annotate scripts/linear-algebra/linsolve.m @ 17795:0a8c35ae5ce1

maint: Fix various problems with GPL copyright statements. * libgui/qterminal/libqterminal/QTerminal.cc, libgui/qterminal/libqterminal/QTerminal.h, libgui/qterminal/libqterminal/win32/QTerminalColors.cpp, libgui/qterminal/libqterminal/win32/QTerminalColors.h, libgui/qterminal/libqterminal/win32/QWinTerminalImpl.cpp, libgui/qterminal/libqterminal/win32/QWinTerminalImpl.h: Replace "Foobar" with "This program" in GPL statement. * scripts/linear-algebra/linsolve.m: Replace "This program" with "Octave" in * GPL statement. * scripts/miscellaneous/getappdata.m, scripts/miscellaneous/isappdata.m, scripts/miscellaneous/rmappdata.m, scripts/miscellaneous/setappdata.m: Add "This file is part of Octave" line. Replace "This program" with "Octave" in GPL statement. Update GPL version to 3. * scripts/plot/util/copyobj.m, scripts/plot/util/hdl2struct.m, scripts/plot/util/struct2hdl.m, scripts/polynomial/ppder.m, scripts/polynomial/ppint.m, scripts/polynomial/ppjumps.m, scripts/sparse/bicg.m, scripts/strings/untabify.m: Replace "This program" with "Octave" in GPL statement.
author Rik <rik@octave.org>
date Tue, 29 Oct 2013 12:31:57 -0700
parents b66f068e4468
children 446c46af4b42
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
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1 ## Copyright (C) 2013 Nir Krakauer
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2 ##
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3 ## This file is part of Octave.
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4 ##
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5 ## Octave is free software; you can redistribute it and/or modify
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6 ## it under the terms of the GNU General Public License as published by
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7 ## the Free Software Foundation; either version 3 of the License, or
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8 ## (at your option) any later version.
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9 ##
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10 ## Octave is distributed in the hope that it will be useful,
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11 ## but WITHOUT ANY WARRANTY; without even the implied warranty of
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12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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13 ## GNU General Public License for more details.
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14 ##
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15 ## You should have received a copy of the GNU General Public License
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16 ## along with Octave; If not, see <http://www.gnu.org/licenses/>.
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17
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18 ## -*- texinfo -*-
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19 ## @deftypefn {Function File} {@var{x} =} linsolve (@var{A}, @var{b})
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20 ## @deftypefnx {Function File} {@var{x} =} linsolve (@var{A}, @var{b}, @var{opts})
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21 ## @deftypefnx {Function File} {[@var{x}, @var{R}] =} linsolve (@dots{})
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22 ## Solve the linear system @code{A*x = b}.
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23 ##
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24 ## With no options, this function is equivalent to the left division operator
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25 ## @w{(@code{x = A \ b})} or the matrix-left-divide function
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26 ## @w{(@code{x = mldivide (A, b)})}.
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27 ##
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28 ## Octave ordinarily examines the properties of the matrix @var{A} and chooses
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29 ## a solver that best matches the matrix. By passing a structure @var{opts}
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30 ## to @code{linsolve} you can inform Octave directly about the matrix @var{A}.
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31 ## In this case Octave will skip the matrix examination and proceed directly
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32 ## to solving the linear system.
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33 ##
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34 ## @strong{Warning:} If the matrix @var{A} does not have the properties
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35 ## listed in the @var{opts} structure then the result will not be accurate
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36 ## AND no warning will be given. When in doubt, let Octave examine the matrix
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37 ## and choose the appropriate solver as this step takes little time and the
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38 ## result is cached so that it is only done once per linear system.
