Mercurial > octave
annotate libinterp/corefcn/sqrtm.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 | 796f54d4ddbf |
| children | aac27ad79be6 |
| rev | line source |
|---|---|
|
27923
bd51beb6205e
update formatting of copyright notices
John W. Eaton <jwe@octave.org>
parents:
27919
diff
changeset
|
1 //////////////////////////////////////////////////////////////////////// |
|
bd51beb6205e
update formatting of copyright notices
John W. Eaton <jwe@octave.org>
parents:
27919
diff
changeset
|
2 // |
|
30564
796f54d4ddbf
update Octave Project Developers copyright for the new year
John W. Eaton <jwe@octave.org>
parents:
30445
diff
changeset
|
3 // Copyright (C) 2001-2022 The Octave Project Developers |
|
27923
bd51beb6205e
update formatting of copyright notices
John W. Eaton <jwe@octave.org>
parents:
27919
diff
changeset
|
4 // |
|
bd51beb6205e
update formatting of copyright notices
John W. Eaton <jwe@octave.org>
parents:
27919
diff
changeset
|
5 // See the file COPYRIGHT.md in the top-level directory of this |
|
bd51beb6205e
update formatting of copyright notices
John W. Eaton <jwe@octave.org>
parents:
27919
diff
changeset
|
6 // distribution or <https://octave.org/copyright/>. |
|
bd51beb6205e
update formatting of copyright notices
John W. Eaton <jwe@octave.org>
parents:
27919
diff
changeset
|
7 // |
|
bd51beb6205e
update formatting of copyright notices
John W. Eaton <jwe@octave.org>
parents:
27919
diff
changeset
|
8 // This file is part of Octave. |
|
bd51beb6205e
update formatting of copyright notices
John W. Eaton <jwe@octave.org>
parents:
27919
diff
changeset
|
9 // |
|
bd51beb6205e
update formatting of copyright notices
John W. Eaton <jwe@octave.org>
parents:
27919
diff
changeset
|
10 // Octave is free software: you can redistribute it and/or modify it |
|
bd51beb6205e
update formatting of copyright notices
John W. Eaton <jwe@octave.org>
parents:
27919
diff
changeset
|
11 // under the terms of the GNU General Public License as published by |
|
bd51beb6205e
update formatting of copyright notices
John W. Eaton <jwe@octave.org>
parents:
27919
diff
changeset
|
12 // the Free Software Foundation, either version 3 of the License, or |
|
bd51beb6205e
update formatting of copyright notices
John W. Eaton <jwe@octave.org>
parents:
27919
diff
changeset
|
13 // (at your option) any later version. |
|
bd51beb6205e
update formatting of copyright notices
John W. Eaton <jwe@octave.org>
parents:
27919
diff
changeset
|
14 // |
|
bd51beb6205e
update formatting of copyright notices
John W. Eaton <jwe@octave.org>
parents:
27919
diff
changeset
|
15 // Octave is distributed in the hope that it will be useful, but |
|
bd51beb6205e
update formatting of copyright notices
John W. Eaton <jwe@octave.org>
parents:
27919
diff
changeset
|
16 // WITHOUT ANY WARRANTY; without even the implied warranty of |
|
bd51beb6205e
update formatting of copyright notices
John W. Eaton <jwe@octave.org>
parents:
27919
diff
changeset
|
17 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
|
bd51beb6205e
update formatting of copyright notices
John W. Eaton <jwe@octave.org>
parents:
27919
diff
changeset
|
18 // GNU General Public License for more details. |
|
bd51beb6205e
update formatting of copyright notices
John W. Eaton <jwe@octave.org>
parents:
27919
diff
changeset
|
19 // |
|
bd51beb6205e
update formatting of copyright notices
John W. Eaton <jwe@octave.org>
parents:
27919
diff
changeset
|
20 // You should have received a copy of the GNU General Public License |
|
bd51beb6205e
update formatting of copyright notices
John W. Eaton <jwe@octave.org>
parents:
27919
diff
changeset
|
21 // along with Octave; see the file COPYING. If not, see |
|
bd51beb6205e
update formatting of copyright notices
John W. Eaton <jwe@octave.org>
parents:
27919
diff
changeset
|
22 // <https://www.gnu.org/licenses/>. |
|
bd51beb6205e
update formatting of copyright notices
John W. Eaton <jwe@octave.org>
parents:
27919
diff
changeset
|
23 // |
|
bd51beb6205e
update formatting of copyright notices
John W. Eaton <jwe@octave.org>
parents:
27919
diff
changeset
|
24 //////////////////////////////////////////////////////////////////////// |
| 4331 | 25 |
|
21724
aba2e6293dd8
use "#if ..." consistently instead of "#ifdef" and "#ifndef"
John W. Eaton <jwe@octave.org>
parents:
21575
diff
changeset
|
26 #if defined (HAVE_CONFIG_H) |
|
21301
40de9f8f23a6
Use '#include "config.h"' rather than <config.h>.
