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1 <!doctype html public "-//IETF//DTD HTML Strict//EN"> |
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2 <html> |
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3 <head> |
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4 <title> Octave -- a high-level language for numerical computations </title> |
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5 </head> |
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6 |
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7 <h1>A Brief Introduction to Octave</h1> |
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8 |
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9 <ul> |
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10 <li><a href="readme.html#Overview">Overview</a></li> |
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11 <li><a href="readme.html#Language Features">Language Features</a></li> |
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12 <li><a href="readme.html#Distribution Terms">Distribution Terms</a></li> |
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13 <li><a href="readme.html#Availability">Availability</a></li> |
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14 <li><a href="readme.html#Installation and Bugs">Installation and Bugs</a></li> |
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15 <li><a href="readme.html#Documentation">Documentation</a></li> |
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16 <li><a href="readme.html#Implementation">Implementation</a></li> |
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17 </ul> |
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18 <hr> |
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19 |
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20 <h2><a name="Overview">Overview</a></h2> |
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21 <p> |
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22 Octave is a high-level language, primarily intended for numerical |
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23 computations. It provides a convenient command line interface for |
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24 solving linear and nonlinear problems numerically, and for performing |
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25 other numerical experiments. It may also be used as a batch-oriented |
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26 language. |
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27 </p> |
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28 |
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29 <h2><a name="Language Features">Language Features</a></h2> |
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30 <p> |
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31 The best way to introduce Octave's language is probably to show a few |
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32 simple examples. |
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33 </p> |
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34 |
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35 <p> |
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36 If you are new to Octave, I recommend that you try these examples to |
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37 begin learning Octave by using it. Lines marked with |
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38 <tt>octave:13></tt> are lines you type, ending each with a carriage |
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39 return. Octave will respond with an answer, or by displaying a graph. |
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40 </p> |
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41 |
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42 <h3>Creating a Matrix</h3> |
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43 |
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44 <p> |
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45 To create a new matrix and store it in a variable so that it you can |
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46 refer to it later, type the command |
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47 |
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48 <pre> |
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49 octave:1> a = [ 1, 1, 2; 3, 5, 8; 13, 21, 34 ] |
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50 </pre> |
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51 |
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52 Octave will respond by printing the matrix in neatly aligned columns. |
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53 Ending a command with a semicolon tells Octave to not print the result |
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54 of a command. For example |
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55 |
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56 <pre> |
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57 octave:2> b = rand (3, 2); |
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58 </pre> |
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59 |
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60 will create a 3 row, 2 column matrix with each element set to a random |
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61 value between zero and one. |
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62 </p> |
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63 |
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64 <p> |
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65 To display the value of any variable, simply type the name of the |
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66 variable. For example, to display the value stored in the matrix |
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67 <tt>b</tt>, type the command |
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68 |
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69 <pre> |
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70 octave:3> b |
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71 </pre> |
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72 |
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73 <h3>Matrix Arithmetic</h3> |
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74 |
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75 <p> |
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76 Octave has a convenient operator notation for performing matrix |
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77 arithmetic. For example, to multiply the matrix <tt>a</tt> by a |
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78 scalar value, type the command |
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79 |
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80 <pre> |
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81 octave:4> 2 * a |
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82 </pre> |
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83 |
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84 <p> |
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85 To multiply the two matrices <tt>a</tt> and <tt>b</tt>, type the |
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86 command |
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87 |
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88 <pre> |
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89 octave:5> a * b |
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90 </pre> |
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91 |
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92 <p> |
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93 To form the matrix product <tt>transpose (a) * a</tt>, type the command |
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94 |
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95 <pre> |
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96 octave:6> a' * a |
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97 </pre> |
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98 </p> |
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99 |
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100 <h3>Solving Linear Equations</h3> |
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101 |
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102 <p> |
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103 To solve the set of linear equations <tt>Ax = b</tt> use the left |
