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Improve/correct documentation for splinefit.m * splinefit.m: Clarify and correct documentation. * doc/interpreter/poly.txi: ditto.
author Ben Abbott <bpabbott@mac.com>
date Wed, 11 Apr 2012 19:34:53 -0400
parents 8985cbbd2fe4
children cd375519eab0
comparison
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14550:bc4c574ab3b6 14551:60ed9260399a
25 ## 25 ##
26 ## The fitted spline is returned as a piece-wise polynomial, @var{pp}, and 26 ## The fitted spline is returned as a piece-wise polynomial, @var{pp}, and
27 ## may be evaluated using @code{ppval}. 27 ## may be evaluated using @code{ppval}.
28 ## 28 ##
29 ## @deftypefnx {Function File} {@var{pp} =} splinefit (@var{x}, @var{y}, @var{p}) 29 ## @deftypefnx {Function File} {@var{pp} =} splinefit (@var{x}, @var{y}, @var{p})
30 ## @var{p} is a positive integer defining the number of linearly spaced 30 ## @var{p} is a positive integer defining the number of intervals along @var{x},
31 ## intervals along @var{x}. @var{p} is the number of intervalas and 31 ## and @var{p}+1 is the number of breaks. The number of points in each interval
32 ## @var{p}+1 is the number of breaks. 32 ## differ by no more than 1.
33 ## 33 ##
34 ## @deftypefnx {Function File} {@var{pp} =} splinefit (@dots{}, "periodic", @var{periodic}) 34 ## @deftypefnx {Function File} {@var{pp} =} splinefit (@dots{}, "periodic", @var{periodic})
35 ## @deftypefnx {Function File} {@var{pp} =} splinefit (@dots{}, "robust", @var{robust}) 35 ## @deftypefnx {Function File} {@var{pp} =} splinefit (@dots{}, "robust", @var{robust})
36 ## @deftypefnx {Function File} {@var{pp} =} splinefit (@dots{}, "beta", @var{beta}) 36 ## @deftypefnx {Function File} {@var{pp} =} splinefit (@dots{}, "beta", @var{beta})
37 ## @deftypefnx {Function File} {@var{pp} =} splinefit (@dots{}, "order", @var{order}) 37 ## @deftypefnx {Function File} {@var{pp} =} splinefit (@dots{}, "order", @var{order})
51 ## value is @var{beta} = 1/2. Values close to 0 give all data equal 51 ## value is @var{beta} = 1/2. Values close to 0 give all data equal
52 ## weighting. Increasing values of @var{beta} reduce the influence of 52 ## weighting. Increasing values of @var{beta} reduce the influence of
53 ## outlying data. Values close to unity may cause instability or rank 53 ## outlying data. Values close to unity may cause instability or rank
54 ## deficiency. 54 ## deficiency.
55 ## 55 ##
56 ## @var{order} sets the order polynomials used to construct the spline. 56 ## The splines are constructed of polynomials with degree @var{order}.
57 ## The default is a cubic, @var{order}=3. A spline with P pieces has 57 ## The default is a cubic, @var{order}=3. A spline with P pieces has
58 ## P+@var{order} degrees of freedom. With periodic boundary conditions 58 ## P+@var{order} degrees of freedom. With periodic boundary conditions
59 ## the degrees of freedom are reduced to P. 59 ## the degrees of freedom are reduced to P.
60 ## 60 ##
61 ## The optional property, @var{constraints}, is a structure specifying 61 ## The optional property, @var{constaints}, is a structure specifying
62 ## linear constraints on the fit. The structure has three fields, "xc", 62 ## linear constraints on the fit. The structure has three fields, "xc",
63 ## "yc", and "cc". 63 ## "yc", and "cc".
64 ## 64 ##
65 ## @table @asis 65 ## @table @asis
66 ## @item "xc" 66 ## @item "xc"
67 ## x-locations of the constraints (vector) with a size identical to @var{x}. 67 ## Vector of the x-locations of the constraints.
68 ## @item "yc" 68 ## @item "yc"
69 ## Constraining values with a size identical to @var{y}. The default 69 ## Constaining values at the locations, @var{xc}.
70 ## is an array of zeros. 70 ## The default is an array of zeros.
71 ## @item "cc" 71 ## @item "cc"
72 ## Coefficients (matrix). The default is an array of ones. The number of 72 ## Coefficients (matrix). The default is an array of ones. The number of
73 ## rows is limited to the order of the piece-wise polynomials, @var{order}. 73 ## rows is limited to the order of the piece-wise polynomials, @var{order}.
74 ## @end table 74 ## @end table
75 ## 75 ##
77 ## @var{order}-1 according to 77 ## @var{order}-1 according to
78 ## 78 ##
79 ## @example 79 ## @example
80 ## @group 80 ## @group
81 ## @tex 81 ## @tex
82 ## $cc(1,j) \cdot y(x) + cc(2,j) \cdot y\prime(x) + ... = yc(:,\dots,:,j), \quad x = xc(j)$. 82 ## $cc(1,j) \cdot y(xc(j)) + cc(2,j) \cdot y\prime(xc(j)) + ... = yc(:,\dots,:,j)$.
83 ## @end tex 83 ## @end tex
84 ## @ifnottex 84 ## @ifnottex
85 ## cc(1,j) * y(x) + cc(2,j) * y'(x) + ... = yc(:,...,:,j), x = xc(j). 85 ## cc(1,j) * y(xc(j)) + cc(2,j) * y'(xc(j)) + ... = yc(:,...,:,j).
86 ## @end ifnottex 86 ## @end ifnottex
87 ## @end group 87 ## @end group
88 ## @end example 88 ## @end example
89 ## 89 ##
90 ## @seealso{interp1, unmkpp, ppval, spline, pchip, ppder, ppint, ppjumps} 90 ## @seealso{interp1, unmkpp, ppval, spline, pchip, ppder, ppint, ppjumps}
128 %! % Noisy data 128 %! % Noisy data
129 %! x = linspace (0, 2*pi, 100); 129 %! x = linspace (0, 2*pi, 100);
130 %! y = sin (x) + 0.1 * randn (size (x)); 130 %! y = sin (x) + 0.1 * randn (size (x));
131 %! % Breaks 131 %! % Breaks
132 %! breaks = [0:5, 2*pi]; 132 %! breaks = [0:5, 2*pi];
133 %! % Constraints: y(0) = 0, y"(0) = 1 and y(3) + y"(3) = 0 133 %! % Constraints: y(0) = 0, y'(0) = 1 and y(3) + y"(3) = 0
134 %! xc = [0 0 3]; 134 %! xc = [0 0 3];
135 %! yc = [0 1 0]; 135 %! yc = [0 1 0];
136 %! cc = [1 0 1; 0 1 0; 0 0 1]; 136 %! cc = [1 0 1; 0 1 0; 0 0 1];
137 %! con = struct ("xc", xc, "yc", yc, "cc", cc); 137 %! con = struct ("xc", xc, "yc", yc, "cc", cc);
138 %! % Fit a cubic spline with 8 pieces and constraints 138 %! % Fit a cubic spline with 8 pieces and constraints