Mercurial > octave-nkf
annotate libinterp/corefcn/balance.cc @ 17744:d63878346099
maint: Update copyright notices for release.
author | John W. Eaton <jwe@octave.org> |
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date | Wed, 23 Oct 2013 22:09:27 -0400 |
parents | bc924baa2c4e |
children | 175b392e91fe |
rev | line source |
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2928 | 1 /* |
2 | |
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3 Copyright (C) 1996-2013 John W. Eaton |
11523 | 4 Copyright (C) 2008-2009 Jaroslav Hajek |
2928 | 5 |
6 This file is part of Octave. | |
7 | |
8 Octave is free software; you can redistribute it and/or modify it | |
9 under the terms of the GNU General Public License as published by the | |
7016 | 10 Free Software Foundation; either version 3 of the License, or (at your |
11 option) any later version. | |
2928 | 12 |
13 Octave is distributed in the hope that it will be useful, but WITHOUT | |
14 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or | |
15 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License | |
16 for more details. | |
17 | |
18 You should have received a copy of the GNU General Public License | |
7016 | 19 along with Octave; see the file COPYING. If not, see |
20 <http://www.gnu.org/licenses/>. | |
2928 | 21 |
22 */ | |
23 | |
3911 | 24 // Author: A. S. Hodel <scotte@eng.auburn.edu> |
2928 | 25 |
26 #ifdef HAVE_CONFIG_H | |
27 #include <config.h> | |
28 #endif | |
29 | |
30 #include <string> | |
31 | |
32 #include "CmplxAEPBAL.h" | |
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33 #include "fCmplxAEPBAL.h" |
2928 | 34 #include "dbleAEPBAL.h" |
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35 #include "floatAEPBAL.h" |
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36 #include "CmplxGEPBAL.h" |
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37 #include "fCmplxGEPBAL.h" |
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38 #include "dbleGEPBAL.h" |
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39 #include "floatGEPBAL.h" |
4153 | 40 #include "quit.h" |
2928 | 41 |
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42 #include "defun.h" |
2928 | 43 #include "error.h" |
3181 | 44 #include "f77-fcn.h" |
2928 | 45 #include "gripes.h" |
46 #include "oct-obj.h" | |
47 #include "utils.h" | |
48 | |
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49 DEFUN (balance, args, nargout, |
3548 | 50 "-*- texinfo -*-\n\ |
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51 @deftypefn {Built-in Function} {@var{AA} =} balance (@var{A})\n\ |
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52 @deftypefnx {Built-in Function} {@var{AA} =} balance (@var{A}, @var{opt})\n\ |
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53 @deftypefnx {Built-in Function} {[@var{DD}, @var{AA}] =} balance (@var{A}, @var{opt})\n\ |
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54 @deftypefnx {Built-in Function} {[@var{D}, @var{P}, @var{AA}] =} balance (@var{A}, @var{opt})\n\ |
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55 @deftypefnx {Built-in Function} {[@var{CC}, @var{DD}, @var{AA}, @var{BB}] =} balance (@var{A}, @var{B}, @var{opt})\n\ |
2928 | 56 \n\ |
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57 Compute @code{@var{AA} = @var{DD} \\ @var{A} * @var{DD}} in which @var{AA}\n\ |
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58 is a matrix whose row and column norms are roughly equal in magnitude, and\n\ |
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59 @code{@var{DD} = @var{P} * @var{D}}, in which @var{P} is a permutation\n\ |
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60 matrix and @var{D} is a diagonal matrix of powers of two. This allows the\n\ |
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61 equilibration to be computed without round-off. Results of eigenvalue\n\ |
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62 calculation are typically improved by balancing first.\n\ |
2928 | 63 \n\ |
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64 If two output values are requested, @code{balance} returns\n\ |
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65 the diagonal @var{D} and the permutation @var{P} separately as vectors.\n\ |
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66 In this case, @code{@var{DD} = eye(n)(:,@var{P}) * diag (@var{D})}, where\n\ |
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67 @math{n} is the matrix size.\n\ |
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68 \n\ |
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69 If four output values are requested, compute @code{@var{AA} =\n\ |
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70 @var{CC}*@var{A}*@var{DD}} and @code{@var{BB} = @var{CC}*@var{B}*@var{DD}},\n\ |
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71 in which @var{AA} and @var{BB} have non-zero elements of approximately the\n\ |
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72 same magnitude and @var{CC} and @var{DD} are permuted diagonal matrices as\n\ |
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73 in @var{DD} for the algebraic eigenvalue problem.\n\ |
3372 | 74 \n\ |
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75 The eigenvalue balancing option @var{opt} may be one of:\n\ |
2928 | 76 \n\ |
3372 | 77 @table @asis\n\ |
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78 @item @qcode{\"noperm\"}, @qcode{\"S\"}\n\ |
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79 Scale only; do not permute.\n\ |
3372 | 80 \n\ |
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81 @item @qcode{\"noscal\"}, @qcode{\"P\"}\n\ |
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82 Permute only; do not scale.\n\ |
3372 | 83 @end table\n\ |
2928 | 84 \n\ |
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85 Algebraic eigenvalue balancing uses standard @sc{lapack} routines.\n\ |
3372 | 86 \n\ |
87 Generalized eigenvalue problem balancing uses Ward's algorithm\n\ | |
88 (SIAM Journal on Scientific and Statistical Computing, 1981).\n\ | |
89 @end deftypefn") | |
2928 | 90 { |
91 octave_value_list retval; | |
92 | |
93 int nargin = args.length (); | |
94 | |
95 if (nargin < 1 || nargin > 3 || nargout < 0 || nargout > 4) | |
96 { | |
5823 | 97 print_usage (); |
2928 | 98 return retval; |
99 } | |
100 | |
3181 | 101 // determine if it's AEP or GEP |
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102 bool AEPcase = nargin == 1 || args(1).is_string (); |
2928 | 103 |
3181 | 104 // problem dimension |
5275 | 105 octave_idx_type nn = args(0).rows (); |
2928 | 106 |
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107 if (nn != args(0).columns ()) |
3185 | 108 { |
109 gripe_square_matrix_required ("balance"); | |
110 return retval; | |
111 } | |
2928 | 112 |
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113 bool isfloat = args(0).is_single_type () || |
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114 (! AEPcase && args(1).is_single_type ()); |
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115 |
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116 bool complex_case = (args(0).is_complex_type () || |
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117 (! AEPcase && args(1).is_complex_type ())); |
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118 |
2928 | 119 // Extract argument 1 parameter for both AEP and GEP. |
120 Matrix aa; | |
121 ComplexMatrix caa; | |
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122 FloatMatrix faa; |
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123 FloatComplexMatrix fcaa; |
3185 | 124 |
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125 if (isfloat) |
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126 { |
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127 if (complex_case) |
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128 fcaa = args(0).float_complex_matrix_value (); |
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129 else |
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130 faa = args(0).float_matrix_value (); |
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131 } |
3185 | 132 else |
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133 { |
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134 if (complex_case) |
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135 caa = args(0).complex_matrix_value (); |
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136 else |
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137 aa = args(0).matrix_value (); |
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138 } |
3185 | 139 |
140 if (error_state) | |
141 return retval; | |
2928 | 142 |
143 // Treat AEP/GEP cases. | |
3185 | 144 if (AEPcase) |
