Mercurial > octave
annotate libinterp/corefcn/balance.cc @ 23807:336f89b6208b
Use character literals 'c' rather than string literals "c" when possible.
Better performance when string constructor isn't required.
* Figure.cc, __init_qt__.cc, files-dock-widget.cc, file-editor-tab.cc,
file-editor.cc, octave-qscintilla.cc, main-window.cc, octave-dock-widget.cc,
octave-qt-link.cc, parser.cc, webinfo.cc, resource-manager.cc,
settings-dialog.cc, workspace-view.cc, __magick_read__.cc, balance.cc,
debug.cc, dynamic-ld.cc, ft-text-renderer.cc, gl-render.cc, gl2ps-print.cc,
graphics.cc, hook-fcn.h, input.cc, load-path.cc, load-save.cc, ls-hdf5.cc,
oct-hist.cc, oct-stream.cc, pager.cc, pr-output.cc, qz.cc, symtab.cc, symtab.h,
tril.cc, __delaunayn__.cc, __init_fltk__.cc, __voronoi__.cc, audioread.cc,
ccolamd.cc, colamd.cc, convhulln.cc, ov-base-int.cc, ov-base-mat.cc,
ov-base-scalar.cc, ov-base.cc, ov-bool-mat.cc, ov-cell.cc, ov-class.cc,
ov-classdef.cc, ov-colon.cc, ov-complex.cc, ov-cx-mat.cc, ov-fcn-handle.cc,
ov-fcn-inline.cc, ov-fcn.h, ov-flt-cx-mat.cc, ov-flt-re-mat.cc, ov-java.cc,
ov-oncleanup.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, octave.cc, bp-table.cc, jit-ir.cc,
jit-ir.h, jit-typeinfo.cc, pt-funcall.cc, pt-idx.cc, pt-pr-code.cc, pt.h,
Array.cc, CDiagMatrix.cc, CMatrix.cc, CNDArray.cc, CRowVector.cc, CSparse.cc,
Range.cc, boolSparse.cc, dDiagMatrix.cc, dMatrix.cc, dNDArray.cc,
dRowVector.cc, dSparse.cc, fCDiagMatrix.cc, fCMatrix.cc, fCNDArray.cc,
fCRowVector.cc, fDiagMatrix.cc, fMatrix.cc, fNDArray.cc, fRowVector.cc,
idx-vector.cc, intNDArray.cc, CollocWt.cc, DASPK.cc, DASRT.cc, DASSL.cc,
LSODE.cc, oct-time.cc, cmd-hist.cc, kpse.cc, lo-array-errwarn.cc, lo-regexp.cc,
lo-utils.cc, str-vec.cc, url-transfer.cc, main-cli.cc, main-gui.cc,
mkoctfile.in.cc:
Replace 1-character string literals "c" with the character literal 'c'.
author | Rik <rik@octave.org> |
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date | Fri, 28 Jul 2017 15:40:00 -0700 |
parents | c3075ae020e1 |
children | d69021d58a61 |
rev | line source |
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2928 | 1 /* |
2 | |
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3 Copyright (C) 1996-2017 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 | |
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9 under the terms of the GNU General Public License as published by |
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10 the Free Software Foundation; either version 3 of the License, or |
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11 (at your option) any later version. |
2928 | 12 |
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13 Octave is distributed in the hope that it will be useful, but |
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14 WITHOUT ANY WARRANTY; without even the implied warranty of |
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15 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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16 GNU General Public License for more details. |
2928 | 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 |
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26 #if defined (HAVE_CONFIG_H) |
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27 # include "config.h" |
2928 | 28 #endif |
29 | |
30 #include <string> | |
31 | |
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32 #include "CMatrix.h" |
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33 #include "aepbalance.h" |
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34 #include "dMatrix.h" |
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35 #include "fCMatrix.h" |
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36 #include "fMatrix.h" |
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37 #include "gepbalance.h" |
4153 | 38 #include "quit.h" |
2928 | 39 |
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40 #include "defun.h" |
2928 | 41 #include "error.h" |
3181 | 42 #include "f77-fcn.h" |
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43 #include "errwarn.h" |
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44 #include "ovl.h" |
2928 | 45 #include "utils.h" |
46 | |
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47 DEFUN (balance, args, nargout, |
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48 doc: /* -*- texinfo -*- |
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49 @deftypefn {} {@var{AA} =} balance (@var{A}) |
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50 @deftypefnx {} {@var{AA} =} balance (@var{A}, @var{opt}) |
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51 @deftypefnx {} {[@var{DD}, @var{AA}] =} balance (@var{A}, @var{opt}) |
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52 @deftypefnx {} {[@var{D}, @var{P}, @var{AA}] =} balance (@var{A}, @var{opt}) |
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53 @deftypefnx {} {[@var{CC}, @var{DD}, @var{AA}, @var{BB}] =} balance (@var{A}, @var{B}, @var{opt}) |
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54 |
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55 Balance the matrix @var{A} to reduce numerical errors in future |
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56 calculations. |
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57 |
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58 Compute @code{@var{AA} = @var{DD} \ @var{A} * @var{DD}} in which @var{AA} |
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59 is a matrix whose row and column norms are roughly equal in magnitude, and |
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60 @code{@var{DD} = @var{P} * @var{D}}, in which @var{P} is a permutation |
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61 matrix and @var{D} is a diagonal matrix of powers of two. This allows the |
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62 equilibration to be computed without round-off. Results of eigenvalue |
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63 calculation are typically improved by balancing first. |
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64 |
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65 If two output values are requested, @code{balance} returns |
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66 the diagonal @var{D} and the permutation @var{P} separately as vectors. |
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67 In this case, @code{@var{DD} = eye(n)(:,@var{P}) * diag (@var{D})}, where |
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68 @math{n} is the matrix size. |
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69 |
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70 If four output values are requested, compute @code{@var{AA} = |
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71 @var{CC}*@var{A}*@var{DD}} and @code{@var{BB} = @var{CC}*@var{B}*@var{DD}}, |
