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annotate scripts/polynomial/spline.m @ 20216:aa36fb998a4d stable

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maint: Remove unnecessary whitespace at end of lines. * libgui/Makefile.am, libgui/graphics/Canvas.cc, libgui/graphics/EditControl.cc, libgui/graphics/Figure.cc, libgui/graphics/MouseModeActionGroup.cc, libgui/graphics/annotation-dialog.cc, libgui/graphics/annotation-dialog.h, libgui/graphics/gl-select.cc, libgui/graphics/module.mk, libgui/kb-layouts/default.keytab, libgui/kb-layouts/linux.keytab, libgui/kb-layouts/vt420pc.keytab, libgui/src/m-editor/find-dialog.cc, libgui/src/main-window.cc, libgui/src/octave-qt-link.cc, libgui/src/octave-qt-link.h, libgui/src/shortcut-manager.h, libinterp/corefcn/error.cc, libinterp/corefcn/find.cc, libinterp/corefcn/gl2ps-renderer.cc, libinterp/corefcn/graphics.cc, libinterp/corefcn/graphics.in.h, libinterp/corefcn/octave-link.cc, libinterp/corefcn/quadcc.cc, libinterp/corefcn/strfns.cc, libinterp/corefcn/syscalls.cc, libinterp/corefcn/sysdep.cc, libinterp/corefcn/urlwrite.cc, libinterp/corefcn/utils.cc, libinterp/corefcn/variables.cc, libinterp/dldfcn/__init_fltk__.cc, libinterp/dldfcn/ccolamd.cc, libinterp/dldfcn/colamd.cc, libinterp/octave-value/ov-bool-sparse.cc, libinterp/octave-value/ov-classdef.cc, libinterp/octave-value/ov-re-sparse.cc, libinterp/octave-value/ov-struct.cc, libinterp/parse-tree/pt-arg-list.cc, scripts/audio/@audiorecorder/play.m, scripts/audio/wavwrite.m, scripts/general/cart2sph.m, scripts/geometry/inpolygon.m, scripts/gui/listdlg.m, scripts/gui/msgbox.m, scripts/gui/private/message_dialog.m, scripts/help/get_first_help_sentence.m, scripts/help/lookfor.m, scripts/image/imshow.m, scripts/io/strread.m, scripts/java/javamem.m, scripts/miscellaneous/dir.m, scripts/miscellaneous/edit.m, scripts/miscellaneous/genvarname.m, scripts/miscellaneous/gzip.m, scripts/miscellaneous/private/__w2mpth__.m, scripts/plot/appearance/annotation.m, scripts/plot/draw/colorbar.m, scripts/plot/draw/quiver3.m, scripts/plot/util/hold.m, scripts/plot/util/print.m, scripts/polynomial/mkpp.m, scripts/polynomial/polyder.m, scripts/polynomial/spline.m, scripts/polynomial/unmkpp.m, scripts/signal/arma_rnd.m, scripts/sparse/gplot.m, scripts/statistics/tests/t_test.m, scripts/statistics/tests/t_test_regression.m, scripts/strings/mat2str.m, scripts/strings/strsplit.m, scripts/strings/strtrunc.m, scripts/strings/untabify.m, scripts/testfun/assert.m: maint: Remove unnecessary whitespace at end of lines.
author Rik <rik@octave.org>
date Tue, 12 May 2015 09:22:01 -0700
parents 4f45eaf83908
children
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
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4197fc428c7d maint: Update copyright notices for 2015.
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1 ## Copyright (C) 2000-2015 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.
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28 ##
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29 ## When called with a third input argument, @code{spline} evaluates the spline
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30 ## at the points @var{xi}. The third calling form
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31 ## @code{spline (@var{x}, @var{y}, @var{xi})} is equivalent to
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32 ## @code{ppval (spline (@var{x}, @var{y}), @var{xi})}.
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33 ##
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34 ## The variable @var{x} must be a vector of length @var{n}.
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35 ##
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36 ## @var{y} can be either a vector or array. If @var{y} is a vector it must
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37 ## have a length of either @var{n} or @code{@var{n} + 2}. If the length of
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38 ## @var{y} is @var{n}, then the @qcode{"not-a-knot"} end condition is used.
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39 ## If the length of @var{y} is @code{@var{n} + 2}, then the first and last
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40 ## values of the vector @var{y} are the values of the first derivative of the
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41 ## cubic spline at the endpoints.
