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1 @c Copyright (C) 2007 John W. Eaton, David Bateman |
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2 @c This is part of the Octave manual. |
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3 @c For copying conditions, see the file gpl.texi. |
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4 |
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5 @macro examplefile{file} |
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6 @example |
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7 @group |
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8 @verbatiminclude @value{top_srcdir}/examples/\file\ |
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9 @end group |
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10 @end example |
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11 @end macro |
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12 |
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13 @node Dynamically Linked Functions |
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14 @appendix Dynamically Linked Functions |
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15 @cindex dynamic-linking |
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16 |
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17 Octave has the possibility of including compiled code as dynamically |
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18 linked extensions and then using these extensions as if they were part |
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19 of Octave itself. Octave has the option of directly calling C++ code |
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20 through its native oct-file interface or C code through its mex |
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21 interface. It can also indirectly call functions written in any other |
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22 language through a simple wrapper. The reasons to write code in a |
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23 compiled language might be either to link to an existing piece of code |
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24 and allow it to be used within Octave, or to allow improved performance |
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25 for key pieces of code. |
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26 |
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27 Before going further, you should first determine if you really need to |
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28 use dynamically linked functions at all. Before proceeding with writing |
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29 any dynamically linked function to improve performance you should |
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30 address ask yourself |
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31 |
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32 @itemize @bullet |
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33 @item |
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34 Can I get the same functionality using the Octave scripting language only. |
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35 @item |
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36 Is it thoroughly optimized Octave code? Vectorization of Octave code, |
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37 doesn't just make it concise, it generally significantly improves its |
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38 performance. Above all, if loops must be used, make sure that the |
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39 allocation of space for variables takes place outside the loops using an |
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40 assignment to a like matrix or zeros. |
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41 @item |
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42 Does it make as much use as possible of existing built-in library |
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43 routines? These are highly optimized and many do not carry the overhead |
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44 of being interpreted. |
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45 @item |
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46 Does writing a dynamically linked function represent useful investment |
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47 of your time, relative to staying in Octave? |
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48 @end itemize |
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49 |
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50 Also, as oct- and mex-files are dynamically linked to octave, they |
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51 introduce to possibility of having Octave abort due to coding errors in |
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52 the user code. For example a segmentation violation in the users code |
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53 will cause Octave to abort. |
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54 |
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55 @menu |
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56 * Oct-Files:: |
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57 * Mex-Files:: |
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58 * Standalone Programs:: |
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59 @end menu |
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60 |
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61 @node Oct-Files |
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62 @section Oct-Files |
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63 @cindex oct-files |
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64 @cindex mkoctfile |
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65 @cindex oct |
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66 |
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67 @menu |
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68 * Getting Started with Oct-Files:: |
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69 * Matrices and Arrays in Oct-Files:: |
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70 * Character Strings in Oct-Files:: |
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71 * Cell Arrays in Oct-Files:: |
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72 * Structures in Oct-Files:: |
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73 * Sparse Matrices in Oct-Files:: |
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74 * Accessing Global Variables in Oct-Files:: |
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75 * Calling Octave Functions from Oct-Files:: |
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76 * Calling External Code from Oct-Files:: |
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77 * Allocating Local Memory in Oct-Files:: |
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78 * Input Parameter Checking in Oct-Files:: |
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79 * Exception and Error Handling in Oct-Files:: |
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80 * Documentation and Test of Oct-Files:: |
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81 * Application Programming Interface for Oct-Files:: |
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82 @end menu |
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83 |
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84 @node Getting Started with Oct-Files |
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85 @subsection Getting Started with Oct-Files |
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86 |
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87 The basic command to build oct-files is @code{mkoctfile} and it can be |
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88 call from within octave or from the command line. |
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89 |
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90 @DOCSTRING(mkoctfile) |
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91 |
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92 Consider the short example |
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93 |
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94 @examplefile{helloworld.cc} |
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95 |
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96 This example although short introduces the basics of writing a C++ |
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97 function that can be dynamically linked to Octave. The easiest way to |
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98 make available most of the definitions that might be necessary for an |
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99 oct-file in Octave is to use the @code{#include <octave/oct.h>} |
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100 header. |
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101 |
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102 The macro that defines the entry point into the dynamically loaded |
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103 function is @code{DEFUN_DLD}. This macro takes four arguments, these being |
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104 |
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105 @enumerate 1 |
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106 @item The function name as it will be seen in Octave, |
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107 @item The list of arguments to the function of type @code{octave_value_list}, |
