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annotate liboctave/numeric/oct-norm.cc @ 17769:49a5a4be04a1

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maint: Use GNU style coding conventions for code in liboctave/ * liboctave/array/Array-C.cc, liboctave/array/Array-b.cc, liboctave/array/Array-ch.cc, liboctave/array/Array-d.cc, liboctave/array/Array-f.cc, liboctave/array/Array-fC.cc, liboctave/array/Array-util.cc, liboctave/array/Array-util.h, liboctave/array/Array.cc, liboctave/array/Array.h, liboctave/array/Array3.h, liboctave/array/CColVector.cc, liboctave/array/CColVector.h, liboctave/array/CDiagMatrix.cc, liboctave/array/CDiagMatrix.h, liboctave/array/CMatrix.cc, liboctave/array/CMatrix.h, liboctave/array/CNDArray.cc, liboctave/array/CNDArray.h, liboctave/array/CRowVector.cc, liboctave/array/CRowVector.h, liboctave/array/CSparse.cc, liboctave/array/CSparse.h, liboctave/array/DiagArray2.h, liboctave/array/MArray.cc, liboctave/array/MArray.h, liboctave/array/MDiagArray2.cc, liboctave/array/MDiagArray2.h, liboctave/array/MSparse.cc, liboctave/array/MSparse.h, liboctave/array/MatrixType.cc, liboctave/array/MatrixType.h, liboctave/array/PermMatrix.h, liboctave/array/Range.cc, liboctave/array/Range.h, liboctave/array/Sparse.cc, liboctave/array/Sparse.h, liboctave/array/boolMatrix.cc, liboctave/array/boolMatrix.h, liboctave/array/boolNDArray.cc, liboctave/array/boolNDArray.h, liboctave/array/boolSparse.cc, liboctave/array/boolSparse.h, liboctave/array/chMatrix.cc, liboctave/array/chMatrix.h, liboctave/array/chNDArray.cc, liboctave/array/chNDArray.h, liboctave/array/dColVector.h, liboctave/array/dDiagMatrix.cc, liboctave/array/dDiagMatrix.h, liboctave/array/dMatrix.cc, liboctave/array/dMatrix.h, liboctave/array/dNDArray.cc, liboctave/array/dNDArray.h, liboctave/array/dRowVector.h, liboctave/array/dSparse.cc, liboctave/array/dSparse.h, liboctave/array/dim-vector.cc, liboctave/array/dim-vector.h, liboctave/array/fCColVector.cc, liboctave/array/fCColVector.h, liboctave/array/fCDiagMatrix.cc, liboctave/array/fCDiagMatrix.h, liboctave/array/fCMatrix.cc, liboctave/array/fCMatrix.h, liboctave/array/fCNDArray.cc, liboctave/array/fCNDArray.h, liboctave/array/fCRowVector.cc, liboctave/array/fCRowVector.h, liboctave/array/fColVector.h, liboctave/array/fDiagMatrix.cc, liboctave/array/fDiagMatrix.h, liboctave/array/fMatrix.cc, liboctave/array/fMatrix.h, liboctave/array/fNDArray.cc, liboctave/array/fNDArray.h, liboctave/array/fRowVector.h, liboctave/array/idx-vector.cc, liboctave/array/idx-vector.h, liboctave/array/intNDArray.cc, liboctave/array/intNDArray.h, liboctave/cruft/misc/blaswrap.c, liboctave/cruft/misc/quit.cc, liboctave/numeric/CmplxCHOL.cc, liboctave/numeric/CmplxCHOL.h, liboctave/numeric/CmplxGEPBAL.cc, liboctave/numeric/CmplxGEPBAL.h, liboctave/numeric/CmplxHESS.h, liboctave/numeric/CmplxLU.cc, liboctave/numeric/CmplxLU.h, liboctave/numeric/CmplxQR.cc, liboctave/numeric/CmplxQRP.cc, liboctave/numeric/CmplxQRP.h, liboctave/numeric/CmplxSCHUR.h, liboctave/numeric/CmplxSVD.cc, liboctave/numeric/CmplxSVD.h, liboctave/numeric/CollocWt.h, liboctave/numeric/DAE.h, liboctave/numeric/DAEFunc.h, liboctave/numeric/DAERT.h, liboctave/numeric/DAERTFunc.h, liboctave/numeric/DASPK.cc, liboctave/numeric/DASRT.cc, liboctave/numeric/DASRT.h, liboctave/numeric/DASSL.cc, liboctave/numeric/DET.h, liboctave/numeric/EIG.cc, liboctave/numeric/EIG.h, liboctave/numeric/LSODE.cc, liboctave/numeric/ODE.h, liboctave/numeric/ODEFunc.h, liboctave/numeric/ODES.h, liboctave/numeric/ODESFunc.h, liboctave/numeric/Quad.cc, liboctave/numeric/Quad.h, liboctave/numeric/SparseCmplxCHOL.h, liboctave/numeric/SparseCmplxLU.cc, liboctave/numeric/SparseCmplxLU.h, liboctave/numeric/SparseCmplxQR.cc, liboctave/numeric/SparseCmplxQR.h, liboctave/numeric/SparseQR.cc, liboctave/numeric/SparseQR.h, liboctave/numeric/SparsedbleCHOL.h, liboctave/numeric/SparsedbleLU.cc, liboctave/numeric/SparsedbleLU.h, liboctave/numeric/base-aepbal.h, liboctave/numeric/base-dae.h, liboctave/numeric/base-de.h, liboctave/numeric/base-lu.cc, liboctave/numeric/base-lu.h, liboctave/numeric/base-min.h, liboctave/numeric/base-qr.h, liboctave/numeric/bsxfun.h, liboctave/numeric/dbleCHOL.cc, liboctave/numeric/dbleCHOL.h, liboctave/numeric/dbleGEPBAL.h, liboctave/numeric/dbleHESS.h, liboctave/numeric/dbleLU.cc, liboctave/numeric/dbleLU.h, liboctave