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104 division operator, <tt>\</tt>: |
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105 |
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106 <pre> |
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107 octave:7> a \ b |
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108 </pre> |
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109 |
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110 This is conceptually equivalent to <tt>inv (A) * b</tt>, but avoids |
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111 computing the inverse of a matrix directly. |
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112 </p> |
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113 |
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114 <p> |
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115 If the coefficient matrix is singular, Octave will print a warning |
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116 message and compute a minimum norm solution. |
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117 </p> |
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118 |
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119 <h3>Integrating Differential Equations</h3> |
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120 |
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121 <p> |
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122 Octave has built-in functions for solving nonlinear differential |
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123 equations of the form |
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124 |
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125 <pre> |
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126 dx |
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127 -- = f (x, t) |
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128 dt |
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129 </pre> |
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130 |
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131 with the initial condition |
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132 |
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133 <pre> |
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134 x(t = t0) = x0 |
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135 </pre> |
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136 </p> |
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137 |
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138 <p> |
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139 For Octave to integrate equations of this form, you must first provide a |
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140 definition of the function <tt> f (x, t)</tt>. This is |
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141 straightforward, and may be accomplished by entering the function body |
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142 directly on the command line. For example, the following commands |
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143 define the right hand side function for an interesting pair of |
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144 nonlinear differential equations. Note that while you are entering a |
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145 function, Octave responds with a different prompt, to indicate that it |
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146 is waiting for you to complete your input. |
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147 |
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148 <pre> |
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149 octave:8> function xdot = f (x, t) |
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150 > |
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151 > r = 0.25; |
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152 > k = 1.4; |
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153 > a = 1.5; |
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154 > b = 0.16; |
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155 > c = 0.9; |
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156 > d = 0.8; |
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157 > |
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158 > xdot(1) = r*x(1)*(1 - x(1)/k) - a*x(1)*x(2)/(1 + b*x(1)); |
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159 > xdot(2) = c*a*x(1)*x(2)/(1 + b*x(1)) - d*x(2); |
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160 > |
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161 > endfunction |
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162 </pre> |
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163 </p> |
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164 |
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165 <p> |
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166 Given the initial condition |
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167 |
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168 <pre> |
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169 x0 = [1; 2]; |
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170 </pre> |
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171 |
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172 and the set of output times as a column vector (note that the first |
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173 output time corresponds to the initial condition given above) |
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174 |
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175 <pre> |
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176 t = linspace (0, 50, 200)'; |
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177 </pre> |
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178 |
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179 it is easy to integrate the set of differential equations: |
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180 |
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181 <pre> |
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182 x = lsode ("f", x0, t); |
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183 </pre> |
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184 |
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185 <p> |
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186 The function <tt>lsode</tt> uses the Livermore Solver for Ordinary |
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187 Differential Equations, described in A. C. Hindmarsh, <em>ODEPACK, a |
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188 Systematized Collection of ODE Solvers</em>, in: Scientific Computing, |
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189 R. S. Stepleman et al. (Eds.), North-Holland, Amsterdam, 1983, pages |
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190 55-64. |
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191 </p> |
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192 |
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193 <h3>Producing Graphical Output</h3> |
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194 |
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195 <p> |
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196 To display the solution of the previous example graphically, use the |
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197 command |
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198 |
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199 <pre> |
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200 plot (t, x) |
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201 </pre> |
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202 </p> |
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203 |
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204 <p> |
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205 If you are using the X Window System, Octave will automatically create |
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206 a separate window to display the plot. If you are using a terminal that |
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207 supports some other graphics commands, you will need to tell Octave what |
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208 kind of terminal you have. Type the command |
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209 </p> |
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210 |
