Mercurial > octave
annotate libinterp/corefcn/inv.cc @ 31605:e88a07dec498 stable
maint: Use macros to begin/end C++ namespaces.
* oct-conf-post-public.in.h: Define two macros (OCTAVE_BEGIN_NAMESPACE,
OCTAVE_END_NAMESPACE) that can be used to start/end a namespace.
* mk-opts.pl, build-env.h, build-env.in.cc, __betainc__.cc, __contourc__.cc,
__dsearchn__.cc, __eigs__.cc, __expint__.cc, __ftp__.cc, __gammainc__.cc,
__ichol__.cc, __ilu__.cc, __isprimelarge__.cc, __lin_interpn__.cc,
__magick_read__.cc, __pchip_deriv__.cc, __qp__.cc, amd.cc, auto-shlib.cc,
auto-shlib.h, balance.cc, base-text-renderer.cc, base-text-renderer.h,
besselj.cc, bitfcns.cc, bsxfun.cc, c-file-ptr-stream.cc, c-file-ptr-stream.h,
call-stack.cc, call-stack.h, ccolamd.cc, cellfun.cc, chol.cc, colamd.cc,
colloc.cc, conv2.cc, daspk.cc, dasrt.cc, dassl.cc, data.cc, data.h, debug.cc,
defaults.cc, defaults.h, defun-int.h, defun.cc, det.cc, dirfns.cc, display.cc,
display.h, dlmread.cc, dmperm.cc, dot.cc, dynamic-ld.cc, dynamic-ld.h, eig.cc,
ellipj.cc, environment.cc, environment.h, error.cc, error.h, errwarn.h,
event-manager.cc, event-manager.h, event-queue.cc, event-queue.h, fcn-info.cc,
fcn-info.h, fft.cc, fft2.cc, fftn.cc, file-io.cc, filter.cc, find.cc,
ft-text-renderer.cc, ft-text-renderer.h, gcd.cc, getgrent.cc, getpwent.cc,
getrusage.cc, givens.cc, gl-render.cc, gl-render.h, gl2ps-print.cc,
gl2ps-print.h, graphics-toolkit.cc, graphics-toolkit.h, graphics.cc,
graphics.in.h, gsvd.cc, gtk-manager.cc, gtk-manager.h, hash.cc, help.cc,
help.h, hess.cc, hex2num.cc, hook-fcn.cc, hook-fcn.h, input.cc, input.h,
interpreter-private.cc, interpreter-private.h, interpreter.cc, interpreter.h,
inv.cc, jsondecode.cc, jsonencode.cc, kron.cc, latex-text-renderer.cc,
latex-text-renderer.h, load-path.cc, load-path.h, load-save.cc, load-save.h,
lookup.cc, ls-ascii-helper.cc, ls-ascii-helper.h, ls-oct-text.cc, ls-utils.cc,
ls-utils.h, lsode.cc, lu.cc, mappers.cc, matrix_type.cc, max.cc, mex-private.h,
mex.cc, mgorth.cc, nproc.cc, oct-fstrm.cc, oct-fstrm.h, oct-hdf5-types.cc,
oct-hdf5-types.h, oct-hist.cc, oct-hist.h, oct-iostrm.cc, oct-iostrm.h,
oct-opengl.h, oct-prcstrm.cc, oct-prcstrm.h, oct-procbuf.cc, oct-procbuf.h,
oct-process.cc, oct-process.h, oct-stdstrm.h, oct-stream.cc, oct-stream.h,
oct-strstrm.cc, oct-strstrm.h, oct-tex-lexer.in.ll, oct-tex-parser.yy,
ordqz.cc, ordschur.cc, pager.cc, pager.h, pinv.cc, pow2.cc, pr-flt-fmt.cc,
pr-output.cc, procstream.cc, procstream.h, psi.cc, qr.cc, quad.cc, quadcc.cc,
qz.cc, rand.cc, rcond.cc, regexp.cc, schur.cc, settings.cc, settings.h,
sighandlers.cc, sighandlers.h, sparse-xdiv.cc, sparse-xdiv.h, sparse-xpow.cc,
