Mercurial > octave-nkf
annotate libinterp/corefcn/sqrtm.cc @ 17787:175b392e91fe
Use GNU style coding conventions for code in libinterp/
* libinterp/corefcn/Cell.h, libinterp/corefcn/__contourc__.cc,
libinterp/corefcn/__dispatch__.cc, libinterp/corefcn/__lin_interpn__.cc,
libinterp/corefcn/__pchip_deriv__.cc, libinterp/corefcn/__qp__.cc,
libinterp/corefcn/balance.cc, libinterp/corefcn/besselj.cc,
libinterp/corefcn/betainc.cc, libinterp/corefcn/bitfcns.cc,
libinterp/corefcn/bsxfun.cc, libinterp/corefcn/c-file-ptr-stream.cc,
libinterp/corefcn/c-file-ptr-stream.h, libinterp/corefcn/cellfun.cc,
libinterp/corefcn/colloc.cc, libinterp/corefcn/comment-list.h,
libinterp/corefcn/conv2.cc, libinterp/corefcn/daspk.cc,
libinterp/corefcn/dasrt.cc, libinterp/corefcn/dassl.cc,
libinterp/corefcn/data.cc, libinterp/corefcn/debug.cc,
libinterp/corefcn/defaults.cc, libinterp/corefcn/defaults.in.h,
libinterp/corefcn/defun-int.h, libinterp/corefcn/defun.cc,
libinterp/corefcn/det.cc, libinterp/corefcn/dirfns.cc,
libinterp/corefcn/display.cc, libinterp/corefcn/dlmread.cc,
libinterp/corefcn/dot.cc, libinterp/corefcn/dynamic-ld.cc,
libinterp/corefcn/dynamic-ld.h, libinterp/corefcn/eig.cc,
libinterp/corefcn/ellipj.cc, libinterp/corefcn/error.cc,
libinterp/corefcn/error.h, libinterp/corefcn/event-queue.h,
libinterp/corefcn/fft.cc, libinterp/corefcn/fft2.cc, libinterp/corefcn/fftn.cc,
libinterp/corefcn/file-io.cc, libinterp/corefcn/filter.cc,
libinterp/corefcn/find.cc, libinterp/corefcn/gammainc.cc,
libinterp/corefcn/gcd.cc, libinterp/corefcn/getgrent.cc,
libinterp/corefcn/getpwent.cc, libinterp/corefcn/getrusage.cc,
libinterp/corefcn/givens.cc, libinterp/corefcn/gl-render.cc,
libinterp/corefcn/gl2ps-renderer.cc, libinterp/corefcn/gl2ps-renderer.h,
libinterp/corefcn/graphics.cc, libinterp/corefcn/graphics.in.h,
libinterp/corefcn/gripes.cc, libinterp/corefcn/gripes.h,
libinterp/corefcn/help.cc, libinterp/corefcn/hess.cc,
libinterp/corefcn/hex2num.cc, libinterp/corefcn/input.cc,
libinterp/corefcn/input.h, libinterp/corefcn/inv.cc,
libinterp/corefcn/jit-ir.h, libinterp/corefcn/jit-typeinfo.cc,
libinterp/corefcn/jit-typeinfo.h, libinterp/corefcn/jit-util.h,
libinterp/corefcn/kron.cc, libinterp/corefcn/load-path.cc,
libinterp/corefcn/load-path.h, libinterp/corefcn/load-save.cc,
libinterp/corefcn/load-save.h, libinterp/corefcn/lookup.cc,
libinterp/corefcn/ls-ascii-helper.cc, libinterp/corefcn/ls-hdf5.cc,
libinterp/corefcn/ls-hdf5.h, libinterp/corefcn/ls-mat-ascii.cc,
libinterp/corefcn/ls-mat-ascii.h, libinterp/corefcn/ls-mat4.cc,
libinterp/corefcn/ls-mat5.cc, libinterp/corefcn/ls-mat5.h,
libinterp/corefcn/ls-oct-ascii.cc, libinterp/corefcn/lsode.cc,
libinterp/corefcn/lu.cc, libinterp/corefcn/luinc.cc,
libinterp/corefcn/mappers.cc, libinterp/corefcn/matrix_type.cc,
libinterp/corefcn/max.cc, libinterp/corefcn/md5sum.cc,
libinterp/corefcn/mex.cc, libinterp/corefcn/mexproto.h,
libinterp/corefcn/mgorth.cc, libinterp/corefcn/mxarray.in.h,
libinterp/corefcn/nproc.cc, libinterp/corefcn/oct-hist.cc,
libinterp/corefcn/oct-lvalue.h, libinterp/corefcn/oct-map.cc,
libinterp/corefcn/oct-map.h, libinterp/corefcn/oct-obj.h,
libinterp/corefcn/oct-prcstrm.h, libinterp/corefcn/oct-stdstrm.h,
libinterp/corefcn/oct-stream.cc, libinterp/corefcn/oct-stream.h,
libinterp/corefcn/octave-link.cc, libinterp/corefcn/octave-link.h,
libinterp/corefcn/pager.cc, libinterp/corefcn/pinv.cc,
libinterp/corefcn/pr-output.cc, libinterp/corefcn/procstream.h,
