annotate scripts/linear-algebra/linsolve.m @ 28789:28de41192f3c

Eliminate unneeded verification of nargin, nargout in m-files. * FIRfilter.m, FIRfilter_aggregation.m, get.m, polynomial.m, polynomial_superiorto.m, polynomial2.m, makeUniqueStrings.m, base64decode.m, base64encode.m, cd.m, lin2mu.m, record.m, sound.m, soundsc.m, accumarray.m, accumdim.m, bitcmp.m, bitset.m, cart2pol.m, celldisp.m, circshift.m, cplxpair.m, cumtrapz.m, flip.m, idivide.m, interpft.m, logspace.m, pol2cart.m, polyarea.m, postpad.m, prepad.m, rat.m, rot90.m, rotdim.m, shift.m, shiftdim.m, sortrows.m, trapz.m, dsearch.m, dsearchn.m, getappdata.m, getpixelposition.m, guidata.m, guihandles.m, isappdata.m, listfonts.m, uigetdir.m, waitforbuttonpress.m, __makeinfo__.m, doc.m, get_first_help_sentence.m, autumn.m, bone.m, brighten.m, cmpermute.m, cmunique.m, colorcube.m, contrast.m, cool.m, copper.m, cubehelix.m, flag.m, gray.m, gray2ind.m, hot.m, hsv.m, im2double.m, im2frame.m, imformats.m, jet.m, lines.m, ocean.m, pink.m, prism.m, rainbow.m, rgbplot.m, spinmap.m, spring.m, summer.m, viridis.m, white.m, winter.m, beep.m, importdata.m, is_valid_file_id.m, javachk.m, javaclasspath.m, findstr.m, genvarname.m, strmatch.m, bandwidth.m, commutation_matrix.m, cond.m, cross.m, isdefinite.m, ishermitian.m, issymmetric.m, krylov.m, linsolve.m, logm.m, lscov.m, null.m, ordeig.m, orth.m, rank.m, rref.m, vecnorm.m, bunzip2.m, citation.m, computer.m, copyfile.m, dir.m, dos.m, fileattrib.m, gunzip.m, inputParser.m, inputname.m, ismac.m, ispc.m, isunix.m, license.m, list_primes.m, methods.m, mkdir.m, movefile.m, nargchk.m, news.m, orderfields.m, recycle.m, tar.m, unix.m, unpack.m, untar.m, unzip.m, ver.m, version.m, what.m, zip.m, decic.m, fminbnd.m, fminunc.m, fsolve.m, fzero.m, glpk.m, humps.m, lsqnonneg.m, optimget.m, pqpnonneg.m, sqp.m, pathdef.m, camlookat.m, hidden.m, specular.m, plotmatrix.m, smooth3.m, sombrero.m, stemleaf.m, __gnuplot_drawnow__.m, __opengl_info__.m, ancestor.m, cla.m, close.m, closereq.m, copyobj.m, gca.m, gcf.m, ginput.m, graphics_toolkit.m, groot.m, hgload.m, hgsave.m, isgraphics.m, ishold.m, linkaxes.m, meshgrid.m, newplot.m, refresh.m, refreshdata.m, rotate.m, saveas.m, struct2hdl.m, conv.m, mkpp.m, mpoles.m, padecoef.m, pchip.m, polyder.m, polyfit.m, polygcd.m, polyint.m, polyout.m, polyval.m, ppder.m, ppint.m, getpref.m, ispref.m, rmpref.m, profexport.m, profshow.m, powerset.m, arch_fit.m, arma_rnd.m, blackman.m, detrend.m, diffpara.m, fftconv.m, fftfilt.m, filter2.m, freqz.m, freqz_plot.m, hamming.m, hanning.m, sinetone.m, sinewave.m, spectral_adf.m, spectral_xdf.m, stft.m, unwrap.m, gplot.m, ichol.m, ilu.m, spdiags.m, sprand.m, sprandn.m, spstats.m, svds.m, treelayout.m, treeplot.m, betainc.m, betaincinv.m, ellipke.m, gammainc.m, gammaincinv.m, legendre.m, pow2.m, hankel.m, pascal.m, rosser.m, toeplitz.m, bounds.m, corr.m, cov.m, histc.m, kendall.m, kurtosis.m, mad.m, mode.m, moment.m, prctile.m, quantile.m, range.m, ranks.m, run_count.m, skewness.m, spearman.m, std.m, var.m, zscore.m, dec2base.m, dec2bin.m, dec2hex.m, index.m, mat2str.m, native2unicode.m, ostrsplit.m, strjoin.m, strjust.m, strtok.m, substr.m, unicode2native.m, untabify.m, __debug_octave__.m, demo.m, example.m, fail.m, oruntests.m, dump_demos.m, speed.m, test.m, date.m, datenum.m, datestr.m, datevec.m, is_leap_year.m, now.m, weekday.m: Eliminate unneeded verification of nargin, nargout in m-files now that the interpreter checks these values.
author Rik <rik@octave.org>
date Thu, 24 Sep 2020 14:44:58 -0700
parents a4268efb7334
children 90fea9cc9caa
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1 ########################################################################
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2 ##
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3 ## Copyright (C) 2013-2020 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 ## @deftypefn {} {@var{x} =} linsolve (@var{A}, @var{b})
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28 ## @deftypefnx {} {@var{x} =} linsolve (@var{A}, @var{b}, @var{opts})
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29 ## @deftypefnx {} {[@var{x}, @var{R}] =} linsolve (@dots{})
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30 ## Solve the linear system @code{A*x = b}.
