Mercurial > octave
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> |
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date | Sun, 14 Aug 2022 18:24:07 +0200 |
parents | 796f54d4ddbf |
children | 597f3ee61a48 |
rev | line source |
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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) |