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72 in which @var{AA} and @var{BB} have nonzero elements of approximately the |
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73 same magnitude and @var{CC} and @var{DD} are permuted diagonal matrices as |
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74 in @var{DD} for the algebraic eigenvalue problem. |
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75 |
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76 The eigenvalue balancing option @var{opt} may be one of: |
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77 |
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78 @table @asis |
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79 @item @qcode{"noperm"}, @qcode{"S"} |
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80 Scale only; do not permute. |
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81 |
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82 @item @qcode{"noscal"}, @qcode{"P"} |
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83 Permute only; do not scale. |
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84 @end table |
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85 |
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86 Algebraic eigenvalue balancing uses standard @sc{lapack} routines. |
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87 |
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88 Generalized eigenvalue problem balancing uses Ward's algorithm |
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89 (SIAM Journal on Scientific and Statistical Computing, 1981). |
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90 @end deftypefn */) |
2928 | 91 { |
92 int nargin = args.length (); | |
93 | |
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94 if (nargin < 1 || nargin > 3 || nargout < 0) |
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95 print_usage (); |
2928 | 96 |
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97 octave_value_list retval; |
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98 |
3181 | 99 // determine if it's AEP or GEP |
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100 bool AEPcase = nargin == 1 || args(1).is_string (); |
2928 | 101 |
3181 | 102 // problem dimension |
5275 | 103 octave_idx_type nn = args(0).rows (); |
2928 | 104 |
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105 if (nn != args(0).columns ()) |
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106 err_square_matrix_required ("balance", "A"); |
2928 | 107 |
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108 bool isfloat = args(0).is_single_type () |
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109 || (! AEPcase && args(1).is_single_type ()); |
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110 |
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111 bool complex_case = args(0).iscomplex () |
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112 || (! AEPcase && args(1).iscomplex ()); |
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113 |
2928 | 114 // Extract argument 1 parameter for both AEP and GEP. |
115 Matrix aa; | |
116 ComplexMatrix caa; | |
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117 FloatMatrix faa; |
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118 FloatComplexMatrix fcaa; |
3185 | 119 |
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120 if (isfloat) |
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121 { |
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122 if (complex_case) |
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123 fcaa = args(0).float_complex_matrix_value (); |
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124 else |
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125 faa = args(0).float_matrix_value (); |
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126 } |
3185 | 127 else |
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128 { |
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129 if (complex_case) |
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130 caa = args(0).complex_matrix_value (); |
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131 else |
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132 aa = args(0).matrix_value (); |
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133 } |
3185 | 134 |
2928 | 135 // Treat AEP/GEP cases. |
3185 | 136 if (AEPcase) |
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137 { |
3185 | 138 // Algebraic eigenvalue problem. |
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139 bool noperm = false; |
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140 bool noscal = false; |
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141 if (nargin > 1) |
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142 { |
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143 std::string a1s = args(1).string_value (); |
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144 noperm = a1s == "noperm" || a1s == "S"; |
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145 noscal = a1s == "noscal" || a1s == "P"; |
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146 } |
3185 | 147 |
148 // balance the AEP | |
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149 if (isfloat) |
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150 { |
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151 if (complex_case) |
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152 { |
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153 octave::math::aepbalance<FloatComplexMatrix> result (fcaa, noperm, noscal); |
2928 | 154 |
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155 if (nargout == 0 || nargout == 1) |
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156 retval = ovl (result.balanced_matrix ()); |
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157 else if (nargout == 2) |
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158 retval = ovl (result.balancing_matrix (), |
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159 result.balanced_matrix ()); |
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160 else |
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161 retval = ovl (result.scaling_vector (), |
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162 result.permuting_vector (), |
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163 result.balanced_matrix ()); |
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164 } |
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165 else |
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166 { |
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167 octave::math::aepbalance<FloatMatrix> result (faa, noperm, noscal); |
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168 |
