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annotate scripts/sparse/spdiags.m @ 19252:edf5d63c82e1

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Deprecate strmatch function. * scripts/deprecated/strmatch.m: Moved from scripts/strings. Add deprecation warning to code and to docstring. * strings.txi: Remove from manual * scripts/deprecated/module.mk: Add to build system in deprecated directory. * scripts/strings/module.mk: Remove from build system in strings directory.
author Rik <rik@octave.org>
date Fri, 29 Aug 2014 20:41:58 -0700
parents 9ac2357f19bc
children 4197fc428c7d
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
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d63878346099 maint: Update copyright notices for release.
John W. Eaton <jwe@octave.org>
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1 ## Copyright (C) 2000-2013 Paul Kienzle
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2 ##
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3 ## This file is part of Octave.
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4 ##
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5 ## Octave is free software; you can redistribute it and/or modify it
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6 ## under the terms of the GNU General Public License as published by
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7 ## the Free Software Foundation; either version 3 of the License, or (at
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8 ## your option) any later version.
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9 ##
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10 ## Octave is distributed in the hope that it will be useful, but
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11 ## WITHOUT ANY WARRANTY; without even the implied warranty of
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12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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13 ## General Public License for more details.
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14 ##
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15 ## You should have received a copy of the GNU General Public License
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16 ## along with Octave; see the file COPYING. If not, see
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17 ## <http://www.gnu.org/licenses/>.
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18
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19 ## -*- texinfo -*-
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20 ## @deftypefn {Function File} {@var{B} =} spdiags (@var{A})
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21 ## @deftypefnx {Function File} {[@var{B}, @var{d}] =} spdiags (@var{A})
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22 ## @deftypefnx {Function File} {@var{B} =} spdiags (@var{A}, @var{d})
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23 ## @deftypefnx {Function File} {@var{A} =} spdiags (@var{v}, @var{d}, @var{A})
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24 ## @deftypefnx {Function File} {@var{A} =} spdiags (@var{v}, @var{d}, @var{m}, @var{n})
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25 ## A generalization of the function @code{diag}. Called with a single
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26 ## input argument, the nonzero diagonals @var{d} of @var{A} are extracted.
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27 ## With two arguments the diagonals to extract are given by the vector
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28 ## @var{d}.
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29 ##
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30 ## The other two forms of @code{spdiags} modify the input matrix by
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31 ## replacing the diagonals. They use the columns of @var{v} to replace
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32 ## the diagonals represented by the vector @var{d}. If the sparse matrix
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33 ## @var{A} is defined then the diagonals of this matrix are replaced.
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34 ## Otherwise a matrix of @var{m} by @var{n} is created with the
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35 ## diagonals given by the columns of @var{v}.
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36 ##
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37 ## Negative values of @var{d} represent diagonals below the main
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38 ## diagonal, and positive values of @var{d} diagonals above the main
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39 ## diagonal.
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40 ##
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41 ## For example:
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42 ##
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43 ## @example
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44 ## @group
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45 ## spdiags (reshape (1:12, 4, 3), [-1 0 1], 5, 4)
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46 ## @result{} 5 10 0 0
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47 ## 1 6 11 0
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48 ## 0 2 7 12
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49 ## 0 0 3 8
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50 ## 0 0 0 4
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51 ## @end group
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52 ## @end example
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53 ##
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54 ## @seealso{diag}
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55 ## @end deftypefn
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56
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57 function [B, d] = spdiags (v, d, m, n)
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58
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59 if (nargin < 1 || nargin > 4)
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60 print_usage ();
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61 endif
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62
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63 if (nargin == 1 || nargin == 2)
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64 ## extract nonzero diagonals of A into B,d
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65 [nr, nc] = size (v);
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66 [i, j] = find (v);
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67
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68 if (nargin == 1)
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69 ## d contains the active diagonals
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70 d = unique (j-i);
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71 endif
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72
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73 ## FIXME: Maybe this could be done faster using [i,j,v] = find (v)
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74 ## and then massaging the indices i, j. However, some
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75 ## benchmarking has shown that diag() written in C++ makes
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76 ## the following code faster even with the for loop.