Rik <rik@octave.org>
parents:
21266
diff
changeset
|
27 # include "config.h" |
| 4331 | 28 #endif |
| 29 | |
|
21266
e69eaee28737
make better use of templates for Schur decomposition
John W. Eaton <jwe@octave.org>
parents:
21200
diff
changeset
|
30 #include "schur.h" |
| 4331 | 31 #include "lo-ieee.h" |
| 32 #include "lo-mappers.h" | |
| 10608 | 33 #include "oct-norm.h" |
| 4331 | 34 |
|
15039
e753177cde93
maint: Move non-dynamically linked functions from DLD-FUNCTIONS/ to corefcn/ directory
Rik <rik@octave.org>
parents:
14501
diff
changeset
|
35 #include "defun.h" |
| 4331 | 36 #include "error.h" |
|
21100
e39e05d90788
Switch gripe_XXX to either err_XXX or warn_XXX naming scheme.
Rik <rik@octave.org>
parents:
21017
diff
changeset
|
37 #include "errwarn.h" |
| 4331 | 38 #include "utils.h" |
| 10608 | 39 #include "xnorm.h" |
| 4331 | 40 |
|
31605
e88a07dec498
maint: Use macros to begin/end C++ namespaces.
Rik <rik@octave.org>
parents:
30564
diff
changeset
|
41 OCTAVE_BEGIN_NAMESPACE(octave) |
|
29958
32c3a5805893
move DEFUN and DEFMETHOD functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents:
29874
diff
changeset
|
42 |
|
21139
538b57866b90
consistently use "typename" intead of "class" in template declarations
John W. Eaton <jwe@octave.org>
parents:
21110
diff
changeset
|
43 template <typename Matrix> |
| 10608 | 44 static void |
| 45 sqrtm_utri_inplace (Matrix& T) | |
| 4331 | 46 { |
| 10608 | 47 typedef typename Matrix::element_type element_type; |
| 4331 | 48 |
| 10608 | 49 const element_type zero = element_type (); |
| 4331 | 50 |
| 10608 | 51 bool singular = false; |
|
7789
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
7017
diff
changeset
|
52 |
|
12902
b9c66f891281
maint: style fixes for sqrtm
John W. Eaton <jwe@octave.org>
parents:
12829
diff
changeset
|
53 // The following code is equivalent to this triple loop: |
|
b9c66f891281
maint: style fixes for sqrtm
John W. Eaton <jwe@octave.org>
parents:
12829
diff
changeset
|
54 // |
|
b9c66f891281
maint: style fixes for sqrtm
John W. Eaton <jwe@octave.org>
parents:
12829
diff
changeset
|
55 // n = rows (T); |
|
b9c66f891281
maint: style fixes for sqrtm
John W. Eaton <jwe@octave.org>
parents:
12829
diff
changeset
|
56 // for j = 1:n |
|
b9c66f891281
maint: style fixes for sqrtm
John W. Eaton <jwe@octave.org>
parents:
12829
diff
changeset
|
57 // T(j,j) = sqrt (T(j,j)); |
|
b9c66f891281
maint: style fixes for sqrtm
John W. Eaton <jwe@octave.org>
parents:
12829
diff
changeset
|
58 // for i = j-1:-1:1 |
|
29777
90d7137b7dc6
sqrtm: Fix for input with eigenvalues 0 (bug #60797).
Markus Mützel <markus.muetzel@gmx.de>
parents:
29358
diff
changeset
|
59 // if T(i,j) != 0 |
|
90d7137b7dc6
sqrtm: Fix for input with eigenvalues 0 (bug #60797).
Markus Mützel <markus.muetzel@gmx.de>
parents:
29358
diff
changeset
|
60 // T(i,j) /= (T(i,i) + T(j,j)); |
|
90d7137b7dc6
sqrtm: Fix for input with eigenvalues 0 (bug #60797).
