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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 Expressions, Evaluation, Variables, Top |
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6 @chapter Expressions |
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7 @cindex expressions |
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8 |
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9 Expressions are the basic building block of statements in Octave. An |
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10 expression evaluates to a value, which you can print, test, store in a |
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11 variable, pass to a function, or assign a new value to a variable with |
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12 an assignment operator. |
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13 |
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14 An expression can serve as a statement on its own. Most other kinds of |
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15 statements contain one or more expressions which specify data to be |
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16 operated on. As in other languages, expressions in Octave include |
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17 variables, array references, constants, and function calls, as well as |
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18 combinations of these with various operators. |
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19 |
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20 @menu |
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21 * Index Expressions:: |
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22 * Calling Functions:: |
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23 * Arithmetic Ops:: |
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24 * Comparison Ops:: |
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25 * Boolean Expressions:: |
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26 * Assignment Ops:: |
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27 * Increment Ops:: |
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28 * Operator Precedence:: |
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29 @end menu |
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30 |
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31 @node Index Expressions, Calling Functions, Expressions, Expressions |
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32 @section Index Expressions |
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33 |
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34 @opindex ( |
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35 @opindex ) |
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36 |
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37 An @dfn{index expression} allows you to reference or extract selected |
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38 elements of a matrix or vector. |
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39 |
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40 Indices may be scalars, vectors, ranges, or the special operator |
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41 @samp{:}, which may be used to select entire rows or columns. |
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42 |
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43 Vectors are indexed using a single expression. Matrices require two |
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44 indices unless the value of the built-in variable |
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45 @code{do_fortran_indexing} is nonzero, in which case matrices may |
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46 also be indexed by a single expression. |
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47 |
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48 @DOCSTRING(do_fortran_indexing) |
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49 |
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50 Given the matrix |
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51 |
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52 @example |
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53 a = [1, 2; 3, 4] |
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54 @end example |
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55 |
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56 @noindent |
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57 all of the following expressions are equivalent |
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58 |
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59 @example |
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60 @group |
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61 a (1, [1, 2]) |
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62 a (1, 1:2) |
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63 a (1, :) |
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64 @end group |
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65 @end example |
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66 |
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67 @noindent |
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68 and select the first row of the matrix. |
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69 |
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70 A special form of indexing may be used to select elements of a matrix or |
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71 vector. If the indices are vectors made up of only ones and zeros, the |
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72 result is a new matrix whose elements correspond to the elements of the |
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73 index vector that are equal to one. For example, |
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74 |
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75 @example |
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76 @group |
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77 a = [1, 2; 3, 4]; |
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78 a ([1, 0], :) |
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79 @end group |
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80 @end example |
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81 |
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82 @noindent |
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83 selects the first row of the matrix @code{a}. |
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84 |
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85 This operation can be useful for selecting elements of a matrix based on |
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86 some condition, since the comparison operators return matrices of ones |
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87 and zeros. |
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88 |
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89 This special zero-one form of indexing leads to a conflict with the |
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90 standard indexing operation. For example, should the following |
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91 statements |
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92 |
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93 @example |
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94 @group |
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95 a = [1, 2; 3, 4]; |
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96 a ([1, 1], :) |
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97 @end group |
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98 @end example |
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99 |
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100 @noindent |
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101 return the original matrix, or the matrix formed by selecting the first |
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102 row twice? Although this conflict is not likely to arise very often in |