sparse-xpow.h, sparse.cc, spparms.cc, sqrtm.cc, stack-frame.cc, stack-frame.h,
stream-euler.cc, strfind.cc, strfns.cc, sub2ind.cc, svd.cc, sylvester.cc,
symbfact.cc, syminfo.cc, syminfo.h, symrcm.cc, symrec.cc, symrec.h,
symscope.cc, symscope.h, symtab.cc, symtab.h, syscalls.cc, sysdep.cc, sysdep.h,
text-engine.cc, text-engine.h, text-renderer.cc, text-renderer.h, time.cc,
toplev.cc, tril.cc, tsearch.cc, typecast.cc, url-handle-manager.cc,
url-handle-manager.h, urlwrite.cc, utils.cc, utils.h, variables.cc,
variables.h, xdiv.cc, xdiv.h, xnorm.cc, xnorm.h, xpow.cc, xpow.h,
__delaunayn__.cc, __fltk_uigetfile__.cc, __glpk__.cc, __init_fltk__.cc,
__init_gnuplot__.cc, __ode15__.cc, __voronoi__.cc, audiodevinfo.cc,
audioread.cc, convhulln.cc, fftw.cc, gzip.cc, mk-build-env-features.sh,
mk-builtins.pl, cdef-class.cc, cdef-class.h, cdef-fwd.h, cdef-manager.cc,
cdef-manager.h, cdef-method.cc, cdef-method.h, cdef-object.cc, cdef-object.h,
cdef-package.cc, cdef-package.h, cdef-property.cc, cdef-property.h,
cdef-utils.cc, cdef-utils.h, ov-base.cc, ov-base.h, ov-bool-mat.cc,
ov-builtin.h, ov-cell.cc, ov-class.cc, ov-class.h, ov-classdef.cc,
ov-classdef.h, ov-complex.cc, ov-fcn-handle.cc, ov-fcn-handle.h, ov-fcn.h,
ov-java.cc, ov-java.h, ov-mex-fcn.h, ov-null-mat.cc, ov-oncleanup.cc,
ov-struct.cc, ov-typeinfo.cc, ov-typeinfo.h, ov-usr-fcn.cc, ov-usr-fcn.h,
ov.cc, ov.h, octave.cc, octave.h, mk-ops.sh, op-b-b.cc, op-b-bm.cc,
op-b-sbm.cc, op-bm-b.cc, op-bm-bm.cc, op-bm-sbm.cc, op-cdm-cdm.cc, op-cell.cc,
op-chm.cc, op-class.cc, op-cm-cm.cc, op-cm-cs.cc, op-cm-m.cc, op-cm-s.cc,
op-cm-scm.cc, op-cm-sm.cc, op-cs-cm.cc, op-cs-cs.cc, op-cs-m.cc, op-cs-s.cc,
op-cs-scm.cc, op-cs-sm.cc, op-dm-dm.cc, op-dm-scm.cc, op-dm-sm.cc,
op-dm-template.cc, op-dms-template.cc, op-fcdm-fcdm.cc, op-fcm-fcm.cc,
op-fcm-fcs.cc, op-fcm-fm.cc, op-fcm-fs.cc, op-fcn.cc, op-fcs-fcm.cc,
op-fcs-fcs.cc, op-fcs-fm.cc, op-fcs-fs.cc, op-fdm-fdm.cc, op-fm-fcm.cc,
op-fm-fcs.cc, op-fm-fm.cc, op-fm-fs.cc, op-fs-fcm.cc, op-fs-fcs.cc,
op-fs-fm.cc, op-fs-fs.cc, op-i16-i16.cc, op-i32-i32.cc, op-i64-i64.cc,
op-i8-i8.cc, op-int-concat.cc, op-m-cm.cc, op-m-cs.cc, op-m-m.cc, op-m-s.cc,
op-m-scm.cc, op-m-sm.cc, op-mi.cc, op-pm-pm.cc, op-pm-scm.cc, op-pm-sm.cc,
op-pm-template.cc, op-range.cc, op-s-cm.cc, op-s-cs.cc, op-s-m.cc, op-s-s.cc,
op-s-scm.cc, op-s-sm.cc, op-sbm-b.cc, op-sbm-bm.cc, op-sbm-sbm.cc,
op-scm-cm.cc, op-scm-cs.cc, op-scm-m.cc, op-scm-s.cc, op-scm-scm.cc,
op-scm-sm.cc, op-sm-cm.cc, op-sm-cs.cc, op-sm-m.cc, op-sm-s.cc, op-sm-scm.cc,
op-sm-sm.cc, op-str-m.cc, op-str-s.cc, op-str-str.cc, op-struct.cc,
op-ui16-ui16.cc, op-ui32-ui32.cc, op-ui64-ui64.cc, op-ui8-ui8.cc, ops.h,