libinterp/corefcn/profiler.cc, libinterp/corefcn/pt-jit.cc,
libinterp/corefcn/pt-jit.h, libinterp/corefcn/quad.cc,
libinterp/corefcn/quadcc.cc, libinterp/corefcn/qz.cc,
libinterp/corefcn/rand.cc, libinterp/corefcn/rcond.cc,
libinterp/corefcn/regexp.cc, libinterp/corefcn/schur.cc,
libinterp/corefcn/sighandlers.cc, libinterp/corefcn/sighandlers.h,
libinterp/corefcn/sparse-xdiv.cc, libinterp/corefcn/sparse-xdiv.h,
libinterp/corefcn/sparse-xpow.cc, libinterp/corefcn/sparse.cc,
libinterp/corefcn/spparms.cc, libinterp/corefcn/sqrtm.cc,
libinterp/corefcn/str2double.cc, libinterp/corefcn/strfind.cc,
libinterp/corefcn/strfns.cc, libinterp/corefcn/sub2ind.cc,
libinterp/corefcn/svd.cc, libinterp/corefcn/syl.cc,
libinterp/corefcn/symtab.cc, libinterp/corefcn/symtab.h,
libinterp/corefcn/syscalls.cc, libinterp/corefcn/sysdep.cc,
libinterp/corefcn/sysdep.h, libinterp/corefcn/time.cc,
libinterp/corefcn/toplev.cc, libinterp/corefcn/toplev.h,
libinterp/corefcn/tril.cc, libinterp/corefcn/txt-eng-ft.cc,
libinterp/corefcn/txt-eng-ft.h, libinterp/corefcn/txt-eng.h,
libinterp/corefcn/typecast.cc, libinterp/corefcn/urlwrite.cc,
libinterp/corefcn/utils.cc, libinterp/corefcn/variables.cc,
libinterp/corefcn/variables.h, libinterp/corefcn/xdiv.cc,
libinterp/corefcn/xdiv.h, libinterp/corefcn/xnorm.h, libinterp/corefcn/xpow.cc,
libinterp/corefcn/xpow.h, libinterp/corefcn/zfstream.cc,
libinterp/corefcn/zfstream.h, libinterp/dldfcn/__delaunayn__.cc,
libinterp/dldfcn/__dsearchn__.cc, libinterp/dldfcn/__eigs__.cc,
libinterp/dldfcn/__fltk_uigetfile__.cc, libinterp/dldfcn/__glpk__.cc,
libinterp/dldfcn/__init_fltk__.cc, libinterp/dldfcn/__init_gnuplot__.cc,
libinterp/dldfcn/__magick_read__.cc, libinterp/dldfcn/__voronoi__.cc,
libinterp/dldfcn/amd.cc, libinterp/dldfcn/ccolamd.cc, libinterp/dldfcn/chol.cc,
libinterp/dldfcn/colamd.cc, libinterp/dldfcn/convhulln.cc,
libinterp/dldfcn/dmperm.cc, libinterp/dldfcn/fftw.cc, libinterp/dldfcn/qr.cc,
libinterp/dldfcn/symbfact.cc, libinterp/dldfcn/symrcm.cc,
libinterp/dldfcn/tsearch.cc, libinterp/octave-value/ov-base-diag.cc,
libinterp/octave-value/ov-base-diag.h, libinterp/octave-value/ov-base-int.cc,
libinterp/octave-value/ov-base-int.h, libinterp/octave-value/ov-base-mat.h,
libinterp/octave-value/ov-base-scalar.cc,
libinterp/octave-value/ov-base-scalar.h,
libinterp/octave-value/ov-base-sparse.cc,
libinterp/octave-value/ov-base-sparse.h, libinterp/octave-value/ov-base.cc,
libinterp/octave-value/ov-base.h, libinterp/octave-value/ov-bool-mat.cc,
libinterp/octave-value/ov-bool-mat.h, libinterp/octave-value/ov-bool-sparse.cc,
libinterp/octave-value/ov-bool-sparse.h, libinterp/octave-value/ov-bool.cc,
libinterp/octave-value/ov-bool.h, libinterp/octave-value/ov-builtin.cc,
libinterp/octave-value/ov-builtin.h, libinterp/octave-value/ov-cell.cc,
libinterp/octave-value/ov-cell.h, libinterp/octave-value/ov-ch-mat.cc,
libinterp/octave-value/ov-ch-mat.h, libinterp/octave-value/ov-class.cc,
libinterp/octave-value/ov-class.h, libinterp/octave-value/ov-colon.h,
libinterp/octave-value/ov-complex.cc, libinterp/octave-value/ov-complex.h,
libinterp/octave-value/ov-cx-diag.cc, libinterp/octave-value/ov-cx-diag.h,
libinterp/octave-value/ov-cx-mat.cc, libinterp/octave-value/ov-cx-mat.h,
libinterp/octave-value/ov-cx-sparse.cc, libinterp/octave-value/ov-cx-sparse.h,
libinterp/octave-value/ov-dld-fcn.h, libinterp/octave-value/ov-fcn-handle.cc,