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77 Brows = min (nr, nc);
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78 B = zeros (Brows, length (d));
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79 for k = 1:length (d)
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80 dn = d(k);
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81 if (dn <= -nr || dn > nc)
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82 continue;
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83 endif
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84 dv = diag (v, dn);
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85 len = rows (dv);
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86 ## Put sub/super-diagonals in the right place based on matrix size (MxN)
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87 if (nr >= nc)
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88 if (dn > 0)
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89 offset = Brows - len + 1;
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90 B(offset:Brows, k) = dv;
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91 else
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92 B(1:len, k) = dv;
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93 endif
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94 else
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95 if (dn < 0)
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96 offset = Brows - len + 1;
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97 B(offset:Brows, k) = dv;
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98 else
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99 B(1:len, k) = dv;
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100 endif
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101 endif
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102 endfor
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103
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104 elseif (nargin == 3)
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105 ## Replace specific diagonals d of m with v,d
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106 [nr, nc] = size (m);
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107 A = spdiags (m, d);
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108 B = m - spdiags (A, d, nr, nc) + spdiags (v, d, nr, nc);
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109
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110 else
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111 ## Create new matrix of size mxn using v,d
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112 [j, i, v] = find (v);
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113 if (m >= n)
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114 offset = max (min (d(:), n-m), 0);
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115 else
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116 offset = d(:);
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117 endif
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118 j = j(:) + offset(i(:));
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119 i = j - d(:)(i(:));
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120 idx = i > 0 & i <= m & j > 0 & j <= n;
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121 B = sparse (i(idx), j(idx), v(idx), m, n);
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122
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123 endif
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124
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125 endfunction
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126
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127
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128 %!test
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129 %! [B,d] = spdiags (magic (3));
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130 %! assert (d, [-2 -1 0 1 2]');
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131 %! assert (B, [4 3 8 0 0
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132 %! 0 9 5 1 0
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133 %! 0 0 2 7 6]);
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134 %! B = spdiags (magic (3), [-2 1]);
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135 %! assert (B, [4 0; 0 1; 0 7]);
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136
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137 ## Test zero filling for supra- and super-diagonals
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138 %!test
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139 %! ## Case 1: M = N
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140 %! A = sparse (zeros (3,3));
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141 %! A(1,3) = 13;
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142 %! A(3,1) = 31;
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143 %! [B, d] = spdiags (A);
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144 %! assert (d, [-2 2]');
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145 %! assert (B, [31 0; 0 0; 0 13]);
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146 %! assert (spdiags (B, d, 3,3), A)
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147
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148 %!test
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149 %! ## Case 1: M > N
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150 %! A = sparse (zeros (4,3));
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151 %! A(1,3) = 13;
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152 %! A(3,1) = 31;
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153 %! [B, d] = spdiags (A);
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154 %! assert (d, [-2 2]');
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155 %! assert (B, [31 0; 0 0; 0 13]);
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156 %! assert (spdiags (B, d, 4,3), A)
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157
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158 %!test
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159 %! ## Case 1: M < N
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160 %! A = sparse (zeros (3,4));
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161 %! A(1,3) = 13;
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162 %! A(3,1) = 31;
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163 %! [B, d] = spdiags (A);
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164 %! assert (d, [-2 2]');
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165 %! assert (B, [0 13; 0 0; 31 0]);
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166 %! assert (spdiags (B, d, 3,4), A)
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167
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168 %!assert (spdiags (zeros (1,0),1,1,1), sparse (0))
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169 %!assert (spdiags (zeros (0,1),1,1,1), sparse (0))
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170 %!assert (spdiags ([0.5 -1 0.5], 0:2, 1, 1), sparse (0.5))
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171
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172 %% Test input validation
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173 %!error spdiags ()
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174 %!error spdiags (1,2,3,4,5)
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175