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108 @item The number of output arguments, which can and often is omitted if |
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109 not used, and |
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110 @item The string that will be seen as the help text of the function. |
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111 @end enumerate |
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112 |
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113 The return type of functions defined with @code{DEFUN_DLD} is always |
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114 @code{octave_value_list}. |
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115 |
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116 There are a couple of important considerations in the choice of function |
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117 name. Firstly, it must be a valid Octave function name and so must be a |
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118 sequence of letters, digits and underscores, not starting with a |
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119 digit. Secondly, as Octave uses the function name to define the filename |
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120 it attempts to find the function in, the function name in the @code{DEFUN_DLD} |
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121 macro must match the filename of the oct-file. Therefore, the above |
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122 function should be in a file @file{helloworld.cc}, and it should be |
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123 compiled to an oct-file using the command |
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124 |
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125 @example |
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126 mkoctfile helloworld.cc |
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127 @end example |
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128 |
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129 This will create a file call helloworld.oct, that is the compiled |
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130 version of the function. It should be noted that it is perfectly |
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131 acceptable to have more than one @code{DEFUN_DLD} function in a source |
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132 file. However, there must either be a symbolic link to the oct-file for |
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133 each of the functions defined in the source code with the @code{DEFUN_DLD} |
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134 macro or the autoload (@ref{Function Files}) function should be used. |
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135 |
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136 The rest of this function then shows how to find the number of input |
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137 arguments, how to print through the octave pager, and return from the |
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138 function. After compiling this function as above, an example of its use |
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139 is |
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140 |
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141 @example |
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142 @group |
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143 helloworld (1, 2, 3) |
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144 @print{} Hello World has 3 input arguments and 0 output arguments. |
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145 @end group |
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146 @end example |
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147 |
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148 @node Matrices and Arrays in Oct-Files |
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149 @subsection Matrices and Arrays in Oct-Files |
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150 |
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151 Octave supports a number of different array and matrix classes, the |
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152 majority of which are based on the Array class. The exception is the |
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153 sparse matrix types discussed separately below. There are three basic |
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154 matrix types |
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155 |
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156 @table @code |
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157 @item Matrix |
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158 A double precision matrix class defined in dMatrix.h, |
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159 @item ComplexMatrix |
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160 A complex matrix class defined in CMatrix.h, and |
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161 @item BoolMatrix |
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162 A boolean matrix class defined in boolMatrix.h. |
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163 @end table |
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164 |
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165 These are the basic two-dimensional matrix types of octave. In |
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166 additional there are a number of multi-dimensional array types, these |
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167 being |
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168 |
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169 @table @code |
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170 @item NDArray |
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171 A double precision array class defined in @file{dNDArray.h} |
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172 @item ComplexNDarray |
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173 A complex array class defined in @file{CNDArray.h} |
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174 @item boolNDArray |
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175 A boolean array class defined in @file{boolNDArray.h} |
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176 @item int8NDArray |
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177 @itemx int16NDArray |
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178 @itemx int32NDArray |
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179 @itemx int64NDArray |
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180 8, 16, 32 and 64-bit signed array classes defined in |
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181 @file{int8NDArray.h}, @file{int16NDArray.h}, etc. |
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182 @item uint8NDArray |
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183 @itemx uint16NDArray |
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184 @itemx uint32NDArray |
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185 @itemx uint64NDArray |
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186 8, 16, 32 and 64-bit unsigned array classes defined in |
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187 @file{uint8NDArray.h}, @file{uint16NDArray.h}, etc. |
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188 @end table |
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189 |
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190 There are several basic means of constructing matrices of |
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191 multi-dimensional arrays. Considering the @code{Matrix} type as an |
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192 example |
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193 |
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194 @itemize @bullet |
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195 @item |
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196 We can create an empty matrix or array with the empty constructor. For |
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197 example |
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198 |
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199 @example |
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200 Matrix a; |
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201 @end example |
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202 |
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203 This can be used on all matrix and array types |
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204 @item |
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205 Define the dimensions of the matrix or array with a dim_vector. For |
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206 example |
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207 |
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208 @example |
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209 @group |
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210 dim_vector dv (2); |
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211 dv(0) = 2; dv(1) = 2; |
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212 Matrix a (dv); |
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213 @end group |
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214 @end example |
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215 |
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216 This can be used on all matrix and array types |
