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stairs.m: Overhaul function. * scripts/plot/stairs.m: Clean up indentation. Fix input validation for size mismatch and linestyle arguments. Correctly implement color rotation for multiple columns. Accept linestyle argument to change line and marker properties. Add titles to %!demos. Add %!error tests for input validation.
author Rik <rik@octave.org>
date Wed, 18 Sep 2013 13:01:48 -0700
parents 1c89599167a6
children
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1 ## Copyright (C) 2001-2012 Kai Habel
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2 ##
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3 ## This file is part of Octave.
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4 ##
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5 ## Octave is free software; you can redistribute it and/or modify it
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6 ## under the terms of the GNU General Public License as published by
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7 ## the Free Software Foundation; either version 3 of the License, or (at
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8 ## your option) any later version.
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9 ##
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10 ## Octave is distributed in the hope that it will be useful, but
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11 ## WITHOUT ANY WARRANTY; without even the implied warranty of
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12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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13 ## General Public License for more details.
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14 ##
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15 ## You should have received a copy of the GNU General Public License
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16 ## along with Octave; see the file COPYING. If not, see
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17 ## <http://www.gnu.org/licenses/>.
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18
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19 ## -*- texinfo -*-
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20 ## @deftypefn {Function File} {@var{pp} =} pchip (@var{x}, @var{y})
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21 ## @deftypefnx {Function File} {@var{yi} =} pchip (@var{x}, @var{y}, @var{xi})
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22 ## Return the Piecewise Cubic Hermite Interpolating Polynomial (pchip) of
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23 ## points @var{x} and @var{y}.
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24 ##
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25 ## If 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{pchip} evaluates
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28 ## the pchip polynomial at the points @var{xi}. The third calling form is
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29 ## equivalent to @code{ppval (pchip (@var{x}, @var{y}), @var{xi})}.
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30 ##
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31 ## The variable @var{x} must be a strictly monotonic vector (either
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32 ## increasing or decreasing) of length @var{n}. @var{y} can be either a
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33 ## vector or array. If @var{y} is a vector then it must be the same length
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34 ## @var{n} as @var{x}. If @var{y} is an array then the size of @var{y} must
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35 ## have the form
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36 ## @tex
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37 ## $$[s_1, s_2, \cdots, s_k, n]$$
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38 ## @end tex
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39 ## @ifnottex
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40 ## @code{[@var{s1}, @var{s2}, @dots{}, @var{sk}, @var{n}]}
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41 ## @end ifnottex
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42 ## The array is reshaped internally to a matrix where the leading
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43 ## dimension is given by
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44 ## @tex
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45 ## $$s_1 s_2 \cdots s_k$$
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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}}
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49 ## @end ifnottex
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50 ## and each row of this matrix is then treated separately. Note that this
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51 ## is exactly opposite to @code{interp1} but is done for @sc{matlab}
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52 ## compatibility.
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53 ##
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54 ## @seealso{spline, ppval, mkpp, unmkpp}
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55 ## @end deftypefn
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56
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57 ## Author: Kai Habel <kai.habel@gmx.de>
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58 ## Date: 9. mar 2001
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59 ##
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60 ## S_k = a_k + b_k*x + c_k*x^2 + d_k*x^3; (spline polynom)
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61 ##
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62 ## 4 conditions:
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63 ## S_k(x_k) = y_k;
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64 ## S_k(x_k+1) = y_k+1;
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65 ## S_k'(x_k) = y_k';
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66 ## S_k'(x_k+1) = y_k+1';
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67
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68 function ret = pchip (x, y, xi)
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69
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70 if (nargin < 2 || nargin > 3)
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71 print_usage ();
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72 endif
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73
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74 ## make row vector
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75 x = x(:).';
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76 n = length (x);
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77
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78 ## Check the size and shape of y
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79 if (isvector (y))
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80 y = y(:).'; ##row vector
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81 szy = size (y);
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82 if (! size_equal (x, y))
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83 error ("pchip: length of X and Y must match");
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84 endif
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85 else
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86 szy = size (y);
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87 if (n != szy(end))
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88 error ("pchip: length of X and last dimension of Y must match");
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89 endif
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90 y = reshape (y, [prod(szy(1:end-1)), szy(end)]);
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91 endif
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92
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93 h = diff (x);
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94 if (all (h < 0))
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95 x = fliplr (x);
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96 h = diff (x);
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97 y = fliplr (y);
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98 elseif (any (h <= 0))
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99 error ("pchip: X must be strictly monotonic");
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100 endif
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101
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102 f1 = y(:, 1:n-1);
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103
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104 ## Compute derivatives.