/numeric/dbleQR.cc, liboctave/numeric/dbleQRP.cc, liboctave/numeric/dbleQRP.h, liboctave/numeric/dbleSCHUR.cc, liboctave/numeric/dbleSCHUR.h, liboctave/numeric/dbleSVD.cc, liboctave/numeric/dbleSVD.h, liboctave/numeric/eigs-base.cc, liboctave/numeric/fCmplxAEPBAL.cc, liboctave/numeric/fCmplxAEPBAL.h, liboctave/numeric/fCmplxCHOL.cc, liboctave/numeric/fCmplxCHOL.h, liboctave/numeric/fCmplxGEPBAL.cc, liboctave/numeric/fCmplxGEPBAL.h, liboctave/numeric/fCmplxHESS.h, liboctave/numeric/fCmplxLU.cc, liboctave/numeric/fCmplxLU.h, liboctave/numeric/fCmplxQR.cc, liboctave/numeric/fCmplxQR.h, liboctave/numeric/fCmplxQRP.cc, liboctave/numeric/fCmplxQRP.h, liboctave/numeric/fCmplxSCHUR.cc, liboctave/numeric/fCmplxSCHUR.h, liboctave/numeric/fCmplxSVD.h, liboctave/numeric/fEIG.cc, liboctave/numeric/fEIG.h, liboctave/numeric/floatCHOL.cc, liboctave/numeric/floatCHOL.h, liboctave/numeric/floatGEPBAL.cc, liboctave/numeric/floatGEPBAL.h, liboctave/numeric/floatHESS.h, liboctave/numeric/floatLU.cc, liboctave/numeric/floatLU.h, liboctave/numeric/floatQR.cc, liboctave/numeric/floatQRP.cc, liboctave/numeric/floatQRP.h, liboctave/numeric/floatSCHUR.cc, liboctave/numeric/floatSCHUR.h, liboctave/numeric/floatSVD.cc, liboctave/numeric/floatSVD.h, liboctave/numeric/lo-mappers.cc, liboctave/numeric/lo-mappers.h, liboctave/numeric/lo-specfun.cc, liboctave/numeric/lo-specfun.h, liboctave/numeric/oct-convn.cc, liboctave/numeric/oct-fftw.cc, liboctave/numeric/oct-fftw.h, liboctave/numeric/oct-norm.cc, liboctave/numeric/oct-rand.cc, liboctave/numeric/oct-rand.h, liboctave/numeric/randgamma.c, liboctave/numeric/randgamma.h, liboctave/numeric/randmtzig.c, liboctave/numeric/randpoisson.c, liboctave/numeric/randpoisson.h, liboctave/numeric/sparse-base-chol.h, liboctave/numeric/sparse-base-lu.h, liboctave/numeric/sparse-dmsolve.cc, liboctave/operators/Sparse-diag-op-defs.h, liboctave/operators/Sparse-op-defs.h, liboctave/operators/mx-inlines.cc, liboctave/system/dir-ops.h, liboctave/system/file-ops.cc, liboctave/system/file-stat.cc, liboctave/system/file-stat.h, liboctave/system/lo-sysdep.cc, liboctave/system/lo-sysdep.h, liboctave/system/mach-info.cc, liboctave/system/mach-info.h, liboctave/system/oct-env.cc, liboctave/system/oct-group.cc, liboctave/system/oct-syscalls.cc, liboctave/system/oct-syscalls.h, liboctave/system/oct-time.h, liboctave/system/tempname.c, liboctave/util/action-container.h, liboctave/util/base-list.h, liboctave/util/cmd-edit.cc, liboctave/util/cmd-edit.h, liboctave/util/cmd-hist.cc, liboctave/util/cmd-hist.h, liboctave/util/data-conv.cc, liboctave/util/data-conv.h, liboctave/util/kpse.cc, liboctave/util/lo-array-gripes.cc, liboctave/util/lo-cieee.c, liboctave/util/lo-regexp.cc, liboctave/util/lo-utils.cc, liboctave/util/oct-alloc.cc, liboctave/util/oct-base64.cc, liboctave/util/oct-binmap.h, liboctave/util/oct-cmplx.h, liboctave/util/oct-glob.cc, liboctave/util/oct-inttypes.cc, liboctave/util/oct-inttypes.h, liboctave/util/oct-locbuf.cc, liboctave/util/oct-locbuf.h, liboctave/util/oct-mem.h, liboctave/util/oct-mutex.cc, liboctave/util/oct-refcount.h, liboctave/util/oct-shlib.cc, liboctave/util/oct-shlib.h, liboctave/util/oct-sort.cc, liboctave/util/oct-sort.h, liboctave/util/pathsearch.cc, liboctave/util/pathsearch.h, liboctave/util/sparse-util.cc, liboctave/util/str-vec.cc, liboctave/util/str-vec.h, liboctave/util/unwind-prot.h, liboctave/util/url-transfer.cc, liboctave/util/url-transfer.h: Use GNU style coding conventions.
author Rik <rik@octave.org>
date Sat, 26 Oct 2013 18:57:05 -0700
parents d63878346099
children 8e056300994b
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1 /*
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2
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3 Copyright (C) 2008-2013 VZLU Prague, a.s.
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4
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5 This file is part of Octave.
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6
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7 Octave is free software; you can redistribute it and/or modify it
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8 under the terms of the GNU General Public License as published by the
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9 Free Software Foundation; either version 3 of the License, or (at your