Markus Mützel <markus.muetzel@gmx.de>
parents:
29358
diff
changeset
|
61 // endif |
|
12902
b9c66f891281
maint: style fixes for sqrtm
John W. Eaton <jwe@octave.org>
parents:
12829
diff
changeset
|
62 // k = 1:i-1; |
|
b9c66f891281
maint: style fixes for sqrtm
John W. Eaton <jwe@octave.org>
parents:
12829
diff
changeset
|
63 // T(k,j) -= T(k,i) * T(i,j); |
|
b9c66f891281
maint: style fixes for sqrtm
John W. Eaton <jwe@octave.org>
parents:
12829
diff
changeset
|
64 // endfor |
|
b9c66f891281
maint: style fixes for sqrtm
John W. Eaton <jwe@octave.org>
parents:
12829
diff
changeset
|
65 // endfor |
|
b9c66f891281
maint: style fixes for sqrtm
John W. Eaton <jwe@octave.org>
parents:
12829
diff
changeset
|
66 // |
|
b9c66f891281
maint: style fixes for sqrtm
John W. Eaton <jwe@octave.org>
parents:
12829
diff
changeset
|
67 // this is an in-place, cache-aligned variant of the code |
|
b9c66f891281
maint: style fixes for sqrtm
John W. Eaton <jwe@octave.org>
parents:
12829
diff
changeset
|
68 // given in Higham's paper. |
| 4331 | 69 |
| 10608 | 70 const octave_idx_type n = T.rows (); |
| 71 element_type *Tp = T.fortran_vec (); | |
| 5275 | 72 for (octave_idx_type j = 0; j < n; j++) |
| 4331 | 73 { |
| 10608 | 74 element_type *colj = Tp + n*j; |
| 75 if (colj[j] != zero) | |
| 76 colj[j] = sqrt (colj[j]); | |
| 77 else | |
| 78 singular = true; | |
| 4331 | 79 |
| 10608 | 80 for (octave_idx_type i = j-1; i >= 0; i--) |
| 81 { | |
| 82 const element_type *coli = Tp + n*i; | |
|
29777
90d7137b7dc6
sqrtm: Fix for input with eigenvalues 0 (bug #60797).
Markus Mützel <markus.muetzel@gmx.de>
parents:
29358
diff
changeset
|
83 if (colj[i] != zero) |
|
90d7137b7dc6
sqrtm: Fix for input with eigenvalues 0 (bug #60797).
Markus Mützel <markus.muetzel@gmx.de>
parents:
29358
diff
changeset
|
84 colj[i] /= (coli[i] + colj[j]); |
|
90d7137b7dc6
sqrtm: Fix for input with eigenvalues 0 (bug #60797).
Markus Mützel <markus.muetzel@gmx.de>
parents:
29358
diff
changeset
|
85 const element_type colji = colj[i]; |
| 10608 | 86 for (octave_idx_type k = 0; k < i; k++) |
| 87 colj[k] -= coli[k] * colji; | |
|
10154
40dfc0c99116
DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents:
9064
diff
changeset
|
88 } |
| 4331 | 89 } |
| 90 | |
| 10608 | 91 if (singular) |
|
10629
b7c4954e1c00
add specific ID for sqrtm singularity warning
Jaroslav Hajek <highegg@gmail.com>
parents:
10619
diff
changeset
|
92 warning_with_id ("Octave:sqrtm:SingularMatrix", |
|
b7c4954e1c00
add specific ID for sqrtm singularity warning
Jaroslav Hajek <highegg@gmail.com>
parents:
10619
diff
changeset
|
93 "sqrtm: matrix is singular, may not have a square root"); |
| 4331 | 94 } |
| 95 | |
|
21139
538b57866b90
consistently use "typename" intead of "class" in template declarations
John W. Eaton <jwe@octave.org>
parents:
21110
diff
changeset
|
96 template <typename Matrix, typename ComplexMatrix, typename ComplexSCHUR> |
| 10608 | 97 static octave_value |
| 98 do_sqrtm (const octave_value& arg) | |
|
7789
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
7017
diff
changeset
|
99 { |
| 10608 | 100 |
| 101 octave_value retval; | |
|
7789
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
7017
diff
changeset
|
102 |
| 10608 | 103 MatrixType mt = arg.matrix_type (); |
| 104 | |
|
23581
c3075ae020e1
maint: Deprecate is_complex_type and replace with iscomplex.
Rik <rik@octave.org>
parents:
23534
diff
changeset
|
105 bool iscomplex = arg.iscomplex (); |
|
7789
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
7017
diff
changeset
|
106 |
| 10608 | 107 typedef typename Matrix::element_type real_type; |
| 108 | |
|
18100
6a71e5030df5
Follow coding convention of defining and initializing only 1 variable per line in liboctinterp.
Rik <rik@octave.org>
parents:
17787
diff
changeset
|
109 real_type cutoff = 0; |
|
6a71e5030df5
Follow coding convention of defining and initializing only 1 variable per line in liboctinterp.