anon-fcn-validator.cc, anon-fcn-validator.h, bp-table.cc, bp-table.h,
comment-list.cc, comment-list.h, filepos.h, lex.h, lex.ll, oct-lvalue.cc,
oct-lvalue.h, oct-parse.yy, parse.h, profiler.cc, profiler.h,
pt-anon-scopes.cc, pt-anon-scopes.h, pt-arg-list.cc, pt-arg-list.h,
pt-args-block.cc, pt-args-block.h, pt-array-list.cc, pt-array-list.h,
pt-assign.cc, pt-assign.h, pt-binop.cc, pt-binop.h, pt-bp.cc, pt-bp.h,
pt-cbinop.cc, pt-cbinop.h, pt-cell.cc, pt-cell.h, pt-check.cc, pt-check.h,
pt-classdef.cc, pt-classdef.h, pt-cmd.h, pt-colon.cc, pt-colon.h, pt-const.cc,
pt-const.h, pt-decl.cc, pt-decl.h, pt-eval.cc, pt-eval.h, pt-except.cc,
pt-except.h, pt-exp.cc, pt-exp.h, pt-fcn-handle.cc, pt-fcn-handle.h, pt-id.cc,
pt-id.h, pt-idx.cc, pt-idx.h, pt-jump.h, pt-loop.cc, pt-loop.h, pt-mat.cc,
pt-mat.h, pt-misc.cc, pt-misc.h, pt-pr-code.cc, pt-pr-code.h, pt-select.cc,
pt-select.h, pt-spmd.cc, pt-spmd.h, pt-stmt.cc, pt-stmt.h, pt-tm-const.cc,
pt-tm-const.h, pt-unop.cc, pt-unop.h, pt-vm-eval.cc, pt-walk.cc, pt-walk.h,
pt.cc, pt.h, token.cc, token.h, Range.cc, Range.h, idx-vector.cc, idx-vector.h,
range-fwd.h, CollocWt.cc, CollocWt.h, aepbalance.cc, aepbalance.h, chol.cc,
chol.h, gepbalance.cc, gepbalance.h, gsvd.cc, gsvd.h, hess.cc, hess.h,
lo-mappers.cc, lo-mappers.h, lo-specfun.cc, lo-specfun.h, lu.cc, lu.h,
oct-convn.cc, oct-convn.h, oct-fftw.cc, oct-fftw.h, oct-norm.cc, oct-norm.h,
oct-rand.cc, oct-rand.h, oct-spparms.cc, oct-spparms.h, qr.cc, qr.h, qrp.cc,
qrp.h, randgamma.cc, randgamma.h, randmtzig.cc, randmtzig.h, randpoisson.cc,
randpoisson.h, schur.cc, schur.h, sparse-chol.cc, sparse-chol.h, sparse-lu.cc,
sparse-lu.h, sparse-qr.cc, sparse-qr.h, svd.cc, svd.h, child-list.cc,
child-list.h, dir-ops.cc, dir-ops.h, file-ops.cc, file-ops.h, file-stat.cc,
file-stat.h, lo-sysdep.cc, lo-sysdep.h, lo-sysinfo.cc, lo-sysinfo.h,
mach-info.cc, mach-info.h, oct-env.cc, oct-env.h, oct-group.cc, oct-group.h,
oct-password.cc, oct-password.h, oct-syscalls.cc, oct-syscalls.h, oct-time.cc,
oct-time.h, oct-uname.cc, oct-uname.h, action-container.cc, action-container.h,
base-list.h, cmd-edit.cc, cmd-edit.h, cmd-hist.cc, cmd-hist.h, f77-fcn.h,
file-info.cc, file-info.h, lo-array-errwarn.cc, lo-array-errwarn.h, lo-hash.cc,
lo-hash.h, lo-ieee.h, lo-regexp.cc, lo-regexp.h, lo-utils.cc, lo-utils.h,
oct-base64.cc, oct-base64.h, oct-glob.cc, oct-glob.h, oct-inttypes.h,
oct-mutex.cc, oct-mutex.h, oct-refcount.h, oct-shlib.cc, oct-shlib.h,
oct-sparse.cc, oct-sparse.h, oct-string.h, octave-preserve-stream-state.h,
pathsearch.cc, pathsearch.h, quit.cc, quit.h, unwind-prot.cc, unwind-prot.h,
url-transfer.cc, url-transfer.h : Use new macros to begin/end C++ namespaces.