libinterp/octave-value/ov-fcn-handle.h,
libinterp/octave-value/ov-fcn-inline.cc,
libinterp/octave-value/ov-fcn-inline.h, libinterp/octave-value/ov-fcn.h,
libinterp/octave-value/ov-float.cc, libinterp/octave-value/ov-float.h,
libinterp/octave-value/ov-flt-complex.cc,
libinterp/octave-value/ov-flt-complex.h,
libinterp/octave-value/ov-flt-cx-diag.cc,
libinterp/octave-value/ov-flt-cx-diag.h,
libinterp/octave-value/ov-flt-cx-mat.cc,
libinterp/octave-value/ov-flt-cx-mat.h,
libinterp/octave-value/ov-flt-re-diag.cc,
libinterp/octave-value/ov-flt-re-diag.h,
libinterp/octave-value/ov-flt-re-mat.cc,
libinterp/octave-value/ov-flt-re-mat.h, libinterp/octave-value/ov-int16.cc,
libinterp/octave-value/ov-int32.cc, libinterp/octave-value/ov-int64.cc,
libinterp/octave-value/ov-int8.cc, libinterp/octave-value/ov-intx.h,
libinterp/octave-value/ov-java.cc, libinterp/octave-value/ov-lazy-idx.h,
libinterp/octave-value/ov-mex-fcn.cc, libinterp/octave-value/ov-mex-fcn.h,
libinterp/octave-value/ov-null-mat.cc, libinterp/octave-value/ov-null-mat.h,
libinterp/octave-value/ov-oncleanup.cc, libinterp/octave-value/ov-perm.cc,
libinterp/octave-value/ov-perm.h, libinterp/octave-value/ov-range.cc,
libinterp/octave-value/ov-range.h, libinterp/octave-value/ov-re-diag.cc,
libinterp/octave-value/ov-re-diag.h, libinterp/octave-value/ov-re-mat.cc,
libinterp/octave-value/ov-re-mat.h, libinterp/octave-value/ov-re-sparse.cc,
libinterp/octave-value/ov-re-sparse.h, libinterp/octave-value/ov-scalar.cc,
libinterp/octave-value/ov-scalar.h, libinterp/octave-value/ov-str-mat.cc,
libinterp/octave-value/ov-str-mat.h, libinterp/octave-value/ov-struct.cc,
libinterp/octave-value/ov-struct.h, libinterp/octave-value/ov-type-conv.h,
libinterp/octave-value/ov-typeinfo.cc, libinterp/octave-value/ov-typeinfo.h,
libinterp/octave-value/ov-uint16.cc, libinterp/octave-value/ov-uint32.cc,
libinterp/octave-value/ov-uint64.cc, libinterp/octave-value/ov-uint8.cc,
libinterp/octave-value/ov-usr-fcn.cc, libinterp/octave-value/ov-usr-fcn.h,
libinterp/octave-value/ov.cc, libinterp/octave-value/ov.h, libinterp/octave.cc,
libinterp/operators/op-b-bm.cc, libinterp/operators/op-b-sbm.cc,
libinterp/operators/op-bm-b.cc, libinterp/operators/op-bm-bm.cc,
libinterp/operators/op-cdm-cdm.cc, libinterp/operators/op-chm.cc,
libinterp/operators/op-class.cc, libinterp/operators/op-cm-cm.cc,
libinterp/operators/op-cm-cs.cc, libinterp/operators/op-cm-s.cc,
libinterp/operators/op-cm-scm.cc, libinterp/operators/op-cm-sm.cc,
libinterp/operators/op-cs-cm.cc, libinterp/operators/op-cs-cs.cc,
libinterp/operators/op-cs-scm.cc, libinterp/operators/op-cs-sm.cc,
libinterp/operators/op-dm-dm.cc, libinterp/operators/op-dm-scm.cc,
libinterp/operators/op-double-conv.cc, libinterp/operators/op-fcdm-fcdm.cc,
libinterp/operators/op-fcm-fcm.cc, libinterp/operators/op-fcm-fcs.cc,
libinterp/operators/op-fcm-fm.cc, libinterp/operators/op-fcm-fs.cc,
libinterp/operators/op-fcs-fcm.cc, libinterp/operators/op-fcs-fcs.cc,
libinterp/operators/op-fcs-fm.cc, libinterp/operators/op-fcs-fs.cc,
libinterp/operators/op-fdm-fdm.cc, libinterp/operators/op-float-conv.cc,
libinterp/operators/op-fm-fcm.cc, libinterp/operators/op-fm-fcs.cc,
libinterp/operators/op-fm-fm.cc, libinterp/operators/op-fm-fs.cc,
libinterp/operators/op-fs-fcm.cc, libinterp/operators/op-fs-fcs.cc,
libinterp/operators/op-fs-fm.cc, libinterp/operators/op-fs-fs.cc,
libinterp/operators/op-m-cm.cc, libinterp/operators/op-m-cs.cc,