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217 @item |
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218 Define the number of rows and columns in the matrix. For example |
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219 |
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220 @example |
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221 Matrix a (2, 2) |
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222 @end example |
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223 |
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224 However, this constructor can only be used with the matrix types. |
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225 @end itemize |
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226 |
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227 These types all share a number of basic methods and operators, a |
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228 selection of which include |
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229 |
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230 @deftypefn Method T& {operator ()} (octave_idx_type) |
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231 @deftypefnx Method T& elem (octave_idx_type) |
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232 The @code{()} operator or @code{elem} method allow the values of the |
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233 matrix or array to be read or set. These can take a single argument, |
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234 which is of type @code{octave_idx_type}, that is the index into the matrix or |
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235 array. Additionally, the matrix type allows two argument versions of the |
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236 @code{()} operator and elem method, giving the row and column index of the |
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237 value to obtain or set. |
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238 @end deftypefn |
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239 |
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240 Note that these function do significant error checking and so in some |
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241 circumstances the user might prefer the access the data of the array or |
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242 matrix directly through the fortran_vec method discussed below. |
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243 |
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244 @deftypefn Method octave_idx_type nelem (void) const |
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245 The total number of elements in the matrix or array. |
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246 @end deftypefn |
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247 |
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248 @deftypefn Method size_t byte_size (void) const |
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249 The number of bytes used to store the matrix or array. |
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250 @end deftypefn |
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251 |
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252 @deftypefn Method dim_vector dims (void) const |
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253 The dimensions of the matrix or array in value of type dim_vector. |
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254 @end deftypefn |
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255 |
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256 @deftypefn Method void resize (const dim_vector&) |
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257 A method taking either an argument of type @code{dim_vector}, or in the |
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258 case of a matrix two arguments of type @code{octave_idx_type} defining |
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259 the number of rows and columns in the matrix. |
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260 @end deftypefn |
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261 |
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262 @deftypefn Method T* fortran_vec (void) |
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263 This method returns a pointer to the underlying data of the matrix or a |
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264 array so that it can be manipulated directly, either within Octave or by |
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265 an external library. |
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266 @end deftypefn |
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267 |
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268 Operators such an @code{+}, @code{-}, or @code{*} can be used on the |
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269 majority of the above types. In addition there are a number of methods |
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270 that are of interest only for matrices such as @code{transpose}, |
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271 @code{hermitian}, @code{solve}, etc. |
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272 |
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273 The typical way to extract a matrix or array from the input arguments of |
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274 @code{DEFUN_DLD} function is as follows |
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275 |
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276 @examplefile{addtwomatrices.cc} |
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277 |
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278 To avoid segmentation faults causing Octave to abort, this function |
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279 explicitly checks that there are sufficient arguments available before |
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280 accessing these arguments. It then obtains two multi-dimensional arrays |
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281 of type @code{NDArray} and adds these together. Note that the array_value |
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282 method is called without using the @code{is_matrix_type} type, and instead the |
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283 error_state is checked before returning @code{A + B}. The reason to |
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284 prefer this is that the arguments might be a type that is not an |
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285 @code{NDArray}, but it would make sense to convert it to one. The |
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286 @code{array_value} method allows this conversion to be performed |
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287 transparently if possible, and sets @code{error_state} if it is not. |
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288 |
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289 @code{A + B}, operating on two @code{NDArray}'s returns an |
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290 @code{NDArray}, which is cast to an @code{octave_value} on the return |
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291 from the function. An example of the use of this demonstration function |
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292 is |
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293 |
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294 @example |
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295 @group |
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296 addtwomatrices (ones (2, 2), ones (2, 2)) |
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297 @result{} 2 2 |
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298 2 2 |
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299 @end group |
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300 @end example |
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301 |
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302 A list of the basic @code{Matrix} and @code{Array} types, the methods to |
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303 extract these from an @code{octave_value} and the associated header is |
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304 listed below. |
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305 |
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306 @multitable @columnfractions .3 .4 .3 |
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307 @item @code{RowVector} @tab @code{row_vector_value} @tab @file{dRowVector.h} |
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308 @item @code{ComplexRowVector} @tab @code{complex_row_vector_value} @tab @file{CRowVector.h} |
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309 @item @code{ColumnVector} @tab @code{column_vector_value} @tab @file{dColVector.h} |
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310 @item @code{ComplexColumnVector} @tab @code{complex_column_vector_value} @tab @file{CColVector.h} |
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311 @item @code{Matrix} @tab @code{matrix_value} @tab @file{dMatrix.h} |
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312 @item @code{ComplexMatrix} @tab @code{complex_matrix_value} @tab @file{CMatrix.h} |
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313 @item @code{boolMatrix} @tab @code{bool_matrix_value} @tab @file{boolMatrix.h} |
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314 @item @code{charMatrix} @tab @code{char_matrix_value} @tab @file{chMatrix.h} |
