1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
|
########################################################################
##
## Copyright (C) 2000-2024 The Octave Project Developers
##
## See the file COPYRIGHT.md in the top-level directory of this
## distribution or <https://octave.org/copyright/>.
##
## This file is part of Octave.
##
## Octave is free software: you can redistribute it and/or modify it
## under the terms of the GNU General Public License as published by
## the Free Software Foundation, either version 3 of the License, or
## (at your option) any later version.
##
## Octave is distributed in the hope that it will be useful, but
## WITHOUT ANY WARRANTY; without even the implied warranty of
## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
## GNU General Public License for more details.
##
## You should have received a copy of the GNU General Public License
## along with Octave; see the file COPYING. If not, see
## <https://www.gnu.org/licenses/>.
##
########################################################################
## -*- texinfo -*-
## @deftypefn {} {@var{B} =} spdiags (@var{A})
## @deftypefnx {} {[@var{B}, @var{d}] =} spdiags (@var{A})
## @deftypefnx {} {@var{B} =} spdiags (@var{A}, @var{d})
## @deftypefnx {} {@var{A} =} spdiags (@var{v}, @var{d}, @var{A})
## @deftypefnx {} {@var{A} =} spdiags (@var{v}, @var{d}, @var{m}, @var{n})
## A generalization of the function @code{diag}.
##
## Called with a single input argument, the nonzero diagonals @var{d} of
## @var{A} are extracted.
##
## With two arguments the diagonals to extract are given by the vector @var{d}.
##
## The other two forms of @code{spdiags} modify the input matrix by replacing
## the diagonals. They use the columns of @var{v} to replace the diagonals
## represented by the vector @var{d}. If the sparse matrix @var{A} is
## defined then the diagonals of this matrix are replaced. Otherwise a
## matrix of @var{m} by @var{n} is created with the diagonals given by the
## columns of @var{v}.
##
## Negative values of @var{d} represent diagonals below the main diagonal, and
## positive values of @var{d} diagonals above the main diagonal.
##
## For example:
##
## @example
## @group
## spdiags (reshape (1:12, 4, 3), [-1 0 1], 5, 4)
## @result{} 5 10 0 0
## 1 6 11 0
## 0 2 7 12
## 0 0 3 8
## 0 0 0 4
## @end group
## @end example
##
## @seealso{diag}
## @end deftypefn
function [B, d] = spdiags (v, d, m, n)
if (nargin < 1)
print_usage ();
endif
if (nargin == 1 || nargin == 2)
## extract nonzero diagonals of A into B,d
[nr, nc] = size (v);
[i, j] = find (v);
if (nargin == 1)
## d contains the active diagonals
d = unique (j-i);
endif
## FIXME: Maybe this could be done faster using [i,j,v] = find (v)
## and then massaging the indices i, j. However, some
## benchmarking has shown that diag() written in C++ makes
## the following code faster even with the for loop.
Brows = min (nr, nc);
B = zeros (Brows, length (d));
for k = 1:length (d)
dn = d(k);
if (dn <= -nr || dn > nc)
continue;
endif
dv = diag (v, dn);
len = rows (dv);
## Put sub/super-diagonals in the right place based on matrix size (MxN)
if (nr >= nc)
if (dn > 0)
offset = Brows - len + 1;
B(offset:Brows, k) = dv;
else
B(1:len, k) = dv;
endif
else
if (dn < 0)
offset = Brows - len + 1;
B(offset:Brows, k) = dv;
else
B(1:len, k) = dv;
endif
endif
endfor
elseif (nargin == 3)
## Replace specific diagonals d of m with v,d
[nr, nc] = size (m);
A = spdiags (m, d);
B = m - spdiags (A, d, nr, nc) + spdiags (v, d, nr, nc);
else
## Create new matrix of size mxn using v,d
[j, i, v] = find (v);
if (m >= n)
offset = max (min (d(:), n-m), 0);
else
offset = d(:);
endif
j = j(:) + offset(i(:));
i = j - d(:)(i(:));
idx = i > 0 & i <= m & j > 0 & j <= n;
B = sparse (i(idx), j(idx), v(idx), m, n);
endif
endfunction
%!test
%! [B,d] = spdiags (magic (3));
%! assert (d, [-2 -1 0 1 2]');
%! assert (B, [4 3 8 0 0
%! 0 9 5 1 0
%! 0 0 2 7 6]);
%! B = spdiags (magic (3), [-2 1]);
%! assert (B, [4 0; 0 1; 0 7]);
## Test zero filling for supra- and super-diagonals
%!test
%! ## Case 1: M = N
%! A = sparse (zeros (3,3));
%! A(1,3) = 13;
%! A(3,1) = 31;
%! [B, d] = spdiags (A);
%! assert (d, [-2 2]');
%! assert (B, [31 0; 0 0; 0 13]);
%! assert (spdiags (B, d, 3,3), A);
%!test
%! ## Case 1: M > N
%! A = sparse (zeros (4,3));
%! A(1,3) = 13;
%! A(3,1) = 31;
%! [B, d] = spdiags (A);
%! assert (d, [-2 2]');
%! assert (B, [31 0; 0 0; 0 13]);
%! assert (spdiags (B, d, 4,3), A);
%!test
%! ## Case 1: M < N
%! A = sparse (zeros (3,4));
%! A(1,3) = 13;
%! A(3,1) = 31;
%! [B, d] = spdiags (A);
%! assert (d, [-2 2]');
%! assert (B, [0 13; 0 0; 31 0]);
%! assert (spdiags (B, d, 3,4), A);
%!assert (spdiags (zeros (1,0),1,1,1), sparse (0))
%!assert (spdiags (zeros (0,1),1,1,1), sparse (0))
%!assert (spdiags ([0.5 -1 0.5], 0:2, 1, 1), sparse (0.5))
## Test input validation
%!error <Invalid call> spdiags ()
|
