annotate scripts/help/slash.m @ 31191:bb9d776eafac stable

Fix wrong color in PDF printout of some latex strings (bug #62884) * octave-svgconvert (draw): For "rect" elements only set brush color if necessary and eventually restore to previous color.
author Pantxo Diribarne <pantxo.diribarne@gmail.com>
date Sun, 14 Aug 2022 18:24:07 +0200
parents 796f54d4ddbf
children 597f3ee61a48
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
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1 ########################################################################
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2 ##
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3 ## Copyright (C) 2017-2022 The Octave Project Developers
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4 ##
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5 ## See the file COPYRIGHT.md in the top-level directory of this
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6 ## distribution or <https://octave.org/copyright/>.
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7 ##
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8 ## This file is part of Octave.
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9 ##
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10 ## Octave is free software: you can redistribute it and/or modify it
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11 ## under the terms of the GNU General Public License as published by
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12 ## the Free Software Foundation, either version 3 of the License, or
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13 ## (at your option) any later version.
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14 ##
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15 ## Octave is distributed in the hope that it will be useful, but
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16 ## WITHOUT ANY WARRANTY; without even the implied warranty of
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17 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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18 ## GNU General Public License for more details.
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19 ##
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20 ## You should have received a copy of the GNU General Public License
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21 ## along with Octave; see the file COPYING. If not, see
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22 ## <https://www.gnu.org/licenses/>.
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23 ##
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24 ########################################################################
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25
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26 ## -*- texinfo -*-
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27 ## @documentencoding UTF-8
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28 ## @defvr {Documentation} slash
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29 ## Backslash and slash perform various sorts of division.
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30 ##
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31 ## @table @asis
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32 ## @item @code{\} Matrix Left Division (``backslash'')
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33 ## Solve systems of equations
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34 ## @iftex
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35 ## $Ax = b$ for $x$.
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36 ## @end iftex
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37 ## @ifnottex
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38 ## Ax = b for x.
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39 ## @end ifnottex
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40 ## @code{A \ b} is conceptually equivalent to @code{inv (A) * b} but is
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41 ## computed more efficiently and accurately, without forming the matrix
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42 ## inverse directly.
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43 ##
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44 ## Example:
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45 ##
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46 ## @example
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47 ## @group
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48 ## A = [1 2; 3 4];
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49 ## b = [4; 2];
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50 ## x = A \ b
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51 ## @result{} x =
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52 ## -6
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53 ## 5
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54 ## isequal (A*x, b)
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55 ## @result{} 1
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56 ## @end group
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57 ## @end example
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58 ##
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59 ## If the system is not square, or if the matrix is singular, a minimum-norm
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60 ## solution is computed (@code{norm (A*x - b)}).
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61 ##
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62 ## For dense matrices, backslash uses the Gaussian Elimination algorithm
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63 ## with partial pivoting. For sparse matrices, backslash uses a direct
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64 ## method to compute an LU factorization (@pxref{XREFlu,,@code{lu}}). The
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65 ## direct method tries to minimize ``fill-in'' of zeros but it could
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66 ## nonetheless use a lot of memory; if this is a concern, consider an iterative
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67 ## method (@pxref{XREFcgs,,@code{cgs}} or @pxref{XREFgmres,,@code{gmres}}).
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68 ##
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69 ## @item @code{/} Matrix Right Division
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70 ## The forward slash notation can be used to solve systems of the form
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71 ## @iftex
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72 ## $AB = C$ for $A$
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73 ## @end iftex
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74 ## @ifnottex
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75 ## AB = C for A
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76 ## @end ifnottex
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77 ## using @code{A = C / B}.
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78 ##
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79 ## @item @code{./} and @code{.\} Component-wise ``Hadamard'' Division
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80 ## The ``dot slash'' operators perform element-by-element division, for
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81 ## example:
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82 ##
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83 ## @example
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84 ## @group
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85 ## A = [1 10 12; 24 30 42];
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86 ## B = [1 5 4; 6 6 7];
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87 ## A ./ B
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88 ## @result{}
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89 ## 1 2 3
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90 ## 4 5 6
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91 ## @end group
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92 ## @end example
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93 ##
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94 ## If the sizes are not the same, ``broadcasting'' may apply
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95 ## (@pxref{Broadcasting}):
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96 ##
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97 ## @example
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98 ## @group
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99 ## 420 ./ B
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100 ## @result{}
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101 ## 420 84 105
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102 ## 70 70 60
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103 ## [20; 42] ./ B
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104 ## @result{}
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105 ## 20 4 5
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106 ## 7 7 6
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107 ## @end group
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108 ## @end example
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109 ##
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110 ## @end table
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111 ##
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112 ## @seealso{mldivide, mrdivide, ldivide, rdivide, linsolve}
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113 ## @end defvr
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114
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115
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116 ## Mark file as being tested. No real test needed for a documentation .m file
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117 %!assert (1)