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annotate scripts/optimization/lsqnonneg.m @ 31551:fd29c7a50a78 stable

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maint: use commas, semicolons consistently with Octave conventions. * makeValidName.m: Remove %!test and move BIST %!asserts to column 1. * base64decode.m, base64encode.m, which.m, logm.m, uniquetol.m, perms.m: Delete semicolon (';') at end of %!assert BIST. * lin2mu.m, interp2.m, interpn.m, lsqnonneg.m, pqpnonneg.m, uniquetol.m, betainc.m, normalize.m: Add semicolon (';') to end of assert statement within %!test BIST. * __memoize__.m, tar_is_bsd.m, publish.m: Add semicolon (';') to line with keyword "persistent". * stft.m: Use comma (',') after "case" keyword when code immediately follows. * gallery.m: Align commas used in case statements in massive switch block. Remove unnecessary parentheses around a numeric case argument. * ranks.m: Remove semicolon (';') from case statemnt argument.
author Rik <rik@octave.org>
date Sat, 26 Nov 2022 06:32:08 -0800
parents 10a813492497
children 597f3ee61a48
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1 ########################################################################
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2 ##
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3 ## Copyright (C) 2008-2022 The Octave Project Developers
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4 ##
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5 ## See the file COPYRIGHT.md in the top-level directory of this
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6 ## distribution or <https://octave.org/copyright/>.
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7 ##
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8 ## This file is part of Octave.
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9 ##
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10 ## Octave is free software: you can redistribute it and/or modify it
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11 ## under the terms of the GNU General Public License as published by
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12 ## the Free Software Foundation, either version 3 of the License, or
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13 ## (at your option) any later version.
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14 ##
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15 ## Octave is distributed in the hope that it will be useful, but
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16 ## WITHOUT ANY WARRANTY; without even the implied warranty of
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17 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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18 ## GNU General Public License for more details.
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19 ##
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20 ## You should have received a copy of the GNU General Public License
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21 ## along with Octave; see the file COPYING. If not, see
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22 ## <https://www.gnu.org/licenses/>.
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23 ##
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24 ########################################################################
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25
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26 ## -*- texinfo -*-
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27 ## @deftypefn {} {@var{x} =} lsqnonneg (@var{c}, @var{d})
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28 ## @deftypefnx {} {@var{x} =} lsqnonneg (@var{c}, @var{d}, @var{x0})
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29 ## @deftypefnx {} {@var{x} =} lsqnonneg (@var{c}, @var{d}, @var{x0}, @var{options})
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30 ## @deftypefnx {} {[@var{x}, @var{resnorm}] =} lsqnonneg (@dots{})
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31 ## @deftypefnx {} {[@var{x}, @var{resnorm}, @var{residual}] =} lsqnonneg (@dots{})
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32 ## @deftypefnx {} {[@var{x}, @var{resnorm}, @var{residual}, @var{exitflag}] =} lsqnonneg (@dots{})
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33 ## @deftypefnx {} {[@var{x}, @var{resnorm}, @var{residual}, @var{exitflag}, @var{output}] =} lsqnonneg (@dots{})
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34 ## @deftypefnx {} {[@var{x}, @var{resnorm}, @var{residual}, @var{exitflag}, @var{output}, @var{lambda}] =} lsqnonneg (@dots{})
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35 ##
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36 ## Minimize @code{norm (@var{c}*@var{x} - @var{d})} subject to
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37 ## @code{@var{x} >= 0}.
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38 ##
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39 ## @var{c} and @var{d} must be real matrices.
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40 ##
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41 ## @var{x0} is an optional initial guess for the solution @var{x}.
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42 ##
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43 ## @var{options} is an options structure to change the behavior of the
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44 ## algorithm (@pxref{XREFoptimset,,@code{optimset}}). @code{lsqnonneg}
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45 ## recognizes these options: @qcode{"MaxIter"}, @qcode{"TolX"}.
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46 ##
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47 ## Outputs:
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48 ##
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49 ## @table @var
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50 ## @item resnorm
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51 ## The squared 2-norm of the residual: @code{norm (@var{c}*@var{x}-@var{d})^2}
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52 ##
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53 ## @item residual
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54 ## The residual: @code{@var{d}-@var{c}*@var{x}}
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55 ##
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56 ## @item exitflag
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57 ## An indicator of convergence. 0 indicates that the iteration count was
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58 ## exceeded, and therefore convergence was not reached; >0 indicates that the
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59 ## algorithm converged. (The algorithm is stable and will converge given
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60 ## enough iterations.)
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61 ##
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62 ## @item output
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63 ## A structure with two fields:
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64 ##
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65 ## @itemize @bullet
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66 ## @item @qcode{"algorithm"}: The algorithm used (@qcode{"nnls"})
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67 ##
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68 ## @item @qcode{"iterations"}: The number of iterations taken.
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69 ## @end itemize
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70 ##
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71 ## @item lambda
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72 ## Lagrange multipliers. If these are nonzero, the corresponding @var{x}
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73 ## values should be zero, indicating the solution is pressed up against a
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74 ## coordinate plane. The magnitude indicates how much the residual would
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75 ## improve if the @code{@var{x} >= 0} constraints were relaxed in that
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76 ## direction.
