Mercurial > octave
annotate libinterp/corefcn/sqrtm.cc @ 21724:aba2e6293dd8
use "#if ..." consistently instead of "#ifdef" and "#ifndef"
* configure.ac, Doxyfile.in, make_int.cc, Backend.cc, BaseControl.cc,
ButtonControl.cc, Canvas.cc, CheckBoxControl.cc, Container.cc,
ContextMenu.cc, EditControl.cc, Figure.cc, FigureWindow.cc,
GLCanvas.cc, KeyMap.cc, ListBoxControl.cc, Logger.cc, Menu.cc,
MouseModeActionGroup.cc, Object.cc, ObjectFactory.cc,
ObjectProxy.cc, Panel.cc, PopupMenuControl.cc, PushButtonControl.cc,
PushTool.cc, QtHandlesUtils.cc, RadioButtonControl.cc,
SliderControl.cc, TextControl.cc, TextEdit.cc,
ToggleButtonControl.cc, ToggleTool.cc, ToolBar.cc, __init_qt__.cc,
annotation-dialog.cc, gl-select.cc, module.mk, color-picker.cc,
dialog.cc, documentation-dock-widget.cc, files-dock-widget.cc,
find-files-dialog.cc, find-files-model.cc, history-dock-widget.cc,
liboctgui-build-info.in.cc, file-editor-tab.cc, file-editor.cc,
find-dialog.cc, marker.cc, marker.h, octave-qscintilla.cc,
octave-txt-lexer.cc, main-window.cc, octave-cmd.cc,
octave-dock-widget.cc, octave-gui.cc, octave-interpreter.cc,
octave-qt-link.cc, parser.cc, webinfo.cc, resource-manager.cc,
settings-dialog.cc, shortcut-manager.cc, terminal-dock-widget.cc,
thread-manager.cc, welcome-wizard.cc, workspace-model.cc,
workspace-view.cc, build-env.in.cc, Cell.cc, __contourc__.cc,
__dispatch__.cc, __dsearchn__.cc, __ichol__.cc, __ilu__.cc,
__lin_interpn__.cc, __luinc__.cc, __magick_read__.cc,
__pchip_deriv__.cc, __qp__.cc, balance.cc, besselj.cc, betainc.cc,
bitfcns.cc, bsxfun.cc, c-file-ptr-stream.cc, c-file-ptr-stream.h,
cdisplay.c, cdisplay.h, cellfun.cc, coct-hdf5-types.c, colloc.cc,
comment-list.cc, conv2.cc, daspk.cc, dasrt.cc, dassl.cc, data.cc,
debug.cc, defaults.cc, defaults.in.h, defun.cc, det.cc, dirfns.cc,
display.cc, dlmread.cc, dot.cc, dynamic-ld.cc, eig.cc, ellipj.cc,
error.cc, errwarn.cc, event-queue.cc, fft.cc, fft2.cc, fftn.cc,
file-io.cc, filter.cc, find.cc, ft-text-renderer.cc, gammainc.cc,
gcd.cc, getgrent.cc, getpwent.cc, getrusage.cc, givens.cc,
gl-render.cc, gl2ps-print.cc, graphics.cc, gripes.cc, hash.cc,
help.cc, hess.cc, hex2num.cc, input.cc, inv.cc, jit-ir.cc, jit-ir.h,
jit-typeinfo.cc, jit-typeinfo.h, jit-util.cc, jit-util.h, kron.cc,
load-path.cc, load-save.cc, lookup.cc, ls-ascii-helper.cc,
ls-hdf5.cc, ls-mat-ascii.cc, ls-mat4.cc, ls-mat5.cc,
ls-oct-binary.cc, ls-oct-text.cc, ls-oct-text.h, ls-utils.cc,
lsode.cc, lu.cc, mappers.cc, matrix_type.cc, max.cc, mex.cc, mex.h,
mexproto.h, mgorth.cc, nproc.cc, oct-errno.in.cc, oct-fstrm.cc,
oct-hdf5-types.cc, oct-hdf5-types.h, oct-hist.cc, oct-iostrm.cc,
oct-lvalue.cc, oct-map.cc, oct-prcstrm.cc, oct-procbuf.cc,
