Mercurial > octave
annotate libinterp/corefcn/hess.cc @ 21200:fcac5dbbf9ed
maint: Indent #ifdef blocks in libinterp.
* builtins.h, Cell.cc, __contourc__.cc, __dispatch__.cc, __dsearchn__.cc,
__ichol__.cc, __ilu__.cc, __lin_interpn__.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, cellfun.cc, colloc.cc,
comment-list.cc, conv2.cc, daspk.cc, dasrt.cc, dassl.cc, data.cc, debug.cc,
defaults.cc, defaults.in.h, defun-dld.h, defun.cc, defun.h, 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, gammainc.cc, gcd.cc, getgrent.cc, getpwent.cc, getrusage.cc,
givens.cc, gl-render.cc, gl2ps-print.cc, graphics.cc, graphics.in.h, gripes.cc,
hash.cc, help.cc, hess.cc, hex2num.cc, input.cc, inv.cc, jit-ir.cc,
jit-typeinfo.cc, 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,
ls-utils.h, lsode.cc, lu.cc, luinc.cc, mappers.cc, matrix_type.cc, max.cc,
mex.h, mexproto.h, mgorth.cc, nproc.cc, oct-errno.in.cc, oct-fstrm.cc,
oct-hdf5-types.cc, oct-hdf5.h, oct-hist.cc, oct-iostrm.cc, oct-lvalue.cc,
oct-map.cc, oct-prcstrm.cc, oct-procbuf.cc, oct-stream.cc, oct-strstrm.cc,
octave-link.cc, ordschur.cc, pager.cc, pinv.cc, pr-output.cc, procstream.cc,
profiler.cc, psi.cc, pt-jit.cc, quad.cc, quadcc.cc, qz.cc, rand.cc, rcond.cc,
regexp.cc, schur.cc, sighandlers.cc, 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, sysdep.h, time.cc, toplev.cc,
tril.cc, tsearch.cc, txt-eng-ft.cc, txt-eng.cc, typecast.cc, urlwrite.cc,
utils.cc, variables.cc, xdiv.cc, xnorm.cc, xpow.cc, zfstream.cc,
__delaunayn__.cc, __eigs__.cc, __fltk_uigetfile__.cc, __glpk__.cc,
__init_fltk__.cc, __init_gnuplot__.cc, __magick_read__.cc, __osmesa_print__.cc,
__voronoi__.cc, amd.cc, audiodevinfo.cc, audioread.cc, ccolamd.cc, chol.cc,
colamd.cc, convhulln.cc, dmperm.cc, fftw.cc, oct-qhull.h, qr.cc, symbfact.cc,
symrcm.cc, oct-conf.in.cc, ov-base-diag.cc, ov-base-int.cc, ov-base-mat.cc,
ov-base-scalar.cc, ov-base-sparse.cc, 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.cc, ovl.cc, octave.cc, op-b-b.cc, op-b-bm.cc,
op-b-sbm.cc, op-bm-b.cc, op-bm-bm.cc, op-bm-sbm.cc, op-cdm-cdm.cc, op-cell.cc,
op-chm.cc, op-class.cc, op-cm-cm.cc, op-cm-cs.cc, op-cm-m.cc, op-cm-s.cc,
op-cm-scm.cc, op-cm-sm.cc, op-cs-cm.cc, op-cs-cs.cc, op-cs-m.cc, op-cs-s.cc,
op-cs-scm.cc, op-cs-sm.cc, op-dm-dm.cc, op-dm-scm.cc, op-dm-sm.cc,
op-dm-template.cc, op-dms-template.cc, op-double-conv.cc, op-fcdm-fcdm.cc,
op-fcdm-fdm.cc, op-fcm-fcm.cc, op-fcm-fcs.cc, op-fcm-fm.cc, op-fcm-fs.cc,
op-fcn.cc, op-fcs-fcm.cc, op-fcs-fcs.cc, op-fcs-fm.cc, op-fcs-fs.cc,
op-fdm-fdm.cc, op-float-conv.cc, op-fm-fcm.cc, op-fm-fcs.cc, op-fm-fm.cc,
op-fm-fs.cc, op-fs-fcm.cc, op-fs-fcs.cc, op-fs-fm.cc, op-fs-fs.cc,
op-i16-i16.cc, op-i32-i32.cc, op-i64-i64.cc, op-i8-i8.cc, op-int-concat.cc,
op-int-conv.cc, op-m-cm.cc, op-m-cs.cc, op-m-m.cc, op-m-s.cc, op-m-scm.cc,
op-m-sm.cc, op-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, 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-colon.h,
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-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-os.cc, Array-sym.cc, Array-tc.cc, version.cc:
Indent #ifdef blocks in libinterp.
