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annotate scripts/polynomial/spline.m @ 15063:36cbcc37fdb8

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Refactor configure.ac to make it more understandable. Use common syntax for messages in config.h Correct typos, refer to libraries in all caps, use two spaces after period. Follow Autoconf guidelines and place general tests before specific tests. * configure.ac, m4/acinclude.m4: Use common syntax for messages in config.h Correct typos, refer to libraries in all caps, use two spaces after period. Follow Autoconf guidelines and place general tests before specific tests.
author Rik <rik@octave.org>
date Tue, 31 Jul 2012 10:28:51 -0700
parents c2dbdeaa25df
children d63878346099
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
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1 ## Copyright (C) 2000-2012 Kai Habel
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2 ## Copyright (C) 2006 David Bateman
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3 ##
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4 ## This file is part of Octave.
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5 ##
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6 ## Octave is free software; you can redistribute it and/or modify it
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7 ## under the terms of the GNU General Public License as published by
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8 ## the Free Software Foundation; either version 3 of the License, or (at
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9 ## your option) any later version.
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10 ##
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11 ## Octave is distributed in the hope that it will be useful, but
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12 ## WITHOUT ANY WARRANTY; without even the implied warranty of
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13 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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14 ## General Public License for more details.
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15 ##
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16 ## You should have received a copy of the GNU General Public License
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17 ## along with Octave; see the file COPYING. If not, see
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18 ## <http://www.gnu.org/licenses/>.
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19
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20 ## -*- texinfo -*-
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21 ## @deftypefn {Function File} {@var{pp} =} spline (@var{x}, @var{y})
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22 ## @deftypefnx {Function File} {@var{yi} =} spline (@var{x}, @var{y}, @var{xi})
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23 ## Return the cubic spline interpolant of points @var{x} and @var{y}.
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24 ##
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25 ## When called with two arguments, return the piecewise polynomial @var{pp}
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26 ## that may be used with @code{ppval} to evaluate the polynomial at specific
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27 ## points. When called with a third input argument, @code{spline} evaluates
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28 ## the spline at the points @var{xi}. The third calling form @code{spline
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29 ## (@var{x}, @var{y}, @var{xi})} is equivalent to @code{ppval (spline
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30 ## (@var{x}, @var{y}), @var{xi})}.
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31 ##
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32 ## The variable @var{x} must be a vector of length @var{n}. @var{y} can be
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33 ## either a vector or array. If @var{y} is a vector it must have a length of
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34 ## either @var{n} or @code{@var{n} + 2}. If the length of @var{y} is
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35 ## @var{n}, then the "not-a-knot" end condition is used. If the length of
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36 ## @var{y} is @code{@var{n} + 2}, then the first and last values of the
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37 ## vector @var{y} are the values of the first derivative of the cubic spline
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38 ## at the endpoints.
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39 ##
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40 ## If @var{y} is an array, then the size of @var{y} must have the form
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41 ## @tex
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42 ## $$[s_1, s_2, \cdots, s_k, n]$$
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43 ## @end tex
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44 ## @ifnottex
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45 ## @code{[@var{s1}, @var{s2}, @dots{}, @var{sk}, @var{n}]}
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46 ## @end ifnottex
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47 ## or
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48 ## @tex
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49 ## $$[s_1, s_2, \cdots, s_k, n + 2].$$
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50 ## @end tex
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51 ## @ifnottex
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52 ## @code{[@var{s1}, @var{s2}, @dots{}, @var{sk}, @var{n} + 2]}.
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53 ## @end ifnottex
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54 ## The array is reshaped internally to a matrix where the leading
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55 ## dimension is given by
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56 ## @tex
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57 ## $$s_1 s_2 \cdots s_k$$
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58 ## @end tex
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59 ## @ifnottex
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60 ## @code{@var{s1} * @var{s2} * @dots{} * @var{sk}}
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61 ## @end ifnottex
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62 ## and each row of this matrix is then treated separately. Note that this
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63 ## is exactly opposite to @code{interp1} but is done for @sc{matlab}
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64 ## compatibility.
