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gallery.m: clean and vectorize part of qmult. * scripts/special-matrix/gallery.m: make qmult() follow Octave guidelines, vectorize last for loop in qmult().
author Antonio Pino Robles <data.script93@gmail.com>
date Thu, 28 May 2015 18:32:47 +0200
parents 4197fc428c7d
children
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
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4197fc428c7d maint: Update copyright notices for 2015.
John W. Eaton <jwe@octave.org>
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1 @c Copyright (C) 1996-2015 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 Debugging
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20 @chapter Debugging
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21
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22 Octave includes a built-in debugger to aid in the development of
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23 scripts. This can be used to interrupt the execution of an Octave script
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24 at a certain point, or when certain conditions are met. Once execution
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25 has stopped, and debug mode is entered, the symbol table at the point
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26 where execution has stopped can be examined and modified to check for
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27 errors.
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28
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29 The normal command-line editing and history functions are available in
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30 debug mode.
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31
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32 @menu
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33 * Entering Debug Mode::
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34 * Leaving Debug Mode::
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35 * Breakpoints::
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36 * Debug Mode::
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37 * Call Stack::
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38 * Profiling::
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39 * Profiler Example::
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40 @end menu
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41
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42 @node Entering Debug Mode
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43 @section Entering Debug Mode
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44
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45 There are two basic means of interrupting the execution of an Octave
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46 script. These are breakpoints (@pxref{Breakpoints}), discussed in the next
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47 section, and interruption based on some condition.
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48
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49 Octave supports three means to stop execution based on the values set in
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50 the functions @code{debug_on_interrupt}, @code{debug_on_warning}, and
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51 @code{debug_on_error}.
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52
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53 @DOCSTRING(debug_on_interrupt)
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54
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55 @DOCSTRING(debug_on_warning)
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56
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57 @DOCSTRING(debug_on_error)
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58
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59 @node Leaving Debug Mode
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60 @section Leaving Debug Mode
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61
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62 Use either @code{dbcont} or @code{return} to leave the debug mode and
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63 continue the normal execution of the script.
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64
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65 @DOCSTRING(dbcont)
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66
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67 To quit debug mode and return directly to the prompt without executing
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68 any additional code use @code{dbquit}.
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70 @DOCSTRING(dbquit)
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71
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72 Finally, typing @code{exit} or @code{quit} at the debug prompt will
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73 result in Octave terminating normally.
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74
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75 @node Breakpoints
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76 @section Breakpoints
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77
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78 Breakpoints can be set in any m-file function by using the @code{dbstop}
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79 function.
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80
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81 @DOCSTRING(dbstop)
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82
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83 @noindent
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84 Breakpoints in class methods are also supported (e.g.,
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85 @code{dbstop ("@@class/method")}). However, breakpoints cannot be set in
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86 built-in functions (e.g., @code{sin}, etc.) or dynamically loaded functions
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87 (i.e., oct-files).
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88
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89 To set a breakpoint immediately upon entering a function use line number 1, or
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90 omit the line number entirely and just give the function name. When setting
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91 the breakpoint Octave will ignore the leading comment block, and the breakpoint
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92 will be set on the first executable statement in the function. For example:
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93
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94 @example
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95 @group
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96 dbstop ("asind", 1)
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97 @result{} 29
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98 @end group
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99 @end example
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100
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101 @noindent
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102 Note that the return value of @code{29} means that the breakpoint was
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103 effectively set to line 29. The status of breakpoints in a function can
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104 be queried with @code{dbstatus}.
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105
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106 @DOCSTRING(dbstatus)
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107
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108 @noindent
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109 Reusing the previous example, @code{dbstatus ("asind")} will return
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110 29. The breakpoints listed can then be cleared with the @code{dbclear}
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111 function.
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112
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113 @DOCSTRING(dbclear)
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114
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115 @noindent
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116
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117 A breakpoint may also be set in a subfunction. For example, if a file contains
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118 the functions
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119
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120 @example
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121 @group
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122 function y = func1 (x)
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123 y = func2 (x);
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124 endfunction
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125 function y = func2 (x)
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126 y = x + 1;
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127 endfunction
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128 @end group
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129 @end example
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130
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131 @noindent
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132 then a breakpoint can be set at the start of the subfunction directly with
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133
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134 @example
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135 @group
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136 dbstop (["func1", filemarker(), "func2"])
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137 @result{} 5
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138 @end group
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139 @end example
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140
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141 Note that @code{filemarker} returns the character that marks subfunctions from
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142 the file containing them. Unless the default has been changed this character
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143 is @samp{>}. Thus, a quicker and more normal way to set the breakpoint would
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144 be
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145
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146 @example
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147 dbstop func1>func2
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148 @end example
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149
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150 Another simple way of setting a breakpoint in an Octave script is the
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151 use of the @code{keyboard} function.
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152
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153 @DOCSTRING(keyboard)
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154
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155 @noindent
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156 The @code{keyboard} function is placed in a script at the point where the user
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157 desires that the execution be stopped. It automatically sets the running
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158 script into the debug mode.