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145 { |
3185 | 146 // Algebraic eigenvalue problem. |
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147 bool noperm = false, noscal = false; |
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148 if (nargin > 1) |
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149 { |
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150 std::string a1s = args(1).string_value (); |
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151 noperm = a1s == "noperm" || a1s == "S"; |
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152 noscal = a1s == "noscal" || a1s == "P"; |
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153 } |
3185 | 154 |
155 // balance the AEP | |
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156 if (isfloat) |
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157 { |
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158 if (complex_case) |
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159 { |
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160 FloatComplexAEPBALANCE result (fcaa, noperm, noscal); |
2928 | 161 |
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162 if (nargout == 0 || nargout == 1) |
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163 retval(0) = result.balanced_matrix (); |
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164 else if (nargout == 2) |
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165 { |
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166 retval(1) = result.balanced_matrix (); |
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167 retval(0) = result.balancing_matrix (); |
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168 } |
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169 else |
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170 { |
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171 retval(2) = result.balanced_matrix (); |
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172 retval(1) = result.permuting_vector (); |
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173 retval(0) = result.scaling_vector (); |
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174 } |
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175 |
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176 } |
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177 else |
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178 { |
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179 FloatAEPBALANCE result (faa, noperm, noscal); |
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180 |
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181 if (nargout == 0 || nargout == 1) |
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182 retval(0) = result.balanced_matrix (); |
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183 else if (nargout == 2) |
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184 { |
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185 retval(1) = result.balanced_matrix (); |
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186 retval(0) = result.balancing_matrix (); |
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187 } |
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188 else |
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189 { |
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190 retval(2) = result.balanced_matrix (); |
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191 retval(1) = result.permuting_vector (); |
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192 retval(0) = result.scaling_vector (); |
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193 } |
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194 } |
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195 } |
3181 | 196 else |
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197 { |
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198 if (complex_case) |
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199 { |
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200 ComplexAEPBALANCE result (caa, noperm, noscal); |
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202 if (nargout == 0 || nargout == 1) |
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203 retval(0) = result.balanced_matrix (); |
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204 else if (nargout == 2) |
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205 { |
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206 retval(1) = result.balanced_matrix (); |
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207 retval(0) = result.balancing_matrix (); |
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208 } |
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209 else |
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210 { |
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211 retval(2) = result.balanced_matrix (); |
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212 retval(1) = result.permuting_vector (); |
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213 retval(0) = result.scaling_vector (); |
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214 } |
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215 } |
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216 else |
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217 { |
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218 AEPBALANCE result (aa, noperm, noscal); |
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219 |
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220 if (nargout == 0 || nargout == 1) |
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221 retval(0) = result.balanced_matrix (); |
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222 else if (nargout == 2) |
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223 { |
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224 retval(1) = result.balanced_matrix (); |
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225 retval(0) = result.balancing_matrix (); |
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226 } |
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227 else |
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228 { |
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229 retval(2) = result.balanced_matrix (); |
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230 retval(1) = result.permuting_vector (); |
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231 retval(0) = result.scaling_vector (); |
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232 } |
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233 } |
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234 } |
3181 | 235 } |
236 else | |
237 { | |
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238 std::string bal_job; |
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239 if (nargout == 1) |
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240 warning ("balance: used GEP, should have two output arguments"); |
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241 |
3185 | 242 // Generalized eigenvalue problem. |
243 if (nargin == 2) | |
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244 bal_job = "B"; |
3185 | 245 else if (args(2).is_string ()) |
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246 bal_job = args(2).string_value (); |
3185 | 247 else |
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248 { |
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249 error ("balance: OPT argument must be a string"); |
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250 return retval; |
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251 } |
3185 | 252 |
253 if ((nn != args(1).columns ()) || (nn != args(1).rows ())) | |
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254 { |
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255 gripe_nonconformant (); |
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256 return retval; |
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257 } |
3185 | 258 |
259 Matrix bb; | |
260 ComplexMatrix cbb; | |
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261 FloatMatrix fbb; |
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262 FloatComplexMatrix fcbb; |
3185 | 263 |
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264 if (isfloat) |
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265 { |
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266 if (complex_case) |
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267 fcbb = args(1).float_complex_matrix_value (); |
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268 else |
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269 fbb = args(1).float_matrix_value (); |
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270 } |