Rik <rik@octave.org>
parents:
17787
diff
changeset
|
110 real_type one = 1; |
| 10608 | 111 real_type eps = std::numeric_limits<real_type>::epsilon (); |
|
7789
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
7017
diff
changeset
|
112 |
| 10608 | 113 if (! iscomplex) |
| 114 { | |
| 115 Matrix x = octave_value_extract<Matrix> (arg); | |
|
7789
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
7017
diff
changeset
|
116 |
| 10608 | 117 if (mt.is_unknown ()) // if type is not known, compute it now. |
| 118 arg.matrix_type (mt = MatrixType (x)); | |
| 119 | |
| 120 switch (mt.type ()) | |
|
10154
40dfc0c99116
DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents:
9064
diff
changeset
|
121 { |
| 10608 | 122 case MatrixType::Upper: |
| 123 case MatrixType::Diagonal: | |
|
12902
b9c66f891281
maint: style fixes for sqrtm
John W. Eaton <jwe@octave.org>
parents:
12829
diff
changeset
|
124 if (! x.diag ().any_element_is_negative ()) |
| 10608 | 125 { |
|
12902
b9c66f891281
maint: style fixes for sqrtm
John W. Eaton <jwe@octave.org>
parents:
12829
diff
changeset
|
126 // Do it in real arithmetic. |
|
b9c66f891281
maint: style fixes for sqrtm
John W. Eaton <jwe@octave.org>
parents:
12829
diff
changeset
|
127 sqrtm_utri_inplace (x); |
|
b9c66f891281
maint: style fixes for sqrtm
John W. Eaton <jwe@octave.org>
parents:
12829
diff
changeset
|
128 retval = x; |
|
b9c66f891281
maint: style fixes for sqrtm
John W. Eaton <jwe@octave.org>
parents:
12829
diff
changeset
|
129 retval.matrix_type (mt); |
|
b9c66f891281
maint: style fixes for sqrtm
John W. Eaton <jwe@octave.org>
parents:
12829
diff
changeset
|
130 } |
|
b9c66f891281
maint: style fixes for sqrtm
John W. Eaton <jwe@octave.org>
parents:
12829
diff
changeset
|
131 else |
|
b9c66f891281
maint: style fixes for sqrtm
John W. Eaton <jwe@octave.org>
parents:
12829
diff
changeset
|
132 iscomplex = true; |
|
b9c66f891281
maint: style fixes for sqrtm
John W. Eaton <jwe@octave.org>
parents:
12829
diff
changeset
|
133 break; |
|
7789
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
7017
diff
changeset
|
134 |
|
12902
b9c66f891281
maint: style fixes for sqrtm
John W. Eaton <jwe@octave.org>
parents:
12829
diff
changeset
|
135 case MatrixType::Lower: |
|
b9c66f891281
maint: style fixes for sqrtm
John W. Eaton <jwe@octave.org>
parents:
12829
diff
changeset
|
136 if (! x.diag ().any_element_is_negative ()) |
|
b9c66f891281
maint: style fixes for sqrtm
John W. Eaton <jwe@octave.org>
parents:
12829
diff
changeset
|
137 { |
|
b9c66f891281
maint: style fixes for sqrtm
John W. Eaton <jwe@octave.org>
parents:
12829
diff
changeset
|
138 x = x.transpose (); |
|
b9c66f891281
maint: style fixes for sqrtm
John W. Eaton <jwe@octave.org>
parents:
12829
diff
changeset
|
139 sqrtm_utri_inplace (x); |
|
b9c66f891281
maint: style fixes for sqrtm
John W. Eaton <jwe@octave.org>
parents:
12829
diff
changeset
|
140 retval = x.transpose (); |
|
b9c66f891281
maint: style fixes for sqrtm
John W. Eaton <jwe@octave.org>
parents:
12829
diff
changeset
|
141 retval.matrix_type (mt); |
| 10608 | 142 } |
|
12902
b9c66f891281
maint: style fixes for sqrtm
John W. Eaton <jwe@octave.org>
parents:
12829
diff
changeset
|
143 else |
|
b9c66f891281
maint: style fixes for sqrtm
John W. Eaton <jwe@octave.org>
parents:
12829
diff
changeset
|
144 iscomplex = true; |
|
b9c66f891281
maint: style fixes for sqrtm
John W. Eaton <jwe@octave.org>
parents:
12829
diff
changeset
|
145 break; |
|
b9c66f891281
maint: style fixes for sqrtm
John W. Eaton <jwe@octave.org>
parents:
12829
diff
changeset
|
146 |
| 10608 | 147 default: |
|
12902
b9c66f891281
maint: style fixes for sqrtm
John W. Eaton <jwe@octave.org>
parents:
12829
diff
changeset
|
148 iscomplex = true; |
|
b9c66f891281
maint: style fixes for sqrtm
John W. Eaton <jwe@octave.org>
parents:
12829
diff
changeset
|
149 break; |
| 10608 | 150 } |
| 151 | |
| 152 if (iscomplex) | |
|
29961
7d6709900da7
eliminate octave:: namespace tags in DEFUN and DEFMETHOD and more
