Mercurial > octave
annotate libinterp/corefcn/hess.cc @ 23577:80c42f4cca13
maint: Deprecate is_empty and replace with isempty.
* ov.h (is_empty): Use OCTAVE_DEPRECATED macro around function.
* ov.h (isempty): New function.
* Array.h (is_empty): Use OCTAVE_DEPRECATED macro around function.
* Array.h (isempty): New function.
* Range.h (is_empty): Use OCTAVE_DEPRECATED macro around function.
* Range.h (isempty): New function.
* Sparse.h (is_empty): Use OCTAVE_DEPRECATED macro around function.
* Sparse.h (isempty): New function.
* Backend.cc, BaseControl.cc, Canvas.cc, Figure.cc, gl-select.cc,
__magick_read__.cc, __qp__.cc, cellfun.cc, daspk.cc, dasrt.cc, dassl.cc,
data.cc, debug.cc, det.cc, eig.cc, error.cc, fft.cc, filter.cc, find.cc,
ft-text-renderer.cc, gl-render.cc, gl2ps-print.cc, graphics.cc, graphics.in.h,
hess.cc, inv.cc, lsode.cc, lu.cc, max.cc, mex.cc, mxarray.in.h, oct-handle.h,
oct-lvalue.cc, oct-map.cc, oct-map.h, oct-stream.cc, pinv.cc, pr-output.cc,
quadcc.cc, qz.cc, strfind.cc, strfns.cc, sylvester.cc, time.cc, toplev.cc,
tril.cc, urlwrite.cc, utils.cc, utils.h, xnorm.cc, __delaunayn__.cc,
__glpk__.cc, __init_fltk__.cc, __init_gnuplot__.cc, __ode15__.cc,
__voronoi__.cc, chol.cc, convhulln.cc, ov-base-diag.cc, ov-base-mat.cc,
ov-base-sparse.cc, ov-base.cc, ov-base.h, ov-bool-mat.cc, ov-bool-sparse.cc,
ov-cell.cc, ov-class.cc, ov-classdef.cc, ov-cx-sparse.cc, ov-fcn-inline.cc,
ov-flt-re-mat.cc, ov-intx.h, ov-java.cc, ov-perm.cc, ov-range.cc, ov-re-mat.cc,
ov-re-sparse.cc, ov-str-mat.cc, ov-struct.cc, ov-usr-fcn.cc, ov.cc, ov.h,
bp-table.cc, oct-parse.in.yy, pt-eval.cc, pt-tm-const.cc, pt-tm-const.h,
Array.cc, Range.cc, Range.h, Sparse.cc, Sparse.h, chNDArray.cc, dNDArray.cc,
fNDArray.cc, DASPK.cc, DASRT.cc, DASSL.cc, LSODE.cc, bsxfun-defs.cc,
eigs-base.cc, oct-convn.cc, qr.cc:
Replace instances of is_empty with isempty.
author | Rik <rik@octave.org> |
---|---|
date | Sun, 11 Jun 2017 22:14:09 -0700 |
parents | 092078913d54 |
children | c3075ae020e1 |
rev | line source |
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2928 | 1 /* |
2 | |
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3 Copyright (C) 1996-2017 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 | |
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8 under the terms of the GNU General Public License as published by |
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9 the Free Software Foundation; either version 3 of the License, or |
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10 (at your option) any later version. |
2928 | 11 |
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12 Octave is distributed in the hope that it will be useful, but |
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13 WITHOUT ANY WARRANTY; without even the implied warranty of |
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14 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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15 GNU General Public License for more details. |
2928 | 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 | |
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23 #if defined (HAVE_CONFIG_H) |
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24 # include "config.h" |
2928 | 25 #endif |
26 | |
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27 #include "hess.h" |
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29 #include "defun.h" |
2928 | 30 #include "error.h" |
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31 #include "errwarn.h" |
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32 #include "ovl.h" |
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34 DEFUN (hess, args, nargout, |
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35 doc: /* -*- texinfo -*- |
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36 @deftypefn {} {@var{H} =} hess (@var{A}) |
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37 @deftypefnx {} {[@var{P}, @var{H}] =} hess (@var{A}) |
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38 @cindex Hessenberg decomposition |
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39 Compute the Hessenberg decomposition of the matrix @var{A}. |
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40 |
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41 The Hessenberg decomposition is |
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42 @tex |
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43 $$ |
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44 A = PHP^T |
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45 $$ |
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46 where $P$ is a square unitary matrix ($P^TP = I$), and $H$ |
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47 is upper Hessenberg ($H_{i,j} = 0, \forall i > j+1$). |
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48 @end tex |
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49 @ifnottex |
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50 @code{@var{P} * @var{H} * @var{P}' = @var{A}} where @var{P} is a square |
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51 unitary matrix (@code{@var{P}' * @var{P} = I}, using complex-conjugate |
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52 transposition) and @var{H} is upper Hessenberg |
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53 (@code{@var{H}(i, j) = 0 forall i > j+1)}. |
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54 @end ifnottex |
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55 |
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56 The Hessenberg decomposition is usually used as the first step in an |
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57 eigenvalue computation, but has other applications as well |
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58 (see @nospell{Golub, Nash, and Van Loan}, |
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59 IEEE Transactions on Automatic Control, 1979). |
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60 @seealso{eig, chol, lu, qr, qz, schur, svd} |