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103 practice, you may select the behavior you prefer by setting the built-in |
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104 variable @code{prefer_zero_one_indexing}. |
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105 |
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106 @c XXX FIXME XXX -- this variable no longer exists! |
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107 |
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108 @defvr {Built-in Variable} prefer_zero_one_indexing |
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109 If the value of @code{prefer_zero_one_indexing} is nonzero, Octave |
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110 will perform zero-one style indexing when there is a conflict with the |
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111 normal indexing rules. @xref{Index Expressions}. For example, given a |
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112 matrix |
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113 |
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114 @example |
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115 a = [1, 2, 3, 4] |
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116 @end example |
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117 |
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118 @noindent |
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119 with @code{prefer_zero_one_indexing} is set to nonzero, the |
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120 expression |
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121 |
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122 @example |
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123 a ([1, 1, 1, 1]) |
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124 @end example |
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125 |
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126 @noindent |
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127 results in the matrix @code{[ 1, 2, 3, 4 ]}. If the value of |
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128 @code{prefer_zero_one_indexing} set to 0, the result would be |
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129 the matrix @code{[ 1, 1, 1, 1 ]}. |
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130 |
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131 In the first case, Octave is selecting each element corresponding to a |
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132 @samp{1} in the index vector. In the second, Octave is selecting the |
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133 first element multiple times. |
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134 |
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135 The default value for @code{prefer_zero_one_indexing} is 0. |
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136 @end defvr |
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137 |
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138 Finally, indexing a scalar with a vector of ones can be used to create a |
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139 vector the same size as the index vector, with each element equal to |
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140 the value of the original scalar. For example, the following statements |
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141 |
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142 @example |
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143 @group |
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144 a = 13; |
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145 a ([1, 1, 1, 1]) |
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146 @end group |
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147 @end example |
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148 |
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149 @noindent |
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150 produce a vector whose four elements are all equal to 13. |
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151 |
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152 Similarly, indexing a scalar with two vectors of ones can be used to |
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153 create a matrix. For example the following statements |
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154 |
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155 @example |
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156 @group |
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157 a = 13; |
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158 a ([1, 1], [1, 1, 1]) |
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159 @end group |
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160 @end example |
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161 |
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162 @noindent |
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163 create a 2 by 3 matrix with all elements equal to 13. |
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164 |
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165 This is an obscure notation and should be avoided. It is better to |
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166 use the function @code{ones} to generate a matrix of the appropriate |
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167 size whose elements are all one, and then to scale it to produce the |
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168 desired result. @xref{Special Utility Matrices}. |
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169 |
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170 @DOCSTRING(prefer_column_vectors) |
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171 |
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172 @DOCSTRING(resize_on_range_error) |
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173 |
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174 Note that it is quite inefficient to create a vector using a loop like |
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175 the one shown in the example above. In this particular case, it would |
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176 have been much more efficient to use the expression |
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177 |
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178 @example |
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179 a = sqrt (1:10); |
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180 @end example |
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181 |
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182 @noindent |
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183 thus avoiding the loop entirely. In cases where a loop is still |
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184 required, or a number of values must be combined to form a larger |
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185 matrix, it is generally much faster to set the size of the matrix first, |
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186 and then insert elements using indexing commands. For example, given a |
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187 matrix @code{a}, |
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188 |
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189 @example |
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190 @group |
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191 [nr, nc] = size (a); |
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192 x = zeros (nr, n * nc); |
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193 for i = 1:n |
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194 x(:,(i-1)*nc+1:i*nc) = a; |
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195 endfor |
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196 @end group |
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197 @end example |
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198 |
