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1 @node Quadrature, Ordinary Differential Equations, Optimization, Top |
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2 @chapter Quadrature |
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3 @cindex quadrature |
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4 @cindex numerical integration |
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5 @cindex integration |
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6 |
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7 @deftypefn {} {} Quad (integrand_fcn @var{fcn}) |
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8 @deftypefnx {} {} Quad (integrand_fcn @var{fcn}, double @var{abs}, double @var{rel}) |
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9 @end deftypefn |
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10 |
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11 @deftypefn {} {virtual double} integrate (void) |
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12 @deftypefnx {} {virtual double} integrate (int &@var{ier}) |
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13 @deftypefnx {} {virtual double} integrate (int &@var{ier}, int &@var{neval}) |
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14 @deftypefnx {} {virtual double} integrate (int &@var{ier}, int &@var{neval}, double &@var{abserr}) = 0 |
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15 @end deftypefn |
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16 |
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17 @deftypefn {} {} Quad_options (void) |
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18 @deftypefnx {} {} Quad_options (const Quad_options &@var{opt}) |
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19 @end deftypefn |
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20 |
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21 @deftypefn {} Quad_options& {operator =} (const Quad_options &@var{opt}) |
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22 @end deftypefn |
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23 |
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24 @deftypefn {} void init (void) |
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25 @end deftypefn |
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26 |
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27 @deftypefn {} void copy (const Quad_options &@var{opt}) |
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28 @end deftypefn |
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29 |
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30 @deftypefn {} void set_default_options (void) |
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31 @end deftypefn |
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32 |
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33 @deftypefn {} void set_absolute_tolerance (double @var{val}) |
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34 @end deftypefn |
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35 |
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36 @deftypefn {} void set_relative_tolerance (double @var{val}) |
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37 @end deftypefn |
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38 |
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39 @deftypefn {} double absolute_tolerance (void) |
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40 @deftypefnx {} double relative_tolerance (void) |
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41 @end deftypefn |
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42 |
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43 @deftypefn {} {} DefQuad (integrand_fcn @var{fcn}) |
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44 @deftypefnx {} {} DefQuad (integrand_fcn @var{fcn}, double @var{ll}, double @var{ul}) |
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45 @deftypefnx {} {} DefQuad (integrand_fcn @var{fcn}, double @var{ll}, double @var{ul}, double @var{abs}, double @var{rel}) |
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46 @deftypefnx {} {} DefQuad (integrand_fcn @var{fcn}, double @var{ll}, double @var{ul}, const ColumnVector &@var{sing}) |
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47 @deftypefnx {} {} DefQuad (integrand_fcn @var{fcn}, const ColumnVector &@var{sing}, double @var{abs}, double @var{rel}) |
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48 @deftypefnx {} {} DefQuad (integrand_fcn @var{fcn}, const ColumnVector &@var{sing}) |
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49 @deftypefnx {} {} DefQuad (integrand_fcn @var{fcn}, double @var{ll}, double @var{ul}, const ColumnVector &@var{sing}, double @var{abs}, double @var{rel}) |
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50 @end deftypefn |
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51 |
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52 @deftypefn {} {} IndefQuad (integrand_fcn @var{fcn}) |
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53 @deftypefnx {} {} IndefQuad (integrand_fcn @var{fcn}, double @var{b}, IntegralType @var{t}) |
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54 @deftypefnx {} {} IndefQuad (integrand_fcn @var{fcn}, double @var{b}, IntegralType @var{t}, double @var{abs}, double @var{rel}) |
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55 @deftypefnx {} {} IndefQuad (integrand_fcn @var{fcn}, double @var{abs}, double @var{rel}) |
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56 @end deftypefn |
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57 |
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58 @menu |
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59 * Collocation Weights:: |
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60 @end menu |
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61 |
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62 @node Collocation Weights, , Quadrature, Quadrature |
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63 @section Collocation Weights |
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64 @cindex orthogonal collocation |
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65 @cindex collocation weights |
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66 |
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67 @deftypefn {} {} CollocWt (void) |
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68 @deftypefnx {} {} CollocWt (int @var{n}, int @var{inc_l}, int @var{inc_r}) |
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69 @deftypefnx {} {} CollocWt (int @var{n}, int @var{inc_l}, int @var{inc_r}, double @var{l}, double @var{r}) |
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70 @deftypefnx {} {} CollocWt (int @var{n}, double @var{a}, double @var{b}, int @var{inc_l}, int @var{inc_r}) |
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71 @deftypefnx {} {} CollocWt (int @var{n}, int @var{inc_l}, int @var{inc_r}, double @var{l}, double @var{r}) |
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72 @deftypefnx {} {} CollocWt (const CollocWt&) |
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73 @end deftypefn |
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74 |
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75 @deftypefn {} CollocWt& {operator =} (const CollocWt&) |
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76 @end deftypefn |
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77 |
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78 @deftypefn {} CollocWt& resize (int @var{ncol}) |
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79 @end deftypefn |
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80 |
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81 @deftypefn {} CollocWt& add_left (void) |
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82 @deftypefnx {} CollocWt& add_right (void) |
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83 @end deftypefn |
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84 |
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85 @deftypefn {} CollocWt& delete_left (void) |
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86 @deftypefnx {} CollocWt& delete_right (void) |
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87 @end deftypefn |
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88 |
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89 @deftypefn {} CollocWt& set_left (double @var{val}) |
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90 @deftypefnx {} CollocWt& set_right (double @var{val}) |
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91 @end deftypefn |
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92 |
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93 @deftypefn {} CollocWt& set_alpha (double @var{val}) |
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94 @deftypefnx {} CollocWt& set_beta (double @var{val}) |
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95 @end deftypefn |
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96 |
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97 @deftypefn {} int ncol (void) const |
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98 @end deftypefn |
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99 |
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100 @deftypefn {} int left_included (void) const |
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101 @deftypefnx {} int right_included (void) const |
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102 @end deftypefn |
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103 |
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104 @deftypefn {} double left (void) const |
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105 @deftypefnx {} double right (void) const |
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106 @deftypefnx {} double width (void) const |
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107 @end deftypefn |
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108 |
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109 @deftypefn {} double alpha (void) const |
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110 @deftypefnx {} double beta (void) const |
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111 @end deftypefn |
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112 |
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113 @deftypefn {} ColumnVector roots (void) |
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114 @deftypefnx {} ColumnVector quad (void) |
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115 @deftypefnx {} ColumnVector quad_weights (void) |
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116 @end deftypefn |
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117 |
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118 @deftypefn {} Matrix first (void) |
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119 @deftypefnx {} Matrix second (void) |
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120 @end deftypefn |
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121 |
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122 @deftypefn {} {ostream&} {operator <<} (ostream &@var{os}, const CollocWt &@var{c}) |
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123 @end deftypefn |