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31 ##
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32 ## With no options, this function is equivalent to the left division operator
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33 ## @w{(@code{x = A \ b})} or the matrix-left-divide function
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34 ## @w{(@code{x = mldivide (A, b)})}.
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35 ##
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36 ## Octave ordinarily examines the properties of the matrix @var{A} and chooses
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37 ## a solver that best matches the matrix. By passing a structure @var{opts}
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38 ## to @code{linsolve} you can inform Octave directly about the matrix @var{A}.
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39 ## In this case Octave will skip the matrix examination and proceed directly
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40 ## to solving the linear system.
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41 ##
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42 ## @strong{Warning:} If the matrix @var{A} does not have the properties listed
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43 ## in the @var{opts} structure then the result will not be accurate AND no
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44 ## warning will be given. When in doubt, let Octave examine the matrix and
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45 ## choose the appropriate solver as this step takes little time and the result
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46 ## is cached so that it is only done once per linear system.
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47 ##
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48 ## Possible @var{opts} fields (set value to true/false):
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49 ##
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50 ## @table @asis
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51 ## @item LT
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52 ## @var{A} is lower triangular
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53 ##
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54 ## @item UT
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55 ## @var{A} is upper triangular
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56 ##
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57 ## @item UHESS
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58 ## @var{A} is upper Hessenberg (currently makes no difference)
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59 ##
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60 ## @item SYM
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61 ## @var{A} is symmetric or complex Hermitian (currently makes no difference)
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62 ##
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63 ## @item POSDEF
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64 ## @var{A} is positive definite
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65 ##
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66 ## @item RECT
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67 ## @var{A} is general rectangular (currently makes no difference)
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68 ##
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69 ## @item TRANSA
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70 ## Solve @code{A'*x = b} if true rather than @code{A*x = b}
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71 ## @end table
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72 ##
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73 ## The optional second output @var{R} is the inverse condition number of
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74 ## @var{A} (zero if matrix is singular).
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75 ## @seealso{mldivide, matrix_type, rcond}
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76 ## @end deftypefn
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77
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78 function [x, R] = linsolve (A, b, opts)
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79
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80 if (nargin < 2)
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81 print_usage ();
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82 endif
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83
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84 if (! (isnumeric (A) && isnumeric (b)))
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85 error ("linsolve: A and B must be numeric");
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86 endif
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87
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88 trans_A = false;
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89
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90 ## Process any opts
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91 if (nargin > 2)
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92 if (! isstruct (opts))
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93 error ("linsolve: OPTS must be a structure");
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94 endif
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95 if (isfield (opts, "TRANSA") && opts.TRANSA)
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96 trans_A = true;
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97 endif
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98 if (isfield (opts, "POSDEF") && opts.POSDEF)
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99 A = matrix_type (A, "positive definite");
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100 endif
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101 if (isfield (opts, "LT") && opts.LT)
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102 A = matrix_type (A, "lower");
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103 elseif (isfield (opts, "UT") && opts.UT)
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104 A = matrix_type (A, "upper");
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105 endif
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106 endif
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107
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108 ## This way is faster as the transpose is not calculated in Octave,
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109 ## but forwarded as a flag option to BLAS.
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110 if (trans_A)
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111 x = A' \ b;
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112 else
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113 x = A \ b;
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114 endif
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115
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116 if (nargout > 1)
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117 if (issquare (A))
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118 R = rcond (A);
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119 else
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120 R = 0;
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121 endif
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122 endif
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123
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124 endfunction
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125
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126
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127 %!test
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128 %! n = 10;
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129 %! A = rand (n);
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130 %! x = rand (n, 1);
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131 %! b = A * x;
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132 %! assert (linsolve (A, b), A \ b);
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133 %! assert (linsolve (A, b, struct ()), A \ b);
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134
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135 %!test
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136 %! n = 10;
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137 %! A = triu (gallery ("condex", n));
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138 %! x = rand (n, 1);
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139 %! b = A' * x;
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140 %! opts.UT = true;
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141 %! opts.TRANSA = true;
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142 %! assert (linsolve (A, b, opts), A' \ b);
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143
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144 %!error linsolve ()
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145 %!error linsolve (1)
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146 %!error linsolve (1,2,3)
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147 %!error <A and B must be numeric> linsolve ({1},2)
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148 %!error <A and B must be numeric> linsolve (1,{2})
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149 %!error <OPTS must be a structure> linsolve (1,2,3)