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annotate scripts/polynomial/spline.m @ 14575:2e23cd0a9e40

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Fix complete spline with three points (bug #35739) * spline.m: Correctly compute the coefficients of a complete spline with three points. Add two tests to check for this bug.
author Marco Caliari <marco.caliari@univr.it>
date Wed, 11 Apr 2012 12:54:41 +0200
parents f3d52523cde1
children 5d3a684236b0
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
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72c96de7a403 maint: update copyright notices for 2012
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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 (size (a, 1) == 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);
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137 g(n,:) = dfe - (a(n,:) - a(n-1,:)) / h(n-1);
2e23cd0a9e40 Fix complete spline with three points (bug #35739)
Marco Caliari <marco.caliari@univr.it>
parents: 14363
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]],...
2e23cd0a9e40 Fix complete spline with three points (bug #35739)
Marco Caliari <marco.caliari@univr.it>
parents: 14363
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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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
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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
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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
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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
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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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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>
parents: 14237
diff changeset
250 %! y = cos (x) + i*sin (x);
14237
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Rik <octave@nomad.inbox5.com>
parents: 14222
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251 %!assert (spline (x,y,x), y, abserr)
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parents: 14222
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252 %!assert (real (spline (x,y,x)), real (y), abserr)
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc.
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parents: 14222
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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)
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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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
diff changeset
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
diff changeset
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
diff changeset
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
diff changeset
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>
parents: 10549
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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>
parents: 11587
diff changeset
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
diff changeset
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
diff changeset
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
diff changeset
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
diff changeset
279 %! pp = spline (x,y);
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
280 %! [x,P] = unmkpp (pp);
14575
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Marco Caliari <marco.caliari@univr.it>
parents: 14363
diff changeset
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
diff changeset
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
2e23cd0a9e40 Fix complete spline with three points (bug #35739)
Marco Caliari <marco.caliari@univr.it>
parents: 14363
diff changeset
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
diff changeset
289 %! x = [0,1,2];
2e23cd0a9e40 Fix complete spline with three points (bug #35739)
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);
2e23cd0a9e40 Fix complete spline with three points (bug #35739)
Marco Caliari <marco.caliari@univr.it>
parents: 14363
diff changeset
292 %! [x,P] = unmkpp (pp);
2e23cd0a9e40 Fix complete spline with three points (bug #35739)
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
diff changeset
295 %! x = [0,1,2,3];
2e23cd0a9e40 Fix complete spline with three points (bug #35739)
Marco Caliari <marco.caliari@univr.it>
parents: 14363
diff changeset
296 %! y = [0,0,1,1,0,0];
2e23cd0a9e40 Fix complete spline with three points (bug #35739)
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