libinterp/operators/op-m-m.cc, libinterp/operators/op-m-s.cc,
libinterp/operators/op-m-scm.cc, libinterp/operators/op-m-sm.cc,
libinterp/operators/op-pm-scm.cc, libinterp/operators/op-range.cc,
libinterp/operators/op-s-cm.cc, libinterp/operators/op-s-cs.cc,
libinterp/operators/op-s-scm.cc, libinterp/operators/op-sbm-b.cc,
libinterp/operators/op-sbm-bm.cc, libinterp/operators/op-sbm-sbm.cc,
libinterp/operators/op-scm-cm.cc, libinterp/operators/op-scm-cs.cc,
libinterp/operators/op-scm-m.cc, libinterp/operators/op-scm-s.cc,
libinterp/operators/op-scm-scm.cc, libinterp/operators/op-scm-sm.cc,
libinterp/operators/op-sm-cm.cc, libinterp/operators/op-sm-m.cc,
libinterp/operators/op-sm-s.cc, libinterp/operators/op-sm-scm.cc,
libinterp/operators/op-sm-sm.cc, libinterp/operators/op-str-m.cc,
libinterp/operators/op-str-s.cc, libinterp/operators/op-str-str.cc,
libinterp/operators/ops.h, libinterp/parse-tree/lex.h,
libinterp/parse-tree/parse.h, libinterp/parse-tree/pt-arg-list.cc,
libinterp/parse-tree/pt-arg-list.h, libinterp/parse-tree/pt-assign.cc,
libinterp/parse-tree/pt-assign.h, libinterp/parse-tree/pt-binop.cc,
libinterp/parse-tree/pt-binop.h, libinterp/parse-tree/pt-bp.h,
libinterp/parse-tree/pt-cbinop.cc, libinterp/parse-tree/pt-check.cc,
libinterp/parse-tree/pt-colon.cc, libinterp/parse-tree/pt-colon.h,
libinterp/parse-tree/pt-const.cc, libinterp/parse-tree/pt-decl.cc,
libinterp/parse-tree/pt-decl.h, libinterp/parse-tree/pt-eval.cc,
libinterp/parse-tree/pt-except.h, libinterp/parse-tree/pt-exp.h,
libinterp/parse-tree/pt-fcn-handle.cc, libinterp/parse-tree/pt-id.cc,
libinterp/parse-tree/pt-id.h, libinterp/parse-tree/pt-idx.cc,
libinterp/parse-tree/pt-idx.h, libinterp/parse-tree/pt-loop.h,
libinterp/parse-tree/pt-mat.cc, libinterp/parse-tree/pt-misc.cc,
libinterp/parse-tree/pt-misc.h, libinterp/parse-tree/pt-pr-code.cc,
libinterp/parse-tree/pt-select.h, libinterp/parse-tree/pt-stmt.h,
libinterp/parse-tree/token.h, libinterp/version.cc:
Use GNU style coding conventions for code in libinterp/
| author | Rik <rik@octave.org> |
|---|---|
| date | Mon, 28 Oct 2013 19:51:46 -0700 |
| parents | d63878346099 |
| children | 6a71e5030df5 |
| rev | line source |
|---|---|
| 4331 | 1 /* |
| 2 | |
|
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3 Copyright (C) 2001-2013 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 | |
| 24 #ifdef HAVE_CONFIG_H | |
| 25 #include <config.h> | |
| 26 #endif | |
| 27 | |
| 28 #include <float.h> | |
| 29 | |
| 30 #include "CmplxSCHUR.h" | |
|
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31 #include "fCmplxSCHUR.h" |
| 4331 | 32 #include "lo-ieee.h" |
| 33 #include "lo-mappers.h" | |
| 10608 | 34 #include "oct-norm.h" |
| 4331 | 35 |
|
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36 #include "defun.h" |
| 4331 | 37 #include "error.h" |
| 38 #include "gripes.h" | |
| 39 #include "utils.h" | |
| 10608 | 40 #include "xnorm.h" |
| 4331 | 41 |
| 10608 | 42 template <class Matrix> |
| 43 static void | |
| 44 sqrtm_utri_inplace (Matrix& T) | |
| 4331 | 45 { |
| 10608 | 46 typedef typename Matrix::element_type element_type; |
| 4331 | 47 |
| 10608 | 48 const element_type zero = element_type (); |
| 4331 | 49 |
| 10608 | 50 bool singular = false; |
|
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51 |
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52 // The following code is equivalent to this triple loop: |
|