John W. Eaton <jwe@octave.org>
parents:
29958
diff
changeset
|
153 cutoff = 10 * x.rows () * eps * xnorm (x, one); |
| 10608 | 154 } |
| 155 | |
| 156 if (iscomplex) | |
| 157 { | |
| 158 ComplexMatrix x = octave_value_extract<ComplexMatrix> (arg); | |
|
7789
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
7017
diff
changeset
|
159 |
| 10608 | 160 if (mt.is_unknown ()) // if type is not known, compute it now. |
| 161 arg.matrix_type (mt = MatrixType (x)); | |
| 162 | |
| 163 switch (mt.type ()) | |
| 164 { | |
| 165 case MatrixType::Upper: | |
| 166 case MatrixType::Diagonal: | |
|
12902
b9c66f891281
maint: style fixes for sqrtm
John W. Eaton <jwe@octave.org>
parents:
12829
diff
changeset
|
167 sqrtm_utri_inplace (x); |
|
b9c66f891281
maint: style fixes for sqrtm
John W. Eaton <jwe@octave.org>
parents:
12829
diff
changeset
|
168 retval = x; |
|
b9c66f891281
maint: style fixes for sqrtm
John W. Eaton <jwe@octave.org>
parents:
12829
diff
changeset
|
169 retval.matrix_type (mt); |
|
b9c66f891281
maint: style fixes for sqrtm
John W. Eaton <jwe@octave.org>
parents:
12829
diff
changeset
|
170 break; |
| 10608 | 171 |
| 172 case MatrixType::Lower: | |
|
12902
b9c66f891281
maint: style fixes for sqrtm
John W. Eaton <jwe@octave.org>
parents:
12829
diff
changeset
|
173 x = x.transpose (); |
|
b9c66f891281
maint: style fixes for sqrtm
John W. Eaton <jwe@octave.org>
parents:
12829
diff
changeset
|
174 sqrtm_utri_inplace (x); |
|
b9c66f891281
maint: style fixes for sqrtm
John W. Eaton <jwe@octave.org>
parents:
12829
diff
changeset
|
175 retval = x.transpose (); |
|
b9c66f891281
maint: style fixes for sqrtm
John W. Eaton <jwe@octave.org>
parents:
12829
diff
changeset
|
176 retval.matrix_type (mt); |
|
b9c66f891281
maint: style fixes for sqrtm
John W. Eaton <jwe@octave.org>
parents:
12829
diff
changeset
|
177 break; |
|
7789
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
7017
diff
changeset
|
178 |
| 10608 | 179 default: |
|
12902
b9c66f891281
maint: style fixes for sqrtm
John W. Eaton <jwe@octave.org>
parents:
12829
diff
changeset
|
180 { |
|
b9c66f891281
maint: style fixes for sqrtm
John W. Eaton <jwe@octave.org>
parents:
12829
diff
changeset
|
181 ComplexMatrix u; |
|
7789
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
7017
diff
changeset
|
182 |
|
12902
b9c66f891281
maint: style fixes for sqrtm
John W. Eaton <jwe@octave.org>
parents:
12829
diff
changeset
|
183 do |
|
b9c66f891281
maint: style fixes for sqrtm
John W. Eaton <jwe@octave.org>
parents:
12829
diff
changeset
|
184 { |
|
21266
e69eaee28737
make better use of templates for Schur decomposition
John W. Eaton <jwe@octave.org>
parents:
21200
diff
changeset
|
185 ComplexSCHUR schur_fact (x, "", true); |
|
e69eaee28737
make better use of templates for Schur decomposition
John W. Eaton <jwe@octave.org>
parents:
21200
diff
changeset
|
186 x = schur_fact.schur_matrix (); |
|
30073
1e277c6b6626
maint: rename schur member function from "unitary_matrix" to "unitary_schur_matrix"
Rik <rik@octave.org>
parents:
29961
diff
changeset
|
187 u = schur_fact.unitary_schur_matrix (); |
|
12902
b9c66f891281
maint: style fixes for sqrtm
John W. Eaton <jwe@octave.org>
parents:
12829
diff
changeset
|
188 } |
|
b9c66f891281
maint: style fixes for sqrtm
John W. Eaton <jwe@octave.org>
parents:
12829
diff
changeset
|
189 while (0); // schur no longer needed. |
| 10608 | 190 |
|
12902
b9c66f891281
maint: style fixes for sqrtm
John W. Eaton <jwe@octave.org>
parents:
12829
diff
changeset
|
191 sqrtm_utri_inplace (x); |
| 10608 | 192 |
|
12902
b9c66f891281
maint: style fixes for sqrtm
John W. Eaton <jwe@octave.org>
parents:
12829
diff
changeset
|
193 x = u * x; // original x no longer needed. |
|
b9c66f891281
maint: style fixes for sqrtm
John W. Eaton <jwe@octave.org>
parents:
12829
diff
changeset
|
194 ComplexMatrix res = xgemm (x, u, blas_no_trans, blas_conj_trans); |
| 10608 | 195 |
|
29961
7d6709900da7
eliminate octave:: namespace tags in DEFUN and DEFMETHOD and more