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199 @noindent |
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200 is considerably faster than |
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201 |
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202 @example |
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203 @group |
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204 x = a; |
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205 for i = 1:n-1 |
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206 x = [x, a]; |
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207 endfor |
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208 @end group |
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209 @end example |
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210 |
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211 @noindent |
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212 particularly for large matrices because Octave does not have to |
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213 repeatedly resize the result. |
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214 |
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215 @node Calling Functions, Arithmetic Ops, Index Expressions, Expressions |
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216 @section Calling Functions |
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217 |
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218 A @dfn{function} is a name for a particular calculation. Because it has |
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219 a name, you can ask for it by name at any point in the program. For |
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220 example, the function @code{sqrt} computes the square root of a number. |
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221 |
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222 A fixed set of functions are @dfn{built-in}, which means they are |
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223 available in every Octave program. The @code{sqrt} function is one of |
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224 these. In addition, you can define your own functions. |
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225 @xref{Functions and Scripts}, for information about how to do this. |
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226 |
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227 @cindex arguments in function call |
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228 The way to use a function is with a @dfn{function call} expression, |
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229 which consists of the function name followed by a list of |
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230 @dfn{arguments} in parentheses. The arguments are expressions which give |
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231 the raw materials for the calculation that the function will do. When |
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232 there is more than one argument, they are separated by commas. If there |
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233 are no arguments, you can omit the parentheses, but it is a good idea to |
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234 include them anyway, to clearly indicate that a function call was |
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235 intended. Here are some examples: |
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236 |
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237 @example |
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238 @group |
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239 sqrt (x^2 + y^2) # @r{One argument} |
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240 ones (n, m) # @r{Two arguments} |
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241 rand () # @r{No arguments} |
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242 @end group |
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243 @end example |
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244 |
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245 Each function expects a particular number of arguments. For example, the |
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246 @code{sqrt} function must be called with a single argument, the number |
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247 to take the square root of: |
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248 |
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249 @example |
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250 sqrt (@var{argument}) |
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251 @end example |
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252 |
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253 Some of the built-in functions take a variable number of arguments, |
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254 depending on the particular usage, and their behavior is different |
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255 depending on the number of arguments supplied. |
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256 |
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257 Like every other expression, the function call has a value, which is |
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258 computed by the function based on the arguments you give it. In this |
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259 example, the value of @code{sqrt (@var{argument})} is the square root of |
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260 the argument. A function can also have side effects, such as assigning |
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261 the values of certain variables or doing input or output operations. |
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262 |
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263 Unlike most languages, functions in Octave may return multiple values. |
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264 For example, the following statement |
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265 |
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266 @example |
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267 [u, s, v] = svd (a) |
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268 @end example |
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269 |
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270 @noindent |
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271 computes the singular value decomposition of the matrix @code{a} and |
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272 assigns the three result matrices to @code{u}, @code{s}, and @code{v}. |
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273 |
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274 The left side of a multiple assignment expression is itself a list of |
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275 expressions, and is allowed to be a list of variable names or index |
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276 expressions. See also @ref{Index Expressions}, and @ref{Assignment Ops}. |
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277 |
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278 @menu |
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279 * Call by Value:: |
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280 * Recursion:: |
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281 @end menu |
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282 |
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283 @node Call by Value, Recursion, Calling Functions, Calling Functions |
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284 @subsection Call by Value |
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285 |
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286 In Octave, unlike Fortran, function arguments are passed by value, which |
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287 means that each argument in a function call is evaluated and assigned to |