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65 ##
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66 ## @seealso{pchip, ppval, mkpp, unmkpp}
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67 ## @end deftypefn
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68
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69 ## This code is based on csape.m from octave-forge, but has been
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70 ## modified to use the sparse solver code in octave that itself allows
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71 ## special casing of tri-diagonal matrices, modified for NDArrays and
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72 ## for the treatment of vectors y 2 elements longer than x as complete
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73 ## splines.
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74
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75 function ret = spline (x, y, xi)
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76
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77 x = x(:);
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78 n = length (x);
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79 if (n < 2)
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80 error ("spline: requires at least 2 points");
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81 endif
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82
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83 ## Check the size and shape of y
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84 ndy = ndims (y);
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85 szy = size (y);
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86 if (ndy == 2 && (szy(1) == n || szy(2) == n))
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87 if (szy(2) == n)
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88 a = y.';
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89 else
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90 a = y;
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91 szy = fliplr (szy);
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92 endif
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93 else
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94 a = shiftdim (reshape (y, [prod(szy(1:end-1)), szy(end)]), 1);
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95 endif
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96
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97 for k = (1:columns (a))(any (isnan (a)))
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98 ok = ! isnan (a(:,k));
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99 a(!ok,k) = spline (x(ok), a(ok,k), x(!ok));
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100 endfor
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101
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102 complete = false;
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103 if (rows (a) == n + 2)
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104 complete = true;
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105 dfs = a(1,:);
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106 dfe = a(end,:);
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107 a = a(2:end-1,:);
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108 endif
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109
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110 if (! issorted (x))
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111 [x, idx] = sort (x);
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112 a = a(idx,:);
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113 endif
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114
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115 b = c = zeros (size (a));
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116 h = diff (x);
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117 idx = ones (columns (a), 1);
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118
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119 if (complete)
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120
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121 if (n == 2)
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122 d = (dfs + dfe) / (x(2) - x(1)) ^ 2 + ...
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123 2 * (a(1,:) - a(2,:)) / (x(2) - x(1)) ^ 3;
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124 c = (-2 * dfs - dfe) / (x(2) - x(1)) - ...
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125 3 * (a(1,:) - a(2,:)) / (x(2) - x(1)) ^ 2;
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126 b = dfs;
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127 a = a(1,:);
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128
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129 d = d(1:n-1,:);
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130 c = c(1:n-1,:);
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131 b = b(1:n-1,:);
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132 a = a(1:n-1,:);
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133 else
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134 g(1,:) = (a(2,:) - a(1,:)) / h(1) - dfs;
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135 g(2:n-1,:) = (a(3:n,:) - a(2:n-1,:)) ./ h(2:n-1) - ...
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136 (a(2:n-1,:) - a(1:n-2,:)) ./ h(1:n-2);
2e23cd0a9e40 Fix complete spline with three points (bug #35739)
Marco Caliari <marco.caliari@univr.it>
parents: 14363
diff changeset
137 g(n,:) = dfe - (a(n,:) - a(n-1,:)) / h(n-1);
14868
5d3a684236b0 maint: Use Octave coding conventions for cuddling parentheses in scripts directory
Rik <octave@nomad.inbox5.com>
parents: 14575
diff changeset
138 c = spdiags ([[h/6;0],[h(1)/3;(h(1:n-2)+h(2:n-1))/3;h(n-1)/3],[0;h/6]],...
5d3a684236b0 maint: Use Octave coding conventions for cuddling parentheses in scripts directory
Rik <octave@nomad.inbox5.com>
parents: 14575
diff changeset
139 [-1,0,1],n,n) \ (g / 2);
12444
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
140 b(1:n-1,:) = diff (a) ./ h(1:n-1, idx) ...