oct-stdstrm.h, oct-stream.cc, oct-strstrm.cc, oct-tex-lexer.in.ll,
oct-tex-parser.in.yy, octave-link.cc, ordschur.cc, pager.cc,
pinv.cc, pr-output.cc, procstream.cc, profiler.cc, psi.cc,
pt-jit.cc, pt-jit.h, quad.cc, quadcc.cc, qz.cc, rand.cc, rcond.cc,
regexp.cc, schur.cc, sighandlers.cc, sighandlers.h, siglist.c,
siglist.h, sparse-xdiv.cc, sparse-xpow.cc, sparse.cc, spparms.cc,
sqrtm.cc, str2double.cc, strfind.cc, strfns.cc, sub2ind.cc, svd.cc,
sylvester.cc, symtab.cc, syscalls.cc, sysdep.cc, text-renderer.cc,
time.cc, toplev.cc, tril.cc, tsearch.cc, txt-eng.cc, typecast.cc,
urlwrite.cc, utils.cc, variables.cc, xdiv.cc, xgl2ps.c, xnorm.cc,
xpow.cc, zfstream.cc, zfstream.h, __delaunayn__.cc, __eigs__.cc,
__fltk_uigetfile__.cc, __glpk__.cc, __init_fltk__.cc,
__init_gnuplot__.cc, __osmesa_print__.cc, __voronoi__.cc, amd.cc,
audiodevinfo.cc, audioread.cc, ccolamd.cc, chol.cc, colamd.cc,
convhulln.cc, dmperm.cc, fftw.cc, qr.cc, symbfact.cc, symrcm.cc,
liboctinterp-build-info.in.cc, mkbuiltins, mkops, ov-base.cc,
ov-bool-mat.cc, ov-bool-sparse.cc, ov-bool.cc, ov-builtin.cc,
ov-cell.cc, ov-ch-mat.cc, ov-class.cc, ov-classdef.cc, ov-colon.cc,
ov-complex.cc, ov-cs-list.cc, ov-cx-diag.cc, ov-cx-mat.cc,
ov-cx-sparse.cc, ov-dld-fcn.cc, ov-fcn-handle.cc, ov-fcn-inline.cc,
ov-fcn.cc, ov-float.cc, ov-flt-complex.cc, ov-flt-cx-diag.cc,
ov-flt-cx-mat.cc, ov-flt-re-diag.cc, ov-flt-re-mat.cc, ov-int16.cc,
ov-int32.cc, ov-int64.cc, ov-int8.cc, ov-java.cc, ov-lazy-idx.cc,
ov-mex-fcn.cc, ov-null-mat.cc, ov-oncleanup.cc, ov-perm.cc,
ov-range.cc, ov-re-diag.cc, ov-re-mat.cc, ov-re-sparse.cc,
ov-scalar.cc, ov-str-mat.cc, ov-struct.cc, ov-typeinfo.cc,
ov-uint16.cc, ov-uint32.cc, ov-uint64.cc, ov-uint8.cc,
ov-usr-fcn.cc, ov-usr-fcn.h, ov.cc, ovl.cc, octave.cc, octave.h,
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-cdm-cm.cc, op-cdm-dm.cc,
op-cdm-m.cc, op-cell.cc, op-chm.cc, op-class.cc, op-cm-cdm.cc,
op-cm-cm.cc, op-cm-cs.cc, op-cm-dm.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-cdm.cc, op-dm-cm.cc,
op-dm-dm.cc, op-dm-m.cc, op-dm-scm.cc, op-dm-sm.cc,
op-dm-template.cc, op-dms-template.cc, op-double-conv.cc,
op-fcdm-fcdm.cc, op-fcdm-fcm.cc, op-fcdm-fdm.cc, op-fcdm-fm.cc,
op-fcm-fcdm.cc, op-fcm-fcm.cc, op-fcm-fcs.cc, op-fcm-fdm.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-fcdm.cc, op-fdm-fcm.cc,
op-fdm-fdm.cc, op-fdm-fm.cc, op-float-conv.cc, op-fm-fcdm.cc,
op-fm-fcm.cc, op-fm-fcs.cc, op-fm-fdm.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-int-conv.cc, op-m-cdm.cc, op-m-cm.cc, op-m-cs.cc, op-m-dm.cc,
op-m-m.cc, op-m-s.cc, op-m-scm.cc, op-m-sm.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,
lex.ll, oct-parse.in.yy, pt-arg-list.cc, pt-array-list.cc,
pt-assign.cc, pt-binop.cc, pt-bp.cc, pt-cbinop.cc, pt-cell.cc,
