Mercurial > octave
annotate libinterp/corefcn/schur.cc @ 20700:68e3a747ca02
rename octave_value value extractors that accept error message args
* ov.h, ov.cc (octave_value::xcell_value, octave_value::xstring_value,
octave_value::xcellstr_value): Rename functions that accept error
message args. Handle error directly. Only forward to functions that
don't attempt type conversion. Change all uses.
* ov-base.h, ov-base.cc (octave_base_value::xstring_value): Don't do
type conversion.
(octave_base_value::cell_value, octave_base_value::cellstr_value):
Delete versions that accept error message args.
* ov-str-mat.h, ov-str-mat.cc (octave_char_matrix_str::string_value,
octave_char_matrix_str::cell_value): Delete.
author | John W. Eaton <jwe@octave.org> |
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date | Fri, 13 Nov 2015 14:10:26 -0500 |
parents | ba2b07c13913 |
children | 8bb38ba1bad6 |
rev | line source |
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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 | |
24 #include <config.h> | |
25 #endif | |
26 | |
27 #include <string> | |
28 | |
29 #include "CmplxSCHUR.h" | |
30 #include "dbleSCHUR.h" | |
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31 #include "fCmplxSCHUR.h" |
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32 #include "floatSCHUR.h" |
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34 #include "defun.h" |
2928 | 35 #include "error.h" |
36 #include "gripes.h" | |
37 #include "oct-obj.h" | |
38 #include "utils.h" | |
39 | |
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40 template <class Matrix> |
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41 static octave_value |
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42 mark_upper_triangular (const Matrix& a) |
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43 { |
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44 octave_value retval = a; |
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45 |
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46 octave_idx_type n = a.rows (); |
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47 assert (a.columns () == n); |
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48 |
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49 const typename Matrix::element_type zero = typename Matrix::element_type (); |
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50 |
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51 for (octave_idx_type i = 0; i < n; i++) |
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52 if (a(i,i) == zero) |
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53 return retval; |
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54 |
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55 retval.matrix_type (MatrixType::Upper); |
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56 |
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57 return retval; |
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58 } |
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59 |
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60 DEFUN (schur, args, nargout, |
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61 "-*- texinfo -*-\n\ |
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62 @deftypefn {Built-in Function} {@var{S} =} schur (@var{A})\n\ |
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63 @deftypefnx {Built-in Function} {@var{S} =} schur (@var{A}, \"real\")\n\ |
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64 @deftypefnx {Built-in Function} {@var{S} =} schur (@var{A}, \"complex\")\n\ |
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65 @deftypefnx {Built-in Function} {@var{S} =} schur (@var{A}, @var{opt})\n\ |
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66 @deftypefnx {Built-in Function} {[@var{U}, @var{S}] =} schur (@dots{})\n\ |
3372 | 67 @cindex Schur decomposition\n\ |
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68 Compute the Schur@tie{}decomposition of @var{A}.\n\ |
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69 \n\ |
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70 The Schur@tie{}decomposition is defined as\n\ |
3372 | 71 @tex\n\ |
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72 $$\n\ |
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73 S = U^T A U\n\ |
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74 $$\n\ |
3372 | 75 @end tex\n\ |
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76 @ifnottex\n\ |
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77 \n\ |
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78 @example\n\ |
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79 @code{@var{S} = @var{U}' * @var{A} * @var{U}}\n\ |
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80 @end example\n\ |
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81 \n\ |
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82 @end ifnottex\n\ |
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83 where @var{U} is a unitary matrix\n\ |
3372 | 84 @tex\n\ |
85 ($U^T U$ is identity)\n\ | |
86 @end tex\n\ | |
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87 @ifnottex\n\ |
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88 (@code{@var{U}'* @var{U}} is identity)\n\ |
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89 @end ifnottex\n\ |
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90 and @var{S} is upper triangular. The eigenvalues of @var{A} (and @var{S})\n\ |
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91 are the diagonal elements of @var{S}. If the matrix @var{A} is real, then\n\ |
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92 the real Schur@tie{}decomposition is computed, in which the matrix @var{U}\n\ |