author | Rik <rik@octave.org> |
---|---|
date | Thu, 01 Dec 2022 14:23:45 -0800 |
parents | 7802c652081f |
children | aac27ad79be6 |
rev | line source |
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1 //////////////////////////////////////////////////////////////////////// |
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2 // |
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3 // Copyright (C) 1996-2022 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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26 #if defined (HAVE_CONFIG_H) |
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27 # include "config.h" |
2928 | 28 #endif |
29 | |
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30 #include "defun.h" |
2928 | 31 #include "error.h" |
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32 #include "errwarn.h" |
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33 #include "ovl.h" |
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34 #include "ops.h" |
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35 #include "ov-re-diag.h" |
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36 #include "ov-cx-diag.h" |
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37 #include "ov-flt-re-diag.h" |
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38 #include "ov-flt-cx-diag.h" |
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39 #include "ov-perm.h" |
2928 | 40 |
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41 OCTAVE_BEGIN_NAMESPACE(octave) |
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42 |
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43 DEFUN (inv, args, nargout, |
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44 doc: /* -*- texinfo -*- |
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45 @deftypefn {} {@var{x} =} inv (@var{A}) |
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46 @deftypefnx {} {[@var{x}, @var{rcond}] =} inv (@var{A}) |
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47 @deftypefnx {} {[@dots{}] =} inverse (@dots{}) |
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48 Compute the inverse of the square matrix @var{A}. |
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49 |
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50 Return an estimate of the reciprocal condition number if requested, |
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51 otherwise warn of an ill-conditioned matrix if the reciprocal condition |
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52 number is small. |
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53 |
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54 In general it is best to avoid calculating the inverse of a matrix directly. |
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55 For example, it is both faster and more accurate to solve systems of |
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56 equations (@var{A}*@math{x} = @math{b}) with |
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57 @code{@var{y} = @var{A} \ @math{b}}, rather than |
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58 @code{@var{y} = inv (@var{A}) * @math{b}}. |
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59 |
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60 If called with a sparse matrix, then in general @var{x} will be a full |
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61 matrix requiring significantly more storage. Avoid forming the inverse of a |
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62 sparse matrix if possible. |
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63 |
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64 @code{inverse} is an alias and may be used identically in place of @code{inv}. |
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65 @seealso{ldivide, rdivide, pinv} |
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66 @end deftypefn */) |
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68 if (args.length () != 1) |
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69 print_usage (); |
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71 octave_value arg = args(0); | |
72 | |
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73 if (! arg.isnumeric ()) |
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74 err_wrong_type_arg ("inv", arg); |
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75 |
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76 if (arg.isempty ()) |
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77 return ovl (Matrix ()); |
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79 if (arg.rows () != arg.columns ()) |
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80 err_square_matrix_required ("inv", "A"); |
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82 octave_value result; |
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83 octave_idx_type info = 0; |
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84 double rcond = 0.0; |
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85 float frcond = 0.0; |
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86 bool isfloat = arg.is_single_type (); |
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87 |
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88 if (arg.is_diag_matrix ()) |
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89 { |
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90 rcond = 1.0; |
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91 frcond = 1.0f; |
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92 if (arg.iscomplex ()) |
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93 { |
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94 if (isfloat) |
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95 { |
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96 result = arg.float_complex_diag_matrix_value ().inverse (info); |
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97 if (info == -1) |
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98 frcond = 0.0f; |
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99 else if (nargout > 1) |
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100 frcond = arg.float_complex_diag_matrix_value ().rcond (); |
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101 } |
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102 else |
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103 { |
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104 result = arg.complex_diag_matrix_value ().inverse (info); |
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105 if (info == -1) |
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106 rcond = 0.0; |
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107 else if (nargout > 1) |
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108 rcond = arg.complex_diag_matrix_value ().rcond (); |
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109 } |
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110 } |
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111 else |
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112 { |
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113 if (isfloat) |
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114 { |
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115 result = arg.float_diag_matrix_value ().inverse (info); |
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116 if (info == -1) |
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117 frcond = 0.0f; |
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118 else if (nargout > 1) |
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119 frcond = arg.float_diag_matrix_value ().rcond (); |