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53 // |
|
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54 // n = rows (T); |
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55 // for j = 1:n |
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56 // T(j,j) = sqrt (T(j,j)); |
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57 // for i = j-1:-1:1 |
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58 // T(i,j) /= (T(i,i) + T(j,j)); |
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59 // k = 1:i-1; |
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60 // T(k,j) -= T(k,i) * T(i,j); |
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61 // endfor |
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62 // endfor |
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63 // |
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64 // this is an in-place, cache-aligned variant of the code |
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65 // given in Higham's paper. |
| 4331 | 66 |
| 10608 | 67 const octave_idx_type n = T.rows (); |
| 68 element_type *Tp = T.fortran_vec (); | |
| 5275 | 69 for (octave_idx_type j = 0; j < n; j++) |
| 4331 | 70 { |
| 10608 | 71 element_type *colj = Tp + n*j; |
| 72 if (colj[j] != zero) | |
| 73 colj[j] = sqrt (colj[j]); | |
| 74 else | |
| 75 singular = true; | |
| 4331 | 76 |
| 10608 | 77 for (octave_idx_type i = j-1; i >= 0; i--) |
| 78 { | |
| 79 const element_type *coli = Tp + n*i; | |
| 80 const element_type colji = colj[i] /= (coli[i] + colj[j]); | |
| 81 for (octave_idx_type k = 0; k < i; k++) | |
| 82 colj[k] -= coli[k] * colji; | |
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83 } |
| 4331 | 84 } |
| 85 | |
| 10608 | 86 if (singular) |
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87 warning_with_id ("Octave:sqrtm:SingularMatrix", |
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88 "sqrtm: matrix is singular, may not have a square root"); |
| 4331 | 89 } |
| 90 | |
| 10608 | 91 template <class Matrix, class ComplexMatrix, class ComplexSCHUR> |
| 92 static octave_value | |
| 93 do_sqrtm (const octave_value& arg) | |
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94 { |
| 10608 | 95 |
| 96 octave_value retval; | |
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97 |
| 10608 | 98 MatrixType mt = arg.matrix_type (); |
| 99 | |
| 100 bool iscomplex = arg.is_complex_type (); | |
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| 10608 | 102 typedef typename Matrix::element_type real_type; |
| 103 | |
| 104 real_type cutoff = 0, one = 1; | |
| 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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| 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 (x, std::string (), true); |
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180 x = schur.schur_matrix (); |
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181 u = schur.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 {Built-in Function} {@var{s} =} sqrtm (@var{A})\n\ |
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205 @deftypefnx {Built-in Function} {[@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: 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 { |
| 214 octave_value_list retval; | |
| 215 | |
| 216 int nargin = args.length (); | |
| 217 | |
| 218 if (nargin != 1) | |
| 219 { | |
| 5823 | 220 print_usage (); |