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77 ##
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78 ## @end table
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79 ## @seealso{pqpnonneg, lscov, optimset}
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80 ## @end deftypefn
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81
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82 ## PKG_ADD: ## Discard result to avoid polluting workspace with ans at startup.
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83 ## PKG_ADD: [~] = __all_opts__ ("lsqnonneg");
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84
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85 ## This is implemented from Lawson and Hanson's 1973 algorithm on page 161 of
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86 ## Solving Least Squares Problems.
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87
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88 function [x, resnorm, residual, exitflag, output, lambda] = lsqnonneg (c, d, x0 = [], options = struct ())
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89
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90 ## Special case: called to find default optimization options
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91 if (nargin == 1 && ischar (c) && strcmp (c, "defaults"))
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92 x = struct ("MaxIter", 1e5);
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93 return;
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94 endif
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95
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96 if (nargin < 2)
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97 print_usage ();
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98 endif
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99
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100 if (! (isnumeric (c) && ismatrix (c)) || ! (isnumeric (d) && ismatrix (d)))
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101 error ("lsqnonneg: C and D must be numeric matrices");
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102 endif
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103
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104 if (! isstruct (options))
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105 error ("lsqnonneg: OPTIONS must be a struct");
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106 endif
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107
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108 ## Lawson-Hanson Step 1 (LH1): initialize the variables.
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109 m = rows (c);
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110 n = columns (c);
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111 if (isempty (x0))
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112 ## Initial guess is all zeros.
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113 x = zeros (n, 1);
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114 else
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115 ## ensure nonnegative guess.
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116 x = max (x0, 0);
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117 endif
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118
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119 useqr = (m >= n);
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120 max_iter = optimget (options, "MaxIter", 1e5);
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121
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122 ## Initialize P, according to zero pattern of x.
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123 p = find (x > 0).';
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124 if (useqr)
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125 ## Initialize the QR factorization, economized form.
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126 [q, r] = qr (c(:,p), 0);
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127 endif
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128
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129 iter = 0;
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130
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131 ## LH3: test for completion.
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132 while (iter < max_iter)
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133 while (iter < max_iter)
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134 iter += 1;
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135
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136 ## LH6: compute the positive matrix and find the min norm solution
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137 ## of the positive problem.
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138 if (useqr)
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139 xtmp = r \ q'*d;
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140 else
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141 xtmp = c(:,p) \ d;
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142 endif
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143 idx = find (xtmp < 0);
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144
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145 if (isempty (idx))
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146 ## LH7: tmp solution found, iterate.
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147 x(:) = 0;
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148 x(p) = xtmp;
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149 break;
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150 else
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151 ## LH8, LH9: find the scaling factor.
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152 pidx = p(idx);
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153 sf = x(pidx) ./ (x(pidx) - xtmp(idx));
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154 alpha = min (sf);
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155 ## LH10: adjust X.
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156 xx = zeros (n, 1);
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157 xx(p) = xtmp;
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158 x += alpha*(xx - x);
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159 ## LH11: move from P to Z all X == 0.
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160 ## This corresponds to those indices where minimum of sf is attained.
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161 idx = idx(sf == alpha);
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162 p(idx) = [];
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163 if (useqr)
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164 ## update the QR factorization.
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165 [q, r] = qrdelete (q, r, idx);
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166 endif
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167 endif
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168 endwhile
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169
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170 ## compute the gradient.
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171 w = c'*(d - c*x);
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172 w(p) = [];
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173 tolx = optimget (options, "TolX", 10*eps*norm (c, 1)*length (c));
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174 if (! any (w > tolx))
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175 if (useqr)
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176 ## verify the solution achieved using qr updating.
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177 ## in the best case, this should only take a single step.
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178 useqr = false;
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179 continue;
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180 else
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181 ## we're finished.
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182 break;
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183 endif
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184 endif
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185
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186 ## find the maximum gradient.
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187 idx = find (w == max (w));
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188 if (numel (idx) > 1)
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189 warning ("lsqnonneg:nonunique",
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190 "a non-unique solution may be returned due to equal gradients");
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191 idx = idx(1);
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192 endif
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193 ## move the index from Z to P. Keep P sorted.
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194 z = [1:n]; z(p) = [];
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195 zidx = z(idx);
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196 jdx = 1 + lookup (p, zidx);
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197 p = [p(1:jdx-1), zidx, p(jdx:end)];
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198 if (useqr)
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199 ## insert the column into the QR factorization.
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200 [q, r] = qrinsert (q, r, jdx, c(:,zidx));
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201 endif
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202
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203 endwhile
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204 ## LH12: complete.
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205
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206 ## Generate the additional output arguments.