pt-check.cc, pt-classdef.cc, pt-cmd.cc, pt-colon.cc, pt-const.cc,
pt-decl.cc, pt-eval.cc, pt-except.cc, pt-exp.cc, pt-fcn-handle.cc,
pt-funcall.cc, pt-id.cc, pt-idx.cc, pt-jump.cc, pt-loop.cc,
pt-loop.h, pt-mat.cc, pt-misc.cc, pt-pr-code.cc, pt-select.cc,
pt-stmt.cc, pt-unop.cc, pt.cc, token.cc, Array-jit.cc, Array-tc.cc,
version.cc, Array-C.cc, Array-b.cc, Array-ch.cc, Array-d.cc,
Array-f.cc, Array-fC.cc, Array-i.cc, Array-idx-vec.cc, Array-s.cc,
Array-str.cc, Array-util.cc, Array-voidp.cc, Array.cc,
CColVector.cc, CDiagMatrix.cc, CMatrix.cc, CNDArray.cc,
CRowVector.cc, CSparse.cc, MArray-C.cc, MArray-d.cc, MArray-f.cc,
MArray-fC.cc, MArray-i.cc, MArray-s.cc, MSparse-C.cc, MSparse-d.cc,
MatrixType.cc, PermMatrix.cc, Range.cc, Sparse-C.cc, Sparse-b.cc,
Sparse-d.cc, boolMatrix.cc, boolNDArray.cc, boolSparse.cc,
chMatrix.cc, chNDArray.cc, dColVector.cc, dDiagMatrix.cc,
dMatrix.cc, dNDArray.cc, dRowVector.cc, dSparse.cc, dim-vector.cc,
dim-vector.h, fCColVector.cc, fCDiagMatrix.cc, fCMatrix.cc,
fCNDArray.cc, fCRowVector.cc, fColVector.cc, fDiagMatrix.cc,
fMatrix.cc, fNDArray.cc, fRowVector.cc, idx-vector.cc,
int16NDArray.cc, int32NDArray.cc, int64NDArray.cc, int8NDArray.cc,
uint16NDArray.cc, uint32NDArray.cc, uint64NDArray.cc,
uint8NDArray.cc, Faddeeva.cc, blaswrap.c, cquit.c, f77-extern.cc,
f77-fcn.c, f77-fcn.h, lo-error.c, lo-error.h, quit.cc, quit.h,
liboctave-build-info.in.cc, CollocWt.cc, DASPK.cc, DASRT.cc,
DASSL.cc, EIG.cc, LSODE.cc, ODES.cc, Quad.cc, aepbalance.cc,
chol.cc, eigs-base.cc, fEIG.cc, gepbalance.cc, hess.cc,
lo-mappers.cc, lo-specfun.cc, lu.cc, oct-convn.cc, oct-fftw.cc,
oct-norm.cc, oct-rand.cc, oct-spparms.cc, qr.cc, qrp.cc,
randmtzig.cc, randpoisson.cc, schur.cc, sparse-chol.cc,
sparse-dmsolve.cc, sparse-lu.cc, sparse-qr.cc, svd.cc, mk-ops.awk,
mx-defs.h, dir-ops.cc, file-ops.cc, file-stat.cc, lo-sysdep.cc,
mach-info.cc, oct-env.cc, oct-group.cc, oct-passwd.cc,
oct-syscalls.cc, oct-time.cc, oct-uname.cc, pathlen.h, syswait.h,
cmd-edit.cc, cmd-hist.cc, data-conv.cc, f2c-main.c, glob-match.cc,
kpse.cc, lo-array-errwarn.cc, lo-array-gripes.cc, lo-cutils.c,
lo-cutils.h, lo-ieee.cc, lo-ieee.h, lo-regexp.cc, lo-utils.cc,
oct-base64.cc, oct-glob.cc, oct-inttypes.cc, oct-inttypes.h,
oct-locbuf.cc, oct-mutex.cc, oct-rl-edit.c, oct-rl-edit.h,
oct-rl-hist.c, oct-rl-hist.h, oct-shlib.cc, oct-sort.cc,
pathsearch.cc, singleton-cleanup.cc, sparse-sort.cc, sparse-util.cc,
statdefs.h, str-vec.cc, unwind-prot.cc, url-transfer.cc,
acinclude.m4, display-available.c, display-available.h, main-cli.cc,
main-gui.cc, main.in.cc, mkoctfile.in.cc, octave-build-info.in.cc,
octave-config.in.cc, shared-fcns.h:
Use "#if ..." consistently instead of "#ifdef" and "#ifndef".