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10 option) any later version.
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11
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12 Octave is distributed in the hope that it will be useful, but WITHOUT
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13 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
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14 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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15 for more details.
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16
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17 You should have received a copy of the GNU General Public License
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18 along with Octave; see the file COPYING. If not, see
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19 <http://www.gnu.org/licenses/>.
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20
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21 */
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22
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23 // author: Jaroslav Hajek <highegg@gmail.com>
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24
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25 #ifdef HAVE_CONFIG_H
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26 #include <config.h>
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27 #endif
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28
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29 #include <cassert>
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30 #include <cfloat>
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31 #include <cmath>
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32
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33 #include <iostream>
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34 #include <vector>
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35
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36 #include "oct-cmplx.h"
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37 #include "lo-error.h"
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38 #include "lo-ieee.h"
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39 #include "Array.h"
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40 #include "Array-util.h"
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41 #include "CMatrix.h"
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42 #include "dMatrix.h"
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43 #include "fCMatrix.h"
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44 #include "fMatrix.h"
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45 #include "CColVector.h"
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46 #include "dColVector.h"
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47 #include "CRowVector.h"
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48 #include "dRowVector.h"
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49 #include "fCColVector.h"
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50 #include "fColVector.h"
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51 #include "fCRowVector.h"
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52 #include "fRowVector.h"
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53 #include "CSparse.h"
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54 #include "dSparse.h"
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55 #include "dbleSVD.h"
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56 #include "CmplxSVD.h"
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57 #include "floatSVD.h"
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58 #include "fCmplxSVD.h"
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59
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60 // Theory: norm accumulator is an object that has an accum method able
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61 // to handle both real and complex element, and a cast operator
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62 // returning the intermediate norm. Reference: Higham, N. "Estimating
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63 // the Matrix p-Norm." Numer. Math. 62, 539-555, 1992.