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42 ##
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43 ## If @var{y} is an array, then the size of @var{y} must have the form
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44 ## @tex
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45 ## $$[s_1, s_2, \cdots, s_k, n]$$
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46 ## @end tex
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47 ## @ifnottex
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48 ## @code{[@var{s1}, @var{s2}, @dots{}, @var{sk}, @var{n}]}
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49 ## @end ifnottex
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50 ## or
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51 ## @tex
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52 ## $$[s_1, s_2, \cdots, s_k, n + 2].$$
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53 ## @end tex
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54 ## @ifnottex
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55 ## @code{[@var{s1}, @var{s2}, @dots{}, @var{sk}, @var{n} + 2]}.
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56 ## @end ifnottex
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57 ## The array is reshaped internally to a matrix where the leading
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58 ## dimension is given by
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59 ## @tex
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60 ## $$s_1 s_2 \cdots s_k$$
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61 ## @end tex
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62 ## @ifnottex
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63 ## @code{@var{s1} * @var{s2} * @dots{} * @var{sk}}
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64 ## @end ifnottex
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65 ## and each row of this matrix is then treated separately. Note that this is
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66 ## exactly the opposite of @code{interp1} but is done for @sc{matlab}
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67 ## compatibility.
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68 ##
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69 ## @seealso{pchip, ppval, mkpp, unmkpp}
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70 ## @end deftypefn
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71
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72 ## This code is based on csape.m from octave-forge, but has been
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73 ## modified to use the sparse solver code in octave that itself allows
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74 ## special casing of tri-diagonal matrices, modified for NDArrays and
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75 ## for the treatment of vectors y 2 elements longer than x as complete
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76 ## splines.
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77
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78 function ret = spline (x, y, xi)
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79
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80 x = x(:);
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81 n = length (x);
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82 if (n < 2)
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83 error ("spline: requires at least 2 points");
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84 endif
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85
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86 ## Check the size and shape of y
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87 ndy = ndims (y);
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88 szy = size (y);
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89 if (ndy == 2 && (any (szy == n) || any (szy == n+2)))
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90 if (szy(2) == n || szy(2) == n+2)
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91 a = y.';
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92 else
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93 a = y;
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94 szy = szy([2 1]);
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95 endif
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96 else
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97 a = shiftdim (reshape (y, [prod(szy(1:end-1)), szy(end)]), 1);
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98 endif
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99
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100 for k = (1:columns (a))(any (isnan (a)))
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101 ok = ! isnan (a(:,k));
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102 a(!ok,k) = spline (x(ok), a(ok,k), x(!ok));
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103 endfor
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104
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105 complete = false;
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106 if (rows (a) == n + 2)
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107 complete = true;
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108 dfs = a(1,:);
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109 dfe = a(end,:);
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110 a = a(2:end-1,:);
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111 endif
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112
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113 if (! issorted (x))
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114 [x, idx] = sort (x);
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115 a = a(idx,:);
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116 endif
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117
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118 b = c = zeros (size (a));
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119 h = diff (x);
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120 idx = ones (columns (a), 1);
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121
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122 if (complete)
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123
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124 if (n == 2)
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Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
125 d = (dfs + dfe) / (x(2) - x(1)) ^ 2 + ...
12608
59e2460acae1 make piecewise polynomial (pp) functions more compatible
Kai Habel <kai.habel@gmx.de>
parents: 12444
diff changeset
126 2 * (a(1,:) - a(2,:)) / (x(2) - x(1)) ^ 3;
12444
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
127 c = (-2 * dfs - dfe) / (x(2) - x(1)) - ...
12608
59e2460acae1 make piecewise polynomial (pp) functions more compatible
Kai Habel <kai.habel@gmx.de>
parents: 12444
diff changeset
128 3 * (a(1,:) - a(2,:)) / (x(2) - x(1)) ^ 2;
12444
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
129 b = dfs;
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
130 a = a(1,:);
5824
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jwe
parents:
diff changeset
131
12444
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
132 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
133 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
134 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
135 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
136 else
14575
2e23cd0a9e40 Fix complete spline with three points (bug #35739)
Marco Caliari <marco.caliari@univr.it>
parents: 14363
diff changeset
137 g(1,:) = (a(2,:) - a(1,:)) / h(1) - dfs;
2e23cd0a9e40 Fix complete spline with three points (bug #35739)
Marco Caliari <marco.caliari@univr.it>
parents: 14363
diff changeset
138 g(2:n-1,:) = (a(3:n,:) - a(2:n-1,:)) ./ h(2:n-1) - ...