| author | Rik <rik@octave.org> |
|---|---|
| date | Fri, 05 Feb 2016 16:29:08 -0800 |
| parents | 228b65504557 |
| children | f5b8c3aca5f8 |
| rev | line source |
|---|---|
| 2928 | 1 /* |
| 2 | |
|
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3 Copyright (C) 1996-2015 John W. Eaton |
| 2928 | 4 |
| 5 This file is part of Octave. | |
| 6 | |
| 7 Octave is free software; you can redistribute it and/or modify it | |
| 8 under the terms of the GNU General Public License as published by the | |
| 7016 | 9 Free Software Foundation; either version 3 of the License, or (at your |
| 10 option) any later version. | |
| 2928 | 11 |
| 12 Octave is distributed in the hope that it will be useful, but WITHOUT | |
| 13 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or | |
| 14 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License | |
| 15 for more details. | |
| 16 | |
| 17 You should have received a copy of the GNU General Public License | |
| 7016 | 18 along with Octave; see the file COPYING. If not, see |
| 19 <http://www.gnu.org/licenses/>. | |
| 2928 | 20 |
| 21 */ | |
| 22 | |
| 23 #ifdef HAVE_CONFIG_H | |
|
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24 # include <config.h> |
| 2928 | 25 #endif |
| 26 | |
| 27 #include "CmplxHESS.h" | |
| 28 #include "dbleHESS.h" | |
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29 #include "fCmplxHESS.h" |
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30 #include "floatHESS.h" |
| 2928 | 31 |
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32 #include "defun.h" |
| 2928 | 33 #include "error.h" |
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34 #include "errwarn.h" |
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35 #include "ovl.h" |
| 2928 | 36 #include "utils.h" |
| 37 | |
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38 DEFUN (hess, args, nargout, |
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39 "-*- texinfo -*-\n\ |
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40 @deftypefn {} {@var{H} =} hess (@var{A})\n\ |
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41 @deftypefnx {} {[@var{P}, @var{H}] =} hess (@var{A})\n\ |
| 3372 | 42 @cindex Hessenberg decomposition\n\ |
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43 Compute the Hessenberg decomposition of the matrix @var{A}.\n\ |
| 3372 | 44 \n\ |
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45 The Hessenberg decomposition is\n\ |
| 3372 | 46 @tex\n\ |
| 47 $$\n\ | |
| 48 A = PHP^T\n\ | |
| 49 $$\n\ | |
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50 where $P$ is a square unitary matrix ($P^TP = I$), and $H$\n\ |
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51 is upper Hessenberg ($H_{i,j} = 0, \\forall i > j+1$).\n\ |
| 3372 | 52 @end tex\n\ |
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53 @ifnottex\n\ |
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54 @code{@var{P} * @var{H} * @var{P}' = @var{A}} where @var{P} is a square\n\ |
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55 unitary matrix (@code{@var{P}' * @var{P} = I}, using complex-conjugate\n\ |
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56 transposition) and @var{H} is upper Hessenberg\n\ |
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57 (@code{@var{H}(i, j) = 0 forall i > j+1)}.\n\ |
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58 @end ifnottex\n\ |
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59 \n\ |
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60 The Hessenberg decomposition is usually used as the first step in an\n\ |
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61 eigenvalue computation, but has other applications as well\n\ |
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62 (see @nospell{Golub, Nash, and Van Loan},\n\ |
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63 IEEE Transactions on Automatic Control, 1979).\n\ |
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64 @seealso{eig, chol, lu, qr, qz, schur, svd}\n\ |
| 3372 | 65 @end deftypefn") |
| 2928 | 66 { |
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67 if (args.length () != 1) |
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68 print_usage (); |
| 2928 | 69 |
| 70 octave_value arg = args(0); | |
| 71 | |
| 5275 | 72 octave_idx_type nr = arg.rows (); |
| 73 octave_idx_type nc = arg.columns (); | |
| 2928 | 74 |
| 75 int arg_is_empty = empty_arg ("hess", nr, nc); | |
| 76 | |
| 77 if (arg_is_empty < 0) | |
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78 return ovl (); |
| 2928 | 79 else if (arg_is_empty > 0) |
| 80 return octave_value_list (2, Matrix ()); | |
| 81 | |
| 82 if (nr != nc) | |
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83 err_square_matrix_required ("hess", "A"); |
| 2928 | 84 |
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85 octave_value_list retval; |
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86 |
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87 if (arg.is_single_type ()) |
| 2928 | 88 { |
