
---|
2678 | if (sol[i] != NULL) |
---|
2679 | { |
---|
2680 | x = sol[i]; |
---|
2681 | sol[i] = nDiv(x, d->m); |
---|
2682 | nDelete(&x); |
---|
2683 | } |
---|
2684 | i--; |
---|
2685 | } |
---|
2686 | this->smAllDel(); |
---|
2687 | } |
---|
2688 | |
---|
2689 | /* |
---|
2690 | * transform the result to an ideal |
---|
2691 | */ |
---|
2692 | ideal sparse_number_mat::smRes2Ideal() |
---|
2693 | { |
---|
2694 | int i, j; |
---|
2695 | ideal res = idInit(crd, 1); |
---|
2696 | |
---|
2697 | for (i=crd; i; i--) |
---|
2698 | { |
---|
2699 | j = perm[i]-1; |
---|
2700 | res->m[j] = smSmnumber2Poly(sol[i]); |
---|
2701 | } |
---|
2702 | omFreeSize((ADDRESS)sol, sizeof(number)*(crd+1)); |
---|
2703 | return res; |
---|
2704 | } |
---|
2705 | |
---|
2706 | /* ----------------- pivot method ------------------ */ |
---|
2707 | |
---|
2708 | /* |
---|
2709 | * compute pivot |
---|
2710 | */ |
---|
2711 | void sparse_number_mat::smRealPivot() |
---|
2712 | { |
---|
2713 | smnumber a; |
---|
2714 | number x, xo; |
---|
2715 | int i, copt, ropt; |
---|
2716 | |
---|
2717 | xo=nInit(0); |
---|
2718 | for (i=act; i; i--) |
---|
2719 | { |
---|
2720 | a = m_act[i]; |
---|
2721 | while ((a!=NULL) && (a->pos<=tored)) |
---|
2722 | { |
---|
2723 | x = a->m; |
---|
2724 | if (nGreaterZero(x)) |
---|
2725 | { |
---|
2726 | if (nGreater(x,xo)) |
---|
2727 | { |
---|
2728 | nDelete(&xo); |
---|
2729 | xo = nCopy(x); |
---|
2730 | copt = i; |
---|
2731 | ropt = a->pos; |
---|
2732 | } |
---|
2733 | } |
---|
2734 | else |
---|
2735 | { |
---|
2736 | xo = nNeg(xo); |
---|
2737 | if (nGreater(xo,x)) |
---|
2738 | { |
---|
2739 | nDelete(&xo); |
---|
2740 | xo = nCopy(x); |
---|
2741 | copt = i; |
---|
2742 | ropt = a->pos; |
---|
2743 | } |
---|
2744 | xo = nNeg(xo); |
---|
2745 | } |
---|
2746 | a = a->n; |
---|
2747 | } |
---|
2748 | } |
---|
2749 | rpiv = ropt; |
---|
2750 | if (copt != act) |
---|
2751 | { |
---|
2752 | a = m_act[act]; |
---|
2753 | m_act[act] = m_act[copt]; |
---|
2754 | m_act[copt] = a; |
---|
2755 | } |
---|
2756 | nDelete(&xo); |
---|
2757 | } |
---|
2758 | |
---|
2759 | /* ----------------- elimination ------------------ */ |
---|
2760 | |
---|
2761 | /* one step of Gauss-elimination */ |
---|
2762 | void sparse_number_mat::smGElim() |
---|
2763 | { |
---|
2764 | number p = nDiv(one,piv->m); // pivotelement |
---|
2765 | smnumber c = m_act[act]; // pivotcolumn |
---|
2766 | smnumber r = red; // row to reduce |
---|
2767 | smnumber res, a, b; |
---|
2768 | number w, ha, hb; |
---|
2769 | |
---|
2770 | if ((c == NULL) || (r == NULL)) |
---|
2771 | { |
---|
2772 | while (r!=NULL) smNumberDelete(&r); |
---|
2773 | return; |
---|
2774 | } |
---|
2775 | do |
---|
2776 | { |
---|
2777 | a = m_act[r->pos]; |
---|
2778 | res = dumm; |