2e23cd0a9e40 Fix complete spline with three points (bug #35739)
Marco Caliari <marco.caliari@univr.it>
parents: 14363
diff changeset
139 (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
140 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
141 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
142 [-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
143 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
144 - 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
145 d = diff (c) ./ (3 * h(1:n-1, idx));
5824
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jwe
parents:
diff changeset
146
12444
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
147 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
148 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
149 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
150 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
151 endif
5824
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jwe
parents:
diff changeset
152 else
448f9982e7fb [project @ 2006-05-19 06:53:31 by jwe]
jwe
parents:
diff changeset
153
12444
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
154 if (n == 2)
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
155 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
156 a = a(1,:);
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
157 d = [];
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
158 c = [];
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
159 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
160 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
161 elseif (n == 3)
5824
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jwe
parents:
diff changeset
162
11196
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
163 n = 2;
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
164 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
165 + (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
166 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
167 / ((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
168 + (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
169 / ((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
170 a = a(1,:);
12444
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
171 d = [];
11196
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
172 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
173
12444
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
174 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
175 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
176 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
177 else
5824
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jwe
parents:
diff changeset
178
11196
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
179 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
180 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
181 * (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
182 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
183 * (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
184
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
185 if (n > 4)
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 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
188 - 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
189
11196
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
190 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
191 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
192 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
193
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
194 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
195 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
196 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
197 c(2:n-1,:) = spdiags ([[ldg(:); 0], dg, [0; udg(:)]],
10549
95c3e38098bf Untabify .m scripts
Rik <code@nomad.inbox5.com>
parents: 9768
diff changeset
198 [-1, 0, 1], n-2, n-2) \ g;
5824
448f9982e7fb [project @ 2006-05-19 06:53:31 by jwe]
jwe
parents:
diff changeset
199
11196
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
200 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
201
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
202 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
203 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
204 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
205 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
206 [-1, 0, 1], n-2, n-2) \ g;
5824
448f9982e7fb [project @ 2006-05-19 06:53:31 by jwe]
jwe
parents:
diff changeset
207
11196
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
208 endif
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
209
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
210 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
211 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
212 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
213 - 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
214 d = diff (c) ./ (3 * h(1:n-1, idx));
5824
448f9982e7fb [project @ 2006-05-19 06:53:31 by jwe]
jwe
parents:
diff changeset
215
12608
59e2460acae1 make piecewise polynomial (pp) functions more compatible
Kai Habel <kai.habel@gmx.de>
parents: 12444
diff changeset
216 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
217 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
218 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
219 a = a(1:n-1,:);a = a.'(:);
5824
448f9982e7fb [project @ 2006-05-19 06:53:31 by jwe]
jwe
parents:
diff changeset
220 endif
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 endif
12608
59e2460acae1 make piecewise polynomial (pp) functions more compatible
Kai Habel <kai.habel@gmx.de>
parents: 12444
diff changeset
223 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
224
448f9982e7fb [project @ 2006-05-19 06:53:31 by jwe]
jwe
parents:
diff changeset
225 if (nargin == 3)
448f9982e7fb [project @ 2006-05-19 06:53:31 by jwe]
jwe
parents:
diff changeset
226 ret = ppval (ret, xi);
448f9982e7fb [project @ 2006-05-19 06:53:31 by jwe]
jwe
parents:
diff changeset
227 endif
448f9982e7fb [project @ 2006-05-19 06:53:31 by jwe]
jwe
parents:
diff changeset
228
448f9982e7fb [project @ 2006-05-19 06:53:31 by jwe]
jwe
parents:
diff changeset
229 endfunction
448f9982e7fb [project @ 2006-05-19 06:53:31 by jwe]
jwe
parents:
diff changeset
230
14237
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc.
Rik <octave@nomad.inbox5.com>
parents: 14222
diff changeset
231
5824
448f9982e7fb [project @ 2006-05-19 06:53:31 by jwe]
jwe
parents:
diff changeset
232 %!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
233 %! 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
234 %! 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
235 %! 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
236 %! 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
237 %! legend ("original", "interpolation", "interpolation points");
5824
448f9982e7fb [project @ 2006-05-19 06:53:31 by jwe]
jwe
parents:
diff changeset
238 %! %--------------------------------------------------------
448f9982e7fb [project @ 2006-05-19 06:53:31 by jwe]
jwe
parents:
diff changeset
239 %! % confirm that interpolated function matches the original
448f9982e7fb [project @ 2006-05-19 06:53:31 by jwe]
jwe
parents:
diff changeset
240
6686
2aad75fcc93a [project @ 2007-06-03 20:58:28 by dbateman]
dbateman
parents: 6248
diff changeset
241 %!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
242 %! 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
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 (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
245 %!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
246 %!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
247 %!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
248 %!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
249 %!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
250 %!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
251 %!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
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252 %!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
253 %! y = cos (x) + i*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
254 %!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
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 (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
257 %!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
258 %!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
259 %!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
260 %!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
261 %!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
262 %!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
263 %!test
c66a4657d764 spline.m: Ignore NaNs within input vectors.