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93 is orthogonal and @var{S} is block upper triangular with blocks of size at\n\ |
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94 most\n\ |
3372 | 95 @tex\n\ |
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96 $2 \\times 2$\n\ |
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98 @ifnottex\n\ |
3372 | 99 @code{2 x 2}\n\ |
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100 @end ifnottex\n\ |
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101 along the diagonal. The diagonal elements of @var{S}\n\ |
3372 | 102 (or the eigenvalues of the\n\ |
103 @tex\n\ | |
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104 $2 \\times 2$\n\ |
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106 @ifnottex\n\ |
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108 @end ifnottex\n\ |
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109 blocks, when appropriate) are the eigenvalues of @var{A} and @var{S}.\n\ |
2928 | 110 \n\ |
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111 The default for real matrices is a real Schur@tie{}decomposition.\n\ |
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112 A complex decomposition may be forced by passing the flag\n\ |
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113 @qcode{\"complex\"}.\n\ |
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114 \n\ |
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115 The eigenvalues are optionally ordered along the diagonal according to the\n\ |
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116 value of @var{opt}. @code{@var{opt} = \"a\"} indicates that all eigenvalues\n\ |
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117 with negative real parts should be moved to the leading block of @var{S}\n\ |
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118 (used in @code{are}), @code{@var{opt} = \"d\"} indicates that all\n\ |
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119 eigenvalues with magnitude less than one should be moved to the leading\n\ |
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120 block of @var{S} (used in @code{dare}), and @code{@var{opt} = \"u\"}, the\n\ |
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121 default, indicates that no ordering of eigenvalues should occur. The\n\ |
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122 leading @var{k} columns of @var{U} always span the @var{A}-invariant\n\ |
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123 subspace corresponding to the @var{k} leading eigenvalues of @var{S}.\n\ |
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124 \n\ |
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125 The Schur@tie{}decomposition is used to compute eigenvalues of a square\n\ |
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126 matrix, and has applications in the solution of algebraic Riccati equations\n\ |
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127 in control (see @code{are} and @code{dare}).\n\ |
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128 @seealso{rsf2csf, ordschur, lu, chol, hess, qr, qz, svd}\n\ |
3372 | 129 @end deftypefn") |
2928 | 130 { |
131 octave_value_list retval; | |
132 | |
133 int nargin = args.length (); | |
134 | |
135 if (nargin < 1 || nargin > 2 || nargout > 2) | |
136 { | |
5823 | 137 print_usage (); |
2928 | 138 return retval; |
139 } | |
140 | |
141 octave_value arg = args(0); | |
142 | |
3523 | 143 std::string ord; |
2928 | 144 |
145 if (nargin == 2) | |
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146 ord = args(1).xstring_value ("schur: second argument must be a string"); |
2928 | 147 |
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148 bool force_complex = false; |
2928 | 149 |
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150 if (ord == "real") |
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151 { |
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152 ord = std::string (); |
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153 } |
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154 else if (ord == "complex") |
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155 { |
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156 force_complex = true; |
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157 ord = std::string (); |
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158 } |
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159 else |
2928 | 160 { |
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161 char ord_char = ord.empty () ? 'U' : ord[0]; |
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162 |
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163 if (ord_char != 'U' && ord_char != 'A' && ord_char != 'D' |
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164 && ord_char != 'u' && ord_char != 'a' && ord_char != 'd') |
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165 { |
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166 warning ("schur: incorrect ordered schur argument '%s'", |
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167 ord.c_str ()); |
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168 return retval; |
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169 } |
2928 | 170 } |
171 | |
5275 | 172 octave_idx_type nr = arg.rows (); |
173 octave_idx_type nc = arg.columns (); | |
2928 | 174 |
175 if (nr != nc) | |
176 { | |
177 gripe_square_matrix_required ("schur"); | |
178 return retval; | |
179 } | |
180 | |
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181 if (! arg.is_numeric_type ()) |