---|
2779 | res->n = NULL; |
---|
2780 | b = c; |
---|
2781 | w = nMult(r->m, p); |
---|
2782 | nDelete(&r->m); |
---|
2783 | r->m = w; |
---|
2784 | loop // combine the chains a and b: a + w*b |
---|
2785 | { |
---|
2786 | if (a == NULL) |
---|
2787 | { |
---|
2788 | do |
---|
2789 | { |
---|
2790 | res = res->n = smNumberCopy(b); |
---|
2791 | res->m = nMult(b->m, w); |
---|
2792 | b = b->n; |
---|
2793 | } while (b != NULL); |
---|
2794 | break; |
---|
2795 | } |
---|
2796 | if (a->pos < b->pos) |
---|
2797 | { |
---|
2798 | res = res->n = a; |
---|
2799 | a = a->n; |
---|
2800 | } |
---|
2801 | else if (a->pos > b->pos) |
---|
2802 | { |
---|
2803 | res = res->n = smNumberCopy(b); |
---|
2804 | res->m = nMult(b->m, w); |
---|
2805 | b = b->n; |
---|
2806 | } |
---|
2807 | else |
---|
2808 | { |
---|
2809 | hb = nMult(b->m, w); |
---|
2810 | ha = nAdd(a->m, hb); |
---|
2811 | nDelete(&hb); |
---|
2812 | nDelete(&a->m); |
---|
2813 | if (nIsZero(ha)) |
---|
2814 | { |
---|
2815 | smNumberDelete(&a); |
---|
2816 | } |
---|
2817 | else |
---|
2818 | { |
---|
2819 | a->m = ha; |
---|
2820 | res = res->n = a; |
---|
2821 | a = a->n; |
---|
2822 | } |
---|
2823 | b = b->n; |
---|
2824 | } |
---|
2825 | if (b == NULL) |
---|
2826 | { |
---|
2827 | res->n = a; |
---|
2828 | break; |
---|
2829 | } |
---|
2830 | } |
---|
2831 | m_act[r->pos] = dumm->n; |
---|
2832 | smNumberDelete(&r); |
---|
2833 | } while (r != NULL); |
---|
2834 | nDelete(&p); |
---|
2835 | } |
---|
2836 | |
---|
2837 | /* ----------------- transfer ------------------ */ |
---|
2838 | |
---|
2839 | /* |
---|
2840 | * select the pivotrow and store it to red and piv |
---|
2841 | */ |
---|
2842 | void sparse_number_mat::smSelectPR() |
---|
2843 | { |
---|
2844 | smnumber b = dumm; |
---|
2845 | smnumber a, ap; |
---|
2846 | int i; |
---|
2847 | |
---|
2848 | if (TEST_OPT_PROT) |
---|
2849 | { |
---|
2850 | if ((crd+1)%10) |
---|
2851 | PrintS("."); |
---|
2852 | else |
---|
2853 | PrintS(".\n"); |
---|
2854 | } |
---|
2855 | a = m_act[act]; |
---|
2856 | if (a->pos < rpiv) |
---|
2857 | { |
---|
2858 | do |
---|
2859 | { |
---|
2860 | ap = a; |
---|
2861 | a = a->n; |
---|
2862 | } while (a->pos < rpiv); |
---|
2863 | ap->n = a->n; |
---|
2864 | } |
---|
2865 | else |
---|
2866 | m_act[act] = a->n; |
---|
2867 | piv = a; |
---|
2868 | a->n = NULL; |
---|
2869 | for (i=1; i<act; i++) |
---|
2870 | { |
---|
2871 | a = m_act[i]; |
---|
2872 | if (a->pos < rpiv) |
---|
2873 | { |
---|
2874 | loop |
---|
2875 | { |
---|
2876 | ap = a; |
---|
2877 | a = a->n; |
---|
2878 | if ((a == NULL) || (a->pos > rpiv)) |
---|
2879 | break; |
---|
2880 | if (a->pos == rpiv) |
---|
2881 | { |
---|
2882 | ap->n = a->n; |
---|
2883 | a->m = nNeg(a->m); |
---|
2884 | b = b->n = a; |
---|