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211 <pre> |
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212 gset term |
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213 </pre> |
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214 |
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215 to see a list of the supported terminal types. Octave uses |
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216 <tt>gnuplot</tt> to display graphics, and can display graphics on any |
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217 terminal that is supported by <tt>gnuplot</tt>. |
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218 |
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219 <p> |
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220 To capture the output of the plot command in a file rather than sending |
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221 the output directly to your terminal, you can use a set of commands like |
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222 this |
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223 |
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224 <pre> |
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225 gset term postscript |
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226 gset output "foo.ps" |
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227 replot |
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228 </pre> |
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229 |
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230 This will work for other types of output devices as well. Octave's |
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231 <tt>gset</tt> command is really just piped to the <tt>gnuplot</tt> |
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232 subprocess, so that once you have a plot on the screen that you like, |
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233 you should be able to do something like this to create an output file |
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234 suitable for your graphics printer. |
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235 </p> |
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236 |
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237 <p> |
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238 Or, you can eliminate the intermediate file by using commands like this |
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239 |
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240 <pre> |
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241 gset term postscript |
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242 gset output "|lpr -Pname_of_your_graphics_printer" |
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243 replot |
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244 </pre> |
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245 |
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246 <h3>Editing What You Have Typed</h3> |
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247 |
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248 <p> |
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249 At the Octave prompt, you can recall, edit, and reissue previous |
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250 commands using Emacs- or vi-style editing commands. The default |
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251 keybindings use Emacs-style commands. |
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252 </p> |
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253 |
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254 <h3>Getting Help</h3> |
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255 |
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256 <p> |
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257 Octave has an extensive help facility. The same documentation that is |
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258 available in printed form is also available from the Octave prompt, |
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259 because both forms of the documentation are created from the same input |
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260 file. |
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261 </p> |
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262 |
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263 <p> |
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264 In order to get good help you first need to know the name of the command |
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265 that you want to use. This name of the function may not always be |
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266 obvious, but a good place to start is to just type <tt>help</tt>. |
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267 This will show you all the operators, reserved words, functions, |
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268 built-in variables, and function files. You can then get more |
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269 help on anything that is listed by simply including the name as an |
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270 argument to help. For example, |
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271 |
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272 <pre> |
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273 help plot |
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274 </pre> |
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275 |
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276 will display the help text for the <tt>plot</tt> function. |
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277 </p> |
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278 |
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279 <p> |
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280 The complete text of the manual is availabe from Octave's command line |
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281 using the command <tt>help -i</tt>. Because it is written in Texinfo, |
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282 it is also possible to put |
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283 <a href="http://www.che.wisc.edu/cgi-bin/info2www?(octave)">the manual |
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284 on the WWW</a>. |
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285 </p> |
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286 |
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287 <h2><a name="Distribution Terms">Distribution Terms</a></h2> |
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288 <p> |
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289 Octave is free software; you can redistribute it and/or modify it |
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290 under the terms of the |
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291 <a href="http://www.che.wisc.edu/cgi-bin/info2www?(octave)Copying">GNU |
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292 General Public License</a> as published by the Free Software |
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293 Foundation; either version 2, or (at your option) any later version. |
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294 </p> |
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295 |
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296 <p> |
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297 Octave is distributed in the hope that it will be useful, but WITHOUT |
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298 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or |
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299 FITNESS FOR A PARTICULAR PURPOSE. See the file COPYING for more |
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300 details. |
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301 </p> |
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302 |
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303 <h2><a name="Availability">Availability</a></h2> |
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304 <p> |
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305 The latest released version of Octave is always available via |
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306 anonymous ftp from |
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307 <a href="ftp://ftp.che.wisc.edu/pub/octave">ftp://ftp.che.wisc.edu/pub/octave</a>. |
