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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 Matrix Manipulation |
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6 @chapter Matrix Manipulation |
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7 |
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8 There are a number of functions available for checking to see if the |
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9 elements of a matrix meet some condition, and for rearranging the |
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10 elements of a matrix. For example, Octave can easily tell you if all |
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11 the elements of a matrix are finite, or are less than some specified |
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12 value. Octave can also rotate the elements, extract the upper- or |
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13 lower-triangular parts, or sort the columns of a matrix. |
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14 |
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15 @menu |
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16 * Finding Elements and Checking Conditions:: |
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17 * Rearranging Matrices:: |
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18 * Special Utility Matrices:: |
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19 * Famous Matrices:: |
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20 @end menu |
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21 |
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22 @node Finding Elements and Checking Conditions |
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23 @section Finding Elements and Checking Conditions |
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24 |
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25 The functions @code{any} and @code{all} are useful for determining |
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26 whether any or all of the elements of a matrix satisfy some condition. |
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27 The @code{find} function is also useful in determining which elements of |
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28 a matrix meet a specified condition. |
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29 |
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30 @DOCSTRING(any) |
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31 |
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32 @DOCSTRING(all) |
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33 |
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34 Since the comparison operators (@pxref{Comparison Ops}) return matrices |
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35 of ones and zeros, it is easy to test a matrix for many things, not just |
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36 whether the elements are nonzero. For example, |
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37 |
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38 @example |
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39 @group |
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40 all (all (rand (5) < 0.9)) |
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41 @result{} 0 |
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42 @end group |
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43 @end example |
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44 |
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45 @noindent |
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46 tests a random 5 by 5 matrix to see if all of its elements are less |
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47 than 0.9. |
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48 |
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49 Note that in conditional contexts (like the test clause of @code{if} and |
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50 @code{while} statements) Octave treats the test as if you had typed |
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51 @code{all (all (condition))}. |
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52 |
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53 @DOCSTRING(xor) |
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54 |
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55 @DOCSTRING(is_duplicate_entry) |
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56 |
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57 @DOCSTRING(diff) |
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58 |
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59 @DOCSTRING(isinf) |
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60 |
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61 @DOCSTRING(isnan) |
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62 |
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63 @DOCSTRING(finite) |
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64 |
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65 @DOCSTRING(find) |
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66 |
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67 @DOCSTRING(common_size) |
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68 |
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69 @node Rearranging Matrices |
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70 @section Rearranging Matrices |
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71 |
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72 @DOCSTRING(fliplr) |
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73 |
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74 @DOCSTRING(flipud) |
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75 |
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76 @DOCSTRING(flipdim) |
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77 |
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78 @DOCSTRING(rot90) |
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79 |
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80 @DOCSTRING(rotdim) |
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81 |
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82 @DOCSTRING(cat) |
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83 |
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84 @DOCSTRING(horzcat) |
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85 |
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86 @DOCSTRING(vertcat) |
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87 |
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88 @DOCSTRING(permute) |
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89 |
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90 @DOCSTRING(ipermute) |
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91 |
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92 @DOCSTRING(reshape) |
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93 |
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94 @DOCSTRING(circshift) |
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95 |
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96 @DOCSTRING(shiftdim) |
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97 |
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98 @DOCSTRING(shift) |
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99 |
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100 @DOCSTRING(sort) |
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101 |
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102 Since the @code{sort} function does not allow sort keys to be specified, |
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103 it can't be used to order the rows of a matrix according to the values |
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104 of the elements in various columns@footnote{For example, to first sort |
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105 based on the values in column 1, and then, for any values that are |
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106 repeated in column 1, sort based on the values found in column 2, etc.} |
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107 in a single call. Using the second output, however, it is possible to |
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108 sort all rows based on the values in a given column. Here's an example |
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109 that sorts the rows of a matrix based on the values in the second |
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110 column. |
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111 |
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112 @example |
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113 @group |
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114 a = [1, 2; 2, 3; 3, 1]; |
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115 [s, i] = sort (a (:, 2)); |
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116 a (i, :) |