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89 if (arg.is_real_type ()) |
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90 { |
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91 FloatMatrix tmp = arg.float_matrix_value (); |
| 2928 | 92 |
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93 FloatHESS result (tmp); |
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94 |
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95 if (nargout <= 1) |
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96 retval = ovl (result.hess_matrix ()); |
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97 else |
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98 retval = ovl (result.unitary_hess_matrix (), |
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99 result.hess_matrix ()); |
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100 } |
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101 else if (arg.is_complex_type ()) |
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102 { |
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103 FloatComplexMatrix ctmp = arg.float_complex_matrix_value (); |
| 2928 | 104 |
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105 FloatComplexHESS result (ctmp); |
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106 |
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107 if (nargout <= 1) |
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108 retval = ovl (result.hess_matrix ()); |
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109 else |
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110 retval = ovl (result.unitary_hess_matrix (), |
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111 result.hess_matrix ()); |
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112 } |
| 2928 | 113 } |
| 114 else | |
| 115 { | |
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116 if (arg.is_real_type ()) |
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117 { |
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118 Matrix tmp = arg.matrix_value (); |
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119 |
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120 HESS result (tmp); |
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121 |
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122 if (nargout <= 1) |
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123 retval = ovl (result.hess_matrix ()); |
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124 else |
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125 retval = ovl (result.unitary_hess_matrix (), |
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126 result.hess_matrix ()); |
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127 } |
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128 else if (arg.is_complex_type ()) |
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129 { |
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130 ComplexMatrix ctmp = arg.complex_matrix_value (); |
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131 |
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132 ComplexHESS result (ctmp); |
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133 |
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134 if (nargout <= 1) |
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135 retval = ovl (result.hess_matrix ()); |
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136 else |
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137 retval = ovl (result.unitary_hess_matrix (), |
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138 result.hess_matrix ()); |
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139 } |
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140 else |
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141 err_wrong_type_arg ("hess", arg); |
| 2928 | 142 } |
| 143 | |
| 144 return retval; | |
| 145 } | |
| 146 | |
| 147 /* | |
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148 %!test |
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149 %! a = [1, 2, 3; 5, 4, 6; 8, 7, 9]; |
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150 %! [p, h] = hess (a); |
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151 %! assert (p * h * p', a, sqrt (eps)); |
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152 |
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153 %!test |
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154 %! a = single ([1, 2, 3; 5, 4, 6; 8, 7, 9]); |
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155 %! [p, h] = hess (a); |
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156 %! assert (p * h * p', a, sqrt (eps ("single"))); |
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157 |
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158 %!error hess () |
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159 %!error hess ([1, 2; 3, 4], 2) |
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160 %!error <must be a square matrix> hess ([1, 2; 3, 4; 5, 6]) |
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161 */ |