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64
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65 // norm accumulator for the p-norm
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66 template <class R>
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67 class norm_accumulator_p
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68 {
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69 R p,scl,sum;
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70 public:
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71 norm_accumulator_p () {} // we need this one for Array
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72 norm_accumulator_p (R pp) : p(pp), scl(0), sum(1) {}
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73
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74 template<class U>
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75 void accum (U val)
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76 {
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77 octave_quit ();
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78 R t = std::abs (val);
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79 if (scl == t) // we need this to handle Infs properly
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80 sum += 1;
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81 else if (scl < t)
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82 {
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83 sum *= std::pow (scl/t, p);
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84 sum += 1;
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85 scl = t;
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86 }
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87 else if (t != 0)
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88 sum += std::pow (t/scl, p);
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89 }
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90 operator R () { return scl * std::pow (sum, 1/p); }
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91 };
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92
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93 // norm accumulator for the minus p-pseudonorm
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94 template <class R>
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95 class norm_accumulator_mp
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96 {
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97 R p,scl,sum;
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98 public:
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99 norm_accumulator_mp () {} // we need this one for Array
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100 norm_accumulator_mp (R pp) : p(pp), scl(0), sum(1) {}
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101
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102 template<class U>
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103 void accum (U val)
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104 {
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105 octave_quit ();
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106 R t = 1 / std::abs (val);
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107 if (scl == t)
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108 sum += 1;
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109 else if (scl < t)
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110 {
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111 sum *= std::pow (scl/t, p);
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112 sum += 1;
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113 scl = t;
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114 }
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115 else if (t != 0)
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116 sum += std::pow (t/scl, p);
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117 }
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118 operator R () { return scl * std::pow (sum, -1/p); }
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119 };
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120
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121 // norm accumulator for the 2-norm (euclidean)
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122 template <class R>
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123 class norm_accumulator_2
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124 {
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125 R scl,sum;
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126 static R pow2 (R x) { return x*x; }
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127 public:
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128 norm_accumulator_2 () : scl(0), sum(1) {}
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129
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130 void accum (R val)
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131 {
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132 R t = std::abs (val);
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133 if (scl == t)
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134 sum += 1;
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135 else if (scl < t)
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136 {
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137 sum *= pow2 (scl/t);
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138 sum += 1;
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139 scl = t;
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140 }
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141 else if (t != 0)
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142 sum += pow2 (t/scl);
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143 }
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144
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145 void accum (std::complex<R> val)
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146 {
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147 accum (val.real ());
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148 accum (val.imag ());
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149 }
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150
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151 operator R () { return scl * std::sqrt (sum); }
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152 };
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153
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154 // norm accumulator for the 1-norm (city metric)
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155 template <class R>
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156 class norm_accumulator_1
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157 {
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158 R sum;
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159 public:
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160 norm_accumulator_1 () : sum (0) {}
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161 template<class U>
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162 void accum (U val)
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163 {
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164 sum += std::abs (val);
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165 }
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166 operator R () { return sum; }
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167 };
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168
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169 // norm accumulator for the inf-norm (max metric)
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170 template <class R>
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171 class norm_accumulator_inf
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172 {
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173 R max;
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174 public:
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175 norm_accumulator_inf () : max (0) {}
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176 template<class U>
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177 void accum (U val)
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178 {
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179 max = std::max (max, std::abs (val));
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180 }
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181 operator R () { return max; }
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182 };
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183
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184 // norm accumulator for the -inf pseudonorm (min abs value)
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185 template <class R>
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186 class norm_accumulator_minf
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187 {
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188 R min;
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189 public:
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190 norm_accumulator_minf () : min (octave_Inf) {}
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191 template<class U>
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192 void accum (U val)
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193 {
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194 min = std::min (min, std::abs (val));
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195 }
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196 operator R () { return min; }
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197 };
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198
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199 // norm accumulator for the 0-pseudonorm (hamming distance)