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120 } |
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121 else |
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122 { |
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123 result = arg.diag_matrix_value ().inverse (info); |
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124 if (info == -1) |
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125 rcond = 0.0; |
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126 else if (nargout > 1) |
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127 rcond = arg.diag_matrix_value ().rcond (); |
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128 } |
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129 } |
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130 } |
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131 else if (arg.is_perm_matrix ()) |
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132 { |
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133 info = 0; |
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134 rcond = 1.0; |
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135 result = arg.perm_matrix_value ().inverse (); |
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136 } |
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137 else if (isfloat) |
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139 if (arg.isreal ()) |
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140 { |
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141 FloatMatrix m = arg.float_matrix_value (); |
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142 |
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143 MatrixType mattyp = args(0).matrix_type (); |
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144 result = m.inverse (mattyp, info, frcond, true, true); |
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145 args(0).matrix_type (mattyp); |
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146 } |
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147 else if (arg.iscomplex ()) |
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148 { |
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149 FloatComplexMatrix m = arg.float_complex_matrix_value (); |
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150 |
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151 MatrixType mattyp = args(0).matrix_type (); |
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152 result = m.inverse (mattyp, info, frcond, true, true); |
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153 args(0).matrix_type (mattyp); |
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154 } |
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156 else |
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158 if (arg.isreal ()) |
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159 { |
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160 if (arg.issparse ()) |
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161 { |
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162 SparseMatrix m = arg.sparse_matrix_value (); |
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163 |
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164 MatrixType mattyp = args(0).matrix_type (); |
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165 result = m.inverse (mattyp, info, rcond, true, true); |
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166 args(0).matrix_type (mattyp); |
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167 } |
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168 else |
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169 { |
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170 Matrix m = arg.matrix_value (); |
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171 |
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172 MatrixType mattyp = args(0).matrix_type (); |
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173 result = m.inverse (mattyp, info, rcond, true, true); |
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174 args(0).matrix_type (mattyp); |
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175 } |
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176 } |
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177 else if (arg.iscomplex ()) |
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178 { |
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179 if (arg.issparse ()) |
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180 { |
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181 SparseComplexMatrix m = arg.sparse_complex_matrix_value (); |
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182 |
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183 MatrixType mattyp = args(0).matrix_type (); |
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184 result = m.inverse (mattyp, info, rcond, true, true); |
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185 args(0).matrix_type (mattyp); |
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186 } |
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187 else |
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188 { |
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189 ComplexMatrix m = arg.complex_matrix_value (); |
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190 |
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191 MatrixType mattyp = args(0).matrix_type (); |
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192 result = m.inverse (mattyp, info, rcond, true, true); |
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193 args(0).matrix_type (mattyp); |
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194 } |
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195 } |
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196 else |
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197 // Shouldn't get here since we checked for suitable arg earlier. |
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198 // Maybe for some user-defined classes? |
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199 err_wrong_type_arg ("inv", arg); |
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201 |
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202 octave_value_list retval (nargout > 1 ? 2 : 1); |
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203 |
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204 retval(0) = result; |
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205 if (nargout > 1) |
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206 retval(1) = (isfloat ? octave_value (frcond) : octave_value (rcond)); |
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207 |
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208 if (nargout < 2) |
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209 { |
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210 bool is_singular; |
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211 |
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212 if (isfloat) |
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213 is_singular = ((frcond + 1.0f == 1.0f) || octave::math::isnan (frcond)) |
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214 && ! arg.is_scalar_type (); |
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215 else |
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216 is_singular = ((rcond + 1.0 == 1.0) || octave::math::isnan (rcond)) |
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217 && ! arg.is_scalar_type (); |
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218 |
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219 if (info == -1 || is_singular) |