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308 Complete source and binaries for several popular systems are available. |
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309 </p> |
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310 |
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311 <h2><a name="Installation and Bugs">Installation and Bugs</a></h2> |
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312 <p> |
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313 Octave requires approximately 125MB of disk storage to unpack and |
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314 compile from source (significantly less if you don't compile with |
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315 debugging symbols or create shared libraries). Once installed, Octave |
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316 requires approximately 65MB of disk space (again, considerably less if |
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317 you don't build shared libraries or the binaries and libraries do not |
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318 include debugging symbols). |
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319 </p> |
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320 |
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321 <p> |
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322 In order to build Octave, you will need a current version of g++, |
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323 libg++, and GNU make. Recommended versions are g++ 2.7.2 or 2.7.2.1, |
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324 libg++ 2.7.1 or 2.7.2, and make 3.75. |
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325 </p> |
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326 |
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327 <p> |
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328 <b>You must have GNU Make to compile Octave</b>. Octave's Makefiles |
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329 use features of GNU Make that are not present in other versions of |
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330 make. GNU Make is very portable and easy to install. |
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331 </p> |
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332 |
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333 <p> |
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334 See the notes in the files INSTALL and INSTALL.OCTAVE for more |
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335 specific installation instructions, including directions for |
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336 installing Octave from a binary distribution. |
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337 </p> |
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338 |
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339 <p> |
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340 The file BUGS contains a recommended procedure for reporting bugs, as |
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341 well as a list of known problems and possible fixes. |
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342 </p> |
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343 |
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344 <h2><a name="Documentation">Documentation</a></h2> |
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345 |
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346 <p> |
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347 Octave's manual has been revised for version 2.0, but it is lagging a |
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348 bit behind the development of the software. In particular, there is |
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349 currently no complete documentation of the C++ class libraries or the |
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350 support for dynamic linking and user-defined data types. If you |
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351 notice ommissions or inconsistencies, please report them as bugs to |
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352 bug-octave@bevo.che.wisc.edu. Specific suggestions for ways to |
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353 improve Octave and its documentation are always welcome. |
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354 </p> |
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355 |
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356 <h2><a name="Implementation">Implementation</a></h2> |
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357 <p> |
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358 Octave is being developed with the Free Software Foundation's make, |
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359 bison (a replacement for YACC), flex (a replacement for lex), gcc/g++, |
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360 and libg++ on a SPARCstation II and a DECstation 5000/240. It should |
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361 be possible to install it on any machine that runs GCC/G++. It may |
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362 also be possible to install it using other implementations of these |
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363 tools, but it will most certainly require much more work. Do yourself |
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364 a favor and get the GNU development tools, either via anonymous ftp |
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365 from prep.ai.mit.edu or by writing the Free Software Foundation, 675 |
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366 Mass Ave, Cambridge, MA 02139, USA. |
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367 </p> |
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368 |
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369 <p> |
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370 The underlying numerical solvers are currently standard Fortran ones |
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371 like Lapack, Linpack, Odepack, the Blas, etc., packaged in a library |
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372 of C++ classes (see the files in the libcruft and liboctave |
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373 subdirectories). If possible, the Fortran subroutines are compiled |
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374 with the system's Fortran compiler, and called directly from the C++ |
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375 functions. If that's not possible, they are translated with f2c and |
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376 compiled with a C compiler. Better performance is usually achieved if |
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377 the intermediate translation to C is avoided. |
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378 </p> |
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379 |
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380 <p> |
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381 The library of C++ classes may also be useful by itself. |
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382 </p> |
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383 |
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384 <hr> |
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385 <p> |
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386 Back to the <a href="http://www.che.wisc.edu/octave">Octave home page</a>. |
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387 </p> |
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388 <hr> |
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389 <p> |
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390 <a href="http://www.che.wisc.edu/~jwe">John W. Eaton</a><br> |
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391 <a href="mailto:jwe@bevo.che.wisc.edu"><i>jwe@bevo.che.wisc.edu</i></a><br> |
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392 University of Wisconsin<br> |
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393 Department of Chemical Engineering<br> |
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394 Madison WI 53719 |
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395 </p> |
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396 </body> |
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397 </html> |
