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1 @c Copyright (C) 1996, 1997 John W. Eaton |
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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 @node Evaluation |
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6 @chapter Evaluation |
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7 |
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8 Normally, you evaluate expressions simply by typing them at the Octave |
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9 prompt, or by asking Octave to interpret commands that you have saved in |
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10 a file. |
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11 |
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12 Sometimes, you may find it necessary to evaluate an expression that has |
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13 been computed and stored in a string, or use a string as the name of a |
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14 function to call. The @code{eval} and @code{feval} functions allow you |
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15 to do just that, and are necessary in order to evaluate commands that |
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16 are not known until run time, or to write functions that will need to |
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17 call user-supplied functions. |
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18 |
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19 @DOCSTRING(eval) |
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20 |
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21 @DOCSTRING(feval) |
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22 |
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23 Here is a simple-minded function using @code{feval} that finds the root |
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24 of a user-supplied function of one variable using Newton's method. |
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25 |
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26 @example |
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27 @group |
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28 @cindex Fordyce, A. P. |
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29 @findex newtroot |
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30 function result = newtroot (fname, x) |
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31 |
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32 # usage: newtroot (fname, x) |
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33 # |
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34 # fname : a string naming a function f(x). |
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35 # x : initial guess |
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36 |
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37 delta = tol = sqrt (eps); |
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38 maxit = 200; |
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39 fx = feval (fname, x); |
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40 for i = 1:maxit |
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41 if (abs (fx) < tol) |
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42 result = x; |
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43 return; |
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44 else |
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45 fx_new = feval (fname, x + delta); |
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46 deriv = (fx_new - fx) / delta; |
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47 x = x - fx / deriv; |
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48 fx = fx_new; |
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49 endif |
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50 endfor |
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51 |
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52 result = x; |
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53 |
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54 endfunction |
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55 @end group |
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56 @end example |
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57 |
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58 Note that this is only meant to be an example of calling user-supplied |
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59 functions and should not be taken too seriously. In addition to using a |
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60 more robust algorithm, any serious code would check the number and type |
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61 of all the arguments, ensure that the supplied function really was a |
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62 function, etc. See @xref{Predicates for Numeric Objects}, for example, |
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63 for a list of predicates for numeric objects, and @xref{Status of |
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64 Variables}, for a description of the @code{exist} function. |