2885 | b->pos = i; |
---|
2886 | break; |
---|
2887 | } |
---|
2888 | } |
---|
2889 | } |
---|
2890 | else if (a->pos == rpiv) |
---|
2891 | { |
---|
2892 | m_act[i] = a->n; |
---|
2893 | a->m = nNeg(a->m); |
---|
2894 | b = b->n = a; |
---|
2895 | b->pos = i; |
---|
2896 | } |
---|
2897 | } |
---|
2898 | b->n = NULL; |
---|
2899 | red = dumm->n; |
---|
2900 | } |
---|
2901 | |
---|
2902 | /* |
---|
2903 | * store the pivotcol in m_row |
---|
2904 | * m_act[cols][pos(rows)] => m_row[rows][pos(cols)] |
---|
2905 | */ |
---|
2906 | void sparse_number_mat::smColToRow() |
---|
2907 | { |
---|
2908 | smnumber c = m_act[act]; |
---|
2909 | smnumber h; |
---|
2910 | |
---|
2911 | while (c != NULL) |
---|
2912 | { |
---|
2913 | h = c; |
---|
2914 | c = c->n; |
---|
2915 | h->n = m_row[h->pos]; |
---|
2916 | m_row[h->pos] = h; |
---|
2917 | h->pos = crd; |
---|
2918 | } |
---|
2919 | } |
---|
2920 | |
---|
2921 | /* |
---|
2922 | * store the pivot and the assosiated row in m_row |
---|
2923 | * to m_res (result): |
---|
2924 | * piv + m_row[rows][pos(cols)] => m_res[cols][pos(rows)] |
---|
2925 | */ |
---|
2926 | void sparse_number_mat::smRowToCol() |
---|
2927 | { |
---|
2928 | smnumber r = m_row[rpiv]; |
---|
2929 | smnumber a, ap, h; |
---|
2930 | |
---|
2931 | m_row[rpiv] = NULL; |
---|
2932 | perm[crd] = rpiv; |
---|
2933 | piv->pos = crd; |
---|
2934 | m_res[crd] = piv; |
---|
2935 | while (r != NULL) |
---|
2936 | { |
---|
2937 | ap = m_res[r->pos]; |
---|
2938 | loop |
---|
2939 | { |
---|
2940 | a = ap->n; |
---|
2941 | if (a == NULL) |
---|
2942 | { |
---|
2943 | ap->n = h = r; |
---|
2944 | r = r->n; |
---|
2945 | h->n = a; |
---|
2946 | h->pos = crd; |
---|
2947 | break; |
---|
2948 | } |
---|
2949 | ap = a; |
---|
2950 | } |
---|
2951 | } |
---|
2952 | } |
---|
2953 | |
---|
2954 | /* ----------------- C++ stuff ------------------ */ |
---|
2955 | |
---|
2956 | /* |
---|
2957 | * check singularity |
---|
2958 | */ |
---|
2959 | void sparse_number_mat::smZeroToredElim() |
---|
2960 | { |
---|
2961 | smnumber a; |
---|
2962 | int i = act; |
---|
2963 | |
---|
2964 | loop |
---|
2965 | { |
---|
2966 | if (i == 0) return; |
---|
2967 | a = m_act[i]; |
---|
2968 | if ((a==NULL) || (a->pos>tored)) |
---|
2969 | { |
---|
2970 | sing = 1; |
---|
2971 | this->smAllDel(); |
---|
2972 | return; |
---|
2973 | } |
---|
2974 | i--; |
---|
2975 | } |
---|
2976 | } |
---|
2977 | |
---|
2978 | /* |
---|
2979 | * delete all smnumber's |
---|
2980 | */ |
---|
2981 | void sparse_number_mat::smAllDel() |
---|
2982 | { |
---|
2983 | smnumber a; |
---|
2984 | int i; |
---|
2985 | |
---|
2986 | for (i=act; i; i--) |
---|
2987 | { |
---|
2988 | a = m_act[i]; |
---|
2989 | while (a != NULL) |
---|
2990 | smNumberDelete(&a); |
---|
2991 | } |
---|