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315 @item @code{NDArray} @tab @code{array_value} @tab @file{dNDArray.h} |
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316 @item @code{ComplexNDArray} @tab @code{complex_array_value} @tab @file{CNDArray.h} |
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317 @item @code{boolNDArray} @tab @code{bool_array_value} @tab @file{boolNDArray.h} |
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318 @item @code{charNDArray} @tab @code{char_array_value} @tab @file{charNDArray.h} |
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319 @item @code{int8NDArray} @tab @code{int8_array_value} @tab @file{int8NDArray.h} |
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320 @item @code{int16NDArray} @tab @code{int16_array_value} @tab @file{int16NDArray.h} |
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321 @item @code{int32NDArray} @tab @code{int32_array_value} @tab @file{int32NDArray.h} |
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322 @item @code{int64NDArray} @tab @code{int64_array_value} @tab @file{int64NDArray.h} |
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323 @item @code{uint8NDArray} @tab @code{uint8_array_value} @tab @file{uint8NDArray.h} |
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324 @item @code{uint16NDArray} @tab @code{uint16_array_value} @tab @file{uint16NDArray.h} |
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325 @item @code{uint32NDArray} @tab @code{uint32_array_value} @tab @file{uint32NDArray.h} |
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326 @item @code{uint64NDArray} @tab @code{uint64_array_value} @tab @file{uint64NDArray.h} |
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327 @end multitable |
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328 |
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329 @node Character Strings in Oct-Files |
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330 @subsection Character Strings in Oct-Files |
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331 |
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332 In Octave a character string is just a special @code{Array} class. |
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333 Consider the example |
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334 |
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335 @examplefile{stringdemo.cc} |
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336 |
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337 An example of the of the use of this function is |
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338 |
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339 @example |
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340 @group |
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341 s0 = ["First String"; "Second String"]; |
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342 [s1,s2] = stringdemo (s0) |
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343 @result{} s1 = Second String |
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344 First String |
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345 |
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346 @result{} s2 = First String |
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347 Second String |
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348 |
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349 typeinfo (s2) |
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350 @result{} sq_string |
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351 typeinfo (s1) |
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352 @result{} string |
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353 @end group |
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354 @end example |
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355 |
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356 One additional complication of strings in Octave is the difference |
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357 between single quoted and double quoted strings. To find out if an |
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358 @code{octave_value} contains a single or double quoted string an example is |
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359 |
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360 @example |
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361 @group |
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362 if (args(0).is_sq_string ()) |
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363 octave_stdout << "First argument is a singularly quoted string\n"; |
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364 else if (args(0).is_dq_string ()) |
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365 octave_stdout << "First argument is a doubly quoted string\n"; |
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366 @end group |
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367 @end example |
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368 |
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369 Note however, that both types of strings are represented by the |
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370 @code{charNDArray} type, and so when assigning to an |
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371 @code{octave_value}, the type of string should be specified. For example |
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372 |
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373 @example |
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374 @group |
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375 octave_value_list retval; |
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376 charNDArray c; |
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377 @dots{} |
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378 // Create single quoted string |
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379 retval(1) = octave_value (ch, true, '\''); |
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380 |
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381 // Create a double quoted string |
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382 retval(0) = octave_value (ch, true); |
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383 @end group |
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384 @end example |
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385 |
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386 @node Cell Arrays in Oct-Files |
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387 @subsection Cell Arrays in Oct-Files |
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388 |
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389 Octave's cell type is equally accessible within an oct-files. A cell |
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390 array is just an array of @code{octave_value}s, and so each element of the cell |
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391 array can then be treated just like any other @code{octave_value}. A simple |
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392 example is |
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393 |
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394 @examplefile{celldemo.cc} |
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395 |
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396 Note that cell arrays are used less often in standard oct-files and so |
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397 the @file{Cell.h} header file must be explicitly included. The rest of this |
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398 example extracts the @code{octave_value}s one by one from the cell array and |
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399 returns be as individual return arguments. For example consider |
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400 |
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401 @example |
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402 @group |
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403 [b1, b2, b3] = celldemo (@{1, [1, 2], "test"@}) |
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404 @result{} |
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405 b1 = 1 |
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406 b2 = |
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407 |
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408 1 2 |
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409 |
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410 b3 = test |
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411 @end group |
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412 @end example |
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413 |
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414 @node Structures in Oct-Files |
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415 @subsection Structures in Oct-Files |
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416 |
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417 A structure in Octave is map between a number of fields represented and |
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418 their values. The Standard Template Library @code{map} class is used, |
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419 with the pair consisting of a @code{std::string} and an octave |
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420 @code{Cell} variable. |
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421 |
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422 A simple example demonstrating the use of structures within oct-files is |