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159
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160 @node Debug Mode
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161 @section Debug Mode
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162
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163 There are three additional support functions that allow the user to
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164 find out where in the execution of a script Octave entered the debug
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165 mode, and to print the code in the script surrounding the point where
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166 Octave entered debug mode.
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167
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168 @DOCSTRING(dbwhere)
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169
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170 @DOCSTRING(dbtype)
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171
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172 @DOCSTRING(dblist)
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173
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174 You may also use @code{isdebugmode} to determine whether the debugger is
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175 currently active.
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176
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177 @DOCSTRING(isdebugmode)
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178
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179 Debug mode also allows single line stepping through a function using
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180 the command @code{dbstep}.
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181
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182 @DOCSTRING(dbstep)
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183
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184 When in debug mode the @key{RETURN} key will execute the last entered command.
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185 This is useful, for example, after hitting a breakpoint and entering
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186 @code{dbstep} once. After that, one can advance line by line through the code
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187 with only a single key stroke.
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188
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189 @node Call Stack
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190 @section Call Stack
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191
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192 The function being debugged may be the leaf node of a series of function calls.
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193 After examining values in the current subroutine it may turn out that the
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194 problem occurred in earlier pieces of code. Use @code{dbup} and @code{dbdown}
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195 to move up and down through the series of function calls to locate where
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196 variables first took on the wrong values. @code{dbstack} shows the entire
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197 series of function calls and at what level debugging is currently taking place.
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198
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199 @DOCSTRING(dbstack)
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200
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201 @DOCSTRING(dbup)
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202
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203 @DOCSTRING(dbdown)
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204
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205 @node Profiling
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206 @section Profiling
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207 @cindex profiler
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208 @cindex code profiling
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209
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210 Octave supports profiling of code execution on a per-function level. If
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211 profiling is enabled, each call to a function (supporting built-ins,
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212 operators, functions in oct- and mex-files, user-defined functions in
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213 Octave code and anonymous functions) is recorded while running Octave
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214 code. After that, this data can aid in analyzing the code behavior, and
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215 is in particular helpful for finding ``hot spots'' in the code which use
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216 up a lot of computation time and are the best targets to spend
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217 optimization efforts on.
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218
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219 The main command for profiling is @code{profile}, which can be used to
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220 start or stop the profiler and also to query collected data afterwards.
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221 The data is returned in an Octave data structure which can then be
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222 examined or further processed by other routines or tools.
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223
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224 @DOCSTRING(profile)
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225
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226 An easy way to get an overview over the collected data is
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227 @code{profshow}. This function takes the profiler data returned by
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228 @code{profile} as input and prints a flat profile, for instance:
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229
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230 @example
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231 @group
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232 Function Attr Time (s) Calls
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233 ----------------------------------------
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234 >myfib R 2.195 13529
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235 binary <= 0.061 13529
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236 binary - 0.050 13528
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237 binary + 0.026 6764
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238 @end group
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239 @end example
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240
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241 This shows that most of the run time was spent executing the function
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242 @samp{myfib}, and some minor proportion evaluating the listed binary
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243 operators. Furthermore, it is shown how often the function was called
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244 and the profiler also records that it is recursive.
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245
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246 @DOCSTRING(profshow)
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247
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248 @DOCSTRING(profexplore)
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249
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250 @node Profiler Example
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251 @section Profiler Example
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252
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253 Below, we will give a short example of a profiler session.
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254 @xref{Profiling}, for the documentation of the profiler functions in
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255 detail. Consider the code:
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256
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257 @example
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258 global N A;
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259
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260 N = 300;
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261 A = rand (N, N);
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262
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263 function xt = timesteps (steps, x0, expM)
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264 global N;
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265
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266 if (steps == 0)
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267 xt = NA (N, 0);
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268 else
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269 xt = NA (N, steps);
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270 x1 = expM * x0;
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271 xt(:, 1) = x1;
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272 xt(:, 2 : end) = timesteps (steps - 1, x1, expM);
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273 endif
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274 endfunction
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275
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276 function foo ()
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277 global N A;
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278
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279 initial = @@(x) sin (x);
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280 x0 = (initial (linspace (0, 2 * pi, N)))';
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281
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282 expA = expm (A);
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283 xt = timesteps (100, x0, expA);
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284 endfunction
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285
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286 function fib = bar (N)
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287 if (N <= 2)
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288 fib = 1;
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289 else
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290 fib = bar (N - 1) + bar (N - 2);
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291 endif
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292 endfunction
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293 @end example
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294
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295 If we execute the two main functions, we get:
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296
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297 @example
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298 @group
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299 tic; foo; toc;
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300 @result{} Elapsed time is 2.37338 seconds.
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301
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302 tic; bar (20); toc;
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303 @result{} Elapsed time is 2.04952 seconds.
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304 @end group
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305 @end example
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306
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307 But this does not give much information about where this time is spent;
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308 for instance, whether the single call to @code{expm} is more expensive
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309 or the recursive time-stepping itself. To get a more detailed picture,
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310 we can use the profiler.
