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1 @c Copyright (C) 1996, 1997, 2006, 2007 John W. Eaton |
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2 @c |
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3 @c This file is part of Octave. |
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4 @c |
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5 @c Octave is free software; you can redistribute it and/or modify it |
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6 @c under the terms of the GNU General Public License as published by the |
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7 @c Free Software Foundation; either version 3 of the License, or (at |
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8 @c your option) any later version. |
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9 @c |
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10 @c Octave is distributed in the hope that it will be useful, but WITHOUT |
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11 @c ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or |
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12 @c FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
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13 @c for more details. |
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14 @c |
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15 @c You should have received a copy of the GNU General Public License |
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16 @c along with Octave; see the file COPYING. If not, see |
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17 @c <http://www.gnu.org/licenses/>. |
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18 |
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19 @node Quadrature, Ordinary Differential Equations, Optimization, Top |
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20 @chapter Quadrature |
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21 @cindex quadrature |
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22 @cindex numerical integration |
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23 @cindex integration |
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24 |
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25 @deftypefn {} {} Quad (integrand_fcn @var{fcn}) |
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26 @deftypefnx {} {} Quad (integrand_fcn @var{fcn}, double @var{abs}, double @var{rel}) |
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27 @end deftypefn |
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28 |
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29 @deftypefn {} {virtual double} integrate (void) |
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30 @deftypefnx {} {virtual double} integrate (int &@var{ier}) |
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31 @deftypefnx {} {virtual double} integrate (int &@var{ier}, int &@var{neval}) |
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32 @deftypefnx {} {virtual double} integrate (int &@var{ier}, int &@var{neval}, double &@var{abserr}) = 0 |
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33 @end deftypefn |
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34 |
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35 @deftypefn {} {} Quad_options (void) |
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36 @deftypefnx {} {} Quad_options (const Quad_options &@var{opt}) |
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37 @end deftypefn |
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38 |
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39 @deftypefn {} Quad_options& {operator =} (const Quad_options &@var{opt}) |
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40 @end deftypefn |
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41 |
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42 @deftypefn {} void init (void) |
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43 @end deftypefn |
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44 |
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45 @deftypefn {} void copy (const Quad_options &@var{opt}) |
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46 @end deftypefn |
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47 |
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48 @deftypefn {} void set_default_options (void) |
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49 @end deftypefn |
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50 |
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51 @deftypefn {} void set_absolute_tolerance (double @var{val}) |
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52 @end deftypefn |
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53 |
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54 @deftypefn {} void set_relative_tolerance (double @var{val}) |
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55 @end deftypefn |
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56 |
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57 @deftypefn {} double absolute_tolerance (void) |
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58 @deftypefnx {} double relative_tolerance (void) |
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59 @end deftypefn |
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60 |
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61 @deftypefn {} {} DefQuad (integrand_fcn @var{fcn}) |
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62 @deftypefnx {} {} DefQuad (integrand_fcn @var{fcn}, double @var{ll}, double @var{ul}) |
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63 @deftypefnx {} {} DefQuad (integrand_fcn @var{fcn}, double @var{ll}, double @var{ul}, double @var{abs}, double @var{rel}) |
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64 @deftypefnx {} {} DefQuad (integrand_fcn @var{fcn}, double @var{ll}, double @var{ul}, const ColumnVector &@var{sing}) |
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65 @deftypefnx {} {} DefQuad (integrand_fcn @var{fcn}, const ColumnVector &@var{sing}, double @var{abs}, double @var{rel}) |
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66 @deftypefnx {} {} DefQuad (integrand_fcn @var{fcn}, const ColumnVector &@var{sing}) |
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67 @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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68 @end deftypefn |
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69 |
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70 @deftypefn {} {} IndefQuad (integrand_fcn @var{fcn}) |
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71 @deftypefnx {} {} IndefQuad (integrand_fcn @var{fcn}, double @var{b}, IntegralType @var{t}) |
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72 @deftypefnx {} {} IndefQuad (integrand_fcn @var{fcn}, double @var{b}, IntegralType @var{t}, double @var{abs}, double @var{rel}) |
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73 @deftypefnx {} {} IndefQuad (integrand_fcn @var{fcn}, double @var{abs}, double @var{rel}) |
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74 @end deftypefn |
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75 |
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76 @menu |
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77 * Collocation Weights:: |
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78 @end menu |
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79 |
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80 @node Collocation Weights, , Quadrature, Quadrature |
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81 @section Collocation Weights |
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82 @cindex orthogonal collocation |
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83 @cindex collocation weights |
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84 |
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85 @deftypefn {} {} CollocWt (void) |
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86 @deftypefnx {} {} CollocWt (int @var{n}, int @var{inc_l}, int @var{inc_r}) |
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87 @deftypefnx {} {} CollocWt (int @var{n}, int @var{inc_l}, int @var{inc_r}, double @var{l}, double @var{r}) |
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88 @deftypefnx {} {} CollocWt (int @var{n}, double @var{a}, double @var{b}, int @var{inc_l}, int @var{inc_r}) |
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89 @deftypefnx {} {} CollocWt (int @var{n}, int @var{inc_l}, int @var{inc_r}, double @var{l}, double @var{r}) |
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90 @deftypefnx {} {} CollocWt (const CollocWt&) |
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91 @end deftypefn |
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92 |
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93 @deftypefn {} CollocWt& {operator =} (const CollocWt&) |
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94 @end deftypefn |
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95 |
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96 @deftypefn {} CollocWt& resize (int @var{ncol}) |
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97 @end deftypefn |
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98 |
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99 @deftypefn {} CollocWt& add_left (void) |
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100 @deftypefnx {} CollocWt& add_right (void) |
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101 @end deftypefn |
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102 |
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103 @deftypefn {} CollocWt& delete_left (void) |
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104 @deftypefnx {} CollocWt& delete_right (void) |
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105 @end deftypefn |
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106 |
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107 @deftypefn {} CollocWt& set_left (double @var{val}) |
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108 @deftypefnx {} CollocWt& set_right (double @var{val}) |
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109 @end deftypefn |
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110 |
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111 @deftypefn {} CollocWt& set_alpha (double @var{val}) |
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112 @deftypefnx {} CollocWt& set_beta (double @var{val}) |
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113 @end deftypefn |
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114 |
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115 @deftypefn {} int ncol (void) const |
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116 @end deftypefn |
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117 |
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118 @deftypefn {} int left_included (void) const |
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119 @deftypefnx {} int right_included (void) const |
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120 @end deftypefn |
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121 |
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122 @deftypefn {} double left (void) const |
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123 @deftypefnx {} double right (void) const |
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124 @deftypefnx {} double width (void) const |
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125 @end deftypefn |
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126 |
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127 @deftypefn {} double alpha (void) const |
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128 @deftypefnx {} double beta (void) const |
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129 @end deftypefn |
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130 |
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131 @deftypefn {} ColumnVector roots (void) |
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132 @deftypefnx {} ColumnVector quad (void) |
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133 @deftypefnx {} ColumnVector quad_weights (void) |
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134 @end deftypefn |
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135 |
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136 @deftypefn {} Matrix first (void) |
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137 @deftypefnx {} Matrix second (void) |
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138 @end deftypefn |
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139 |
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140 @deftypefn {} {ostream&} {operator <<} (ostream &@var{os}, const CollocWt &@var{c}) |
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141 @end deftypefn |