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200 template <class R>
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201 class norm_accumulator_0
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202 {
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203 unsigned int num;
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204 public:
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205 norm_accumulator_0 () : num (0) {}
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206 template<class U>
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207 void accum (U val)
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208 {
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209 if (val != static_cast<U> (0)) ++num;
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210 }
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211 operator R () { return num; }
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212 };
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213
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214
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215 // OK, we're armed :) Now let's go for the fun
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216
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217 template <class T, class R, class ACC>
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218 inline void vector_norm (const Array<T>& v, R& res, ACC acc)
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219 {
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220 for (octave_idx_type i = 0; i < v.numel (); i++)
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221 acc.accum (v(i));
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222
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223 res = acc;
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224 }
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225
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226 // dense versions
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227 template <class T, class R, class ACC>
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228 void column_norms (const MArray<T>& m, MArray<R>& res, ACC acc)
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229 {
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230 res = MArray<R> (dim_vector (1, m.columns ()));
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231 for (octave_idx_type j = 0; j < m.columns (); j++)
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232 {
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233 ACC accj = acc;
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234 for (octave_idx_type i = 0; i < m.rows (); i++)
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235 accj.accum (m(i, j));
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236
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237 res.xelem (j) = accj;
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238 }
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239 }
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240
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241 template <class T, class R, class ACC>
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242 void row_norms (const MArray<T>& m, MArray<R>& res, ACC acc)
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243 {
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244 res = MArray<R> (dim_vector (m.rows (), 1));
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245 std::vector<ACC> acci (m.rows (), acc);
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246 for (octave_idx_type j = 0; j < m.columns (); j++)
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247 {
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248 for (octave_idx_type i = 0; i < m.rows (); i++)
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249 acci[i].accum (m(i, j));
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250 }
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251
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252 for (octave_idx_type i = 0; i < m.rows (); i++)
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253 res.xelem (i) = acci[i];
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254 }
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255
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256 // sparse versions
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257 template <class T, class R, class ACC>
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258 void column_norms (const MSparse<T>& m, MArray<R>& res, ACC acc)
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259 {
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260 res = MArray<R> (dim_vector (1, m.columns ()));
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261 for (octave_idx_type j = 0; j < m.columns (); j++)
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262 {
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263 ACC accj = acc;
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264 for (octave_idx_type k = m.cidx (j); k < m.cidx (j+1); k++)
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265 accj.accum (m.data (k));
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266
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267 res.xelem (j) = accj;
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268 }
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269 }
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270
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271 template <class T, class R, class ACC>
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272 void row_norms (const MSparse<T>& m, MArray<R>& res, ACC acc)
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273 {
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274 res = MArray<R> (dim_vector (m.rows (), 1));
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275 std::vector<ACC> acci (m.rows (), acc);
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276 for (octave_idx_type j = 0; j < m.columns (); j++)
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277 {
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278 for (octave_idx_type k = m.cidx (j); k < m.cidx (j+1); k++)
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279 acci[m.ridx (k)].accum (m.data (k));
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280 }
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281
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282 for (octave_idx_type i = 0; i < m.rows (); i++)
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283 res.xelem (i) = acci[i];
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284 }
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285
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286 // now the dispatchers
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287 #define DEFINE_DISPATCHER(FUNC_NAME, ARG_TYPE, RES_TYPE) \
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288 template <class T, class R> \
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289 RES_TYPE FUNC_NAME (const ARG_TYPE& v, R p) \
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290 { \
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291 RES_TYPE res; \
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292 if (p == 2) \
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293 FUNC_NAME (v, res, norm_accumulator_2<R> ()); \
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294 else if (p == 1) \
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295 FUNC_NAME (v, res, norm_accumulator_1<R> ()); \
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296 else if (lo_ieee_isinf (p)) \
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297 { \
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298 if (p > 0) \
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299 FUNC_NAME (v, res, norm_accumulator_inf<R> ()); \
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300 else \
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301 FUNC_NAME (v, res, norm_accumulator_minf<R> ()); \
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302 } \
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303 else if (p == 0) \
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304 FUNC_NAME (v, res, norm_accumulator_0<R> ()); \
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305 else if (p > 0) \
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306 FUNC_NAME (v, res, norm_accumulator_p<R> (p)); \
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307 else \
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308 FUNC_NAME (v, res, norm_accumulator_mp<R> (p)); \
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309 return res; \
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310 }
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311
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312 DEFINE_DISPATCHER (vector_norm, MArray<T>, R)
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313 DEFINE_DISPATCHER (column_norms, MArray<T>, MArray<R>)
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314 DEFINE_DISPATCHER (row_norms, MArray<T>, MArray<R>)
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315 DEFINE_DISPATCHER (column_norms, MSparse<T>, MArray<R>)
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316 DEFINE_DISPATCHER (row_norms, MSparse<T>, MArray<R>)
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317
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318 // The approximate subproblem in Higham's method. Find lambda and mu such that
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319 // norm ([lambda, mu], p) == 1 and norm (y*lambda + col*mu, p) is maximized.
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320 // Real version. As in Higham's paper.