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288 a temporary location in memory before being passed to the function. |
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289 There is currently no way to specify that a function parameter should be |
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290 passed by reference instead of by value. This means that it is |
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291 impossible to directly alter the value of function parameter in the |
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292 calling function. It can only change the local copy within the function |
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293 body. For example, the function |
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294 |
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295 @example |
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296 @group |
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297 function f (x, n) |
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298 while (n-- > 0) |
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299 disp (x); |
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300 endwhile |
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301 endfunction |
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302 @end group |
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303 @end example |
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304 |
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305 @noindent |
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306 displays the value of the first argument @var{n} times. In this |
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307 function, the variable @var{n} is used as a temporary variable without |
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308 having to worry that its value might also change in the calling |
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309 function. Call by value is also useful because it is always possible to |
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310 pass constants for any function parameter without first having to |
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311 determine that the function will not attempt to modify the parameter. |
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312 |
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313 The caller may use a variable as the expression for the argument, but |
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314 the called function does not know this: it only knows what value the |
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315 argument had. For example, given a function called as |
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316 |
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317 @example |
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318 @group |
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319 foo = "bar"; |
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320 fcn (foo) |
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321 @end group |
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322 @end example |
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323 |
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324 @noindent |
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325 you should not think of the argument as being ``the variable |
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326 @code{foo}.'' Instead, think of the argument as the string value, |
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327 @code{"bar"}. |
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328 |
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329 Even though Octave uses pass-by-value semantics for function arguments, |
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330 values are not copied unnecessarily. For example, |
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331 |
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332 @example |
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333 @group |
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334 x = rand (1000); |
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335 f (x); |
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336 @end group |
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337 @end example |
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338 |
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339 @noindent |
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340 does not actually force two 1000 by 1000 element matrices to exist |
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341 @emph{unless} the function @code{f} modifies the value of its |
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342 argument. Then Octave must create a copy to avoid changing the |
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343 value outside the scope of the function @code{f}, or attempting (and |
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344 probably failing!) to modify the value of a constant or the value of a |
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345 temporary result. |
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346 |
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347 @node Recursion, , Call by Value, Calling Functions |
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348 @subsection Recursion |
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349 @cindex factorial function |
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350 |
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351 With some restrictions@footnote{Some of Octave's function are |
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352 implemented in terms of functions that cannot be called recursively. |
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353 For example, the ODE solver @code{lsode} is ultimately implemented in a |
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354 Fortran subroutine that cannot be called recursively, so @code{lsode} |
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355 should not be called either directly or indirectly from within the |
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356 user-supplied function that @code{lsode} requires. Doing so will result |
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357 in undefined behavior.}, recursive function calls are allowed. A |
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358 @dfn{recursive function} is one which calls itself, either directly or |
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359 indirectly. For example, here is an inefficient@footnote{It would be |
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360 much better to use @code{prod (1:n)}, or @code{gamma (n+1)} instead, |
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361 after first checking to ensure that the value @code{n} is actually a |
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362 positive integer.} way to compute the factorial of a given integer: |
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363 |
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364 @example |
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365 @group |
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366 function retval = fact (n) |
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367 if (n > 0) |
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368 retval = n * fact (n-1); |
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369 else |
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370 retval = 1; |
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371 endif |
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372 endfunction |
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373 @end group |
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374 @end example |
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375 |
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376 This function is recursive because it calls itself directly. It |