2992 | for (i=crd; i; i--) |
---|
2993 | { |
---|
2994 | a = m_res[i]; |
---|
2995 | while (a != NULL) |
---|
2996 | smNumberDelete(&a); |
---|
2997 | } |
---|
2998 | if (act) |
---|
2999 | { |
---|
3000 | for (i=nrows; i; i--) |
---|
3001 | { |
---|
3002 | a = m_row[i]; |
---|
3003 | while (a != NULL) |
---|
3004 | smNumberDelete(&a); |
---|
3005 | } |
---|
3006 | } |
---|
3007 | } |
---|
3008 | |
---|
3009 | /* ----------------- internal 'C' stuff ------------------ */ |
---|
3010 | |
---|
3011 | static void smNumberDelete(smnumber *r) |
---|
3012 | { |
---|
3013 | smnumber a = *r, b = a->n; |
---|
3014 | |
---|
3015 | nDelete(&a->m); |
---|
3016 | omFreeBin((ADDRESS)a, smnrec_bin); |
---|
3017 | *r = b; |
---|
3018 | } |
---|
3019 | |
---|
3020 | static smnumber smNumberCopy(smnumber a) |
---|
3021 | { |
---|
3022 | smnumber r = (smnumber)omAllocBin(smnrec_bin); |
---|
3023 | memcpy(r, a, sizeof(smnrec)); |
---|
3024 | return r; |
---|
3025 | } |
---|
3026 | |
---|
3027 | /* |
---|
3028 | * from poly to smnumber |
---|
3029 | * do not destroy p |
---|
3030 | */ |
---|
3031 | static smnumber smPoly2Smnumber(poly q) |
---|
3032 | { |
---|
3033 | smnumber a, res; |
---|
3034 | poly p = q; |
---|
3035 | |
---|
3036 | if (p == NULL) |
---|
3037 | return NULL; |
---|
3038 | a = res = (smnumber)omAllocBin(smnrec_bin); |
---|
3039 | a->pos = pGetComp(p); |
---|
3040 | a->m = pGetCoeff(p); |
---|
3041 | nNew(&pGetCoeff(p)); |
---|
3042 | loop |
---|
3043 | { |
---|
3044 | pIter(p); |
---|
3045 | if (p == NULL) |
---|
3046 | { |
---|
3047 | pDelete(&q); |
---|
3048 | a->n = NULL; |
---|
3049 | return res; |
---|
3050 | } |
---|
3051 | a = a->n = (smnumber)omAllocBin(smnrec_bin); |
---|
3052 | a->pos = pGetComp(p); |
---|
3053 | a->m = pGetCoeff(p); |
---|
3054 | nNew(&pGetCoeff(p)); |
---|
3055 | } |
---|
3056 | } |
---|
3057 | |
---|
3058 | /* |
---|
3059 | * from smnumber to poly |
---|
3060 | * destroy a |
---|
3061 | */ |
---|
3062 | static poly smSmnumber2Poly(number a) |
---|
3063 | { |
---|
3064 | poly res; |
---|
3065 | |
---|
3066 | if (a == NULL) return NULL; |
---|
3067 | res = pInit(); |
---|
3068 | pSetCoeff0(res, a); |
---|
3069 | return res; |
---|
3070 | } |
---|
3071 | |
---|
3072 | /*2 |
---|
3073 | * check the input |
---|
3074 | */ |
---|
3075 | static BOOLEAN smCheckSolv(ideal I) |
---|
3076 | { int i = I->ncols; |
---|
3077 | if ((i == 0) || (i != I->rank-1)) |
---|
3078 | { |
---|
3079 | WerrorS("wrong dimensions for linsolv"); |
---|
3080 | return TRUE; |
---|
3081 | } |
---|
3082 | for(;i;i--) |
---|
3083 | { |
---|
3084 | if(I->m[i-1] == NULL) |
---|
3085 | { |
---|
3086 | WerrorS("singular input for linsolv"); |
---|
3087 | return TRUE; |
---|
3088 | } |
---|
3089 | } |
---|
3090 | return FALSE; |
---|
3091 | } |
---|