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321 template <class ColVectorT, class R>
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322 static void
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323 higham_subp (const ColVectorT& y, const ColVectorT& col,
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324 octave_idx_type nsamp, R p, R& lambda, R& mu)
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325 {
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326 R nrm = 0;
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327 for (octave_idx_type i = 0; i < nsamp; i++)
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328 {
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329 octave_quit ();
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330 R fi = i*M_PI/nsamp, lambda1 = cos (fi), mu1 = sin (fi);
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331 R lmnr = std::pow (std::pow (std::abs (lambda1), p) +
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332 std::pow (std::abs (mu1), p), 1/p);
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333 lambda1 /= lmnr; mu1 /= lmnr;
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334 R nrm1 = vector_norm (lambda1 * y + mu1 * col, p);
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335 if (nrm1 > nrm)
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336 {
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337 lambda = lambda1;
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338 mu = mu1;
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339 nrm = nrm1;
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340 }
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341 }
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342 }
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343
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344 // Complex version. Higham's paper does not deal with complex case, so we use a
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345 // simple extension. First, guess the magnitudes as in real version, then try
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346 // to rotate lambda to improve further.
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347 template <class ColVectorT, class R>
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348 static void
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349 higham_subp (const ColVectorT& y, const ColVectorT& col,
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350 octave_idx_type nsamp, R p,
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351 std::complex<R>& lambda, std::complex<R>& mu)
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352 {
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353 typedef std::complex<R> CR;
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354 R nrm = 0;
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355 lambda = 1.0;
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356 CR lamcu = lambda / std::abs (lambda);
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357 // Probe magnitudes
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358 for (octave_idx_type i = 0; i < nsamp; i++)
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359 {
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360 octave_quit ();
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361 R fi = i*M_PI/nsamp, lambda1 = cos (fi), mu1 = sin (fi);
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362 R lmnr = std::pow (std::pow (std::abs (lambda1), p) +
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363 std::pow (std::abs (mu1), p), 1/p);
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364 lambda1 /= lmnr; mu1 /= lmnr;
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365 R nrm1 = vector_norm (lambda1 * lamcu * y + mu1 * col, p);
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366 if (nrm1 > nrm)
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367 {
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368 lambda = lambda1 * lamcu;
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369 mu = mu1;
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370 nrm = nrm1;
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371 }
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372 }
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373 R lama = std::abs (lambda);
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374 // Probe orientation
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375 for (octave_idx_type i = 0; i < nsamp; i++)
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376 {
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377 octave_quit ();
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378 R fi = i*M_PI/nsamp;
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379 lamcu = CR (cos (fi), sin (fi));
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380 R nrm1 = vector_norm (lama * lamcu * y + mu * col, p);
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381 if (nrm1 > nrm)
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382 {
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383 lambda = lama * lamcu;
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384 nrm = nrm1;
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385 }
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386 }
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387 }
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388
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389 // the p-dual element (should work for both real and complex)
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390 template <class T, class R>
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391 inline T elem_dual_p (T x, R p)
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392 {
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393 return signum (x) * std::pow (std::abs (x), p-1);
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394 }
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395
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396 // the VectorT is used for vectors, but actually it has to be
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397 // a Matrix type to allow all the operations. For instance SparseMatrix
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398 // does not support multiplication with column/row vectors.
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399 // the dual vector
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400 template <class VectorT, class R>
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401 VectorT dual_p (const VectorT& x, R p, R q)
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402 {
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403 VectorT res (x.dims ());
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404 for (octave_idx_type i = 0; i < x.numel (); i++)
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405 res.xelem (i) = elem_dual_p (x(i), p);
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406 return res / vector_norm (res, q);
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407 }
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408
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409 // Higham's hybrid method
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410 template <class MatrixT, class VectorT, class R>
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diff changeset
411 R higham (const MatrixT& m, R p, R tol, int maxiter,
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diff changeset
412 VectorT& x)
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413 {
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parents:
diff changeset
414 x.resize (m.columns (), 1);
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parents:
diff changeset
415 // the OSE part
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parents:
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416 VectorT y(m.rows (), 1, 0), z(m.rows (), 1);
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417 typedef typename VectorT::element_type RR;
14520
c4ed0fdf2b62 Fix initialization in Higham's method for norm estimate (bug #36031).