John W. Eaton <jwe@octave.org>
parents:
29958
diff
changeset
|
196 if (cutoff > 0 && xnorm (imag (res), one) <= cutoff) |
|
12902
b9c66f891281
maint: style fixes for sqrtm
John W. Eaton <jwe@octave.org>
parents:
12829
diff
changeset
|
197 retval = real (res); |
|
b9c66f891281
maint: style fixes for sqrtm
John W. Eaton <jwe@octave.org>
parents:
12829
diff
changeset
|
198 else |
|
b9c66f891281
maint: style fixes for sqrtm
John W. Eaton <jwe@octave.org>
parents:
12829
diff
changeset
|
199 retval = res; |
|
b9c66f891281
maint: style fixes for sqrtm
John W. Eaton <jwe@octave.org>
parents:
12829
diff
changeset
|
200 } |
|
b9c66f891281
maint: style fixes for sqrtm
John W. Eaton <jwe@octave.org>
parents:
12829
diff
changeset
|
201 break; |
|
10154
40dfc0c99116
DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents:
9064
diff
changeset
|
202 } |
|
7789
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
7017
diff
changeset
|
203 } |
|
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
7017
diff
changeset
|
204 |
| 10608 | 205 return retval; |
|
7789
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
7017
diff
changeset
|
206 } |
|
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
7017
diff
changeset
|
207 |
|
15039
e753177cde93
maint: Move non-dynamically linked functions from DLD-FUNCTIONS/ to corefcn/ directory
Rik <rik@octave.org>
parents:
14501
diff
changeset
|
208 DEFUN (sqrtm, args, nargout, |
|
21966
112b20240c87
move docstrings in C++ files out of C strings and into comments
John W. Eaton <jwe@octave.org>
parents:
21912
diff
changeset
|
209 doc: /* -*- texinfo -*- |
|
112b20240c87
move docstrings in C++ files out of C strings and into comments
John W. Eaton <jwe@octave.org>
parents:
21912
diff
changeset
|
210 @deftypefn {} {@var{s} =} sqrtm (@var{A}) |
|
112b20240c87
move docstrings in C++ files out of C strings and into comments
John W. Eaton <jwe@octave.org>
parents:
21912
diff
changeset
|
211 @deftypefnx {} {[@var{s}, @var{error_estimate}] =} sqrtm (@var{A}) |
|
112b20240c87
move docstrings in C++ files out of C strings and into comments
John W. Eaton <jwe@octave.org>
parents:
21912
diff
changeset
|
212 Compute the matrix square root of the square matrix @var{A}. |
|
112b20240c87
move docstrings in C++ files out of C strings and into comments
John W. Eaton <jwe@octave.org>
parents:
21912
diff
changeset
|
213 |
|
112b20240c87
move docstrings in C++ files out of C strings and into comments
John W. Eaton <jwe@octave.org>
parents:
21912
diff
changeset
|
214 Ref: @nospell{N.J. Higham}. @cite{A New sqrtm for @sc{matlab}}. Numerical |
|
27800
5a6a19a4e3da
doc: Use Texinfo non-sentence ending periods in citations.
Rik <rik@octave.org>
parents:
26376
diff
changeset
|
215 Analysis Report No.@: 336, Manchester @nospell{Centre} for Computational |
|
21966
112b20240c87
move docstrings in C++ files out of C strings and into comments
John W. Eaton <jwe@octave.org>
parents:
21912
diff
changeset
|
216 Mathematics, Manchester, England, January 1999. |
|
112b20240c87
move docstrings in C++ files out of C strings and into comments
John W. Eaton <jwe@octave.org>
parents:
21912
diff
changeset
|
217 @seealso{expm, logm} |
|
112b20240c87
move docstrings in C++ files out of C strings and into comments
John W. Eaton <jwe@octave.org>
parents:
21912
diff
changeset
|
218 @end deftypefn */) |
| 4331 | 219 { |
|
20819
f428cbe7576f
eliminate unnecessary uses of nargin
John W. Eaton <jwe@octave.org>
parents:
20801
diff
changeset
|
220 if (args.length () != 1) |
|
20801
a542a9bf177e
eliminate return statements after calls to print_usage
John W. Eaton <jwe@octave.org>
parents:
20555
diff
changeset
|
221 print_usage (); |
| 4331 | 222 |
| 223 octave_value arg = args(0); | |
| 224 | |
| 5275 | 225 octave_idx_type n = arg.rows (); |
| 226 octave_idx_type nc = arg.columns (); | |
| 4331 | 227 |
| 10608 | 228 if (n != nc || arg.ndims () > 2) |
|
21110
3d0d84305600
Use err_square_matrix_required more widely.