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61 @end deftypefn */) |
2928 | 62 { |
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63 if (args.length () != 1) |
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64 print_usage (); |
2928 | 65 |
66 octave_value arg = args(0); | |
67 | |
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68 if (arg.isempty ()) |
2928 | 69 return octave_value_list (2, Matrix ()); |
70 | |
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71 if (arg.rows () != arg.columns ()) |
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72 err_square_matrix_required ("hess", "A"); |
2928 | 73 |
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74 octave_value_list retval; |
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75 |
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76 if (arg.is_single_type ()) |
2928 | 77 { |
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78 if (arg.is_real_type ()) |
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79 { |
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80 FloatMatrix tmp = arg.float_matrix_value (); |
2928 | 81 |
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82 octave::math::hess<FloatMatrix> result (tmp); |
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83 |
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84 if (nargout <= 1) |
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85 retval = ovl (result.hess_matrix ()); |
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86 else |
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87 retval = ovl (result.unitary_hess_matrix (), |
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88 result.hess_matrix ()); |
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89 } |
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90 else if (arg.is_complex_type ()) |
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91 { |
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92 FloatComplexMatrix ctmp = arg.float_complex_matrix_value (); |
2928 | 93 |
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94 octave::math::hess<FloatComplexMatrix> result (ctmp); |
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95 |
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96 if (nargout <= 1) |
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97 retval = ovl (result.hess_matrix ()); |
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98 else |
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99 retval = ovl (result.unitary_hess_matrix (), |
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100 result.hess_matrix ()); |
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101 } |
2928 | 102 } |
103 else | |
104 { | |
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105 if (arg.is_real_type ()) |
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106 { |
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107 Matrix tmp = arg.matrix_value (); |
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108 |
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109 octave::math::hess<Matrix> result (tmp); |
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110 |
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111 if (nargout <= 1) |
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112 retval = ovl (result.hess_matrix ()); |
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113 else |
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114 retval = ovl (result.unitary_hess_matrix (), |
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115 result.hess_matrix ()); |
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116 } |
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117 else if (arg.is_complex_type ()) |
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118 { |
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119 ComplexMatrix ctmp = arg.complex_matrix_value (); |
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120 |
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121 octave::math::hess<ComplexMatrix> result (ctmp); |
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122 |
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123 if (nargout <= 1) |
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124 retval = ovl (result.hess_matrix ()); |
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125 else |
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126 retval = ovl (result.unitary_hess_matrix (), |
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127 result.hess_matrix ()); |
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128 } |
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129 else |
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130 err_wrong_type_arg ("hess", arg); |
2928 | 131 } |
132 | |
133 return retval; | |
134 } | |
135 | |
136 /* | |
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137 %!test |
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138 %! a = [1, 2, 3; 5, 4, 6; 8, 7, 9]; |
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139 %! [p, h] = hess (a); |
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140 %! assert (p * h * p', a, sqrt (eps)); |
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141 |
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142 %!test |
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143 %! a = single ([1, 2, 3; 5, 4, 6; 8, 7, 9]); |
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144 %! [p, h] = hess (a); |
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145 %! assert (p * h * p', a, sqrt (eps ("single"))); |
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146 |
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147 %!error hess () |
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148 %!error hess ([1, 2; 3, 4], 2) |
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149 %!error <must be a square matrix> hess ([1, 2; 3, 4; 5, 6]) |
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150 */ |