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377 eventually terminates because each time it calls itself, it uses an |
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378 argument that is one less than was used for the previous call. Once the |
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379 argument is no longer greater than zero, it does not call itself, and |
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380 the recursion ends. |
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381 |
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382 The built-in variable @code{max_recursion_depth} specifies a limit to |
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383 the recursion depth and prevents Octave from recursing infinitely. |
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384 |
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385 @DOCSTRING(max_recursion_depth) |
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386 |
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387 @node Arithmetic Ops, Comparison Ops, Calling Functions, Expressions |
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388 @section Arithmetic Operators |
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389 @cindex arithmetic operators |
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390 @cindex operators, arithmetic |
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391 @cindex addition |
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392 @cindex subtraction |
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393 @cindex multiplication |
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394 @cindex matrix multiplication |
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395 @cindex division |
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396 @cindex quotient |
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397 @cindex negation |
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398 @cindex unary minus |
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399 @cindex exponentiation |
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400 @cindex transpose |
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401 @cindex Hermitian operator |
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402 @cindex transpose, complex-conjugate |
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403 @cindex complex-conjugate transpose |
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404 |
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405 The following arithmetic operators are available, and work on scalars |
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406 and matrices. |
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407 |
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408 @table @code |
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409 @item @var{x} + @var{y} |
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410 @opindex + |
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411 Addition. If both operands are matrices, the number of rows and columns |
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412 must both agree. If one operand is a scalar, its value is added to |
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413 all the elements of the other operand. |
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414 |
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415 @item @var{x} .+ @var{y} |
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416 @opindex .+ |
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417 Element by element addition. This operator is equivalent to @code{+}. |
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418 |
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419 @item @var{x} - @var{y} |
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420 @opindex - |
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421 Subtraction. If both operands are matrices, the number of rows and |
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422 columns of both must agree. |
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423 |
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424 @item @var{x} .- @var{y} |
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425 Element by element subtraction. This operator is equivalent to @code{-}. |
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426 |
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427 @item @var{x} * @var{y} |
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428 @opindex * |
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429 Matrix multiplication. The number of columns of @var{x} must agree |
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430 with the number of rows of @var{y}. |
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431 |
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432 @item @var{x} .* @var{y} |
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433 @opindex .* |
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434 Element by element multiplication. If both operands are matrices, the |
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435 number of rows and columns must both agree. |
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436 |
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437 @item @var{x} / @var{y} |
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438 @opindex / |
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439 Right division. This is conceptually equivalent to the expression |
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440 |
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441 @example |
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442 (inverse (y') * x')' |
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443 @end example |
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444 |
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445 @noindent |
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446 but it is computed without forming the inverse of @var{y'}. |
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447 |
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448 If the system is not square, or if the coefficient matrix is singular, |
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449 a minimum norm solution is computed. |
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450 |
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451 @item @var{x} ./ @var{y} |
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452 @opindex ./ |
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453 Element by element right division. |
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454 |
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455 @item @var{x} \ @var{y} |
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456 @opindex \ |
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457 Left division. This is conceptually equivalent to the expression |
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458 |
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459 @example |
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460 inverse (x) * y |
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461 @end example |
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462 |
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463 @noindent |
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464 but it is computed without forming the inverse of @var{x}. |
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465 |
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466 If the system is not square, or if the coefficient matrix is singular, |
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467 a minimum norm solution is computed. |
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468 |
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469 @item @var{x} .\ @var{y} |
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470 @opindex .\ |
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471 Element by element left division. Each element of @var{y} is divided |
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472 by each corresponding element of @var{x}. |
