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
182
183
184
185
186
187
188
189
190
191
192
|
########################################################################
##
## Copyright (C) 2003-2024 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{c} =} contourc (@var{z})
## @deftypefnx {} {@var{c} =} contourc (@var{z}, @var{vn})
## @deftypefnx {} {@var{c} =} contourc (@var{x}, @var{y}, @var{z})
## @deftypefnx {} {@var{c} =} contourc (@var{x}, @var{y}, @var{z}, @var{vn})
## @deftypefnx {} {[@var{c}, @var{lev}] =} contourc (@dots{})
## Compute contour lines (isolines of constant Z value).
##
## The matrix @var{z} contains height values above the rectangular grid
## determined by @var{x} and @var{y}. If only a single input @var{z} is
## provided then @var{x} is taken to be @code{1:columns (@var{z})} and @var{y}
## is taken to be @code{1:rows (@var{z})}. The minimum data size is 2x2.
##
## The optional input @var{vn} is either a scalar denoting the number of
## contour lines to compute or a vector containing the Z values where lines
## will be computed. When @var{vn} is a vector the number of contour lines
## is @code{numel (@var{vn})}. However, to compute a single contour line
## at a given value use @code{@var{vn} = [val, val]}. If @var{vn} is omitted
## it defaults to 10.
##
## The return value @var{c} is a 2x@var{n} matrix containing the contour lines
## in the following format
##
## @example
## @group
## @var{c} = [lev1, x1, x2, @dots{}, levn, x1, x2, ...
## len1, y1, y2, @dots{}, lenn, y1, y2, @dots{}]
## @end group
## @end example
##
## @noindent
## in which contour line @var{n} has a level (height) of @var{levn} and length
## of @var{lenn}.
##
## The optional return value @var{lev} is a vector with the Z values of the
## contour levels.
##
## Example:
##
## @example
## @group
## x = 0:2;
## y = x;
## z = x' * y;
## c = contourc (x, y, z, 2:3)
## @result{} c =
## 2.0000 1.0000 1.0000 2.0000 2.0000 3.0000 1.5000 2.0000
## 4.0000 2.0000 2.0000 1.0000 1.0000 2.0000 2.0000 1.5000
## @end group
## @end example
## @seealso{contour, contourf, contour3, clabel}
## @end deftypefn
function [c, lev] = contourc (varargin)
if (nargin < 1 || nargin > 4)
print_usage ();
endif
if (nargin == 1)
z = varargin{1};
x = 1:columns (z);
y = 1:rows (z);
vn = 10;
elseif (nargin == 2)
z = varargin{1};
x = 1:columns (z);
y = 1:rows (z);
vn = varargin{2};
elseif (nargin == 3)
x = varargin{1};
y = varargin{2};
z = varargin{3};
vn = 10;
elseif (nargin == 4)
x = varargin{1};
y = varargin{2};
z = varargin{3};
vn = varargin{4};
endif
if (! (isnumeric (z) && isnumeric (x) && isnumeric (y))
|| ! (ismatrix (z) && ismatrix (x) && ismatrix (y))
|| ! (isreal (z) && isreal (x) && isreal (y)))
error ("contourc: X, Y, and Z must be real numeric matrices");
endif
if (rows (z) < 2 || columns (z) < 2)
error ("contourc: Z data must have at least 2 rows and 2 columns");
endif
if (isscalar (vn))
lev = linspace (min (z(:)), max (z(:)), vn+2)(2:end-1);
else
lev = unique (sort (vn));
endif
if (isvector (x) && isvector (y))
c = __contourc__ (x(:)', y(:)', z, lev);
elseif (! any (bsxfun (@minus, x, x(1,:))(:))
&& ! any (bsxfun (@minus, y, y(:,1))(:)))
## x,y are uniform grid (such as from meshgrid)
c = __contourc__ (x(1,:), y(:,1)', z, lev);
else
## Data is sampled over non-uniform mesh.
## Algorithm calculates contours for uniform grid
## and then interpolates values back to the non-uniform mesh.
## Uniform grid for __contourc__.
[nr, nc] = size (z);
ii = 1:nc;
jj = 1:nr;
c = __contourc__ (ii, jj, z, lev);
## Map the contour lines from index space (i,j)
## back to the original grid (x,y)
i = 1;
while (i < columns (c))
clen = c(2, i);
idx = i + (1:clen);
ci = c(1, idx);
cj = c(2, idx);
## Due to rounding errors, some elements of ci and cj can fall out of the
## range of ii and jj and interp2 would return NA for those values.
## The permitted range is enforced here:
ci = max (ci, 1); ci = min (ci, nc);
cj = max (cj, 1); cj = min (cj, nr);
c(1, idx) = interp2 (ii, jj, x, ci, cj);
c(2, idx) = interp2 (ii, jj, y, ci, cj);
i += (clen + 1);
endwhile
endif
endfunction
%!test
%! x = 0:2;
%! y = x;
%! z = x' * y;
%! c_exp = [2, 1, 1, 2, 2, 3, 1.5, 2; 4, 2, 2, 1, 1, 2, 2, 1.5];
%! lev_exp = [2 3];
%! [c_obs, lev_obs] = contourc (x, y, z, 2:3);
%! assert (c_obs, c_exp, eps);
%! assert (lev_obs, lev_exp, eps);
## Test input validation
%!error <Invalid call> contourc ()
%!error <Invalid call> contourc (1,2,3,4,5)
%!error <X, Y, and Z must be .* numeric> contourc ({3})
%!error <X, Y, and Z must be .* numeric> contourc ({1}, 2, 3)
%!error <X, Y, and Z must be .* numeric> contourc (1, {2}, 3)
%!error <X, Y, and Z must be .* matrices> contourc (ones (3,3,3))
%!error <X, Y, and Z must be .* matrices> contourc (ones (3,3,3), 2, 3)
%!error <X, Y, and Z must be .* matrices> contourc (1, ones (3,3,3), 3)
%!error <X, Y, and Z must be real> contourc (3i)
%!error <X, Y, and Z must be real> contourc (1i, 2, 3)
%!error <X, Y, and Z must be real> contourc (1, 2i, 3)
%!error <Z data must have at least 2 rows> contourc ([1, 2])
%!error <Z data must have at least .* 2 columns> contourc ([1; 2])
|