| author | John W. Eaton <jwe@octave.org> |
|---|---|
| date | Tue, 17 May 2016 12:09:30 -0400 |
| parents | bc9aa534bc29 |
| children | d92dcbcd7691 |
| rev | line source |
|---|---|
| 4331 | 1 /* |
| 2 | |
|
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3 Copyright (C) 2001-2015 Ross Lippert and Paul Kienzle |
| 10608 | 4 Copyright (C) 2010 VZLU Prague |
| 4331 | 5 |
| 7016 | 6 This file is part of Octave. |
| 4331 | 7 |
| 7016 | 8 Octave is free software; you can redistribute it and/or modify it |
| 9 under the terms of the GNU General Public License as published by the | |
| 10 Free Software Foundation; either version 3 of the License, or (at your | |
| 11 option) any later version. | |
| 12 | |
| 13 Octave is distributed in the hope that it will be useful, but WITHOUT | |
| 14 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or | |
| 15 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License | |
| 16 for more details. | |
| 4331 | 17 |
| 18 You should have received a copy of the GNU General Public License | |
| 7016 | 19 along with Octave; see the file COPYING. If not, see |
| 20 <http://www.gnu.org/licenses/>. | |
| 4331 | 21 |
| 22 */ | |
| 23 | |
|
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24 #if defined (HAVE_CONFIG_H) |
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25 # include "config.h" |
| 4331 | 26 #endif |
| 27 | |
| 28 #include <float.h> | |
| 29 | |
|
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30 #include "schur.h" |
| 4331 | 31 #include "lo-ieee.h" |
| 32 #include "lo-mappers.h" | |
| 10608 | 33 #include "oct-norm.h" |
| 4331 | 34 |
|
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35 #include "defun.h" |
| 4331 | 36 #include "error.h" |
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37 #include "errwarn.h" |
| 4331 | 38 #include "utils.h" |
| 10608 | 39 #include "xnorm.h" |
| 4331 | 40 |
|
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41 template <typename Matrix> |
| 10608 | 42 static void |
| 43 sqrtm_utri_inplace (Matrix& T) | |
| 4331 | 44 { |
| 10608 | 45 typedef typename Matrix::element_type element_type; |
| 4331 | 46 |
| 10608 | 47 const element_type zero = element_type (); |
| 4331 | 48 |
| 10608 | 49 bool singular = false; |
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50 |
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51 // The following code is equivalent to this triple loop: |
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52 // |
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53 // n = rows (T); |
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54 // for j = 1:n |
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55 // T(j,j) = sqrt (T(j,j)); |
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56 // for i = j-1:-1:1 |
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57 // T(i,j) /= (T(i,i) + T(j,j)); |
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58 // k = 1:i-1; |
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59 // T(k,j) -= T(k,i) * T(i,j); |
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60 // endfor |
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61 // endfor |
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62 // |
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63 // this is an in-place, cache-aligned variant of the code |
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64 // given in Higham's paper. |
| 4331 | 65 |
| 10608 | 66 const octave_idx_type n = T.rows (); |
| 67 element_type *Tp = T.fortran_vec (); | |
| 5275 | 68 for (octave_idx_type j = 0; j < n; j++) |
| 4331 | 69 { |
| 10608 | 70 element_type *colj = Tp + n*j; |
| 71 if (colj[j] != zero) | |
| 72 colj[j] = sqrt (colj[j]); | |
| 73 else | |
| 74 singular = true; | |
| 4331 | 75 |
| 10608 | 76 for (octave_idx_type i = j-1; i >= 0; i--) |
| 77 { | |
| 78 const element_type *coli = Tp + n*i; | |
| 79 const element_type colji = colj[i] /= (coli[i] + colj[j]); | |
| 80 for (octave_idx_type k = 0; k < i; k++) | |
| 81 colj[k] -= coli[k] * colji; | |
|
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82 } |
| 4331 | 83 } |
| 84 | |
| 10608 | 85 if (singular) |
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86 warning_with_id ("Octave:sqrtm:SingularMatrix", |
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87 "sqrtm: matrix is singular, may not have a square root"); |
| 4331 | 88 } |
| 89 | |
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90 template <typename Matrix, typename ComplexMatrix, typename ComplexSCHUR> |
| 10608 | 91 static octave_value |
| 92 do_sqrtm (const octave_value& arg) | |
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93 { |
| 10608 | 94 |
| 95 octave_value retval; | |
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96 |
| 10608 | 97 MatrixType mt = arg.matrix_type (); |
| 98 | |
| 99 bool iscomplex = arg.is_complex_type (); | |
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100 |
| 10608 | 101 typedef typename Matrix::element_type real_type; |
| 102 | |
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103 real_type cutoff = 0; |
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104 real_type one = 1; |
| 10608 | 105 real_type eps = std::numeric_limits<real_type>::epsilon (); |