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169 if (nargout == 0 || nargout == 1) |
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170 retval = ovl (result.balanced_matrix ()); |
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171 else if (nargout == 2) |
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172 retval = ovl (result.balancing_matrix (), |
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173 result.balanced_matrix ()); |
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174 else |
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175 retval = ovl (result.scaling_vector (), |
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176 result.permuting_vector (), |
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177 result.balanced_matrix ()); |
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178 } |
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179 } |
3181 | 180 else |
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181 { |
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182 if (complex_case) |
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183 { |
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184 octave::math::aepbalance<ComplexMatrix> result (caa, noperm, noscal); |
3185 | 185 |
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186 if (nargout == 0 || nargout == 1) |
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187 retval = ovl (result.balanced_matrix ()); |
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188 else if (nargout == 2) |
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189 retval = ovl (result.balancing_matrix (), |
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190 result.balanced_matrix ()); |
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191 else |
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192 retval = ovl (result.scaling_vector (), |
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193 result.permuting_vector (), |
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194 result.balanced_matrix ()); |
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195 } |
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196 else |
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197 { |
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198 octave::math::aepbalance<Matrix> result (aa, noperm, noscal); |
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199 |
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200 if (nargout == 0 || nargout == 1) |
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201 retval = ovl (result.balanced_matrix ()); |
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202 else if (nargout == 2) |
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203 retval = ovl (result.balancing_matrix (), |
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204 result.balanced_matrix ()); |
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205 else |
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206 retval = ovl (result.scaling_vector (), |
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207 result.permuting_vector (), |
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208 result.balanced_matrix ()); |
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209 } |
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210 } |
3181 | 211 } |
212 else | |
213 { | |
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214 std::string bal_job; |
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215 if (nargout == 1) |
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216 warning ("balance: used GEP, should have two output arguments"); |
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217 |
3185 | 218 // Generalized eigenvalue problem. |
219 if (nargin == 2) | |
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220 bal_job = 'B'; |
3185 | 221 else |
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222 bal_job = args(2).xstring_value ("balance: OPT argument must be a string"); |
3185 | 223 |
224 if ((nn != args(1).columns ()) || (nn != args(1).rows ())) | |
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225 err_nonconformant (); |
3185 | 226 |
227 Matrix bb; | |
228 ComplexMatrix cbb; | |
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229 FloatMatrix fbb; |
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230 FloatComplexMatrix fcbb; |
3185 | 231 |
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232 if (isfloat) |
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233 { |
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234 if (complex_case) |
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235 fcbb = args(1).float_complex_matrix_value (); |
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236 else |
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237 fbb = args(1).float_matrix_value (); |
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238 } |
3185 | 239 else |
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240 { |
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241 if (complex_case) |
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242 cbb = args(1).complex_matrix_value (); |
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243 else |
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244 bb = args(1).matrix_value (); |
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245 } |
4153 | 246 |
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247 // balance the GEP |
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248 if (isfloat) |
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249 { |
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250 if (complex_case) |
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251 { |
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252 octave::math::gepbalance<FloatComplexMatrix> result (fcaa, fcbb, bal_job); |
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253 |
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254 switch (nargout) |
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255 { |
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256 case 4: |
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257 retval(3) = result.balanced_matrix2 (); |
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258 // fall through |
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259 case 3: |
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260 retval(2) = result.balanced_matrix (); |
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261 retval(1) = result.balancing_matrix2 (); |
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262 retval(0) = result.balancing_matrix (); |
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263 break; |
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264 case 2: |
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265 retval(1) = result.balancing_matrix2 (); |