Rik <rik@octave.org>
parents:
21100
diff
changeset
|
229 err_square_matrix_required ("sqrtm", "A"); |
| 4331 | 230 |
| 20892 | 231 octave_value_list retval (nargout > 1 ? 3 : 1); |
| 232 | |
|
14022
de90542b7afc
Return retval(1) before retval(0) to avoid re-sizing call on retval.
Rik <octave@nomad.inbox5.com>
parents:
12926
diff
changeset
|
233 if (nargout > 1) |
|
de90542b7afc
Return retval(1) before retval(0) to avoid re-sizing call on retval.
Rik <octave@nomad.inbox5.com>
parents:
12926
diff
changeset
|
234 { |
| 20892 | 235 // FIXME: Octave does not calculate a condition number with respect to |
| 236 // sqrtm. Should this return NaN instead of -1? | |
|
14022
de90542b7afc
Return retval(1) before retval(0) to avoid re-sizing call on retval.
Rik <octave@nomad.inbox5.com>
parents:
12926
diff
changeset
|
237 retval(2) = -1.0; |
|
de90542b7afc
Return retval(1) before retval(0) to avoid re-sizing call on retval.
Rik <octave@nomad.inbox5.com>
parents:
12926
diff
changeset
|
238 } |
|
de90542b7afc
Return retval(1) before retval(0) to avoid re-sizing call on retval.
Rik <octave@nomad.inbox5.com>
parents:
12926
diff
changeset
|
239 |
| 10608 | 240 if (arg.is_diag_matrix ()) |
|
12902
b9c66f891281
maint: style fixes for sqrtm
John W. Eaton <jwe@octave.org>
parents:
12829
diff
changeset
|
241 // sqrtm of a diagonal matrix is just sqrt. |
|
b9c66f891281
maint: style fixes for sqrtm
John W. Eaton <jwe@octave.org>
parents:
12829
diff
changeset
|
242 retval(0) = arg.sqrt (); |
| 10608 | 243 else if (arg.is_single_type ()) |
|
21266
e69eaee28737
make better use of templates for Schur decomposition
John W. Eaton <jwe@octave.org>
parents:
21200
diff
changeset
|
244 retval(0) = do_sqrtm<FloatMatrix, FloatComplexMatrix, |
|
29961
7d6709900da7
eliminate octave:: namespace tags in DEFUN and DEFMETHOD and more
John W. Eaton <jwe@octave.org>
parents:
29958
diff
changeset
|
245 math::schur<FloatComplexMatrix>> (arg); |
|
23586
f6c5db0a02e7
maint: Deprecate is_numeric_type and replace with isnumeric.
Rik <rik@octave.org>
parents:
23581
diff
changeset
|
246 else if (arg.isnumeric ()) |
|
22317
6ca3acf5fad8
move some new numeric classes to namespace octave::math
John W. Eaton <jwe@octave.org>
parents:
21966
diff
changeset
|
247 retval(0) = do_sqrtm<Matrix, ComplexMatrix, |
|
29961
7d6709900da7
eliminate octave:: namespace tags in DEFUN and DEFMETHOD and more
John W. Eaton <jwe@octave.org>
parents:
29958
diff
changeset
|
248 math::schur<ComplexMatrix>> (arg); |
| 4331 | 249 |
|
20555
f90c8372b7ba
eliminate many more simple uses of error_state
John W. Eaton <jwe@octave.org>
parents:
19697
diff
changeset
|
250 if (nargout > 1) |
|
7789
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
7017
diff
changeset
|
251 { |
| 10608 | 252 // This corresponds to generic code |
|
12902
b9c66f891281
maint: style fixes for sqrtm
John W. Eaton <jwe@octave.org>
parents:
12829
diff
changeset
|
253 // |
| 10608 | 254 // norm (s*s - x, "fro") / norm (x, "fro"); |
|
7789
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
7017
diff
changeset
|
255 |
| 10608 | 256 octave_value s = retval(0); |
| 257 retval(1) = xfrobnorm (s*s - arg) / xfrobnorm (arg); | |
|
7789
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
7017
diff
changeset
|
258 } |
| 4331 | 259 |
| 260 return retval; | |
| 261 } | |
|
12829
ab529124f516
codesprint: Wrote 3 tests for sqrtm.cc
Jordi Gutiérrez Hermoso <jordigh@gmail.com>
parents:
12584
diff
changeset
|
262 |
|
ab529124f516
codesprint: Wrote 3 tests for sqrtm.cc
Jordi Gutiérrez Hermoso <jordigh@gmail.com>
parents:
12584
diff
changeset
|
263 /* |
|
ab529124f516
codesprint: Wrote 3 tests for sqrtm.cc
Jordi Gutiérrez Hermoso <jordigh@gmail.com>
parents:
12584
diff
changeset
|
264 %!assert (sqrtm (2*ones (2)), ones (2), 3*eps) |
|
30445
56eddda69c0e
sqrtm: Fix syntax error in test markup. Increase tolerance in test (bug #60797).