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473 |
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474 @item @var{x} ^ @var{y} |
|
|
475 @itemx @var{x} ** @var{y} |
|
|
476 @opindex ** |
|
|
477 @opindex ^ |
|
|
478 Power operator. If @var{x} and @var{y} are both scalars, this operator |
|
|
479 returns @var{x} raised to the power @var{y}. If @var{x} is a scalar and |
|
|
480 @var{y} is a square matrix, the result is computed using an eigenvalue |
|
|
481 expansion. If @var{x} is a square matrix. the result is computed by |
|
|
482 repeated multiplication if @var{y} is an integer, and by an eigenvalue |
|
|
483 expansion if @var{y} is not an integer. An error results if both |
|
|
484 @var{x} and @var{y} are matrices. |
|
|
485 |
|
|
486 The implementation of this operator needs to be improved. |
|
|
487 |
|
|
488 @item @var{x} .^ @var{y} |
|
|
489 @item @var{x} .** @var{y} |
|
|
490 @opindex .** |
|
|
491 @opindex .^ |
|
|
492 Element by element power operator. If both operands are matrices, the |
|
|
493 number of rows and columns must both agree. |
|
|
494 |
|
|
495 @item -@var{x} |
|
|
496 @opindex - |
|
|
497 Negation. |
|
|
498 |
|
|
499 @item +@var{x} |
|
|
500 @opindex + |
|
|
501 Unary plus. This operator has no effect on the operand. |
|
|
502 |
|
|
503 @item @var{x}' |
|
|
504 @opindex ' |
|
|
505 Complex conjugate transpose. For real arguments, this operator is the |
|
|
506 same as the transpose operator. For complex arguments, this operator is |
|
|
507 equivalent to the expression |
|
|
508 |
|
|
509 @example |
|
|
510 conj (x.') |
|
|
511 @end example |
|
|
512 |
|
|
513 @item @var{x}.' |
|
|
514 @opindex .' |
|
|
515 Transpose. |
|
|
516 @end table |
|
|
517 |
|
|
518 Note that because Octave's element by element operators begin with a |
|
|
519 @samp{.}, there is a possible ambiguity for statements like |
|
|
520 |
|
|
521 @example |
|
|
522 1./m |
|
|
523 @end example |
|
|
524 |
|
|
525 @noindent |
|
|
526 because the period could be interpreted either as part of the constant |
|
|
527 or as part of the operator. To resolve this conflict, Octave treats the |
|
|
528 expression as if you had typed |
|
|
529 |
|
|
530 @example |
|
|
531 (1) ./ m |
|
|
532 @end example |
|
|
533 |
|
|
534 @noindent |
|
|
535 and not |
|
|
536 |
|
|
537 @example |
|
|
538 (1.) / m |
|
|
539 @end example |
|
|
540 |
|
|
541 @noindent |
|
|
542 Although this is inconsistent with the normal behavior of Octave's |
|
|
543 lexer, which usually prefers to break the input into tokens by |
|
|
544 preferring the longest possible match at any given point, it is more |
|
|
545 useful in this case. |
|
|
546 |
|
3371
|
547 @DOCSTRING(warn_divide_by_zero) |
|
3294
|
548 |
|
|
549 @node Comparison Ops, Boolean Expressions, Arithmetic Ops, Expressions |
|
|
550 @section Comparison Operators |
|
|
551 @cindex comparison expressions |
|
|
552 @cindex expressions, comparison |
|
|
553 @cindex relational operators |
|
|
554 @cindex operators, relational |
|
|
555 @cindex less than operator |
|
|
556 @cindex greater than operator |
|
|
557 @cindex equality operator |
|
|
558 @cindex tests for equality |
|
|
559 @cindex equality, tests for |
|
|
560 |
|
|
561 @dfn{Comparison operators} compare numeric values for relationships |
|
|
562 such as equality. They are written using |
|
|
563 @emph{relational operators}. |
|
|
564 |
|
|
565 All of Octave's comparison operators return a value of 1 if the |
|
|
566 comparison is true, or 0 if it is false. For matrix values, they all |
|
|
567 work on an element-by-element basis. For example, |
|
|
568 |
|
|
569 @example |
|
|
570 @group |
|
|
571 [1, 2; 3, 4] == [1, 3; 2, 4] |
|
|
572 @result{} 1 0 |
|
|
573 0 1 |
|
|
574 @end group |
|
|
575 @end example |
|
|
576 |
|
|
577 If one operand is a scalar and the other is a matrix, the scalar is |
|
|
578 compared to each element of the matrix in turn, and the result is the |
|
|
579 same size as the matrix. |
|
|
580 |
|
|
581 @table @code |
|
|
582 @item @var{x} < @var{y} |
|
|
583 @opindex < |
|
|
584 True if @var{x} is less than @var{y}. |
|
|
585 |
|
|
586 @item @var{x} <= @var{y} |
|
|
587 @opindex <= |
|
|
588 True if @var{x} is less than or equal to @var{y}. |
|
|
589 |
|
|
590 @item @var{x} == @var{y} |
|
|
591 @opindex == |
|
|
592 True if @var{x} is equal to @var{y}. |
|
|
593 |
|
|
594 @item @var{x} >= @var{y} |
|
|
595 @opindex >= |
|
|
596 True if @var{x} is greater than or equal to @var{y}. |
|
|
597 |
|
|
598 @item @var{x} > @var{y} |
|
|
599 @opindex > |
|
|
600 True if @var{x} is greater than @var{y}. |
|
|
601 |
|
|
602 @item @var{x} != @var{y} |
|
|
603 @itemx @var{x} ~= @var{y} |
|
|
604 @itemx @var{x} <> @var{y} |
|
|
605 @opindex != |
|
|
606 @opindex ~= |
|
|
607 @opindex <> |
|
|
608 True if @var{x} is not equal to @var{y}. |
|
|
609 @end table |
|
|
610 |
|
|
611 String comparisons may also be performed with the @code{strcmp} |
|
|
612 function, not with the comparison operators listed above. |
|
|
613 @xref{Strings}. |
|
|
614 |
|
|
615 @node Boolean Expressions, Assignment Ops, Comparison Ops, Expressions |
|
|
616 @section Boolean Expressions |
|
|
617 @cindex expressions, boolean |
|
|
618 @cindex boolean expressions |
|
|
619 @cindex expressions, logical |
|
|
620 @cindex logical expressions |
|
|
621 @cindex operators, boolean |
|
|
622 @cindex boolean operators |
|
|
623 @cindex logical operators |
|
|
624 @cindex operators, logical |
|
|
625 @cindex and operator |
|
|
626 @cindex or operator |
|
|
627 @cindex not operator |
|
|
628 |
|
|
629 @menu |
|
|
630 * Element-by-element Boolean Operators:: |
|
|
631 * Short-circuit Boolean Operators:: |
|
|
632 @end menu |
|
|
633 |
|
|
634 @node Element-by-element Boolean Operators, Short-circuit Boolean Operators, Boolean Expressions, Boolean Expressions |
|
|
635 @subsection Element-by-element Boolean Operators |
|
|
636 @cindex element-by-element evaluation |
|
|
637 |
|
|
638 An @dfn{element-by-element boolean expression} is a combination of |
|
|
639 comparison expressions using the boolean |
|
|
640 operators ``or'' (@samp{|}), ``and'' (@samp{&}), and ``not'' (@samp{!}), |
|
|
641 along with parentheses to control nesting. The truth of the boolean |
|
|
642 expression is computed by combining the truth values of the |
|
|
643 corresponding elements of the component expressions. A value is |
|
|
644 considered to be false if it is zero, and true otherwise. |
|
|
645 |
|
|
646 Element-by-element boolean expressions can be used wherever comparison |
|
|
647 expressions can be used. They can be used in @code{if} and @code{while} |
|
|
648 statements. However, if a matrix value used as the condition in an |
|
|
649 @code{if} or @code{while} statement is only true if @emph{all} of its |
|
|
650 elements are nonzero. |
|
|
651 |
|
|
652 Like comparison operations, each element of an element-by-element |
|
|
653 boolean expression also has a numeric value (1 if true, 0 if false) that |
|
|
654 comes into play if the result of the boolean expression is stored in a |
|
|
655 variable, or used in arithmetic. |
|
|
656 |
|
|
657 Here are descriptions of the three element-by-element boolean operators. |
|
|
658 |
|
|
659 @table @code |
|
|
660 @item @var{boolean1} & @var{boolean2} |
|
|
661 @opindex & |
|
|
662 Elements of the result are true if both corresponding elements of |
|
|
663 @var{boolean1} and @var{boolean2} are true. |
|
|
664 |
|
|
665 @item @var{boolean1} | @var{boolean2} |
|
|
666 @opindex | |
|
|
667 Elements of the result are true if either of the corresponding elements |
|
|
668 of @var{boolean1} or @var{boolean2} is true. |
|
|
669 |
|
|
670 @item ! @var{boolean} |
|
|
671 @itemx ~ @var{boolean} |
|
|
672 @opindex ~ |
|
|
673 @opindex ! |
|
|
674 Each element of the result is true if the corresponding element of |
|
|
675 @var{boolean} is false. |
|
|
676 @end table |
|
|
677 |
|
|
678 For matrix operands, these operators work on an element-by-element |
|
|
679 basis. For example, the expression |
|
|
680 |
|
|
681 @example |
|
|
682 [1, 0; 0, 1] & [1, 0; 2, 3] |
|
|
683 @end example |
|
|
684 |
|
|
685 @noindent |
|
|
686 returns a two by two identity matrix. |
|
|
687 |
|
|
688 For the binary operators, the dimensions of the operands must conform if |
