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comparison scripts/polynomial/spline.m @ 11587:c792872f8942

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all script files: untabify and strip trailing whitespace
author John W. Eaton <jwe@octave.org>
date Thu, 20 Jan 2011 17:35:29 -0500
parents 702dbd0c53f5
children 07e102029d2a
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11586:12df7854fa7c 11587:c792872f8942
19 19
20 ## -*- texinfo -*- 20 ## -*- texinfo -*-
21 ## @deftypefn {Function File} {@var{pp} =} spline (@var{x}, @var{y}) 21 ## @deftypefn {Function File} {@var{pp} =} spline (@var{x}, @var{y})
22 ## @deftypefnx {Function File} {@var{yi} =} spline (@var{x}, @var{y}, @var{xi}) 22 ## @deftypefnx {Function File} {@var{yi} =} spline (@var{x}, @var{y}, @var{xi})
23 ## 23 ##
24 ## Return the cubic spline interpolant of @var{y} at points @var{x}. 24 ## Return the cubic spline interpolant of @var{y} at points @var{x}.
25 ## If called with two arguments, @code{spline} returns the piecewise 25 ## If called with two arguments, @code{spline} returns the piecewise
26 ## polynomial @var{pp} that may later be used with @code{ppval} to 26 ## polynomial @var{pp} that may later be used with @code{ppval} to
27 ## evaluate the polynomial at specific points. 27 ## evaluate the polynomial at specific points.
28 ## If called with a third input argument, @code{spline} evaluates the 28 ## If called with a third input argument, @code{spline} evaluates the
29 ## spline at the points @var{xi}. There is an equivalence 29 ## spline at the points @var{xi}. There is an equivalence
30 ## between @code{ppval (spline (@var{x}, @var{y}), @var{xi})} and 30 ## between @code{ppval (spline (@var{x}, @var{y}), @var{xi})} and
31 ## @code{spline (@var{x}, @var{y}, @var{xi})}. 31 ## @code{spline (@var{x}, @var{y}, @var{xi})}.
32 ## 32 ##
33 ## The variable @var{x} must be a vector of length @var{n}, and @var{y} 33 ## The variable @var{x} must be a vector of length @var{n}, and @var{y}
51 ## @end tex 51 ## @end tex
52 ## @ifnottex 52 ## @ifnottex
53 ## @code{[@var{s1}, @var{s2}, @dots{}, @var{sk}, @var{n} + 2]}. 53 ## @code{[@var{s1}, @var{s2}, @dots{}, @var{sk}, @var{n} + 2]}.
54 ## @end ifnottex 54 ## @end ifnottex
55 ## The array is then reshaped internally to a matrix where the leading 55 ## The array is then reshaped internally to a matrix where the leading
56 ## dimension is given by 56 ## dimension is given by
57 ## @tex 57 ## @tex
58 ## $$s_1 s_2 \cdots s_k$$ 58 ## $$s_1 s_2 \cdots s_k$$
59 ## @end tex 59 ## @end tex
60 ## @ifnottex 60 ## @ifnottex
61 ## @code{@var{s1} * @var{s2} * @dots{} * @var{sk}} 61 ## @code{@var{s1} * @var{s2} * @dots{} * @var{sk}}
75 function ret = spline (x, y, xi) 75 function ret = spline (x, y, xi)
76 76
77 x = x(:); 77 x = x(:);
78 n = length (x); 78 n = length (x);
79 if (n < 3) 79 if (n < 3)
80 error ("spline: requires at least 3 points"); 80 error ("spline: requires at least 3 points");
81 endif 81 endif
82 82
83 ## Check the size and shape of y 83 ## Check the size and shape of y
84 ndy = ndims (y); 84 ndy = ndims (y);
85 szy = size (y); 85 szy = size (y);
91 szy = fliplr (szy); 91 szy = fliplr (szy);
92 endif 92 endif
93 else 93 else
94 a = reshape (y, [prod(szy(1:end-1)), szy(end)]).'; 94 a = reshape (y, [prod(szy(1:end-1)), szy(end)]).';
95 endif 95 endif
96 96
97 for k = (1:columns (a))(any (isnan (a))) 97 for k = (1:columns (a))(any (isnan (a)))
98 ok = ! isnan (a(:,k)); 98 ok = ! isnan (a(:,k));
99 a(!ok,k) = spline (x(ok), a(ok,k), x(!ok)); 99 a(!ok,k) = spline (x(ok), a(ok,k), x(!ok));
100 endfor 100 endfor
101 101
102 complete = false; 102 complete = false;
103 if (size (a, 1) == n + 2) 103 if (size (a, 1) == n + 2)
104 complete = true; 104 complete = true;
105 dfs = a(1,:); 105 dfs = a(1,:);
106 dfe = a(end,:); 106 dfe = a(end,:);