Markus Mützel <markus.muetzel@gmx.de>
parents:
30443
diff
changeset
|
265 %!assert <*60797> (sqrtm (ones (4))^2, ones (4), 5*eps) |
|
12829
ab529124f516
codesprint: Wrote 3 tests for sqrtm.cc
Jordi Gutiérrez Hermoso <jordigh@gmail.com>
parents:
12584
diff
changeset
|
266 |
|
ab529124f516
codesprint: Wrote 3 tests for sqrtm.cc
Jordi Gutiérrez Hermoso <jordigh@gmail.com>
parents:
12584
diff
changeset
|
267 ## The following two tests are from the reference in the docstring above. |
|
12926
838ada8779a5
Fix brain-o in sqrtm test
Jordi Gutiérrez Hermoso <jordigh@gmail.com>
parents:
12917
diff
changeset
|
268 %!test |
|
21575
bc9aa534bc29
maint: Clean up BIST tests so they don't produce warnings.
Rik <rik@octave.org>
parents:
21301
diff
changeset
|
269 %! warning ("off", "Octave:sqrtm:SingularMatrix", "local"); |
|
12926
838ada8779a5
Fix brain-o in sqrtm test
Jordi Gutiérrez Hermoso <jordigh@gmail.com>
parents:
12917
diff
changeset
|
270 %! x = [0 1; 0 0]; |
|
14501
60e5cf354d80
Update %!tests in DLD-FUNCTIONS/ directory with Octave coding conventions.
Rik <octave@nomad.inbox5.com>
parents:
14138
diff
changeset
|
271 %! assert (any (isnan (sqrtm (x))(:))); |
|
12829
ab529124f516
codesprint: Wrote 3 tests for sqrtm.cc
Jordi Gutiérrez Hermoso <jordigh@gmail.com>
parents:
12584
diff
changeset
|
272 |
|
ab529124f516
codesprint: Wrote 3 tests for sqrtm.cc
Jordi Gutiérrez Hermoso <jordigh@gmail.com>
parents:
12584
diff
changeset
|
273 %!test |
|
14501
60e5cf354d80
Update %!tests in DLD-FUNCTIONS/ directory with Octave coding conventions.
Rik <octave@nomad.inbox5.com>
parents:
14138
diff
changeset
|
274 %! x = eye (4); x(2,2) = x(3,3) = 2^-26; x(1,4) = 1; |
|
60e5cf354d80
Update %!tests in DLD-FUNCTIONS/ directory with Octave coding conventions.
Rik <octave@nomad.inbox5.com>
parents:
14138
diff
changeset
|
275 %! z = eye (4); z(2,2) = z(3,3) = 2^-13; z(1,4) = 0.5; |
|
60e5cf354d80
Update %!tests in DLD-FUNCTIONS/ directory with Octave coding conventions.
Rik <octave@nomad.inbox5.com>
parents:
14138
diff
changeset
|
276 %! [y, err] = sqrtm (x); |
|
60e5cf354d80
Update %!tests in DLD-FUNCTIONS/ directory with Octave coding conventions.
Rik <octave@nomad.inbox5.com>
parents:
14138
diff
changeset
|
277 %! assert (y, z); |
|
17336
b81b9d079515
Use '##' for comments which stand alone on a line.
Rik <rik@octave.org>
parents:
15195
diff
changeset
|
278 %! assert (err, 0); # Yes, this one has to hold exactly |
|
12829
ab529124f516
codesprint: Wrote 3 tests for sqrtm.cc
Jordi Gutiérrez Hermoso <jordigh@gmail.com>
parents:
12584
diff
changeset
|
279 */ |
|
29958
32c3a5805893
move DEFUN and DEFMETHOD functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents:
29874
diff
changeset
|
280 |
|
31605
e88a07dec498
maint: Use macros to begin/end C++ namespaces.
Rik <rik@octave.org>
parents:
30564
diff
changeset
|
281 OCTAVE_END_NAMESPACE(octave) |