Ben Abbott <bpabbott@mac.com>
parents: 10549
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264 %! xnan = 5;
c66a4657d764 spline.m: Ignore NaNs within input vectors.
Ben Abbott <bpabbott@mac.com>
parents: 10549
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265 %! y(x==xnan) = NaN;
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
diff changeset
267 %! 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
268 %!test
c66a4657d764 spline.m: Ignore NaNs within input vectors.
Ben Abbott <bpabbott@mac.com>
parents: 10549
diff changeset
269 %! ok = ! isnan (y);
c66a4657d764 spline.m: Ignore NaNs within input vectors.
Ben Abbott <bpabbott@mac.com>
parents: 10549
diff changeset
270 %! 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
271 %!test
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
272 %! x = [1,2];
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
273 %! y = [1,4];
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
274 %! 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
275 %!test
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
276 %! x = [2,1];
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
277 %! y = [1,4];
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
278 %! 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
279 %!test
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
280 %! x = [1,2];
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
281 %! 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
282 %! pp = spline (x,y);
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
283 %! [x,P] = unmkpp (pp);
14575
2e23cd0a9e40 Fix complete spline with three points (bug #35739)
Marco Caliari <marco.caliari@univr.it>
parents: 14363
diff changeset
284 %! 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
285 %!test
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
286 %! x = [2,1];
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
287 %! 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
288 %! pp = spline (x,y);
17966
3232956a6081 spline.m: Fix problem with transposed "complete" inputs (bug #40584).
Rik <rik@octave.org>
parents: 17744
diff changeset
289 %! pp2 = spline (x', y');
12444
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
290 %! [x,P] = unmkpp (pp);
14575
2e23cd0a9e40 Fix complete spline with three points (bug #35739)
Marco Caliari <marco.caliari@univr.it>
parents: 14363
diff changeset
291 %! assert (P, [7,-9,1,3], abserr);
17966
3232956a6081 spline.m: Fix problem with transposed "complete" inputs (bug #40584).
Rik <rik@octave.org>
parents: 17744
diff changeset
292 %! assert (pp2, pp);
14575
2e23cd0a9e40 Fix complete spline with three points (bug #35739)
Marco Caliari <marco.caliari@univr.it>
parents: 14363
diff changeset
293 %!test
2e23cd0a9e40 Fix complete spline with three points (bug #35739)
Marco Caliari <marco.caliari@univr.it>
parents: 14363
diff changeset
294 %! x = [0,1,2];
2e23cd0a9e40 Fix complete spline with three points (bug #35739)
Marco Caliari <marco.caliari@univr.it>
parents: 14363
diff changeset
295 %! 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
296 %! pp = spline (x,y);
17966
3232956a6081 spline.m: Fix problem with transposed "complete" inputs (bug #40584).
Rik <rik@octave.org>
parents: 17744
diff changeset
297 %! pp2 = spline (x', y');
14575
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, [-2,3,0,0;2,-3,0,1], abserr);
17966
3232956a6081 spline.m: Fix problem with transposed "complete" inputs (bug #40584).
Rik <rik@octave.org>
parents: 17744
diff changeset
300 %! assert (pp2, pp);
14575
2e23cd0a9e40 Fix complete spline with three points (bug #35739)
Marco Caliari <marco.caliari@univr.it>
parents: 14363
diff changeset
301 %!test
2e23cd0a9e40 Fix complete spline with three points (bug #35739)
Marco Caliari <marco.caliari@univr.it>
parents: 14363
diff changeset
302 %! x = [0,1,2,3];
2e23cd0a9e40 Fix complete spline with three points (bug #35739)
Marco Caliari <marco.caliari@univr.it>
parents: 14363
diff changeset
303 %! 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
304 %! pp = spline (x,y);
17966
3232956a6081 spline.m: Fix problem with transposed "complete" inputs (bug #40584).
Rik <rik@octave.org>
parents: 17744
diff changeset
305 %! pp2 = spline (x', y');
14575
2e23cd0a9e40 Fix complete spline with three points (bug #35739)
Marco Caliari <marco.caliari@univr.it>
parents: 14363
diff changeset
306 %! [x,P] = unmkpp (pp);
2e23cd0a9e40 Fix complete spline with three points (bug #35739)
Marco Caliari <marco.caliari@univr.it>
parents: 14363
diff changeset
307 %! assert (P, [-1,2,0,0;0,-1,1,1;1,-1,-1,1], abserr);
17966
3232956a6081 spline.m: Fix problem with transposed "complete" inputs (bug #40584).
Rik <rik@octave.org>
parents: 17744
diff changeset
308 %! assert (pp2, pp);
14237
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc.
Rik <octave@nomad.inbox5.com>
parents: 14222
diff changeset
309