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266 // fall through |
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267 case 1: |
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268 retval(0) = result.balancing_matrix (); |
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269 break; |
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270 default: |
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271 error ("balance: invalid number of output arguments"); |
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272 break; |
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273 } |
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274 } |
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275 else |
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276 { |
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277 octave::math::gepbalance<FloatMatrix> result (faa, fbb, bal_job); |
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278 |
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279 switch (nargout) |
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280 { |
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281 case 4: |
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282 retval(3) = result.balanced_matrix2 (); |
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283 // fall through |
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284 case 3: |
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285 retval(2) = result.balanced_matrix (); |
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286 retval(1) = result.balancing_matrix2 (); |
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287 retval(0) = result.balancing_matrix (); |
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288 break; |
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289 case 2: |
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290 retval(1) = result.balancing_matrix2 (); |
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291 // fall through |
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292 case 1: |
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293 retval(0) = result.balancing_matrix (); |
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294 break; |
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295 default: |
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296 error ("balance: invalid number of output arguments"); |
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297 break; |
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298 } |
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299 } |
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300 } |
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301 else |
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302 { |
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303 if (complex_case) |
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304 { |
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305 octave::math::gepbalance<ComplexMatrix> result (caa, cbb, bal_job); |
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306 |
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307 switch (nargout) |
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308 { |
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309 case 4: |
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310 retval(3) = result.balanced_matrix2 (); |
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311 // fall through |
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312 case 3: |
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313 retval(2) = result.balanced_matrix (); |
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314 retval(1) = result.balancing_matrix2 (); |
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315 retval(0) = result.balancing_matrix (); |
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316 break; |
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317 case 2: |
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318 retval(1) = result.balancing_matrix2 (); |
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319 // fall through |
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320 case 1: |
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321 retval(0) = result.balancing_matrix (); |
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322 break; |
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323 default: |
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324 error ("balance: invalid number of output arguments"); |
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325 break; |
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326 } |
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327 } |
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328 else |
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329 { |
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330 octave::math::gepbalance<Matrix> result (aa, bb, bal_job); |
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331 |
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332 switch (nargout) |
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333 { |
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334 case 4: |
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335 retval(3) = result.balanced_matrix2 (); |
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336 // fall through |
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337 case 3: |
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338 retval(2) = result.balanced_matrix (); |
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339 retval(1) = result.balancing_matrix2 (); |
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340 retval(0) = result.balancing_matrix (); |
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341 break; |
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342 case 2: |
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343 retval(1) = result.balancing_matrix2 (); |
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344 // fall through |
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345 case 1: |
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346 retval(0) = result.balancing_matrix (); |
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347 break; |
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348 default: |
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349 error ("balance: invalid number of output arguments"); |
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350 break; |
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351 } |
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352 } |
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353 } |
2928 | 354 } |
3185 | 355 |
2928 | 356 return retval; |
357 } |