1 | |
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2 | /**************************************************************************\ |
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3 | |
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4 | MODULE: mat_RR |
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5 | |
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6 | SUMMARY: |
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7 | |
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8 | Defines the class mat_RR. |
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9 | |
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10 | \**************************************************************************/ |
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11 | |
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12 | |
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13 | #include <NTL/matrix.h> |
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14 | #include <NTL/vec_vec_RR.h> |
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15 | |
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16 | NTL_matrix_decl(RR,vec_RR,vec_vec_RR,mat_RR) |
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17 | NTL_io_matrix_decl(RR,vec_RR,vec_vec_RR,mat_RR) |
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18 | NTL_eq_matrix_decl(RR,vec_RR,vec_vec_RR,mat_RR) |
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19 | |
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20 | void add(mat_RR& X, const mat_RR& A, const mat_RR& B); |
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21 | // X = A + B |
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22 | |
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23 | void sub(mat_RR& X, const mat_RR& A, const mat_RR& B); |
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24 | // X = A - B |
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25 | |
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26 | void negate(mat_RR& X, const mat_RR& A); |
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27 | // X = - A |
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28 | |
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29 | void mul(mat_RR& X, const mat_RR& A, const mat_RR& B); |
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30 | // X = A * B |
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31 | |
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32 | void mul(vec_RR& x, const mat_RR& A, const vec_RR& b); |
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33 | // x = A * b |
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34 | |
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35 | void mul(vec_RR& x, const vec_RR& a, const mat_RR& B); |
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36 | // x = a * B |
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37 | |
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38 | void mul(mat_RR& X, const mat_RR& A, const RR& b); |
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39 | void mul(mat_RR& X, const mat_RR& A, double b); |
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40 | // X = A * b |
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41 | |
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42 | void mul(mat_RR& X, const RR& a, const mat_RR& B); |
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43 | void mul(mat_RR& X, double a, const mat_RR& B); |
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44 | // X = a * B |
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45 | |
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46 | |
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47 | void determinant(RR& d, const mat_RR& A); |
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48 | RR determinant(const mat_RR& A); |
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49 | // d = determinant(A) |
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50 | |
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51 | |
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52 | void transpose(mat_RR& X, const mat_RR& A); |
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53 | mat_RR transpose(const mat_RR& A); |
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54 | // X = transpose of A |
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55 | |
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56 | void solve(RR& d, vec_RR& X, |
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57 | const mat_RR& A, const vec_RR& b); |
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58 | // A is an n x n matrix, b is a length n vector. Computes d = |
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59 | // determinant(A). If d != 0, solves x*A = b. |
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60 | |
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61 | void inv(RR& d, mat_RR& X, const mat_RR& A); |
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62 | // A is an n x n matrix. Computes d = determinant(A). If d != 0, |
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63 | // computes X = A^{-1}. |
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64 | |
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65 | void sqr(mat_RR& X, const mat_RR& A); |
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66 | mat_RR sqr(const mat_RR& A); |
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67 | // X = A*A |
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68 | |
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69 | void inv(mat_RR& X, const mat_RR& A); |
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70 | mat_RR inv(const mat_RR& A); |
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71 | // X = A^{-1}; error is raised if A is singular |
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72 | |
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73 | void power(mat_RR& X, const mat_RR& A, const ZZ& e); |
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74 | mat_RR power(const mat_RR& A, const ZZ& e); |
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75 | |
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76 | void power(mat_RR& X, const mat_RR& A, long e); |
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77 | mat_RR power(const mat_RR& A, long e); |
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78 | // X = A^e; e may be negative (in which case A must be nonsingular). |
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79 | |
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80 | void ident(mat_RR& X, long n); |
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81 | mat_RR ident_mat_RR(long n); |
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82 | // X = n x n identity matrix |
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83 | |
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84 | long IsIdent(const mat_RR& A, long n); |
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85 | // test if A is the n x n identity matrix |
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86 | |
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87 | void diag(mat_RR& X, long n, const RR& d); |
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88 | mat_RR diag(long n, const RR& d); |
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89 | // X = n x n diagonal matrix with d on diagonal |
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90 | |
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91 | long IsDiag(const mat_RR& A, long n, const RR& d); |
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92 | // test if X is an n x n diagonal matrix with d on diagonal |
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93 | |
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94 | |
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95 | |
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96 | |
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97 | |
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98 | // miscellaneous: |
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99 | |
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100 | void clear(mat_RR& a); |
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101 | // x = 0 (dimension unchanged) |
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102 | |
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103 | long IsZero(const mat_RR& a); |
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104 | // test if a is the zero matrix (any dimension) |
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105 | |
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106 | |
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107 | // operator notation: |
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108 | |
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109 | mat_RR operator+(const mat_RR& a, const mat_RR& b); |
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110 | mat_RR operator-(const mat_RR& a, const mat_RR& b); |
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111 | mat_RR operator*(const mat_RR& a, const mat_RR& b); |
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112 | |
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113 | mat_RR operator-(const mat_RR& a); |
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114 | |
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115 | |
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116 | // matrix/scalar multiplication: |
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117 | |
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118 | mat_RR operator*(const mat_RR& a, const RR& b); |
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119 | mat_RR operator*(const mat_RR& a, double b); |
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120 | |
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121 | mat_RR operator*(const RR& a, const mat_RR& b); |
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122 | mat_RR operator*(double a, const mat_RR& b); |
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123 | |
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124 | |
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125 | // matrix/vector multiplication: |
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126 | |
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127 | vec_RR operator*(const mat_RR& a, const vec_RR& b); |
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128 | |
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129 | vec_RR operator*(const vec_RR& a, const mat_RR& b); |
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130 | |
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131 | |
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132 | // assignment operator notation: |
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133 | |
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134 | mat_RR& operator+=(mat_RR& x, const mat_RR& a); |
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135 | mat_RR& operator-=(mat_RR& x, const mat_RR& a); |
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136 | mat_RR& operator*=(mat_RR& x, const mat_RR& a); |
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137 | |
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138 | mat_RR& operator*=(mat_RR& x, const RR& a); |
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139 | mat_RR& operator*=(mat_RR& x, double a); |
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140 | |
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141 | vec_RR& operator*=(vec_RR& x, const mat_RR& a); |
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142 | |
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143 | |
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144 | |
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