|
|
689 both are matrices. If one of the operands is a scalar and the other a |
|
|
690 matrix, the operator is applied to the scalar and each element of the |
|
|
691 matrix. |
|
|
692 |
|
|
693 For the binary element-by-element boolean operators, both subexpressions |
|
|
694 @var{boolean1} and @var{boolean2} are evaluated before computing the |
|
|
695 result. This can make a difference when the expressions have side |
|
|
696 effects. For example, in the expression |
|
|
697 |
|
|
698 @example |
|
|
699 a & b++ |
|
|
700 @end example |
|
|
701 |
|
|
702 @noindent |
|
|
703 the value of the variable @var{b} is incremented even if the variable |
|
|
704 @var{a} is zero. |
|
|
705 |
|
|
706 This behavior is necessary for the boolean operators to work as |
|
|
707 described for matrix-valued operands. |
|
|
708 |
|
|
709 @node Short-circuit Boolean Operators, , Element-by-element Boolean Operators, Boolean Expressions |
|
|
710 @subsection Short-circuit Boolean Operators |
|
|
711 @cindex short-circuit evaluation |
|
|
712 |
|
|
713 Combined with the implicit conversion to scalar values in @code{if} and |
|
|
714 @code{while} conditions, Octave's element-by-element boolean operators |
|
|
715 are often sufficient for performing most logical operations. However, |
|
|
716 it is sometimes desirable to stop evaluating a boolean expression as |
|
|
717 soon as the overall truth value can be determined. Octave's |
|
|
718 @dfn{short-circuit} boolean operators work this way. |
|
|
719 |
|
|
720 @table @code |
|
|
721 @item @var{boolean1} && @var{boolean2} |
|
|
722 @opindex && |
|
|
723 The expression @var{boolean1} is evaluated and converted to a scalar |
|
|
724 using the equivalent of the operation @code{all (all (@var{boolean1}))}. |
|
|
725 If it is false, the result of the overall expression is 0. If it is |
|
|
726 true, the expression @var{boolean2} is evaluated and converted to a |
|
|
727 scalar using the equivalent of the operation @code{all (all |
|
|
728 (@var{boolean1}))}. If it is true, the result of the overall expression |
|
|
729 is 1. Otherwise, the result of the overall expression is 0. |
|
|
730 |
|
|
731 @item @var{boolean1} || @var{boolean2} |
|
|
732 @opindex || |
|
|
733 The expression @var{boolean1} is evaluated and converted to a scalar |
|
|
734 using the equivalent of the operation @code{all (all (@var{boolean1}))}. |
|
|
735 If it is true, the result of the overall expression is 1. If it is |
|
|
736 false, the expression @var{boolean2} is evaluated and converted to a |
|
|
737 scalar using the equivalent of the operation @code{all (all |
|
|
738 (@var{boolean1}))}. If it is true, the result of the overall expression |
|
|
739 is 1. Otherwise, the result of the overall expression is 0. |
|
|
740 @end table |
|
|
741 |
|
|
742 The fact that both operands may not be evaluated before determining the |
|
|
743 overall truth value of the expression can be important. For example, in |
|
|
744 the expression |
|
|
745 |
|
|
746 @example |
|
|
747 a && b++ |
|
|
748 @end example |
|
|
749 |
|
|
750 @noindent |
|
|
751 the value of the variable @var{b} is only incremented if the variable |
|
|
752 @var{a} is nonzero. |
|
|
753 |
|
|
754 This can be used to write somewhat more concise code. For example, it |
|
|
755 is possible write |
|
|
756 |
|
|
757 @example |
|
|
758 @group |
|
|
759 function f (a, b, c) |
|
|
760 if (nargin > 2 && isstr (c)) |
|
|
761 @dots{} |
|
|
762 @end group |
|
|
763 @end example |
|
|
764 |
|
|
765 @noindent |
|
|
766 instead of having to use two @code{if} statements to avoid attempting to |
|
|
767 evaluate an argument that doesn't exist. For example, without the |
|
|
768 short-circuit feature, it would be necessary to write |
|
|
769 |
|
|
770 @example |
|
|
771 @group |
|
|
772 function f (a, b, c) |
|
|
773 if (nargin > 2) |
|
|
774 if (isstr (c)) |
|
|
775 @dots{} |
|
|
776 @end group |
|
|
777 @end example |
|
|
778 |
|
|
779 Writing |
|
|
780 |
|
|
781 @example |
|
|
782 @group |
|
|
783 function f (a, b, c) |
|
|
784 if (nargin > 2 & isstr (c)) |
|
|
785 @dots{} |
|
|
786 @end group |
|
|
787 @end example |
|
|
788 |
|
|
789 @noindent |
|
|
790 would result in an error if @code{f} were called with one or two |
|
|
791 arguments because Octave would be forced to try to evaluate both of the |
|
|
792 operands for the operator @samp{&}. |
|
|
793 |
|
|
794 @node Assignment Ops, Increment Ops, Boolean Expressions, Expressions |
|
|
795 @section Assignment Expressions |
|
|
796 @cindex assignment expressions |
|
|
797 @cindex assignment operators |
|
|
798 @cindex operators, assignment |
|
|
799 @cindex expressions, assignment |
|
|
800 |
|
|
801 @opindex = |
|
|
802 |
|
|
803 An @dfn{assignment} is an expression that stores a new value into a |
|
|
804 variable. For example, the following expression assigns the value 1 to |
|
|
805 the variable @code{z}: |
|
|
806 |
|
|
807 @example |
|
|
808 z = 1 |
|
|
809 @end example |
|
|
810 |
|
|
811 After this expression is executed, the variable @code{z} has the value 1. |
|
|
812 Whatever old value @code{z} had before the assignment is forgotten. |
|
|
813 The @samp{=} sign is called an @dfn{assignment operator}. |
|
|
814 |
|
|
815 Assignments can store string values also. For example, the following |
|
|
816 expression would store the value @code{"this food is good"} in the |
|
|
817 variable @code{message}: |
|
|
818 |
|
|
819 @example |
|
|
820 @group |
|
|
821 thing = "food" |
|
|
822 predicate = "good" |
|
|
823 message = [ "this " , thing , " is " , predicate ] |
|
|
824 @end group |
|
|
825 @end example |
|
|
826 |
|
|
827 @noindent |
|
|
828 (This also illustrates concatenation of strings.) |
|
|
829 |
|
|
830 @cindex side effect |
|
|
831 Most operators (addition, concatenation, and so on) have no effect |
|
|
832 except to compute a value. If you ignore the value, you might as well |
|
|
833 not use the operator. An assignment operator is different. It does |
|
|
834 produce a value, but even if you ignore the value, the assignment still |
|
|
835 makes itself felt through the alteration of the variable. We call this |
|
|
836 a @dfn{side effect}. |
|
|
837 |
|
|
838 @cindex lvalue |
|
|
839 The left-hand operand of an assignment need not be a variable |
|
|
840 (@pxref{Variables}). It can also be an element of a matrix |
|
|
841 (@pxref{Index Expressions}) or a list of return values |
|
|
842 (@pxref{Calling Functions}). These are all called @dfn{lvalues}, which |
|
|
843 means they can appear on the left-hand side of an assignment operator. |
|
|
844 The right-hand operand may be any expression. It produces the new value |
|
|
845 which the assignment stores in the specified variable, matrix element, |
|
|
846 or list of return values. |
|
|
847 |
|
|
848 It is important to note that variables do @emph{not} have permanent types. |
|
|
849 The type of a variable is simply the type of whatever value it happens |
|
|
850 to hold at the moment. In the following program fragment, the variable |
|
|
851 @code{foo} has a numeric value at first, and a string value later on: |
|
|
852 |
|
|
853 @example |
|
|
854 @group |
|
|
855 octave:13> foo = 1 |
|
|
856 foo = 1 |
|
|
857 octave:13> foo = "bar" |
|
|
858 foo = bar |
|
|
859 @end group |
|
|
860 @end example |
|
|
861 |
|
|
862 @noindent |
|
|
863 When the second assignment gives @code{foo} a string value, the fact that |
|
|
864 it previously had a numeric value is forgotten. |
|
|
865 |
|
|
866 Assignment of a scalar to an indexed matrix sets all of the elements |
|
|
867 that are referenced by the indices to the scalar value. For example, if |
|
|
868 @code{a} is a matrix with at least two columns, |
|
|
869 |
|
|
870 @example |
|
|
871 @group |
|
|
872 a(:, 2) = 5 |
|
|
873 @end group |
|
|
874 @end example |
|
|
875 |
|
|
876 @noindent |
|
|
877 sets all the elements in the second column of @code{a} to 5. |
|
|
878 |
|
|
879 Assigning an empty matrix @samp{[]} works in most cases to allow you to |
|
|
880 delete rows or columns of matrices and vectors. @xref{Empty Matrices}. |
|
|
881 For example, given a 4 by 5 matrix @var{A}, the assignment |
|
|
882 |
|
|
883 @example |
|
|
884 A (3, :) = [] |
|
|
885 @end example |
|
|
886 |
|
|