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117 @result{} 3 1 |
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118 1 2 |
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119 2 3 |
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120 @end group |
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121 @end example |
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122 |
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123 @DOCSTRING(tril) |
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124 |
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125 @DOCSTRING(vec) |
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126 |
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127 @DOCSTRING(vech) |
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128 |
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129 @DOCSTRING(prepad) |
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130 |
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131 @node Special Utility Matrices |
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132 @section Special Utility Matrices |
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133 |
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134 @DOCSTRING(eye) |
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135 |
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136 @DOCSTRING(ones) |
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137 |
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138 @DOCSTRING(zeros) |
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139 |
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140 @DOCSTRING(repmat) |
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141 |
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142 @DOCSTRING(rand) |
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143 |
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144 @DOCSTRING(randn) |
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145 |
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146 @DOCSTRING(rande) |
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147 |
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148 @DOCSTRING(randp) |
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149 |
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150 @DOCSTRING(randg) |
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151 |
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152 The new random generators all use a common Mersenne Twister generator, |
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153 and so the state of only one of the generators needs to be reset. |
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154 The old generator function use separate generators. This ensures that |
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155 |
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156 @example |
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157 @group |
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158 rand ("seed", 13); |
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159 randn ("seed", 13); |
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160 u = rand (100, 1); |
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161 n = randn (100, 1); |
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162 @end group |
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163 @end example |
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164 |
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165 @noindent |
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166 and |
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167 |
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168 @example |
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169 @group |
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170 rand ("seed", 13); |
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171 randn ("seed", 13); |
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172 u = zeros (100, 1); |
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173 n = zeros (100, 1); |
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174 for i = 1:100 |
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175 u(i) = rand (); |
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176 n(i) = randn (); |
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177 end |
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178 @end group |
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179 @end example |
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180 |
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181 @noindent |
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182 produce equivalent results. |
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183 |
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184 Normally, @code{rand} and @code{randn} obtain their initial |
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185 seeds from the system clock, so that the sequence of random numbers is |
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186 not the same each time you run Octave. If you really do need for to |
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187 reproduce a sequence of numbers exactly, you can set the seed to a |
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188 specific value. |
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189 |
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190 If it is invoked without arguments, @code{rand} and @code{randn} return a |
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191 single element of a random sequence. |
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192 |
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193 The @code{rand} and @code{randn} functions use Fortran code from |
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194 @sc{Ranlib}, a library of fortran routines for random number generation, |
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195 compiled by Barry W. Brown and James Lovato of the Department of |
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196 Biomathematics at The University of Texas, M.D. Anderson Cancer Center, |
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197 Houston, TX 77030. |
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198 |
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199 @DOCSTRING(randperm) |
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200 |
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201 @DOCSTRING(diag) |
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202 |
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203 The functions @code{linspace} and @code{logspace} make it very easy to |
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204 create vectors with evenly or logarithmically spaced elements. |
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205 @xref{Ranges}. |
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206 |
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207 @DOCSTRING(linspace) |
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208 |
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209 @DOCSTRING(logspace) |
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210 |
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211 @node Famous Matrices |
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212 @section Famous Matrices |
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213 |
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214 The following functions return famous matrix forms. |
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215 |
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216 @DOCSTRING(hadamard) |
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217 |
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218 @DOCSTRING(hankel) |
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219 |
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220 @DOCSTRING(hilb) |
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221 |
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222 @DOCSTRING(invhilb) |
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223 |
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224 @DOCSTRING(magic) |
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225 |
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226 @DOCSTRING(pascal) |
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227 |
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228 @DOCSTRING(rosser) |
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229 |
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230 @DOCSTRING(sylvester_matrix) |
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231 |
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232 @DOCSTRING(toeplitz) |
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233 |
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234 @DOCSTRING(vander) |
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235 |
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236 @DOCSTRING(wilkinson) |