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423 |
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424 @examplefile{structdemo.cc} |
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425 |
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426 An example of its use is |
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427 |
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428 @example |
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429 @group |
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430 x.a = 1; x.b = "test"; x.c = [1, 2]; |
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431 structdemo (x, "b") |
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432 @result{} selected = test |
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433 @end group |
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434 @end example |
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435 |
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436 The commented code above demonstrates how to iterated over all of the |
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437 fields of the structure, where as the following code demonstrates finding |
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438 a particular field in a more concise manner. |
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439 |
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440 As can be seen the @code{contents} method of the @code{Octave_map} class |
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441 returns a @code{Cell} which allows structure arrays to be represented. |
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442 Therefore, to obtain the underlying @code{octave_value} we write |
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443 |
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444 @example |
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445 octave_value tmp = arg0.contents (p1) (0); |
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446 @end example |
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447 |
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448 where the trailing (0) is the () operator on the @code{Cell} object. |
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449 |
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450 @node Sparse Matrices in Oct-Files |
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451 @subsection Sparse Matrices in Oct-Files |
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452 |
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453 There are three classes of sparse objects that are of interest to the |
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454 user. |
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455 |
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456 @table @code |
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457 @item SparseMatrix |
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458 A double precision sparse matrix class |
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459 @item SparseComplexMatrix |
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460 A complex sparse matrix class |
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461 @item SparseBoolMatrix |
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462 A boolean sparse matrix class |
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463 @end table |
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464 |
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465 All of these classes inherit from the @code{Sparse<T>} template class, |
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466 and so all have similar capabilities and usage. The @code{Sparse<T>} |
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467 class was based on Octave @code{Array<T>} class, and so users familiar |
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468 with Octave's @code{Array} classes will be comfortable with the use of |
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469 the sparse classes. |
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470 |
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471 The sparse classes will not be entirely described in this section, due |
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472 to their similarity with the existing @code{Array} classes. However, |
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473 there are a few differences due the different nature of sparse objects, |
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474 and these will be described. Firstly, although it is fundamentally |
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475 possible to have N-dimensional sparse objects, the Octave sparse classes do |
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476 not allow them at this time. So all operations of the sparse classes |
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477 must be 2-dimensional. This means that in fact @code{SparseMatrix} is |
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478 similar to Octave's @code{Matrix} class rather than its |
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479 @code{NDArray} class. |
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480 |
|
481 @menu |
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|
482 * Array and Sparse Differences:: |
|
483 * Creating Sparse Matrices in Oct-Files:: |
|
484 * Using Sparse Matrices in Oct-Files:: |
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|
485 @end menu |
|
486 |
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|
487 @node Array and Sparse Differences |
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|
488 @subsubsection The Differences between the Array and Sparse Classes |
|
489 |
|
490 The number of elements in a sparse matrix is considered to be the number |
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|
491 of non-zero elements rather than the product of the dimensions. Therefore |
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|
492 |
|
493 @example |
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|
494 @group |
|
495 SparseMatrix sm; |
|
496 @dots{} |
|
497 int nel = sm.nelem (); |
|
498 @end group |
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|
499 @end example |
|
500 |
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|
501 returns the number of non-zero elements. If the user really requires the |
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|
502 number of elements in the matrix, including the non-zero elements, they |
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|
503 should use @code{numel} rather than @code{nelem}. Note that for very |
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|
504 large matrices, where the product of the two dimensions is large that |
|
505 the representation of the an unsigned int, then @code{numel} can overflow. |
|
506 An example is @code{speye(1e6)} which will create a matrix with a million |
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|
507 rows and columns, but only a million non-zero elements. Therefore the |
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|
508 number of rows by the number of columns in this case is more than two |
|
509 hundred times the maximum value that can be represented by an unsigned int. |
|
510 The use of @code{numel} should therefore be avoided useless it is known |
|
511 it won't overflow. |
|
512 |
|
513 Extreme care must be take with the elem method and the "()" operator, |
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|
514 which perform basically the same function. The reason is that if a |
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|
515 sparse object is non-const, then Octave will assume that a |
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|
516 request for a zero element in a sparse matrix is in fact a request |
|
517 to create this element so it can be filled. Therefore a piece of |
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|
518 code like |
|
519 |
|
520 @example |
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|
521 @group |
|
522 SparseMatrix sm; |
|
523 @dots{} |
|
524 for (int j = 0; j < nc; j++) |
|
525 for (int i = 0; i < nr; i++) |
|
526 std::cerr << " (" << i << "," << j << "): " << sm(i,j) |
|
527 << std::endl; |
|
528 @end group |
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|
529 @end example |
|
530 |
|
531 is a great way of turning the sparse matrix into a dense one, and a |
|
532 very slow way at that since it reallocates the sparse object at each |
|
533 zero element in the matrix. |
|
534 |
|
535 An easy way of preventing the above from happening is to create a temporary |
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|
536 constant version of the sparse matrix. Note that only the container for |
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|
537 the sparse matrix will be copied, while the actual representation of the |
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|
538 data will be shared between the two versions of the sparse matrix. So this |
|
539 is not a costly operation. For example, the above would become |
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|
540 |
|
541 @example |
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|
542 @group |
|
543 SparseMatrix sm; |
|
544 @dots{} |
|
545 const SparseMatrix tmp (sm); |
|
546 for (int j = 0; j < nc; j++) |
|
547 for (int i = 0; i < nr; i++) |
|
548 std::cerr << " (" << i << "," << j << "): " << tmp(i,j) |
|
549 << std::endl; |
|
550 @end group |
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|
551 @end example |
|
552 |
|
553 Finally, as the sparse types aren't just represented as a contiguous |