10549
95c3e38098bf Untabify .m scripts
Rik <code@nomad.inbox5.com>
parents: 9768
diff changeset
141 - h(1:n-1,idx) / 3 .* (c(2:n,:) + 2 * c(1:n-1,:));
12444
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
142 d = diff (c) ./ (3 * h(1:n-1, idx));
5824
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jwe
parents:
diff changeset
143
12444
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
144 d = d(1:n-1,:);
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
145 c = c(1:n-1,:);
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
146 b = b(1:n-1,:);
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
147 a = a(1:n-1,:);
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
148 endif
5824
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jwe
parents:
diff changeset
149 else
448f9982e7fb [project @ 2006-05-19 06:53:31 by jwe]
jwe
parents:
diff changeset
150
12444
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
151 if (n == 2)
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
152 b = (a(2,:) - a(1,:)) / (x(2) - x(1));
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
153 a = a(1,:);
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
154 d = [];
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
155 c = [];
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
156 b = b(1:n-1,:);
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
157 a = a(1:n-1,:);
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
158 elseif (n == 3)
5824
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jwe
parents:
diff changeset
159
11196
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
160 n = 2;
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
161 c = (a(1,:) - a(3,:)) / ((x(3) - x(1)) * (x(2) - x(3))) ...
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
162 + (a(2,:) - a(1,:)) / ((x(2) - x(1)) * (x(2) - x(3)));
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
163 b = (a(2,:) - a(1,:)) * (x(3) - x(1)) ...
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
164 / ((x(2) - x(1)) * (x(3) - x(2))) ...
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
165 + (a(1,:) - a(3,:)) * (x(2) - x(1)) ...
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
166 / ((x(3) - x(1)) * (x(3) - x(2)));
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
167 a = a(1,:);
12444
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
168 d = [];
11196
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
169 x = [min(x), max(x)];
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
170
12444
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
171 c = c(1:n-1,:);
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
172 b = b(1:n-1,:);
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
173 a = a(1:n-1,:);
11196
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
174 else
5824
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jwe
parents:
diff changeset
175
11196
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
176 g = zeros (n-2, columns (a));
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
177 g(1,:) = 3 / (h(1) + h(2)) ...
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
178 * (a(3,:) - a(2,:) - h(2) / h(1) * (a(2,:) - a(1,:)));
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
179 g(n-2,:) = 3 / (h(n-1) + h(n-2)) ...
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
180 * (h(n-2) / h(n-1) * (a(n,:) - a(n-1,:)) - (a(n-1,:) - a(n-2,:)));
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
181
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
182 if (n > 4)
5824
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jwe
parents:
diff changeset
183
11196
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
184 g(2:n - 3,:) = 3 * diff (a(3:n-1,:)) ./ h(3:n-2,idx) ...
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
185 - 3 * diff (a(2:n-2,:)) ./ h(2:n - 3,idx);
5824
448f9982e7fb [project @ 2006-05-19 06:53:31 by jwe]
jwe
parents:
diff changeset
186
11196
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
187 dg = 2 * (h(1:n-2) .+ h(2:n-1));
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
188 dg(1) = dg(1) - h(1);
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
189 dg(n-2) = dg(n-2) - h(n-1);
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
190
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
191 ldg = udg = h(2:n-2);
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
192 udg(1) = udg(1) - h(1);
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
193 ldg(n - 3) = ldg(n-3) - h(n-1);
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
194 c(2:n-1,:) = spdiags ([[ldg(:); 0], dg, [0; udg(:)]],
10549
95c3e38098bf Untabify .m scripts
Rik <code@nomad.inbox5.com>
parents: 9768
diff changeset
195 [-1, 0, 1], n-2, n-2) \ g;
5824
448f9982e7fb [project @ 2006-05-19 06:53:31 by jwe]
jwe
parents:
diff changeset
196
11196
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
197 elseif (n == 4)
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
198
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
199 dg = [h(1) + 2 * h(2); 2 * h(2) + h(3)];
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
200 ldg = h(2) - h(3);
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
201 udg = h(2) - h(1);
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
202 c(2:n-1,:) = spdiags ([[ldg(:);0], dg, [0; udg(:)]],
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
203 [-1, 0, 1], n-2, n-2) \ g;
5824
448f9982e7fb [project @ 2006-05-19 06:53:31 by jwe]
jwe
parents:
diff changeset
204
11196
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
205 endif
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
206
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
207 c(1,:) = c(2,:) + h(1) / h(2) * (c(2,:) - c(3,:));
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
208 c(n,:) = c(n-1,:) + h(n-1) / h(n-2) * (c(n-1,:) - c(n-2,:));
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
209 b = diff (a) ./ h(1:n-1, idx) ...