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220 warn_singular_matrix (isfloat ? frcond : rcond); |
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221 } |
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223 return retval; | |
224 } | |
225 | |
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226 /* |
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227 ## Basic test for double/single matrices |
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228 %!assert (inv ([1, 2; 3, 4]), [-2, 1; 1.5, -0.5], 5*eps) |
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229 %!test |
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230 %! [xinv, rcond] = inv ([1,2;3,4]); |
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231 %! assert (xinv, [-2, 1; 1.5, -0.5], 5*eps); |
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232 %! assert (isa (rcond, "double")); |
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233 |
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234 %!assert (inv (single ([1, 2; 3, 4])), single ([-2, 1; 1.5, -0.5]), |
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235 %! 5*eps ("single")) |
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236 %!test |
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237 %! [xinv, rcond] = inv (single ([1,2;3,4])); |
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238 %! assert (xinv, single ([-2, 1; 1.5, -0.5]), 5*eps ("single")); |
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239 %! assert (isa (rcond, "single")); |
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240 |
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241 ## Basic test for integer inputs |
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242 %!assert (inv (int32 (2)), 0.5) |
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243 %!assert (inv (uint32 (2)), 0.5) |
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244 %!assert (inv (int64 (2)), 0.5) |
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245 %!assert (inv (uint64 (2)), 0.5) |
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246 |
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247 ## Normal scalar cases |
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248 %!assert (inv (2), 0.5) |
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249 %!test |
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250 %! [xinv, rcond] = inv (2); |
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251 %! assert (xinv, 0.5); |
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252 %! assert (rcond, 1); |
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253 %!assert (inv (single (2)), single (0.5)) |
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254 %!test |
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255 %! [xinv, rcond] = inv (single (2)); |
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256 %! assert (xinv, single (0.5)); |
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257 %! assert (rcond, single (1)); |
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258 %!assert (inv (complex (1, -1)), 0.5+0.5i) |
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259 %!test |
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260 %! [xinv, rcond] = inv (complex (1, -1)); |
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261 %! assert (xinv, 0.5+0.5i); |
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262 %! assert (rcond, 1); |
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263 %!assert (inv (complex (single (1), -1)), single (0.5+0.5i)) |
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264 %!test |
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265 %! [xinv, rcond] = inv (complex (single (1), -1)); |
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266 %! assert (xinv, single (0.5+0.5i)); |
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267 %! assert (rcond, single (1)); |
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268 |
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269 ## Test special inputs |
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270 ## Empty matrix |
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271 %!assert (inv (zeros (2,0)), []) |
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272 |
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273 ## Scalar "0" |
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274 %!assert (inv (0), Inf) |
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275 %!test |
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276 %! [xinv, rcond] = inv (0); |
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277 %! assert (xinv, Inf); |
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278 %! assert (rcond, 0); |
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279 %!assert (inv (single (0)), single (Inf)) |
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280 %!test |
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281 %! [xinv, rcond] = inv (single (0)); |
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282 %! assert (xinv, single (Inf)); |
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283 %! assert (rcond, single (0)); |
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284 %!assert (inv (complex (0, 0)), Inf) |
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285 %!test |
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286 %! [xinv, rcond] = inv (complex (0, 0)); |
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287 %! assert (xinv, Inf); |
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288 %! assert (rcond, 0); |
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289 %!assert (inv (complex (single (0), 0)), single (Inf)) |
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290 %!test |
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291 %! [xinv, rcond] = inv (complex (single (0), 0)); |
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292 %! assert (xinv, single (Inf)); |
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293 %! assert (rcond, single (0)); |
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294 ## NOTE: Matlab returns +Inf for -0 input, but it returns -Inf for 1/-0. |
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295 ## These should be the same, and in Octave they are. |
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296 %!assert (inv (-0), -Inf) |
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297 %!test |
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298 %! [xinv, rcond] = inv (-0); |
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299 %! assert (xinv, -Inf); |
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300 %! assert (rcond, 0); |
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301 |
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302 ## Scalar "Inf" |
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303 %!assert (inv (Inf), 0) |
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304 %!test |
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305 %! [xinv, rcond] = inv (Inf); |
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306 %! assert (xinv, 0); |
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307 %! assert (rcond, 0); |
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308 %!assert (inv (single (Inf)), single (0)) |
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309 %!test |
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310 %! [xinv, rcond] = inv (single (Inf)); |
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311 %! assert (xinv, single (0)); |
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312 %! assert (rcond, single (0)); |