Marco Caliari <marco.caliari@univr.it>
parents: 14138
diff changeset
418 RR lambda = 0, mu = 1;
8303
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419 for (octave_idx_type k = 0; k < m.columns (); k++)
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parents:
diff changeset
420 {
10142
829e69ec3110 make OCTAVE_QUIT a function
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421 octave_quit ();
8303
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422 VectorT col (m.column (k));
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parents:
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423 if (k > 0)
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424 higham_subp (y, col, 4*k, p, lambda, mu);
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425 for (octave_idx_type i = 0; i < k; i++)
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426 x(i) *= lambda;
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427 x(k) = mu;
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428 y = lambda * y + mu * col;
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429 }
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430
8303
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431 // the PM part
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432 x = x / vector_norm (x, p);
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433 R q = p/(p-1);
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434
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435 R gamma = 0, gamma1;
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436 int iter = 0;
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437 while (iter < maxiter)
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438 {
10142
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439 octave_quit ();
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440 y = m*x;
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441 gamma1 = gamma;
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442 gamma = vector_norm (y, p);
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443 z = dual_p (y, p, q);
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444 z = z.hermitian ();
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445 z = z * m;
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446
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447 if (iter > 0 && (vector_norm (z, q) <= gamma
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448 || (gamma - gamma1) <= tol*gamma))
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449 break;
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450
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451 z = z.hermitian ();
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452 x = dual_p (z, q, p);
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453 iter ++;
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454 }
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455
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456 return gamma;
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457 }
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458
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459 // derive column vector and SVD types
8303
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460
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461 static const char *p_less1_gripe = "xnorm: p must be at least 1";
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462
17769
49a5a4be04a1 maint: Use GNU style coding conventions for code in liboctave/
Rik <rik@octave.org>
parents: 17744
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463 // Static constant to control the maximum number of iterations. 100 seems to
49a5a4be04a1 maint: Use GNU style coding conventions for code in liboctave/
Rik <rik@octave.org>
parents: 17744
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464 // be a good value. Eventually, we can provide a means to change this
49a5a4be04a1 maint: Use GNU style coding conventions for code in liboctave/
Rik <rik@octave.org>
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465 // constant from Octave.
8303
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466 static int max_norm_iter = 100;
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467
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468 // version with SVD for dense matrices
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469 template <class MatrixT, class VectorT, class SVDT, class R>
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470 R matrix_norm (const MatrixT& m, R p, VectorT, SVDT)
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471 {
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472 R res = 0;
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473 if (p == 2)
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474 {
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475 SVDT svd (m, SVD::sigma_only);
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476 res = svd.singular_values () (0,0);
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477 }
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478 else if (p == 1)
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479 res = xcolnorms (m, 1).max ();
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480 else if (lo_ieee_isinf (p))
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481 res = xrownorms (m, 1).max ();
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482 else if (p > 1)
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483 {
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484 VectorT x;
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485 const R sqrteps = std::sqrt (std::numeric_limits<R>::epsilon ());
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486 res = higham (m, p, sqrteps, max_norm_iter, x);
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487 }
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488 else
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489 (*current_liboctave_error_handler) (p_less1_gripe);
8303
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490
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491 return res;
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492 }
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493
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parents:
diff changeset
494 // SVD-free version for sparse matrices
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diff changeset
495 template <class MatrixT, class VectorT, class R>
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496 R matrix_norm (const MatrixT& m, R p, VectorT)
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diff changeset
497 {
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498 R res = 0;
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499 if (p == 1)
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500 res = xcolnorms (m, 1).max ();
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501 else if (lo_ieee_isinf (p))
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502 res = xrownorms (m, 1).max ();
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503 else if (p > 1)
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parents:
diff changeset
504 {
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diff changeset
505 VectorT x;
8995
1b097d86a61a remove a TODO in oct-norm.cc