| 4331 | 221 return retval; |
| 222 } | |
| 223 | |
| 224 octave_value arg = args(0); | |
| 225 | |
| 5275 | 226 octave_idx_type n = arg.rows (); |
| 227 octave_idx_type nc = arg.columns (); | |
| 4331 | 228 |
| 10608 | 229 if (n != nc || arg.ndims () > 2) |
| 4331 | 230 { |
| 231 gripe_square_matrix_required ("sqrtm"); | |
| 232 return retval; | |
| 233 } | |
| 234 | |
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235 if (nargout > 1) |
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236 { |
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237 retval.resize (1, 2); |
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238 retval(2) = -1.0; |
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239 } |
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240 |
| 10608 | 241 if (arg.is_diag_matrix ()) |
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242 // sqrtm of a diagonal matrix is just sqrt. |
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243 retval(0) = arg.sqrt (); |
| 10608 | 244 else if (arg.is_single_type ()) |
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245 retval(0) = do_sqrtm<FloatMatrix, FloatComplexMatrix, FloatComplexSCHUR> |
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246 (arg); |
| 10608 | 247 else if (arg.is_numeric_type ()) |
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248 retval(0) = do_sqrtm<Matrix, ComplexMatrix, ComplexSCHUR> (arg); |
| 4331 | 249 |
| 10608 | 250 if (nargout > 1 && ! error_state) |
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251 { |
| 10608 | 252 // This corresponds to generic code |
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253 // |
| 10608 | 254 // norm (s*s - x, "fro") / norm (x, "fro"); |
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255 |
| 10608 | 256 octave_value s = retval(0); |
| 257 retval(1) = xfrobnorm (s*s - arg) / xfrobnorm (arg); | |
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258 } |
| 4331 | 259 |
| 260 return retval; | |
| 261 } | |
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262 |
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263 /* |
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264 %!assert (sqrtm (2*ones (2)), ones (2), 3*eps) |
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265 |
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266 ## The following two tests are from the reference in the docstring above. |
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267 %!test |
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268 %! x = [0 1; 0 0]; |
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269 %! assert (any (isnan (sqrtm (x))(:))); |
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270 |
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271 %!test |
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272 %! x = eye (4); x(2,2) = x(3,3) = 2^-26; x(1,4) = 1; |
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273 %! z = eye (4); z(2,2) = z(3,3) = 2^-13; z(1,4) = 0.5; |
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274 %! [y, err] = sqrtm (x); |
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275 %! assert (y, z); |
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276 %! assert (err, 0); # Yes, this one has to hold exactly |
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parents:
12584
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277 */ |