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313 %!assert (inv (complex (1, Inf)), 0) |
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314 %!test |
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315 %! [xinv, rcond] = inv (complex (1, Inf)); |
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316 %! assert (xinv, 0); |
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317 %! assert (rcond, 0); |
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318 %!assert (inv (complex (single (1), Inf)), single (0)) |
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319 %!test |
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320 %! [xinv, rcond] = inv (complex (single (1), Inf)); |
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321 %! assert (xinv, single (0)); |
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322 %! assert (rcond, single (0)); |
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323 |
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324 ## Scalar "NaN" |
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325 %!assert (inv (NaN), NaN) |
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326 %!test |
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327 %! [xinv, rcond] = inv (NaN); |
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328 %! assert (xinv, NaN); |
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329 %! assert (rcond, NaN); |
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330 %!assert (inv (single (NaN)), single (NaN)) |
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331 %!test |
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332 %! [xinv, rcond] = inv (single (NaN)); |
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333 %! assert (xinv, single (NaN)); |
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334 %! assert (rcond, single (NaN)); |
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335 %!assert (inv (complex (1, NaN)), complex (NaN, NaN)) |
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336 %!test |
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337 %! [xinv, rcond] = inv (complex (1, NaN)); |
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338 %! assert (xinv, complex (NaN, NaN)); |
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339 %! assert (rcond, NaN); |
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340 %!assert (inv (complex (single (1), NaN)), complex (single (NaN), NaN)) |
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341 %!test |
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342 %! [xinv, rcond] = inv (complex (single (1), NaN)); |
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343 %! assert (xinv, complex (single (NaN), NaN)); |
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344 %! assert (rcond, single (NaN)); |
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345 |
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346 ## Matrix special values |
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347 ## Matrix of all zeroes |
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348 %!warning <matrix singular> assert (inv (zeros (2,2)), Inf (2,2)) |
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349 %!test |
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350 %! [xinv, rcond] = inv (zeros (2,2)); |
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351 %! assert (xinv, Inf (2,2)); |
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352 %! assert (rcond, 0); |
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353 ## Matrix of all Inf |
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354 %!warning <rcond = > assert (inv (Inf (2,2)), NaN (2,2)) |
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355 %!test |
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356 %! [xinv, rcond] = inv (Inf (2,2)); |
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357 %! assert (xinv, NaN (2,2)); |
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358 %! assert (rcond, NaN); |
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359 ## Matrix of all NaN |
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360 %!warning <rcond = > assert (inv (NaN (2,2)), NaN (2,2)) |
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361 %!test |
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362 %! [xinv, rcond] = inv (NaN (2,2)); |
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363 %! assert (xinv, NaN (2,2)); |
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364 %! assert (rcond, NaN); |
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365 |
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366 ## Special diagonal matrices |
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367 %!test |
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368 %! fail ("A = inv (diag ([1, 0, 1]))", "warning", "matrix singular"); |
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369 %! assert (A, diag ([Inf, Inf, Inf])); |
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370 |
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371 ## Special sparse matrices |
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372 %!testif HAVE_UMFPACK <*56232> |
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373 %! fail ("A = inv (sparse ([1, 2;0 ,0]))", "warning", "matrix singular"); |
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374 %! assert (A, sparse ([Inf, Inf; 0, 0])); |
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375 |
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376 %!testif HAVE_UMFPACK <*56232> |
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377 %! fail ("A = inv (sparse ([1i, 2;0 ,0]))", "warning", "matrix singular"); |
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378 %! assert (A, sparse ([Inf, Inf; 0, 0])); |
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379 |
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380 %!testif HAVE_UMFPACK <*56232> |
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381 %! fail ("A = inv (sparse ([1, 0, 0; 0, 0, 0; 0, 0, 1]))", |
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382 %! "warning", "matrix singular"); |
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383 %! assert (A, sparse ([Inf, 0, 0; 0, 0, 0; 0, 0, Inf])); |
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384 |
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385 %!error <Invalid call> inv () |
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386 %!error <Invalid call> inv ([1, 2; 3, 4], 2) |
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387 %!error <wrong type argument> inv ("Hello World") |
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388 %!error <wrong type argument> inv ({1}) |
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389 %!error <wrong type argument> inv (true) |
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390 %!error <must be a square matrix> inv ([1, 2; 3, 4; 5, 6]) |
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391 %!error <inverse of the null matrix not defined> inv (sparse (2, 2, 0)) |
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392 %!error <inverse of the null matrix not defined> inv (diag ([0, 0])) |
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393 %!error <inverse of the null matrix not defined> inv (diag (complex ([0, 0]))) |
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394 */ |
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395 |
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396 DEFALIAS (inverse, inv); |
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397 |
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398 OCTAVE_END_NAMESPACE(octave) |