3185 | 271 else |
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272 { |
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273 if (complex_case) |
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274 cbb = args(1).complex_matrix_value (); |
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275 else |
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276 bb = args(1).matrix_value (); |
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277 } |
4153 | 278 |
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279 // balance the GEP |
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280 if (isfloat) |
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281 { |
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282 if (complex_case) |
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283 { |
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284 FloatComplexGEPBALANCE result (fcaa, fcbb, bal_job); |
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285 |
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286 switch (nargout) |
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287 { |
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288 case 4: |
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289 retval(3) = result.balanced_matrix2 (); |
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290 // fall through |
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291 case 3: |
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292 retval(2) = result.balanced_matrix (); |
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293 retval(1) = result.balancing_matrix2 (); |
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294 retval(0) = result.balancing_matrix (); |
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295 break; |
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296 case 2: |
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297 retval(1) = result.balancing_matrix2 (); |
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298 // fall through |
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299 case 1: |
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300 retval(0) = result.balancing_matrix (); |
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301 break; |
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302 default: |
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303 error ("balance: invalid number of output arguments"); |
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304 break; |
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305 } |
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306 } |
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307 else |
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308 { |
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309 FloatGEPBALANCE result (faa, fbb, bal_job); |
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310 |
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311 switch (nargout) |
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312 { |
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313 case 4: |
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314 retval(3) = result.balanced_matrix2 (); |
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315 // fall through |
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316 case 3: |
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317 retval(2) = result.balanced_matrix (); |
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318 retval(1) = result.balancing_matrix2 (); |
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319 retval(0) = result.balancing_matrix (); |
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320 break; |
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321 case 2: |
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322 retval(1) = result.balancing_matrix2 (); |
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323 // fall through |
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324 case 1: |
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325 retval(0) = result.balancing_matrix (); |
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326 break; |
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327 default: |
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328 error ("balance: invalid number of output arguments"); |
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329 break; |
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330 } |
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331 } |
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332 } |
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333 else |
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334 { |
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335 if (complex_case) |
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336 { |
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337 ComplexGEPBALANCE result (caa, cbb, bal_job); |
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338 |
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339 switch (nargout) |
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340 { |
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341 case 4: |
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342 retval(3) = result.balanced_matrix2 (); |
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343 // fall through |
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344 case 3: |
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345 retval(2) = result.balanced_matrix (); |
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346 retval(1) = result.balancing_matrix2 (); |
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347 retval(0) = result.balancing_matrix (); |
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348 break; |
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349 case 2: |
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350 retval(1) = result.balancing_matrix2 (); |
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351 // fall through |
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352 case 1: |
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353 retval(0) = result.balancing_matrix (); |
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354 break; |
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355 default: |
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356 error ("balance: invalid number of output arguments"); |
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357 break; |
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358 } |
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359 } |
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360 else |
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361 { |
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362 GEPBALANCE result (aa, bb, bal_job); |
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363 |
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364 switch (nargout) |
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365 { |
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366 case 4: |
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367 retval(3) = result.balanced_matrix2 (); |
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368 // fall through |
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369 case 3: |
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370 retval(2) = result.balanced_matrix (); |
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371 retval(1) = result.balancing_matrix2 (); |
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372 retval(0) = result.balancing_matrix (); |
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373 break; |
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374 case 2: |
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375 retval(1) = result.balancing_matrix2 (); |
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376 // fall through |
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377 case 1: |
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378 retval(0) = result.balancing_matrix (); |
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379 break; |
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380 default: |
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381 error ("balance: invalid number of output arguments"); |
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382 break; |
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383 } |
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384 } |
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385 } |
2928 | 386 } |
3185 | 387 |
2928 | 388 return retval; |
389 } |