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106 |
| 10608 | 107 if (! iscomplex) |
| 108 { | |
| 109 Matrix x = octave_value_extract<Matrix> (arg); | |
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110 |
| 10608 | 111 if (mt.is_unknown ()) // if type is not known, compute it now. |
| 112 arg.matrix_type (mt = MatrixType (x)); | |
| 113 | |
| 114 switch (mt.type ()) | |
|
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115 { |
| 10608 | 116 case MatrixType::Upper: |
| 117 case MatrixType::Diagonal: | |
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118 if (! x.diag ().any_element_is_negative ()) |
| 10608 | 119 { |
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120 // Do it in real arithmetic. |
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121 sqrtm_utri_inplace (x); |
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122 retval = x; |
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123 retval.matrix_type (mt); |
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124 } |
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125 else |
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126 iscomplex = true; |
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127 break; |
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128 |
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129 case MatrixType::Lower: |
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130 if (! x.diag ().any_element_is_negative ()) |
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131 { |
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132 x = x.transpose (); |
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133 sqrtm_utri_inplace (x); |
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134 retval = x.transpose (); |
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135 retval.matrix_type (mt); |
| 10608 | 136 } |
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137 else |
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138 iscomplex = true; |
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139 break; |
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140 |
| 10608 | 141 default: |
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142 iscomplex = true; |
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143 break; |
| 10608 | 144 } |
| 145 | |
| 146 if (iscomplex) | |
| 147 cutoff = 10 * x.rows () * eps * xnorm (x, one); | |
| 148 } | |
| 149 | |
| 150 if (iscomplex) | |
| 151 { | |
| 152 ComplexMatrix x = octave_value_extract<ComplexMatrix> (arg); | |
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153 |
| 10608 | 154 if (mt.is_unknown ()) // if type is not known, compute it now. |
| 155 arg.matrix_type (mt = MatrixType (x)); | |
| 156 | |
| 157 switch (mt.type ()) | |
| 158 { | |
| 159 case MatrixType::Upper: | |
| 160 case MatrixType::Diagonal: | |
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161 sqrtm_utri_inplace (x); |
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162 retval = x; |
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163 retval.matrix_type (mt); |
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164 break; |
| 10608 | 165 |
| 166 case MatrixType::Lower: | |
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167 x = x.transpose (); |
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168 sqrtm_utri_inplace (x); |
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169 retval = x.transpose (); |
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170 retval.matrix_type (mt); |
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171 break; |
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172 |
| 10608 | 173 default: |
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174 { |
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175 ComplexMatrix u; |
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176 |
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177 do |
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178 { |
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179 ComplexSCHUR schur_fact (x, "", true); |
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180 x = schur_fact.schur_matrix (); |
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181 u = schur_fact.unitary_matrix (); |
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182 } |
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183 while (0); // schur no longer needed. |
| 10608 | 184 |
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185 sqrtm_utri_inplace (x); |
| 10608 | 186 |
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187 x = u * x; // original x no longer needed. |
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188 ComplexMatrix res = xgemm (x, u, blas_no_trans, blas_conj_trans); |
| 10608 | 189 |
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190 if (cutoff > 0 && xnorm (imag (res), one) <= cutoff) |
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191 retval = real (res); |
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192 else |
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193 retval = res; |
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194 } |