|
554 block of memory, the @code{fortran_vec} method of the @code{Array<T>} |
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|
555 is not available. It is however replaced by three separate methods |
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|
556 @code{ridx}, @code{cidx} and @code{data}, that access the raw compressed |
|
557 column format that the Octave sparse matrices are stored in. |
|
558 Additionally, these methods can be used in a manner similar to @code{elem}, |
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|
559 to allow the matrix to be accessed or filled. However, in that case it is |
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|
560 up to the user to respect the sparse matrix compressed column format |
|
561 discussed previous. |
|
562 |
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|
563 @node Creating Sparse Matrices in Oct-Files |
|
564 @subsubsection Creating Sparse Matrices in Oct-Files |
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|
565 |
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|
566 You have several alternatives for creating a sparse matrix. |
|
567 You can first create the data as three vectors representing the |
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|
568 row and column indexes and the data, and from those create the matrix. |
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|
569 Or alternatively, you can create a sparse matrix with the appropriate |
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|
570 amount of space and then fill in the values. Both techniques have their |
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|
571 advantages and disadvantages. |
|
572 |
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|
573 Here is an example of how to create a small sparse matrix with the first |
|
574 technique |
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|
575 |
|
576 @example |
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|
577 @group |
|
578 int nz = 4, nr = 3, nc = 4; |
|
579 |
|
580 ColumnVector ridx (nz); |
|
581 ColumnVector cidx (nz); |
|
582 ColumnVector data (nz); |
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|
583 |
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|
584 ridx(0) = 0; ridx(1) = 0; ridx(2) = 1; ridx(3) = 2; |
|
585 cidx(0) = 0; cidx(1) = 1; cidx(2) = 3; cidx(3) = 3; |
|
586 data(0) = 1; data(1) = 2; data(2) = 3; data(3) = 4; |
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|
587 |
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|
588 SparseMatrix sm (data, ridx, cidx, nr, nc); |
|
589 @end group |
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|
590 @end example |
|
591 |
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|
592 @noindent |
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|
593 which creates the matrix given in section @ref{Storage}. Note that |
6569
|
594 the compressed matrix format is not used at the time of the creation |
6571
|
595 of the matrix itself, however it is used internally. |
6569
|
596 |
|
597 As previously mentioned, the values of the sparse matrix are stored |
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|
598 in increasing column-major ordering. Although the data passed by the |
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|
599 user does not need to respect this requirement, the pre-sorting the |
|
600 data significantly speeds up the creation of the sparse matrix. |
|
601 |
|
602 The disadvantage of this technique of creating a sparse matrix is |
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|
603 that there is a brief time where two copies of the data exists. Therefore |
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|
604 for extremely memory constrained problems this might not be the right |
|
605 technique to create the sparse matrix. |
|
606 |
|
607 The alternative is to first create the sparse matrix with the desired |
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|
608 number of non-zero elements and then later fill those elements in. The |
|
609 easiest way to do this is |
6569
|
610 |
6571
|
611 @example |
6577
|
612 @group |
|
613 int nz = 4, nr = 3, nc = 4; |
|
614 SparseMatrix sm (nr, nc, nz); |
|
615 sm(0,0) = 1; sm(0,1) = 2; sm(1,3) = 3; sm(2,3) = 4; |
|
616 @end group |
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|
617 @end example |
|
618 |
6571
|
619 That creates the same matrix as previously. Again, although it is not |
6569
|
620 strictly necessary, it is significantly faster if the sparse matrix is |
|
621 created in this manner that the elements are added in column-major |
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|
622 ordering. The reason for this is that if the elements are inserted |
6569
|
623 at the end of the current list of known elements then no element |
|
624 in the matrix needs to be moved to allow the new element to be |
6571
|
625 inserted. Only the column indexes need to be updated. |
6569
|
626 |
|
627 There are a few further points to note about this technique of creating |
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|
628 a sparse matrix. Firstly, it is possible to create a sparse matrix |
6571
|
629 with fewer elements than are actually inserted in the matrix. Therefore |
6569
|
630 |
6571
|
631 @example |
6577
|
632 @group |
|
633 int nz = 4, nr = 3, nc = 4; |
|
634 SparseMatrix sm (nr, nc, 0); |
|
635 sm(0,0) = 1; sm(0,1) = 2; sm(1,3) = 3; sm(2,3) = 4; |
|
636 @end group |
6569
|
637 @end example |
|
638 |
6572
|
639 @noindent |
|
640 is perfectly valid. However it is a very bad idea. The reason is that |
6569
|
641 as each new element is added to the sparse matrix the space allocated |
6571
|
642 to it is increased by reallocating the memory. This is an expensive |
6569
|
643 operation, that will significantly slow this means of creating a sparse |
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|
644 matrix. Furthermore, it is possible to create a sparse matrix with |
|
645 too much storage, so having @var{nz} above equaling 6 is also valid. |
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|
646 The disadvantage is that the matrix occupies more memory than strictly |
|
647 needed. |
|
648 |
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|
649 It is not always easy to know the number of non-zero elements prior |
6571
|
650 to filling a matrix. For this reason the additional storage for the |
6569
|
651 sparse matrix can be removed after its creation with the |
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|
652 @dfn{maybe_compress} function. Furthermore, the maybe_compress can |
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|
653 deallocate the unused storage, but it can equally remove zero elements |
|
654 from the matrix. The removal of zero elements from the matrix is |
|
655 controlled by setting the argument of the @dfn{maybe_compress} function |
6572
|
656 to be @samp{true}. However, the cost of removing the zeros is high because it |
6571
|
657 implies resorting the elements. Therefore, if possible it is better |
|
658 is the user doesn't add the zeros in the first place. An example of |
6569
|
659 the use of @dfn{maybe_compress} is |
|
660 |
|
661 @example |
6577
|
662 @group |
6569
|
663 int nz = 6, nr = 3, nc = 4; |
6577
|
664 |
6569
|
665 SparseMatrix sm1 (nr, nc, nz); |
|
666 sm1(0,0) = 1; sm1(0,1) = 2; sm1(1,3) = 3; sm1(2,3) = 4; |
|
667 sm1.maybe_compress (); // No zero elements were added |
|
668 |
|
669 SparseMatrix sm2 (nr, nc, nz); |
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|
670 sm2(0,0) = 1; sm2(0,1) = 2; sm(0,2) = 0; sm(1,2) = 0; |
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|
671 sm1(1,3) = 3; sm1(2,3) = 4; |
|
672 sm2.maybe_compress (true); // Zero elements were added |
6577
|
673 @end group |
6569
|
674 @end example |
|
675 |
|
676 The use of the @dfn{maybe_compress} function should be avoided if |
|
677 possible, as it will slow the creation of the matrices. |
|
678 |
|
679 A third means of creating a sparse matrix is to work directly with |
6571
|
680 the data in compressed row format. An example of this technique might |
6569
|
681 be |
|
682 |
|
683 @c Note the @verbatim environment is a relatively new addition to texinfo. |
6571
|
684 @c Therefore use the @example environment and replace @, with @@, |
6569
|
685 @c { with @{, etc |
|
686 |
|
687 @example |
6577
|
688 @group |
|
689 octave_value arg; |
|
690 @dots{} |
|
691 int nz = 6, nr = 3, nc = 4; // Assume we know the max no nz |
|
692 SparseMatrix sm (nr, nc, nz); |
|
693 Matrix m = arg.matrix_value (); |
6569
|
694 |
6577
|
695 int ii = 0; |
|
696 sm.cidx (0) = 0; |
|
697 for (int j = 1; j < nc; j++) |
|
698 @{ |
|
699 for (int i = 0; i < nr; i++) |
|
700 @{ |
|
701 double tmp = foo (m(i,j)); |
|
702 if (tmp != 0.) |
|
703 @{ |
|
704 sm.data(ii) = tmp; |
|
705 sm.ridx(ii) = i; |
|
706 ii++; |
|
707 @} |
|
708 @} |
|
709 sm.cidx(j+1) = ii; |
|
710 @} |
|
711 sm.maybe_compress (); // If don't know a-priori the final no of nz. |
|
712 @end group |
6569
|
713 @end example |
|
714 |
6572
|
715 @noindent |
6569
|
716 which is probably the most efficient means of creating the sparse matrix. |
|
717 |
|
718 Finally, it might sometimes arise that the amount of storage initially |
6571
|
719 created is insufficient to completely store the sparse matrix. Therefore, |
6569
|
720 the method @code{change_capacity} exists to reallocate the sparse memory. |
6571
|
721 The above example would then be modified as |
6569
|
722 |
|
723 @example |
6577
|
724 @group |
|
725 octave_value arg; |
|
726 @dots{} |
|
727 int nz = 6, nr = 3, nc = 4; // Assume we know the max no nz |
|
728 SparseMatrix sm (nr, nc, nz); |
|
729 Matrix m = arg.matrix_value (); |
6569
|
730 |
6577
|
731 int ii = 0; |
|
732 sm.cidx (0) = 0; |
|