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
210 - h(1:n-1, idx) / 3 .* (c(2:n,:) + 2 * c(1:n-1,:));
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
211 d = diff (c) ./ (3 * h(1:n-1, idx));
5824
448f9982e7fb [project @ 2006-05-19 06:53:31 by jwe]
jwe
parents:
diff changeset
212
12608
59e2460acae1 make piecewise polynomial (pp) functions more compatible
Kai Habel <kai.habel@gmx.de>
parents: 12444
diff changeset
213 d = d(1:n-1,:);d = d.'(:);
59e2460acae1 make piecewise polynomial (pp) functions more compatible
Kai Habel <kai.habel@gmx.de>
parents: 12444
diff changeset
214 c = c(1:n-1,:);c = c.'(:);
59e2460acae1 make piecewise polynomial (pp) functions more compatible
Kai Habel <kai.habel@gmx.de>
parents: 12444
diff changeset
215 b = b(1:n-1,:);b = b.'(:);
59e2460acae1 make piecewise polynomial (pp) functions more compatible
Kai Habel <kai.habel@gmx.de>
parents: 12444
diff changeset
216 a = a(1:n-1,:);a = a.'(:);
5824
448f9982e7fb [project @ 2006-05-19 06:53:31 by jwe]
jwe
parents:
diff changeset
217 endif
448f9982e7fb [project @ 2006-05-19 06:53:31 by jwe]
jwe
parents:
diff changeset
218
448f9982e7fb [project @ 2006-05-19 06:53:31 by jwe]
jwe
parents:
diff changeset
219 endif
12608
59e2460acae1 make piecewise polynomial (pp) functions more compatible
Kai Habel <kai.habel@gmx.de>
parents: 12444
diff changeset
220 ret = mkpp (x, cat (2, d, c, b, a), szy(1:end-1));
5824
448f9982e7fb [project @ 2006-05-19 06:53:31 by jwe]
jwe
parents:
diff changeset
221
448f9982e7fb [project @ 2006-05-19 06:53:31 by jwe]
jwe
parents:
diff changeset
222 if (nargin == 3)
448f9982e7fb [project @ 2006-05-19 06:53:31 by jwe]
jwe
parents:
diff changeset
223 ret = ppval (ret, xi);
448f9982e7fb [project @ 2006-05-19 06:53:31 by jwe]
jwe
parents:
diff changeset
224 endif
448f9982e7fb [project @ 2006-05-19 06:53:31 by jwe]
jwe
parents:
diff changeset
225
448f9982e7fb [project @ 2006-05-19 06:53:31 by jwe]
jwe
parents:
diff changeset
226 endfunction
448f9982e7fb [project @ 2006-05-19 06:53:31 by jwe]
jwe
parents:
diff changeset
227
14237
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc.
Rik <octave@nomad.inbox5.com>
parents: 14222
diff changeset
228
5824
448f9982e7fb [project @ 2006-05-19 06:53:31 by jwe]
jwe
parents:
diff changeset
229 %!demo
14237
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc.
Rik <octave@nomad.inbox5.com>
parents: 14222
diff changeset
230 %! x = 0:10; y = sin (x);
14363
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14237
diff changeset
231 %! xspline = 0:0.1:10; yspline = spline (x,y,xspline);
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14237
diff changeset
232 %! title ("spline fit to points from sin (x)");
14237
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc.
Rik <octave@nomad.inbox5.com>
parents: 14222
diff changeset
233 %! plot (xspline,sin(xspline),"r", xspline,yspline,"g-", x,y,"b+");
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc.
Rik <octave@nomad.inbox5.com>
parents: 14222
diff changeset
234 %! legend ("original", "interpolation", "interpolation points");
5824
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jwe
parents:
diff changeset
235 %! %--------------------------------------------------------
448f9982e7fb [project @ 2006-05-19 06:53:31 by jwe]
jwe
parents:
diff changeset
236 %! % confirm that interpolated function matches the original
448f9982e7fb [project @ 2006-05-19 06:53:31 by jwe]
jwe
parents:
diff changeset
237
6686
2aad75fcc93a [project @ 2007-06-03 20:58:28 by dbateman]
dbateman
parents: 6248
diff changeset
238 %!shared x,y,abserr
14237
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc.