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311
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312 @example
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313 @group
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314 profile on;
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315 foo;
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316 profile off;
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317
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318 data = profile ("info");
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319 profshow (data, 10);
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320 @end group
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321 @end example
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322
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323 This prints a table like:
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324
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325 @example
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326 @group
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327 # Function Attr Time (s) Calls
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328 ---------------------------------------------
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329 7 expm 1.034 1
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330 3 binary * 0.823 117
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331 41 binary \ 0.188 1
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332 38 binary ^ 0.126 2
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333 43 timesteps R 0.111 101
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334 44 NA 0.029 101
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335 39 binary + 0.024 8
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336 34 norm 0.011 1
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337 40 binary - 0.004 101
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338 33 balance 0.003 1
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339 @end group
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340 @end example
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341
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342 The entries are the individual functions which have been executed (only
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343 the 10 most important ones), together with some information for each of
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344 them. The entries like @samp{binary *} denote operators, while other
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345 entries are ordinary functions. They include both built-ins like
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346 @code{expm} and our own routines (for instance @code{timesteps}). From
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347 this profile, we can immediately deduce that @code{expm} uses up the
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348 largest proportion of the processing time, even though it is only called
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349 once. The second expensive operation is the matrix-vector product in the
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350 routine @code{timesteps}. @footnote{We only know it is the binary
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351 multiplication operator, but fortunately this operator appears only at
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352 one place in the code and thus we know which occurrence takes so much
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353 time. If there were multiple places, we would have to use the
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354 hierarchical profile to find out the exact place which uses up the time
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355 which is not covered in this example.}
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356
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357 Timing, however, is not the only information available from the profile.
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358 The attribute column shows us that @code{timesteps} calls itself
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359 recursively. This may not be that remarkable in this example (since it's
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360 clear anyway), but could be helpful in a more complex setting. As to the
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361 question of why is there a @samp{binary \} in the output, we can easily
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362 shed some light on that too. Note that @code{data} is a structure array
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363 (@ref{Structure Arrays}) which contains the field @code{FunctionTable}.
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364 This stores the raw data for the profile shown. The number in the first
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365 column of the table gives the index under which the shown function can
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366 be found there. Looking up @code{data.FunctionTable(41)} gives:
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367
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368 @example
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369 @group
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370 scalar structure containing the fields:
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371
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372 FunctionName = binary \
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373 TotalTime = 0.18765
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374 NumCalls = 1
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375 IsRecursive = 0
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376 Parents = 7
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377 Children = [](1x0)
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378 @end group
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379 @end example
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380
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381 Here we see the information from the table again, but have additional
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382 fields @code{Parents} and @code{Children}. Those are both arrays, which
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383 contain the indices of functions which have directly called the function
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384 in question (which is entry 7, @code{expm}, in this case) or been called
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385 by it (no functions). Hence, the backslash operator has been used
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386 internally by @code{expm}.
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387
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388 Now let's take a look at @code{bar}. For this, we start a fresh
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389 profiling session (@code{profile on} does this; the old data is removed
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390 before the profiler is restarted):
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391
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392 @example
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393 @group
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394 profile on;
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395 bar (20);
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396 profile off;
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397
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398 profshow (profile ("info"));
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399 @end group
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400 @end example
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401
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402 This gives:
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403
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404 @example
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405 @group
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406 # Function Attr Time (s) Calls
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407 -------------------------------------------------------
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408 1 bar R 2.091 13529
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409 2 binary <= 0.062 13529
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410 3 binary - 0.042 13528
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411 4 binary + 0.023 6764
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412 5 profile 0.000 1
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413 8 false 0.000 1
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414 6 nargin 0.000 1
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415 7 binary != 0.000 1
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416 9 __profiler_enable__ 0.000 1
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417 @end group
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418 @end example
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419
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420 Unsurprisingly, @code{bar} is also recursive. It has been called 13,529
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421 times in the course of recursively calculating the Fibonacci number in a
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422 suboptimal way, and most of the time was spent in @code{bar} itself.
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423
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424 Finally, let's say we want to profile the execution of both @code{foo}
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425 and @code{bar} together. Since we already have the run-time data
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426 collected for @code{bar}, we can restart the profiler without clearing
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427 the existing data and collect the missing statistics about @code{foo}.
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428 This is done by:
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429
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430 @example
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431 @group
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432 profile resume;
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433 foo;
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434 profile off;
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435
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436 profshow (profile ("info"), 10);
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437 @end group
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438 @end example
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439
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440 As you can see in the table below, now we have both profiles mixed
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441 together.
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442
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443 @example
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444 @group
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445 # Function Attr Time (s) Calls
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446 ---------------------------------------------
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447 1 bar R 2.091 13529
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448 16 expm 1.122 1
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449 12 binary * 0.798 117
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450 46 binary \ 0.185 1
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451 45 binary ^ 0.124 2
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452 48 timesteps R 0.115 101
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453 2 binary <= 0.062 13529
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454 3 binary - 0.045 13629
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455 4 binary + 0.041 6772
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456 49 NA 0.036 101
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457 @end group
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458 @end example