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39 ##
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40 ## Possible @var{opts} fields (set value to true/false):
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41 ##
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42 ## @table @asis
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43 ## @item LT
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44 ## @var{A} is lower triangular
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45 ##
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46 ## @item UT
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47 ## @var{A} is upper triangular
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48 ##
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49 ## @item UHESS
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50 ## @var{A} is upper Hessenberg (currently makes no difference)
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51 ##
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52 ## @item SYM
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53 ## @var{A} is symmetric or complex Hermitian (currently makes no difference)
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54 ##
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55 ## @item POSDEF
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56 ## @var{A} is positive definite
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57 ##
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58 ## @item RECT
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59 ## @var{A} is general rectangular (currently makes no difference)
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60 ##
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61 ## @item TRANSA
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62 ## Solve @code{A'*x = b} by @code{transpose (A) \ b}
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63 ## @end table
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64 ##
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65 ## The optional second output @var{R} is the inverse condition number of
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66 ## @var{A} (zero if matrix is singular).
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67 ## @seealso{mldivide, matrix_type, rcond}
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68 ## @end deftypefn
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69
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70 ## Author: Nir Krakauer <nkrakauer@ccny.cuny.edu>
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71
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72 function [x, R] = linsolve (A, b, opts)
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73
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74 if (nargin < 2 || nargin > 3)
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75 print_usage ();
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76 endif
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77
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78 if (! (isnumeric (A) && isnumeric (b)))
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79 error ("linsolve: A and B must be numeric");
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80 endif
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81
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82 ## Process any opts
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83 if (nargin > 2)
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84 if (! isstruct (opts))
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85 error ("linsolve: OPTS must be a structure");
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86 endif
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87 trans_A = false;
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88 if (isfield (opts, "TRANSA") && opts.TRANSA)
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89 trans_A = true;
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90 A = A';
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91 endif
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92 if (isfield (opts, "POSDEF") && opts.POSDEF)
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93 A = matrix_type (A, "positive definite");
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94 endif
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95 if (isfield (opts, "LT") && opts.LT)
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96 if (trans_A)
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97 A = matrix_type (A, "upper");
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98 else
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99 A = matrix_type (A, "lower");
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100 endif
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101 endif
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102 if (isfield (opts, "UT") && opts.UT)
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103 if (trans_A)
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104 A = matrix_type (A, "lower");
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105 else
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106 A = matrix_type (A, "upper");
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107 endif
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108 endif
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109 endif
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110
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111 x = A \ b;
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112
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113 if (nargout > 1)
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114 if (issquare (A))
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115 R = rcond (A);
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116 else
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117 R = 0;
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118 endif
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119 endif
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120 endfunction
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121
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122
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123 %!test
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124 %! n = 4;
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125 %! A = triu (rand (n));
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126 %! x = rand (n, 1);
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127 %! b = A' * x;
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128 %! opts.UT = true;
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129 %! opts.TRANSA = true;
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130 %! assert (linsolve (A, b, opts), A' \ b);
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c3a3532e3d98 linsolve.m: Add new function for Matlab compatibility.
Nir Krakauer < nkrakauer@ccny.cuny.edu>
parents:
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131
17500
b66f068e4468 linsolve.m: Use Octave coding conventions.
Rik <rik@octave.org>
parents: 17499
diff changeset
132 %!error linsolve ()
b66f068e4468 linsolve.m: Use Octave coding conventions.
Rik <rik@octave.org>
parents: 17499
diff changeset
133 %!error linsolve (1)
b66f068e4468 linsolve.m: Use Octave coding conventions.
Rik <rik@octave.org>
parents: 17499
diff changeset
134 %!error linsolve (1,2,3)
b66f068e4468 linsolve.m: Use Octave coding conventions.
Rik <rik@octave.org>
parents: 17499
diff changeset
135 %!error <A and B must be numeric> linsolve ({1},2)
b66f068e4468 linsolve.m: Use Octave coding conventions.
Rik <rik@octave.org>
parents: 17499
diff changeset
136 %!error <A and B must be numeric> linsolve (1,{2})
b66f068e4468 linsolve.m: Use Octave coding conventions.
Rik <rik@octave.org>
parents: 17499
diff changeset
137 %!error <OPTS must be a structure> linsolve (1,2,3)