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195 break; |
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196 } |
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197 } |
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198 |
| 10608 | 199 return retval; |
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200 } |
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201 |
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202 DEFUN (sqrtm, args, nargout, |
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203 "-*- texinfo -*-\n\ |
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204 @deftypefn {} {@var{s} =} sqrtm (@var{A})\n\ |
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205 @deftypefnx {} {[@var{s}, @var{error_estimate}] =} sqrtm (@var{A})\n\ |
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206 Compute the matrix square root of the square matrix @var{A}.\n\ |
| 4331 | 207 \n\ |
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208 Ref: @nospell{N.J. Higham}. @cite{A New sqrtm for @sc{matlab}}. Numerical\n\ |
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209 Analysis Report No. 336, Manchester @nospell{Centre} for Computational\n\ |
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210 Mathematics, Manchester, England, January 1999.\n\ |
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211 @seealso{expm, logm}\n\ |
| 5642 | 212 @end deftypefn") |
| 4331 | 213 { |
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214 if (args.length () != 1) |
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215 print_usage (); |
| 4331 | 216 |
| 217 octave_value arg = args(0); | |
| 218 | |
| 5275 | 219 octave_idx_type n = arg.rows (); |
| 220 octave_idx_type nc = arg.columns (); | |
| 4331 | 221 |
| 10608 | 222 if (n != nc || arg.ndims () > 2) |
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223 err_square_matrix_required ("sqrtm", "A"); |
| 4331 | 224 |
| 20892 | 225 octave_value_list retval (nargout > 1 ? 3 : 1); |
| 226 | |
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227 if (nargout > 1) |
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228 { |
| 20892 | 229 // FIXME: Octave does not calculate a condition number with respect to |
| 230 // sqrtm. Should this return NaN instead of -1? | |
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231 retval(2) = -1.0; |
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232 } |
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233 |
| 10608 | 234 if (arg.is_diag_matrix ()) |
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235 // sqrtm of a diagonal matrix is just sqrt. |
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236 retval(0) = arg.sqrt (); |
| 10608 | 237 else if (arg.is_single_type ()) |
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238 retval(0) = do_sqrtm<FloatMatrix, FloatComplexMatrix, |
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239 schur<FloatComplexMatrix> > (arg); |
| 10608 | 240 else if (arg.is_numeric_type ()) |
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241 retval(0) = do_sqrtm<Matrix, ComplexMatrix, schur<ComplexMatrix> > (arg); |
| 4331 | 242 |
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243 if (nargout > 1) |
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244 { |
| 10608 | 245 // This corresponds to generic code |
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246 // |
| 10608 | 247 // norm (s*s - x, "fro") / norm (x, "fro"); |
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248 |
| 10608 | 249 octave_value s = retval(0); |
| 250 retval(1) = xfrobnorm (s*s - arg) / xfrobnorm (arg); | |
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251 } |
| 4331 | 252 |
| 253 return retval; | |
| 254 } | |
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255 |
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256 /* |
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257 %!assert (sqrtm (2*ones (2)), ones (2), 3*eps) |
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258 |
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259 ## The following two tests are from the reference in the docstring above. |
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260 %!test |
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261 %! warning ("off", "Octave:sqrtm:SingularMatrix", "local"); |
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262 %! x = [0 1; 0 0]; |
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263 %! assert (any (isnan (sqrtm (x))(:))); |
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264 |
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265 %!test |
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266 %! x = eye (4); x(2,2) = x(3,3) = 2^-26; x(1,4) = 1; |
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267 %! z = eye (4); z(2,2) = z(3,3) = 2^-13; z(1,4) = 0.5; |
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268 %! [y, err] = sqrtm (x); |
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269 %! assert (y, z); |
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270 %! assert (err, 0); # Yes, this one has to hold exactly |
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271 */ |