Rik <octave@nomad.inbox5.com>
parents: 14222
diff changeset
239 %! x = [0:10]; y = sin (x); abserr = 1e-14;
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc.
Rik <octave@nomad.inbox5.com>
parents: 14222
diff changeset
240 %!assert (spline (x,y,x), y, abserr)
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc.
Rik <octave@nomad.inbox5.com>
parents: 14222
diff changeset
241 %!assert (spline (x,y,x'), y', abserr)
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc.
Rik <octave@nomad.inbox5.com>
parents: 14222
diff changeset
242 %!assert (spline (x',y',x'), y', abserr)
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc.
Rik <octave@nomad.inbox5.com>
parents: 14222
diff changeset
243 %!assert (spline (x',y',x), y, abserr)
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc.
Rik <octave@nomad.inbox5.com>
parents: 14222
diff changeset
244 %!assert (isempty (spline (x',y',[])))
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc.
Rik <octave@nomad.inbox5.com>
parents: 14222
diff changeset
245 %!assert (isempty (spline (x,y,[])))
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc.
Rik <octave@nomad.inbox5.com>
parents: 14222
diff changeset
246 %!assert (spline (x,[y;y],x), [spline(x,y,x);spline(x,y,x)], abserr)
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc.
Rik <octave@nomad.inbox5.com>
parents: 14222
diff changeset
247 %!assert (spline (x,[y;y],x'), [spline(x,y,x);spline(x,y,x)], abserr)
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc.
Rik <octave@nomad.inbox5.com>
parents: 14222
diff changeset
248 %!assert (spline (x',[y;y],x), [spline(x,y,x);spline(x,y,x)], abserr)
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc.
Rik <octave@nomad.inbox5.com>
parents: 14222
diff changeset
249 %!assert (spline (x',[y;y],x'), [spline(x,y,x);spline(x,y,x)], abserr)
14363
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
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250 %! y = cos (x) + i*sin (x);
14237
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Rik <octave@nomad.inbox5.com>
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251 %!assert (spline (x,y,x), y, abserr)
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc.
Rik <octave@nomad.inbox5.com>
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252 %!assert (real (spline (x,y,x)), real (y), abserr)
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253 %!assert (real (spline (x,y,x.')), real (y).', abserr)
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Rik <octave@nomad.inbox5.com>
parents: 14222
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254 %!assert (real (spline (x.',y.',x.')), real (y).', abserr)
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Rik <octave@nomad.inbox5.com>
parents: 14222
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255 %!assert (real (spline (x.',y,x)), real (y), abserr)
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc.
Rik <octave@nomad.inbox5.com>
parents: 14222
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256 %!assert (imag (spline (x,y,x)), imag (y), abserr)
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc.
Rik <octave@nomad.inbox5.com>
parents: 14222
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257 %!assert (imag (spline (x,y,x.')), imag (y).', abserr)
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc.
Rik <octave@nomad.inbox5.com>
parents: 14222
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258 %!assert (imag (spline (x.',y.',x.')), imag (y).', abserr)
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc.
Rik <octave@nomad.inbox5.com>
parents: 14222
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259 %!assert (imag (spline (x.',y,x)), imag (y), abserr)
10658
c66a4657d764 spline.m: Ignore NaNs within input vectors.
Ben Abbott <bpabbott@mac.com>
parents: 10549
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260 %!test
c66a4657d764 spline.m: Ignore NaNs within input vectors.
Ben Abbott <bpabbott@mac.com>
parents: 10549
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261 %! xnan = 5;
c66a4657d764 spline.m: Ignore NaNs within input vectors.
Ben Abbott <bpabbott@mac.com>
parents: 10549
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262 %! y(x==xnan) = NaN;
c66a4657d764 spline.m: Ignore NaNs within input vectors.