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506 const R sqrteps = std::sqrt (std::numeric_limits<R>::epsilon ());
1b097d86a61a remove a TODO in oct-norm.cc
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diff changeset
507 res = higham (m, p, sqrteps, max_norm_iter, x);
8303
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508 }
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diff changeset
509 else
11586
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parents: 11570
diff changeset
510 (*current_liboctave_error_handler) (p_less1_gripe);
8303
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511
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512 return res;
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parents:
diff changeset
513 }
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parents:
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514
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parents:
diff changeset
515 // and finally, here's what we've promised in the header file
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516
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diff changeset
517 #define DEFINE_XNORM_FUNCS(PREFIX, RTYPE) \
8319
c374691576f6 Fix for MSVC compilation
Michael Goffioul <michael.goffioul@gmail.com>
parents: 8309
diff changeset
518 OCTAVE_API RTYPE xnorm (const PREFIX##ColumnVector& x, RTYPE p) \
8303
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diff changeset
519 { return vector_norm (x, p); } \
8319
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Michael Goffioul <michael.goffioul@gmail.com>
parents: 8309
diff changeset
520 OCTAVE_API RTYPE xnorm (const PREFIX##RowVector& x, RTYPE p) \
8303
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parents:
diff changeset
521 { return vector_norm (x, p); } \
8319
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Michael Goffioul <michael.goffioul@gmail.com>
parents: 8309
diff changeset
522 OCTAVE_API RTYPE xnorm (const PREFIX##Matrix& x, RTYPE p) \
8303
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diff changeset
523 { return matrix_norm (x, p, PREFIX##Matrix (), PREFIX##SVD ()); } \
8319
c374691576f6 Fix for MSVC compilation
Michael Goffioul <michael.goffioul@gmail.com>
parents: 8309
diff changeset
524 OCTAVE_API RTYPE xfrobnorm (const PREFIX##Matrix& x) \
8303
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parents:
diff changeset
525 { return vector_norm (x, static_cast<RTYPE> (2)); }
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parents:
diff changeset
526
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diff changeset
527 DEFINE_XNORM_FUNCS(, double)
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parents:
diff changeset
528 DEFINE_XNORM_FUNCS(Complex, double)
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parents:
diff changeset
529 DEFINE_XNORM_FUNCS(Float, float)
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parents:
diff changeset
530 DEFINE_XNORM_FUNCS(FloatComplex, float)
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parents:
diff changeset
531
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parents:
diff changeset
532 // this is needed to avoid copying the sparse matrix for xfrobnorm
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parents:
diff changeset
533 template <class T, class R>
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parents:
diff changeset
534 inline void array_norm_2 (const T* v, octave_idx_type n, R& res)
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parents:
diff changeset
535 {
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parents:
diff changeset
536 norm_accumulator_2<R> acc;
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parents:
diff changeset
537 for (octave_idx_type i = 0; i < n; i++)
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parents:
diff changeset
538 acc.accum (v[i]);
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parents:
diff changeset
539
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parents:
diff changeset
540 res = acc;
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parents:
diff changeset
541 }
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parents:
diff changeset
542
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parents:
diff changeset
543 #define DEFINE_XNORM_SPARSE_FUNCS(PREFIX, RTYPE) \
8319
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Michael Goffioul <michael.goffioul@gmail.com>
parents: 8309
diff changeset
544 OCTAVE_API RTYPE xnorm (const Sparse##PREFIX##Matrix& x, RTYPE p) \
8303
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parents:
diff changeset
545 { return matrix_norm (x, p, PREFIX##Matrix ()); } \
8319
c374691576f6 Fix for MSVC compilation
Michael Goffioul <michael.goffioul@gmail.com>
parents: 8309
diff changeset
546 OCTAVE_API RTYPE xfrobnorm (const Sparse##PREFIX##Matrix& x) \
8303
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parents:
diff changeset
547 { \
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parents:
diff changeset
548 RTYPE res; \
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parents:
diff changeset
549 array_norm_2 (x.data (), x.nnz (), res); \
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parents:
diff changeset
550 return res; \
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parents:
diff changeset
551 }
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parents:
diff changeset
552
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parents:
diff changeset
553 DEFINE_XNORM_SPARSE_FUNCS(, double)
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parents:
diff changeset
554 DEFINE_XNORM_SPARSE_FUNCS(Complex, double)
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parents:
diff changeset
555
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parents:
diff changeset
556 #define DEFINE_COLROW_NORM_FUNCS(PREFIX, RPREFIX, RTYPE) \
8319
c374691576f6 Fix for MSVC compilation
Michael Goffioul <michael.goffioul@gmail.com>
parents: 8309
diff changeset
557 extern OCTAVE_API RPREFIX##RowVector xcolnorms (const PREFIX##Matrix& m, RTYPE p) \
8303
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parents:
diff changeset
558 { return column_norms (m, p); } \
8319
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Michael Goffioul <michael.goffioul@gmail.com>
parents: 8309
diff changeset
559 extern OCTAVE_API RPREFIX##ColumnVector xrownorms (const PREFIX##Matrix& m, RTYPE p) \
8303
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parents:
diff changeset
560 { return row_norms (m, p); } \
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parents:
diff changeset
561
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parents:
diff changeset
562 DEFINE_COLROW_NORM_FUNCS(, , double)
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parents:
diff changeset
563 DEFINE_COLROW_NORM_FUNCS(Complex, , double)
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
564 DEFINE_COLROW_NORM_FUNCS(Float, Float, float)
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
565 DEFINE_COLROW_NORM_FUNCS(FloatComplex, Float, float)
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
566
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
567 DEFINE_COLROW_NORM_FUNCS(Sparse, , double)
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
568 DEFINE_COLROW_NORM_FUNCS(SparseComplex, , double)
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
569