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105 d = __pchip_deriv__ (x, y, 2);
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106 d1 = d(:, 1:n-1);
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107 d2 = d(:, 2:n);
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108
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109 ## This is taken from SLATEC.
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110 h = diag (h);
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111
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112 delta = diff (y, 1, 2) / h;
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113 del1 = (d1 - delta) / h;
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114 del2 = (d2 - delta) / h;
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115 c3 = del1 + del2;
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116 c2 = -c3 - del1;
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117 c3 = c3 / h;
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118 coeffs = cat (3, c3, c2, d1, f1);
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119
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120 ret = mkpp (x, coeffs, szy(1:end-1));
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121
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122 if (nargin == 3)
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123 ret = ppval (ret, xi);
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124 endif
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125
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126 endfunction
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127
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128
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129 %!demo
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130 %! x = 0:8;
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131 %! y = [1, 1, 1, 1, 0.5, 0, 0, 0, 0];
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132 %! xi = 0:0.01:8;
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133 %! yspline = spline (x,y,xi);
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134 %! ypchip = pchip (x,y,xi);
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135 %! title ("pchip and spline fit to discontinuous function");
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136 %! plot (xi,yspline, xi,ypchip,"-", x,y,"+");
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137 %! legend ("spline", "pchip", "data");
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138 %! %-------------------------------------------------------------------
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139 %! % confirm that pchip agreed better to discontinuous data than spline
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140
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721a4a83cba6 test: Space out %!shared variable declaration for readability
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141 %!shared x, y, y2, pp, yi1, yi2, yi3
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c792872f8942 all script files: untabify and strip trailing whitespace
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142 %! x = 0:8;
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143 %! y = [1, 1, 1, 1, 0.5, 0, 0, 0, 0];
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144 %!assert (pchip (x,y,x), y)
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145 %!assert (pchip (x,y,x'), y')
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146 %!assert (pchip (x',y',x'), y')
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147 %!assert (pchip (x',y',x), y)
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148 %!assert (isempty (pchip (x',y',[])))
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149 %!assert (isempty (pchip (x,y,[])))
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150 %!assert (pchip (x,[y;y],x), [pchip(x,y,x);pchip(x,y,x)])
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151 %!assert (pchip (x,[y;y],x'), [pchip(x,y,x);pchip(x,y,x)])
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152 %!assert (pchip (x',[y;y],x), [pchip(x,y,x);pchip(x,y,x)])
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153 %!assert (pchip (x',[y;y],x'), [pchip(x,y,x);pchip(x,y,x)])
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Kai Habel <kai.habel@gmx.de>
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154 %!test
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155 %! x = (0:8)*pi/4; y = [sin(x); cos(x)];
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156 %! y2(:,:,1) = y; y2(:,:,2) = y+1; y2(:,:,3) = y-1;
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157 %! pp = pchip (x, shiftdim (y2,2));
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158 %! yi1 = ppval (pp, (1:4)*pi/4);
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159 %! yi2 = ppval (pp, repmat ((1:4)*pi/4, [5,1]));
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160 %! yi3 = ppval (pp, [pi/2,pi]);
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161 %!assert (size (pp.coefs), [48,4])
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162 %!assert (pp.pieces, 8)
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163 %!assert (pp.order, 4)
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164 %!assert (pp.dim, [3,2])
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165 %!assert (ppval (pp,pi), [0,-1;1,0;-1,-2], 1e-14)
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166 %!assert (yi3(:,:,2), ppval (pp,pi), 1e-14)
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167 %!assert (yi3(:,:,1), [1,0;2,1;0,-1], 1e-14)
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168 %!assert (squeeze (yi1(1,2,:)), [1/sqrt(2); 0; -1/sqrt(2);-1], 1e-14)
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169 %!assert (size (yi2), [3,2,5,4])
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170 %!assert (squeeze (yi2(1,2,3,:)), [1/sqrt(2); 0; -1/sqrt(2);-1], 1e-14)
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Jordi Gutiérrez Hermoso <jordigh@octave.org>
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171
af552038cc52 Fix segfault in pchip when input array is too small (bug #35835).
Jordi Gutiérrez Hermoso <jordigh@octave.org>
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172 %!error (pchip (1,2));
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Jordi Gutiérrez Hermoso <jordigh@octave.org>
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173 %!error (pchip (1,2,3));
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174