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182 gripe_wrong_type_arg ("schur", arg); |
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183 else if (arg.is_single_type ()) |
2928 | 184 { |
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185 if (! force_complex && arg.is_real_type ()) |
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186 { |
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187 FloatMatrix tmp = arg.float_matrix_value (); |
2928 | 188 |
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189 if (nargout == 0 || nargout == 1) |
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190 { |
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191 FloatSCHUR result (tmp, ord, false); |
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192 retval(0) = result.schur_matrix (); |
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193 } |
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194 else |
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195 { |
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196 FloatSCHUR result (tmp, ord, true); |
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197 retval(1) = result.schur_matrix (); |
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198 retval(0) = result.unitary_matrix (); |
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199 } |
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200 } |
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201 else |
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202 { |
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203 FloatComplexMatrix ctmp = arg.float_complex_matrix_value (); |
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204 |
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205 if (nargout == 0 || nargout == 1) |
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206 { |
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207 FloatComplexSCHUR result (ctmp, ord, false); |
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208 retval(0) = mark_upper_triangular (result.schur_matrix ()); |
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209 } |
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210 else |
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211 { |
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212 FloatComplexSCHUR result (ctmp, ord, true); |
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213 retval(1) = mark_upper_triangular (result.schur_matrix ()); |
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214 retval(0) = result.unitary_matrix (); |
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215 } |
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216 } |
2928 | 217 } |
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218 else |
2928 | 219 { |
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220 if (! force_complex && arg.is_real_type ()) |
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221 { |
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222 Matrix tmp = arg.matrix_value (); |
2928 | 223 |
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224 if (nargout == 0 || nargout == 1) |
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225 { |
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226 SCHUR result (tmp, ord, false); |
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227 retval(0) = result.schur_matrix (); |
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228 } |
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229 else |
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230 { |
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231 SCHUR result (tmp, ord, true); |
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232 retval(1) = result.schur_matrix (); |
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233 retval(0) = result.unitary_matrix (); |
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234 } |
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235 } |
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236 else |
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237 { |
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238 ComplexMatrix ctmp = arg.complex_matrix_value (); |
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239 |
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240 if (nargout == 0 || nargout == 1) |
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241 { |
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242 ComplexSCHUR result (ctmp, ord, false); |
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243 retval(0) = mark_upper_triangular (result.schur_matrix ()); |
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244 } |
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245 else |
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246 { |
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247 ComplexSCHUR result (ctmp, ord, true); |
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248 retval(1) = mark_upper_triangular (result.schur_matrix ()); |
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249 retval(0) = result.unitary_matrix (); |
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250 } |
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251 } |
2928 | 252 } |
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253 |
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254 return retval; |
2928 | 255 } |
256 | |
257 /* | |
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258 %!test |
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259 %! a = [1, 2, 3; 4, 5, 9; 7, 8, 6]; |
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260 %! [u, s] = schur (a); |