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207 if (isargout (2))
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208 resnorm = norm (c*x - d) ^ 2;
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209 endif
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210 if (isargout (3))
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211 residual = d - c*x;
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212 endif
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213 if (isargout (4))
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214 if (iter >= max_iter)
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215 exitflag = 0;
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216 else
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217 exitflag = iter;
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218 endif
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219 endif
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220 if (isargout (5))
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221 output = struct ("algorithm", "nnls", "iterations", iter);
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222 endif
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223 if (isargout (6))
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224 lambda = zeros (size (x));
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225 lambda (setdiff (1:numel(x), p)) = w;
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226 endif
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227
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228 endfunction
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229
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230
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231 %!test
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232 %! C = [1 0;0 1;2 1];
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233 %! d = [1;3;-2];
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234 %! assert (lsqnonneg (C, d), [0;0.5], 100*eps);
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235
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236 %!test
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237 %! C = [0.0372 0.2869;0.6861 0.7071;0.6233 0.6245;0.6344 0.6170];
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238 %! d = [0.8587;0.1781;0.0747;0.8405];
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239 %! xnew = [0;0.6929];
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240 %! assert (lsqnonneg (C, d), xnew, 0.0001);
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241
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242 ## Test Lagrange multiplier duality: x .* lambda == 0
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243
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244 %!test
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245 %! [x, resn, resid, ~, ~, lambda] = lsqnonneg ([1 0; 0 1; 2 1], [1 1 3]');
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246 %! assert (x, [1 1]', 10*eps);
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247 %! assert (resn, 0, 10*eps);
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248 %! assert (resid, [0 0 0]', 10*eps);
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249 %! assert (lambda, [0 0]', 10*eps);
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250 %! assert (x .* lambda, [0 0]');
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251
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252 %!test
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253 %! [x, resn, resid, ~, ~, lambda] = lsqnonneg ([1 0; 0 1; 2 1], [1 -1 1]');
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254 %! assert (x, [0.6 0]', 10*eps);
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255 %! assert (resn, 1.2, 10*eps);
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256 %! assert (resid, [0.4 -1 -0.2]', 10*eps);
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257 %! assert (lambda, [0 -1.2]', 10*eps);
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258 %! assert (x .* lambda, [0 0]');
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259
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260 %!test
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261 %! [x, resn, resid, ~, ~, lambda] = lsqnonneg ([1 0; 0 1; 2 1], [-1 1 -1]');
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262 %! assert (x, [0 0]', 10*eps);
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263 %! assert (resn, 3, 10*eps);
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264 %! assert (resid, [-1 1 -1]', 10*eps);
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265 %! assert (lambda, [-3 0]', 10*eps);
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266 %! assert (x .* lambda, [0 0]');
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267
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268 %!test
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269 %! [x, resn, resid, ~, ~, lambda] = lsqnonneg ([1 0; 0 1; 2 1], [-1 -1 -3]');
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270 %! assert (x, [0 0]', 10*eps);
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271 %! assert (resn, 11, 20*eps);
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272 %! assert (resid, [-1 -1 -3]', 10*eps);
44a68ac1a22f Fix incorrect lambda outputs for lsqnonneg and pqpnonneg (bug #63178)
Arun Giridhar <arungiridhar@gmail.com>
parents: 31266
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273 %! assert (lambda, [-7 -4]', 10*eps);
31551
fd29c7a50a78 maint: use commas, semicolons consistently with Octave conventions.
Rik <rik@octave.org>
parents: 31286
diff changeset
274 %! assert (x .* lambda, [0 0]');
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44a68ac1a22f Fix incorrect lambda outputs for lsqnonneg and pqpnonneg (bug #63178)
Arun Giridhar <arungiridhar@gmail.com>
parents: 31266
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275
28942
fc4bb4bd1d5e maint: Use '##' as lead-in for full-line comments.
Rik <rik@octave.org>
parents: 28896
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276 ## Test input validation
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90fea9cc9caa test: Add expected error message <Invalid call> to BIST tests for nargin.
Rik <rik@octave.org>
parents: 28789
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277 %!error <Invalid call> lsqnonneg ()
90fea9cc9caa test: Add expected error message <Invalid call> to BIST tests for nargin.
Rik <rik@octave.org>
parents: 28789
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278 %!error <Invalid call> lsqnonneg (1)
22769
9bd2ea5703e2 lsqnonneg.m: Overhaul function.
Rik <rik@octave.org>
parents: 22755
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279 %!error <C .* must be numeric matrices> lsqnonneg ({1},2)
9bd2ea5703e2 lsqnonneg.m: Overhaul function.
Rik <rik@octave.org>
parents: 22755
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280 %!error <C .* must be numeric matrices> lsqnonneg (ones (2,2,2),2)
9bd2ea5703e2 lsqnonneg.m: Overhaul function.
Rik <rik@octave.org>
parents: 22755
diff changeset
281 %!error <D must be numeric matrices> lsqnonneg (1,{2})
9bd2ea5703e2 lsqnonneg.m: Overhaul function.
Rik <rik@octave.org>
parents: 22755
diff changeset
282 %!error <D must be numeric matrices> lsqnonneg (1, ones (2,2,2))
9bd2ea5703e2 lsqnonneg.m: Overhaul function.
Rik <rik@octave.org>
parents: 22755
diff changeset
283 %!error <OPTIONS must be a struct> lsqnonneg (1, 2, [], 3)