887 @noindent |
|
|
888 deletes the third row of @var{A}, and the assignment |
|
|
889 |
|
|
890 @example |
|
|
891 A (:, 1:2:5) = [] |
|
|
892 @end example |
|
|
893 |
|
|
894 @noindent |
|
|
895 deletes the first, third, and fifth columns. |
|
|
896 |
|
|
897 An assignment is an expression, so it has a value. Thus, @code{z = 1} |
|
|
898 as an expression has the value 1. One consequence of this is that you |
|
|
899 can write multiple assignments together: |
|
|
900 |
|
|
901 @example |
|
|
902 x = y = z = 0 |
|
|
903 @end example |
|
|
904 |
|
|
905 @noindent |
|
|
906 stores the value 0 in all three variables. It does this because the |
|
|
907 value of @code{z = 0}, which is 0, is stored into @code{y}, and then |
|
|
908 the value of @code{y = z = 0}, which is 0, is stored into @code{x}. |
|
|
909 |
|
|
910 This is also true of assignments to lists of values, so the following is |
|
|
911 a valid expression |
|
|
912 |
|
|
913 @example |
|
|
914 [a, b, c] = [u, s, v] = svd (a) |
|
|
915 @end example |
|
|
916 |
|
|
917 @noindent |
|
|
918 that is exactly equivalent to |
|
|
919 |
|
|
920 @example |
|
|
921 @group |
|
|
922 [u, s, v] = svd (a) |
|
|
923 a = u |
|
|
924 b = s |
|
|
925 c = v |
|
|
926 @end group |
|
|
927 @end example |
|
|
928 |
|
|
929 In expressions like this, the number of values in each part of the |
|
|
930 expression need not match. For example, the expression |
|
|
931 |
|
|
932 @example |
|
|
933 [a, b, c, d] = [u, s, v] = svd (a) |
|
|
934 @end example |
|
|
935 |
|
|
936 @noindent |
|
|
937 is equivalent to the expression above, except that the value of the |
|
|
938 variable @samp{d} is left unchanged, and the expression |
|
|
939 |
|
|
940 @example |
|
|
941 [a, b] = [u, s, v] = svd (a) |
|
|
942 @end example |
|
|
943 |
|
|
944 @noindent |
|
|
945 is equivalent to |
|
|
946 |
|
|
947 @example |
|
|
948 @group |
|
|
949 [u, s, v] = svd (a) |
|
|
950 a = u |
|
|
951 b = s |
|
|
952 @end group |
|
|
953 @end example |
|
|
954 |
|
|
955 You can use an assignment anywhere an expression is called for. For |
|
|
956 example, it is valid to write @code{x != (y = 1)} to set @code{y} to 1 |
|
|
957 and then test whether @code{x} equals 1. But this style tends to make |
|
|
958 programs hard to read. Except in a one-shot program, you should rewrite |
|
|
959 it to get rid of such nesting of assignments. This is never very hard. |
|
|
960 |
|
3428
|
961 @DOCSTRING(print_rhs_assign_val) |
|
|
962 |
|
3294
|
963 @cindex increment operator |
|
|
964 @cindex decrement operator |
|
|
965 @cindex operators, increment |
|
|
966 @cindex operators, decrement |
|
|
967 |
|
|
968 @node Increment Ops, Operator Precedence, Assignment Ops, Expressions |
|
|
969 @section Increment Operators |
|
|
970 |
|
|
971 @emph{Increment operators} increase or decrease the value of a variable |
|
|
972 by 1. The operator to increment a variable is written as @samp{++}. It |
|
|
973 may be used to increment a variable either before or after taking its |
|
|
974 value. |
|
|
975 |
|
|
976 For example, to pre-increment the variable @var{x}, you would write |
|
|
977 @code{++@var{x}}. This would add one to @var{x} and then return the new |
|
|
978 value of @var{x} as the result of the expression. It is exactly the |
|
|
979 same as the expression @code{@var{x} = @var{x} + 1}. |
|
|
980 |
|
|
981 To post-increment a variable @var{x}, you would write @code{@var{x}++}. |
|
|
982 This adds one to the variable @var{x}, but returns the value that |
|
|
983 @var{x} had prior to incrementing it. For example, if @var{x} is equal |
|
|
984 to 2, the result of the expression @code{@var{x}++} is 2, and the new |
|
|
985 value of @var{x} is 3. |
|
|
986 |
|
|
987 For matrix and vector arguments, the increment and decrement operators |
|
|
988 work on each element of the operand. |
|
|
989 |
|
|
990 Here is a list of all the increment and decrement expressions. |
|
|
991 |
|
|
992 @table @code |
|
|
993 @item ++@var{x} |
|
|
994 @opindex ++ |
|
|
995 This expression increments the variable @var{x}. The value of the |
|
|
996 expression is the @emph{new} value of @var{x}. It is equivalent to the |
|
|
997 expression @code{@var{x} = @var{x} + 1}. |
|
|
998 |
|
|
999 @item --@var{x} |
|
|
1000 @opindex @code{--} |
|
|
1001 This expression decrements the variable @var{x}. The value of the |
|
|
1002 expression is the @emph{new} value of @var{x}. It is equivalent to the |
|
|
1003 expression @code{@var{x} = @var{x} - 1}. |
|
|
1004 |
|
|
1005 @item @var{x}++ |
|
|
1006 @opindex ++ |
|
|
1007 This expression causes the variable @var{x} to be incremented. The |
|
|
1008 value of the expression is the @emph{old} value of @var{x}. |
|
|
1009 |
|
|
1010 @item @var{x}-- |
|
|
1011 @opindex @code{--} |
|
|
1012 This expression causes the variable @var{x} to be decremented. The |
|
|
1013 value of the expression is the @emph{old} value of @var{x}. |
|
|
1014 @end table |
|
|
1015 |
|
|
1016 It is not currently possible to increment index expressions. For |
|
|
1017 example, you might expect that the expression @code{@var{v}(4)++} would |
|
|
1018 increment the fourth element of the vector @var{v}, but instead it |
|
|
1019 results in a parse error. This problem may be fixed in a future |
|
|
1020 release of Octave. |
|
|
1021 |
|
|
1022 @node Operator Precedence, , Increment Ops, Expressions |
|
|
1023 @section Operator Precedence |
|
|
1024 @cindex operator precedence |
|
|
1025 |
|
|
1026 @dfn{Operator precedence} determines how operators are grouped, when |
|
|
1027 different operators appear close by in one expression. For example, |
|
|
1028 @samp{*} has higher precedence than @samp{+}. Thus, the expression |
|
|
1029 @code{a + b * c} means to multiply @code{b} and @code{c}, and then add |
|
|
1030 @code{a} to the product (i.e., @code{a + (b * c)}). |
|
|
1031 |
|
|
1032 You can overrule the precedence of the operators by using parentheses. |
|
|
1033 You can think of the precedence rules as saying where the parentheses |
|
|
1034 are assumed if you do not write parentheses yourself. In fact, it is |
|
|
1035 wise to use parentheses whenever you have an unusual combination of |
|
|
1036 operators, because other people who read the program may not remember |
|
|
1037 what the precedence is in this case. You might forget as well, and then |
|
|
1038 you too could make a mistake. Explicit parentheses will help prevent |
|
|
1039 any such mistake. |
|
|
1040 |
|
|
1041 When operators of equal precedence are used together, the leftmost |
|
|
1042 operator groups first, except for the assignment and exponentiation |
|
|
1043 operators, which group in the opposite order. Thus, the expression |
|
|
1044 @code{a - b + c} groups as @code{(a - b) + c}, but the expression |
|
|
1045 @code{a = b = c} groups as @code{a = (b = c)}. |
|
|
1046 |
|
|
1047 The precedence of prefix unary operators is important when another |
|
|
1048 operator follows the operand. For example, @code{-x^2} means |
|
|
1049 @code{-(x^2)}, because @samp{-} has lower precedence than @samp{^}. |
|
|
1050 |
|
|
1051 Here is a table of the operators in Octave, in order of increasing |
|
|
1052 precedence. |
|
|
1053 |
|
|
1054 @table @code |
|
|
1055 @item statement separators |
|
|
1056 @samp{;}, @samp{,}. |
|
|
1057 |
|
|
1058 @item assignment |
|
|
1059 @samp{=}. This operator groups right to left. |
|
|
1060 |
|
|
1061 @item logical "or" and "and" |
|
|
1062 @samp{||}, @samp{&&}. |
|
|
1063 |
|
|
1064 @item element-wise "or" and "and" |
|
|
1065 @samp{|}, @samp{&}. |
|
|
1066 |
|
|
1067 @item relational |
|
|
1068 @samp{<}, @samp{<=}, @samp{==}, @samp{>=}, @samp{>}, @samp{!=}, |
|
|
1069 @samp{~=}, @samp{<>}. |
|
|
1070 |
|
|
1071 @item colon |
|
|
1072 @samp{:}. |
|
|
1073 |
|
|
1074 @item add, subtract |
|
|
1075 @samp{+}, @samp{-}. |
|
|
1076 |
|
|
1077 @item multiply, divide |
|
|
1078 @samp{*}, @samp{/}, @samp{\}, @samp{.\}, @samp{.*}, @samp{./}. |
|
|
1079 |
|
|
1080 @item transpose |
|
|
1081 @samp{'}, @samp{.'} |
|
|
1082 |
|
|
1083 @item unary plus, minus, increment, decrement, and ``not'' |
|
|
1084 @samp{+}, @samp{-}, @samp{++}, @samp{--}, @samp{!}, @samp{~}. |
|
|
1085 |
|
|
1086 @item exponentiation |
|
|
1087 @samp{^}, @samp{**}, @samp{.^}, @samp{.**}. |
|
|
1088 @end table |
