Mercurial > octave
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> |
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date | Thu, 24 Sep 2020 14:44:58 -0700 |
parents | a4268efb7334 |
children | 90fea9cc9caa |
rev | line source |
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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) |