Ben Abbott <bpabbott@mac.com>
parents: 10549
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263 %! ok = ! isnan (y);
c66a4657d764 spline.m: Ignore NaNs within input vectors.
Ben Abbott <bpabbott@mac.com>
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264 %! assert (spline (x, y, x(ok)), y(ok), abserr);
c66a4657d764 spline.m: Ignore NaNs within input vectors.
Ben Abbott <bpabbott@mac.com>
parents: 10549
diff changeset
265 %!test
c66a4657d764 spline.m: Ignore NaNs within input vectors.
Ben Abbott <bpabbott@mac.com>
parents: 10549
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266 %! ok = ! isnan (y);
c66a4657d764 spline.m: Ignore NaNs within input vectors.
Ben Abbott <bpabbott@mac.com>
parents: 10549
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267 %! assert (! isnan (spline (x, y, x(!ok))));
12444
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
268 %!test
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
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269 %! x = [1,2];
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
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270 %! y = [1,4];
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
271 %! assert (spline (x,y,x), [1,4], abserr);
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
272 %!test
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
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273 %! x = [2,1];
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
274 %! y = [1,4];
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
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275 %! assert (spline (x,y,x), [1,4], abserr);
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
276 %!test
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
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277 %! x = [1,2];
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
278 %! y = [1,2,3,4];
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
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279 %! pp = spline (x,y);
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
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280 %! [x,P] = unmkpp (pp);
14575
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Marco Caliari <marco.caliari@univr.it>
parents: 14363
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281 %! assert (P, [3,-3,1,2], abserr);
12444
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
282 %!test
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
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283 %! x = [2,1];
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
284 %! y = [1,2,3,4];
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
285 %! pp = spline (x,y);
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
286 %! [x,P] = unmkpp (pp);
14575
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Marco Caliari <marco.caliari@univr.it>
parents: 14363
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287 %! assert (P, [7,-9,1,3], abserr);
2e23cd0a9e40 Fix complete spline with three points (bug #35739)
Marco Caliari <marco.caliari@univr.it>
parents: 14363
diff changeset
288 %!test
2e23cd0a9e40 Fix complete spline with three points (bug #35739)
Marco Caliari <marco.caliari@univr.it>
parents: 14363
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289 %! x = [0,1,2];
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Marco Caliari <marco.caliari@univr.it>
parents: 14363
diff changeset
290 %! y = [0,0,1,0,0];
2e23cd0a9e40 Fix complete spline with three points (bug #35739)
Marco Caliari <marco.caliari@univr.it>
parents: 14363
diff changeset
291 %! pp = spline (x,y);
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Marco Caliari <marco.caliari@univr.it>
parents: 14363
diff changeset
292 %! [x,P] = unmkpp (pp);
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Marco Caliari <marco.caliari@univr.it>
parents: 14363
diff changeset
293 %! assert (P, [-2,3,0,0;2,-3,0,1], abserr);
2e23cd0a9e40 Fix complete spline with three points (bug #35739)
Marco Caliari <marco.caliari@univr.it>
parents: 14363
diff changeset
294 %!test
2e23cd0a9e40 Fix complete spline with three points (bug #35739)
Marco Caliari <marco.caliari@univr.it>
parents: 14363
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295 %! x = [0,1,2,3];
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Marco Caliari <marco.caliari@univr.it>
parents: 14363
diff changeset
296 %! y = [0,0,1,1,0,0];
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Marco Caliari <marco.caliari@univr.it>
parents: 14363
diff changeset
297 %! pp = spline (x,y);
2e23cd0a9e40 Fix complete spline with three points (bug #35739)
Marco Caliari <marco.caliari@univr.it>
parents: 14363
diff changeset
298 %! [x,P] = unmkpp (pp);
2e23cd0a9e40 Fix complete spline with three points (bug #35739)
Marco Caliari <marco.caliari@univr.it>
parents: 14363
diff changeset
299 %! assert (P, [-1,2,0,0;0,-1,1,1;1,-1,-1,1], abserr);
14237
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Rik <octave@nomad.inbox5.com>
parents: 14222
diff changeset
300