733 for (int j = 1; j < nc; j++) |
|
734 @{ |
|
735 for (int i = 0; i < nr; i++) |
|
736 @{ |
|
737 double tmp = foo (m(i,j)); |
|
738 if (tmp != 0.) |
|
739 @{ |
|
740 if (ii == nz) |
|
741 @{ |
|
742 nz += 2; // Add 2 more elements |
|
743 sm.change_capacity (nz); |
|
744 @} |
|
745 sm.data(ii) = tmp; |
|
746 sm.ridx(ii) = i; |
|
747 ii++; |
|
748 @} |
|
749 @} |
|
750 sm.cidx(j+1) = ii; |
|
751 @} |
|
752 sm.maybe_mutate (); // If don't know a-priori the final no of nz. |
|
753 @end group |
6569
|
754 @end example |
|
755 |
|
756 Note that both increasing and decreasing the number of non-zero elements in |
6571
|
757 a sparse matrix is expensive, as it involves memory reallocation. Also as |
6569
|
758 parts of the matrix, though not its entirety, exist as the old and new copy |
6571
|
759 at the same time, additional memory is needed. Therefore if possible this |
6569
|
760 should be avoided. |
|
761 |
6572
|
762 @node Using Sparse Matrices in Oct-Files |
6569
|
763 @subsubsection Using Sparse Matrices in Oct-Files |
|
764 |
|
765 Most of the same operators and functions on sparse matrices that are |
|
766 available from the Octave are equally available with oct-files. |
|
767 The basic means of extracting a sparse matrix from an @code{octave_value} |
|
768 and returning them as an @code{octave_value}, can be seen in the |
|
769 following example |
|
770 |
|
771 @example |
6577
|
772 @group |
|
773 octave_value_list retval; |
6569
|
774 |
6577
|
775 SparseMatrix sm = args(0).sparse_matrix_value (); |
|
776 SparseComplexMatrix scm = args(1).sparse_complex_matrix_value (); |
|
777 SparseBoolMatrix sbm = args(2).sparse_bool_matrix_value (); |
|
778 @dots{} |
|
779 retval(2) = sbm; |
|
780 retval(1) = scm; |
|
781 retval(0) = sm; |
|
782 @end group |
6569
|
783 @end example |
|
784 |
|
785 The conversion to an octave-value is handled by the sparse |
|
786 @code{octave_value} constructors, and so no special care is needed. |
|
787 |
|
788 @node Accessing Global Variables in Oct-Files |
|
789 @subsection Accessing Global Variables in Oct-Files |
|
790 |
|
791 Global variables allow variables in the global scope to be |
6571
|
792 accessed. Global variables can easily be accessed with oct-files using |
6569
|
793 the support functions @code{get_global_value} and |
6571
|
794 @code{set_global_value}. @code{get_global_value} takes two arguments, |
|
795 the first is a string representing the variable name to obtain. The |
6569
|
796 second argument is a boolean argument specifying what to do in the case |
6571
|
797 that no global variable of the desired name is found. An example of the |
6569
|
798 use of these two functions is |
|
799 |
6578
|
800 @examplefile{globaldemo.cc} |
6569
|
801 |
|
802 An example of its use is |
|
803 |
|
804 @example |
|
805 @group |
|
806 global a b |
|
807 b = 10; |
|
808 globaldemo ("b") |
|
809 @result{} 10 |
|
810 globaldemo ("c") |
|
811 @result{} "Global variable not found" |
|
812 num2str (a) |
|
813 @result{} 42 |
|
814 @end group |
|
815 @end example |
|
816 |
|
817 @node Calling Octave Functions from Oct-Files |
|
818 @subsection Calling Octave Functions from Oct-Files |
|
819 |
|
820 There is often a need to be able to call another octave function from |
|
821 within an oct-file, and there are many examples of such within octave |
6571
|
822 itself. For example the @code{quad} function is an oct-file that |
6569
|
823 calculates the definite integral by quadrature over a user supplied |
|
824 function. |
|
825 |
6571
|
826 There are also many ways in which a function might be passed. It might |
|
827 be passed as one of |
6569
|
828 |
|
829 @enumerate 1 |
|
830 @item Function Handle |
|
831 @item Anonymous Function Handle |
|
832 @item Inline Function |
|
833 @item String |
|
834 @end enumerate |
|
835 |
|
836 The example below demonstrates an example that accepts all four means of |
6571
|
837 passing a function to an oct-file. |
6569
|
838 |
6578
|
839 @examplefile{funcdemo.cc} |
6569
|
840 |
|
841 The first argument to this demonstration is the user supplied function |
|
842 and the following arguments are all passed to the user function. |
|
843 |
|
844 @example |
|
845 @group |
6572
|
846 funcdemo (@@sin,1) |
6569
|
847 @result{} 0.84147 |
6572
|
848 funcdemo (@@(x) sin(x), 1) |
6569
|
849 @result{} 0.84147 |
6572
|
850 funcdemo (inline ("sin(x)"), 1) |
6569
|
851 @result{} 0.84147 |
6572
|
852 funcdemo ("sin",1) |
6569
|
853 @result{} 0.84147 |
|
854 funcdemo (@@atan2, 1, 1) |
|
855 @result{} 0.78540 |
|
856 @end group |
|
857 @end example |
|
858 |
|
859 When the user function is passed as a string, the treatment of the |
6571
|
860 function is different. In some cases it is necessary to always have the |
6572
|
861 user supplied function as an @code{octave_function} object. In that |
|
862 case the string argument can be used to create a temporary function like |
6569
|
863 |
|
864 @example |
|
865 @group |
6577
|
866 std::octave fcn_name = unique_symbol_name ("__fcn__"); |
|
867 std::string fname = "function y = "; |
|
868 fname.append (fcn_name); |
|
869 fname.append ("(x) y = "); |
|
870 fcn = extract_function (args(0), "funcdemo", fcn_name, |
|
871 fname, "; endfunction"); |
|
872 @dots{} |
|
873 if (fcn_name.length ()) |
|
874 clear_function (fcn_name); |
6569
|
875 @end group |
|
876 @end example |
|
877 |
6571
|
878 There are two important things to know in this case. The number of input |
6569
|
879 arguments to the user function is fixed, and in the above is a single |
|
880 argument, and secondly to avoid leaving the temporary function in the |
|
881 Octave symbol table it should be cleared after use. |
|
882 |
|
883 @node Calling External Code from Oct-Files |
|
884 @subsection Calling External Code from Oct-Files |
|
885 |
|
886 Linking external C code to Octave is relatively simple, as the C |
6571
|
887 functions can easily be called directly from C++. One possible issue is |
6569
|
888 the declarations of the external C functions might need to be explicitly |
6571
|
889 defined as C functions to the compiler. If the declarations of the |
6569
|
890 external C functions are in the header @code{foo.h}, then the manner in |
|
891 which to ensure that the C++ compiler treats these declarations as C |
|
892 code is |
|
893 |
|
894 @example |
|
895 @group |
|
896 #ifdef __cplusplus |
6571
|
897 extern "C" |
6569
|
898 @{ |
|
899 #endif |
|
900 #include "foo.h" |
|
901 #ifdef __cplusplus |
|
902 @} /* end extern "C" */ |
|
903 #endif |
|
904 @end group |
|
905 @end example |
|
906 |
6571
|
907 Calling Fortran code however can pose some difficulties. This is due to |
6569
|
908 differences in the manner in compilers treat the linking of Fortran code |
6571
|
909 with C or C++ code. Octave supplies a number of macros that allow |
6569
|
910 consistent behavior across a number of compilers. |
|
911 |
|
912 The underlying Fortran code should use the @code{XSTOPX} function to |
6571
|
913 replace the Fortran @code{STOP} function. @code{XSTOPX} uses the Octave |
6569
|
914 exception handler to treat failing cases in the fortran code |
6571
|
915 explicitly. Note that Octave supplies its own replacement blas |
6569
|
916 @code{XERBLA} function, which uses @code{XSTOPX}. |
|
917 |
6572
|
918 If the underlying code calls @code{XSTOPX}, then the @code{F77_XFCN} |
6571
|
919 macro should be used to call the underlying fortran function. The Fortran |
6569
|
920 exception state can then be checked with the global variable |
6572
|
921 @code{f77_exception_encountered}. If @code{XSTOPX} will not be called, |
6569
|
922 then the @code{F77_FCN} macro should be used instead to call the Fortran |
|
923 code. |
|
924 |
|
925 There is no harm in using @code{F77_XFCN} in all cases, except that for |
|
926 Fortran code that is short running and executes a large number of times, |
6571
|
927 there is potentially an overhead in doing so. However, if @code{F77_FCN} |
6569
|
928 is used with code that calls @code{XSTOP}, Octave can generate a |
|
929 segmentation fault. |
|
930 |
|
931 An example of the inclusion of a Fortran function in an oct-file is |
|
932 given in the following example, where the C++ wrapper is |
|
933 |
6578
|
934 @examplefile{fortdemo.cc} |
6569
|
935 |
6572
|
936 @noindent |
6569
|
937 and the fortran function is |
|
938 |
6578
|
939 @examplefile{fortsub.f} |
6569
|
940 |
|
941 This example demonstrates most of the features needed to link to an |
|
942 external Fortran function, including passing arrays and strings, as well |
6571
|
943 as exception handling. An example of the behavior of this function is |
6569
|
944 |
|
945 @example |
|
946 @group |
6572
|
947 [b, s] = fortdemo (1:3) |
6569
|
948 @result{} |
|
949 b = 1.00000 0.50000 0.33333 |
|
950 s = There are 3 values in the input vector |
|
951 [b, s] = fortdemo(0:3) |
|
952 error: fortsub:divide by zero |
|
953 error: exception encountered in Fortran subroutine fortsub_ |
|
954 error: fortdemo: error in fortran |
|
955 @end group |
|
956 @end example |
|
957 |
|
958 @node Allocating Local Memory in Oct-Files |
|
959 @subsection Allocating Local Memory in Oct-Files |
|
960 |
|
961 Allocating memory within an oct-file might seem easy as the C++ |
6571
|
962 new/delete operators can be used. However, in that case care must be |
|
963 taken to avoid memory leaks. The preferred manner in which to allocate |
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|
964 memory for use locally is to use the @code{OCTAVE_LOCAL_BUFFER} macro. |
|
965 An example of its use is |
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|
966 |
|
967 @example |
|
968 OCTAVE_LOCAL_BUFFER (double, tmp, len) |
|
969 @end example |
|
970 |
|
971 that returns a pointer @code{tmp} of type @code{double *} of length |
|
972 @code{len}. |
|
973 |
|
974 @node Input Parameter Checking in Oct-Files |