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261 %! assert (u' * a * u, s, sqrt (eps)); |
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262 |
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263 %!test |
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264 %! a = single ([1, 2, 3; 4, 5, 9; 7, 8, 6]); |
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265 %! [u, s] = schur (a); |
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266 %! assert (u' * a * u, s, sqrt (eps ("single"))); |
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267 |
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268 %!error schur () |
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269 %!error schur (1,2,3) |
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270 %!error [a,b,c] = schur (1) |
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271 %!error <argument must be a square matrix> schur ([1, 2, 3; 4, 5, 6]) |
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272 %!error <wrong type argument 'cell'> schur ({1}) |
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273 %!warning <incorrect ordered schur argument> schur ([1, 2; 3, 4], "bad_opt"); |
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274 |
2928 | 275 */ |
10822 | 276 |
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277 DEFUN (rsf2csf, args, nargout, |
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278 "-*- texinfo -*-\n\ |
10822 | 279 @deftypefn {Function File} {[@var{U}, @var{T}] =} rsf2csf (@var{UR}, @var{TR})\n\ |
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280 Convert a real, upper quasi-triangular Schur@tie{}form @var{TR} to a complex,\n\ |
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281 upper triangular Schur@tie{}form @var{T}.\n\ |
10822 | 282 \n\ |
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283 Note that the following relations hold:\n\ |
10822 | 284 \n\ |
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285 @tex\n\ |
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286 $UR \\cdot TR \\cdot {UR}^T = U T U^{\\dagger}$ and\n\ |
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287 $U^{\\dagger} U$ is the identity matrix I.\n\ |
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288 @end tex\n\ |
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289 @ifnottex\n\ |
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290 @tcode{@var{UR} * @var{TR} * @var{UR}' = @var{U} * @var{T} * @var{U}'} and\n\ |
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291 @code{@var{U}' * @var{U}} is the identity matrix I.\n\ |
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292 @end ifnottex\n\ |
10822 | 293 \n\ |
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294 Note also that @var{U} and @var{T} are not unique.\n\ |
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295 @seealso{schur}\n\ |
10822 | 296 @end deftypefn") |
297 { | |
298 octave_value_list retval; | |
299 | |
300 if (args.length () == 2 && nargout <= 2) | |
301 { | |
302 if (! args(0).is_numeric_type ()) | |
303 gripe_wrong_type_arg ("rsf2csf", args(0)); | |
304 else if (! args(1).is_numeric_type ()) | |
305 gripe_wrong_type_arg ("rsf2csf", args(1)); | |
306 else if (args(0).is_complex_type () || args(1).is_complex_type ()) | |
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307 error ("rsf2csf: UR and TR must be real matrices"); |
10822 | 308 else |
309 { | |
310 | |
311 if (args(0).is_single_type () || args(1).is_single_type ()) | |
312 { | |
313 FloatMatrix u = args(0).float_matrix_value (); | |
314 FloatMatrix t = args(1).float_matrix_value (); | |
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315 |
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316 FloatComplexSCHUR cs (FloatSCHUR (t, u)); |
10822 | 317 |
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318 retval(1) = cs.schur_matrix (); |
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319 retval(0) = cs.unitary_matrix (); |
10822 | 320 } |
321 else | |
322 { | |
323 Matrix u = args(0).matrix_value (); | |
324 Matrix t = args(1).matrix_value (); | |
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325 |
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326 ComplexSCHUR cs (SCHUR (t, u)); |
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328 retval(1) = cs.schur_matrix (); |
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329 retval(0) = cs.unitary_matrix (); |
10822 | 330 } |
331 } | |
332 } | |
333 else | |
334 print_usage (); | |
335 | |
336 return retval; | |
337 } | |
338 | |
339 /* | |
340 %!test | |
341 %! A = [1, 1, 1, 2; 1, 2, 1, 1; 1, 1, 3, 1; -2, 1, 1, 1]; | |
342 %! [u, t] = schur (A); | |
343 %! [U, T] = rsf2csf (u, t); | |
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344 %! assert (norm (u * t * u' - U * T * U'), 0, 1e-12); |
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345 %! assert (norm (A - U * T * U'), 0, 1e-12); |
10822 | 346 |
347 %!test | |
348 %! A = rand (10); | |
349 %! [u, t] = schur (A); | |
350 %! [U, T] = rsf2csf (u, t); | |
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351 %! assert (norm (tril (T, -1)), 0); |
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352 %! assert (norm (U * U'), 1, 1e-14); |
10822 | 353 |
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354 %!test |
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355 %! A = [0, 1;-1, 0]; |
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356 %! [u, t] = schur (A); |
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357 %! [U, T] = rsf2csf (u,t); |
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358 %! assert (U * T * U', A, 1e-14); |
10822 | 359 */ |