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1 ## Copyright (C) 2000-2001 Paul Kienzle |
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2 ## |
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3 ## This program is free software; you can redistribute it and/or modify |
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4 ## it under the terms of the GNU General Public License as published by |
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5 ## the Free Software Foundation; either version 2 of the License, or |
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6 ## (at your option) any later version. |
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7 ## |
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8 ## This program is distributed in the hope that it will be useful, |
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9 ## but WITHOUT ANY WARRANTY; without even the implied warranty of |
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10 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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11 ## GNU General Public License for more details. |
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12 ## |
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13 ## You should have received a copy of the GNU General Public License |
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14 ## along with this program; if not, write to the Free Software |
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15 ## Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA |
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16 ## 02110-1301 USA |
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17 |
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18 ## -*- texinfo -*- |
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19 ## @deftypefn {function File} {[@var{b}, @var{c}] =} spdiags (@var{a}) |
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20 ## @deftypefnx {function File} {@var{b} =} spdiags (@var{a}, @var{c}) |
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21 ## @deftypefnx {function File} {@var{b} =} spdiags (@var{v}, @var{c}, @var{a}) |
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22 ## @deftypefnx {function File} {@var{b} =} spdiags (@var{v}, @var{c}, @var{m}, @var{n}) |
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23 ## A generalization of the function @code{spdiag}. Called with a single |
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24 ## input argument, the non-zero diagonals @var{c} of @var{A} are extracted. |
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25 ## With two arguments the diagonals to extract are given by the vector |
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26 ## @var{c}. |
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27 ## |
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28 ## The other two forms of @code{spdiags} modify the input matrix by |
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29 ## replacing the diagonals. They use the columns of @var{v} to replace |
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30 ## the columns represented by the vector @var{c}. If the sparse matrix |
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31 ## @var{a} is defined then the diagonals of this matrix are replaced. |
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32 ## Otherwise a matrix of @var{m} by @var{n} is created with the |
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33 ## diagonals given by @var{v}. |
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34 ## |
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35 ## Negative values of @var{c} representive diagonals below the main |
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36 ## diagonal, and positive values of @var{c} diagonals above the main |
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37 ## diagonal. |
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38 ## |
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39 ## For example |
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40 ## |
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41 ## @example |
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42 ## @group |
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43 ## spdiags (reshape (1:12, 4, 3), [-1 0 1], 5, 4) |
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44 ## @result{} 5 10 0 0 |
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45 ## 1 6 11 0 |
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46 ## 0 2 7 12 |
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47 ## 0 0 3 8 |
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48 ## 0 0 0 4 |
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49 ## @end group |
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50 ## @end example |
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51 ## |
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52 ## @end deftypefn |
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53 |
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54 function [A, c] = spdiags (v, c, m, n) |
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55 |
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56 if (nargin == 1 || nargin == 2) |
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57 ## extract nonzero diagonals of v into A,c |
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58 [i, j, v, nr, nc] = spfind (v); |
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59 if (nargin == 1) |
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60 ## c contains the active diagonals |
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61 c = unique (j-i); |
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62 endif |
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63 ## FIXME: we can do this without a loop if we are clever |
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64 offset = max (min (c, nc-nr), 0); |
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65 A = zeros (min (nr, nc), length (c)); |
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66 for k = 1:length (c) |
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67 idx = find (j-i == c(k)); |
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68 A(j(idx)-offset(k),k) = v(idx); |
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69 endfor |
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70 elseif (nargin == 3) |
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71 ## Replace specific diagonals c of m with v,c |
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72 [nr, nc] = size (m); |
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73 B = spdiags (m, c); |
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74 A = m - spdiags (B, c, nr, nc) + spdiags (v, c, nr, nc); |
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75 else |
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76 ## Create new matrix of size mxn using v,c |
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77 [j, i, v] = find (v); |
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78 offset = max (min (c(:), n-m), 0); |
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79 j = j(:) + offset(i); |
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80 i = j-c(:)(i); |
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81 idx = i > 0 & i <= m & j > 0 & j <= n; |
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82 A = sparse (i(idx), j(idx), v(idx), m, n); |
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83 endif |
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84 |
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85 endfunction |