|
975 @subsection Input Parameter Checking in Oct-Files |
|
976 |
|
977 WRITE ME |
|
978 |
|
979 @node Exception and Error Handling in Oct-Files |
|
980 @subsection Exception and Error Handling in Oct-Files |
|
981 |
|
982 Another important feature of Octave is its ability to react to the user |
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|
983 typing @kbd{Control-C} even during calculations. This ability is based on the |
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|
984 C++ exception handler, where memory allocated by the C++ new/delete |
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|
985 methods are automatically released when the exception is treated. When |
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|
986 writing an oct-file, to allow Octave to treat the user typing @kbd{Control-C}, |
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|
987 the @code{OCTAVE_QUIT} macro is supplied. For example |
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|
988 |
|
989 @example |
|
990 @group |
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|
991 for (octave_idx_type i = 0; i < a.nelem (); i++) |
|
992 @{ |
|
993 OCTAVE_QUIT; |
|
994 b.elem(i) = 2. * a.elem(i); |
|
995 @} |
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|
996 @end group |
|
997 @end example |
|
998 |
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|
999 The presence of the @code{OCTAVE_QUIT} macro in the inner loop allows Octave to |
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|
1000 treat the user request with the @kbd{Control-C}. Without this macro, the user |
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|
1001 must either wait for the function to return before the interrupt is |
|
1002 processed, or press @kbd{Control-C} three times to force Octave to exit. |
|
1003 |
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|
1004 The @code{OCTAVE_QUIT} macro does impose a very small speed penalty, and so for |
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|
1005 loops that are known to be small it might not make sense to include |
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|
1006 @code{OCTAVE_QUIT}. |
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|
1007 |
|
1008 When creating an oct-file that uses an external libraries, the function |
|
1009 might spend a significant portion of its time in the external |
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|
1010 library. It is not generally possible to use the @code{OCTAVE_QUIT} macro in |
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|
1011 this case. The alternative in this case is |
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|
1012 |
|
1013 @example |
|
1014 @group |
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|
1015 BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE; |
|
1016 @dots{} some code that calls a "foreign" function @dots{} |
|
1017 END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE; |
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|
1018 @end group |
|
1019 @end example |
|
1020 |
|
1021 The disadvantage of this is that if the foreign code allocates any |
|
1022 memory internally, then this memory might be lost during an interrupt, |
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|
1023 without being deallocated. Therefore, ideally Octave itself should |
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|
1024 allocate any memory that is needed by the foreign code, with either the |
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|
1025 fortran_vec method or the @code{OCTAVE_LOCAL_BUFFER} macro. |
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|
1026 |
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|
1027 The Octave unwind_protect mechanism (@ref{The unwind_protect Statement}) |
|
1028 can also be used in oct-files. In conjunction with the exception |
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|
1029 handling of Octave, it is important to enforce that certain code is run |
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|
1030 to allow variables, etc to be restored even if an exception occurs. An |
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|
1031 example of the use of this mechanism is |
|
1032 |
6578
|
1033 @examplefile{unwinddemo.cc} |
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|
1034 |
|
1035 As can be seen in the example |
|
1036 |
|
1037 @example |
|
1038 @group |
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|
1039 unwinddemo (1, 0) |
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|
1040 @result{} Inf |
|
1041 1 / 0 |
|
1042 @result{} warning: division by zero |
|
1043 Inf |
|
1044 @end group |
|
1045 @end example |
|
1046 |
|
1047 The division by zero (and in fact all warnings) is disabled in the |
|
1048 @code{unwinddemo} function. |
|
1049 |
|
1050 @node Documentation and Test of Oct-Files |
|
1051 @subsection Documentation and Test of Oct-Files |
|
1052 |
6572
|
1053 WRITE ME, reference how to use Texinfo in oct-file and embed test code. |
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|
1054 |
|
1055 @node Application Programming Interface for Oct-Files |
|
1056 @subsection Application Programming Interface for Oct-Files |
|
1057 |
|
1058 WRITE ME, using Coda section 1.3 as a starting point. |
|
1059 |
|
1060 @node Mex-Files |
|
1061 @section Mex-Files |
|
1062 @cindex mex-files |
|
1063 @cindex mex |
|
1064 |
|
1065 Octave includes an interface to allow legacy mex-files to be compiled |
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|
1066 and used with Octave. This interface can also be used to share code |
|
1067 between Octave and non Octave users. However, as mex-files expose the |
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|
1068 intern API of a product alternative to Octave, and the internal |
|
1069 structure of Octave is different to this product, a mex-file can never |
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|
1070 have the same performance in Octave as the equivalent oct-file. In |
6569
|
1071 particular to support the manner in which mex-files access the variables |
|
1072 passed to mex functions, there are a significant number of additional |
6571
|
1073 copies of memory when calling or returning from a mex function. For this |
6569
|
1074 reason, new code should be written using the oct-file interface |
|
1075 discussed above if possible. |
|
1076 |
|
1077 @menu |
6572
|
1078 * Getting Started with Mex-Files:: |
|
1079 * Structures with Mex-Files:: |
|
1080 * Sparse Matrices with Mex-Files:: |
|
1081 * Calling External Functions in Mex-Files:: |
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|
1082 @end menu |
|
1083 |
|
1084 @node Getting Started with Mex-Files |
|
1085 @subsection Getting Started with Mex-Files |
|
1086 |
|
1087 The basic command to build a mex-file is either @code{mkoctfile --mex} or |
6571
|
1088 @code{mex}. The first can either be used from within Octave or from the |
|
1089 commandline. However, to avoid issues with the installation of other |
6569
|
1090 products, the use of the command @code{mex} is limited to within Octave. |
|
1091 |
|
1092 @DOCSTRING(mex) |
|
1093 |
|
1094 @DOCSTRING(mexext) |
|
1095 |
|
1096 One important difference between the use of mex with other products and |
|
1097 with Octave is that the header file "matrix.h" is implicitly included |
6571
|
1098 through the inclusion of "mex.h". This is to avoid a conflict with the |
6569
|
1099 Octave file "Matrix.h" with operating systems and compilers that don't |
|
1100 distinguish between filenames in upper and lower case |
|
1101 |
|
1102 Consider the short example |
|
1103 |
6578
|
1104 @examplefile{firstmexdemo.c} |
6569
|
1105 |
|
1106 This simple example demonstrates the basics of writing a mex-file. |
|
1107 |
|
1108 WRITE ME |
|
1109 |
6572
|
1110 @node Structures with Mex-Files |
|
1111 @subsection Structures with Mex-Files |
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|
1112 |
|
1113 WRITE ME |
|
1114 |
|
1115 @node Sparse Matrices with Mex-Files |
|
1116 @subsection Sparse Matrices with Mex-Files |
|
1117 |
|
1118 WRITE ME |
|
1119 |
|
1120 @node Calling External Functions in Mex-Files |
|
1121 @subsection Calling External Functions in Mex-Files |
|
1122 |
|
1123 WRITE ME |
|
1124 |
|
1125 @node Standalone Programs |
|
1126 @section Standalone Programs |
|
1127 |
|
1128 The libraries Octave itself uses, can be utilized in standalone |
6571
|
1129 applications. These applications then have access, for example, to the |
6569
|
1130 array and matrix classes as well as to all the Octave algorithms. The |
|
1131 following C++ program, uses class Matrix from liboctave.a or |
|
1132 liboctave.so. |
|
1133 |
|
1134 @example |
|
1135 @group |
|
1136 #include <iostream> |
|
1137 #include <octave/oct.h> |
|
1138 int |
|
1139 main (void) |
|
1140 @{ |
|
1141 std::cout << "Hello Octave world!\n"; |
6572
|
1142 int n = 2; |
|
1143 Matrix a_matrix = Matrix (n, n); |
|
1144 for (octave_idx_type i = 0; i < n; i++) |
6569
|
1145 @{ |
6572
|
1146 for (octave_idx_type j = 0; j < n; j++) |
6569
|
1147 @{ |
6572
|
1148 a_matrix(row,column) = (i+1)*10 + (j+1); |
6569
|
1149 @} |
|
1150 @} |
|
1151 std::cout << a_matrix; |
|
1152 return 0; |
|
1153 @} |
|
1154 @end group |
|
1155 @end example |
|
1156 |
|
1157 mkoctfile can then be used to build a standalone application with a |
|
1158 command like |
|
1159 |
|
1160 @example |
|
1161 @group |
|
1162 $ mkoctfile --link-stand-alone hello.cc -o hello |
|
1163 $ ./hello |
|
1164 Hello Octave world! |
|
1165 11 12 |
|
1166 21 22 |
|
1167 $ |
|
1168 @end group |
|
1169 @end example |
|
1170 |
|
1171 Note that the application @code{hello} will be dynamically linked |
|
1172 against the octave libraries and any octave support libraries. |