matlab 2012 vs2010混合编程

 1 function output = spline(x,y,xx)
 2 %SPLINE Cubic spline data interpolation.
 3 %   PP = SPLINE(X,Y) provides the piecewise polynomial form of the 
 4 %   cubic spline interpolant to the data values Y at the data sites X,
 5 %   for use with the evaluator PPVAL and the spline utility UNMKPP.
 6 %   X must be a vector.
 7 %   If Y is a vector, then Y(j) is taken as the value to be matched at X(j), 
 8 %   hence Y must be of the same length as X  -- see below for an exception
 9 %   to this.
10 %   If Y is a matrix or ND array, then Y(:,...,:,j) is taken as the value to
11 %   be matched at X(j),  hence the last dimension of Y must equal length(X) --
12 %   see below for an exception to this.
13 %
14 %   YY = SPLINE(X,Y,XX) is the same as  YY = PPVAL(SPLINE(X,Y),XX), thus
15 %   providing, in YY, the values of the interpolant at XX.  For information
16 %   regarding the size of YY see PPVAL.
17 %
18 %   Ordinarily, the not-a-knot end conditions are used. However, if Y contains
19 %   two more values than X has entries, then the first and last value in Y are
20 %   used as the endslopes for the cubic spline.  If Y is a vector, this
21 %   means:
22 %       f(X) = Y(2:end-1),  Df(min(X))=Y(1),    Df(max(X))=Y(end).
23 %   If Y is a matrix or N-D array with SIZE(Y,N) equal to LENGTH(X)+2, then
24 %   f(X(j)) matches the value Y(:,...,:,j+1) for j=1:LENGTH(X), then
25 %   Df(min(X)) matches Y(:,:,...:,1) and Df(max(X)) matches Y(:,:,...:,end).
26 %
27 %   Example:
28 %   This generates a sine-like spline curve and samples it over a finer mesh:
29 %       x = 0:10;  y = sin(x);
30 %       xx = 0:.25:10;
31 %       yy = spline(x,y,xx);
32 %       plot(x,y,‘o‘,xx,yy)
33 %
34 %   Example:
35 %   This illustrates the use of clamped or complete spline interpolation where
36 %   end slopes are prescribed. In this example, zero slopes at the ends of an 
37 %   interpolant to the values of a certain distribution are enforced:
38 %      x = -4:4; y = [0 .15 1.12 2.36 2.36 1.46 .49 .06 0];
39 %      cs = spline(x,[0 y 0]);
40 %      xx = linspace(-4,4,101);
41 %      plot(x,y,‘o‘,xx,ppval(cs,xx),‘-‘);
42 %
43 %   Class support for inputs x, y, xx:
44 %      float: double, single
45 %
46 %   See also INTERP1, PCHIP, PPVAL, MKPP, UNMKPP.
47 
48 %   Carl de Boor 7-2-86
49 %   Copyright 1984-2010 The MathWorks, Inc.
50 %   $Revision: 5.18.4.6 $  $Date: 2010/09/02 13:36:29 $
51 
52 
53 % Check that data are acceptable and, if not, try to adjust them appropriately
54 [x,y,sizey,endslopes] = mychckxy(x,y);
55 n = length(x); yd = prod(sizey);
56 
57 % Generate the cubic spline interpolant in ppform
58 
59 dd = ones(yd,1); dx = diff(x); divdif = diff(y,[],2)./dx(dd,:); 
60 if n==2
61    if isempty(endslopes) % the interpolant is a straight line
62       pp=mkpp(x,[divdif y(:,1)],sizey);
63    else         % the interpolant is the cubic Hermite polynomial
64       pp = pwch(x,y,endslopes,dx,divdif); pp.dim = sizey;
65    end
66 elseif n==3&&isempty(endslopes) % the interpolant is a parabola
67    y(:,2:3)=divdif;
68    y(:,3)=diff(divdif‘)‘/(x(3)-x(1));
69    y(:,2)=y(:,2)-y(:,3)*dx(1); 
70    pp = mkpp(x([1,3]),y(:,[3 2 1]),sizey);
71 else % set up the sparse, tridiagonal, linear system b = ?*c for the slopes
72    b=zeros(yd,n);
73    b(:,2:n-1)=3*(dx(dd,2:n-1).*divdif(:,1:n-2)+dx(dd,1:n-2).*divdif(:,2:n-1));
74    if isempty(endslopes)
75       x31=x(3)-x(1);xn=x(n)-x(n-2);
76       b(:,1)=((dx(1)+2*x31)*dx(2)*divdif(:,1)+dx(1)^2*divdif(:,2))/x31;
77       b(:,n)=...
78       (dx(n-1)^2*divdif(:,n-2)+(2*xn+dx(n-1))*dx(n-2)*divdif(:,n-1))/xn;
79    else
80       x31 = 0; xn = 0; b(:,[1 n]) = dx(dd,[2 n-2]).*endslopes;
81    end
82    dxt = dx(:);
83    c = spdiags([ [x31;dxt(1:n-2);0] ...
84         [dxt(2);2*(dxt(2:n-1)+dxt(1:n-2));dxt(n-2)] ...
85         [0;dxt(2:n-1);xn] ],[-1 0 1],n,n);
86 
87    % sparse linear equation solution for the slopes
88    mmdflag = spparms(‘autommd‘);
89    spparms(‘autommd‘,0);
90    s=b/c;
91    spparms(‘autommd‘,mmdflag);
92 
93    % construct piecewise cubic Hermite interpolant
94    % to values and computed slopes
95    pp = pwch(x,y,s,dx,divdif); pp.dim = sizey;
96 
97 end
98 
99 if nargin==2, output = pp; else output = ppval(pp,xx); end

  1 function [x,y,sizey,endslopes] = mychckxy(x,y)
  2 %CHCKXY check and adjust input for SPLINE and PCHIP
  3 %   [X,Y,SIZEY] = CHCKXY(X,Y) checks the data sites X and corresponding data
  4 %   values Y, making certain that there are exactly as many sites as values,
  5 %   that no two data sites are the same, removing any data points that involve 
  6 %   NaNs, reordering the sites if necessary to ensure that X is a strictly
  7 %   increasing row vector and reordering the data values correspondingly,
  8 %   and reshaping Y if necessary to make sure that it is a matrix, with Y(:,j)
  9 %   the data value corresponding to the data site X(j), and with SIZEY the
 10 %   actual dimensions of the given values. 
 11 %   This call to CHCKXY is suitable for PCHIP.
 12 %
 13 %   [X,Y,SIZEY,ENDSLOPES] = CHCKXY(X,Y) also considers the possibility that
 14 %   there are two more data values than there are data sites.
 15 %   If there are, then the first and the last data value are removed from Y
 16 %   and returned separately as ENDSLOPES. Otherwise, an empty ENDSLOPES is
 17 %   returned.  This call to CHCKXY is suitable for SPLINE.
 18 %
 19 %   See also PCHIP, SPLINE.
 20 
 21 %   Copyright 1984-2011 The MathWorks, Inc.
 22 
 23 % make sure X is a vector:
 24 if length(find(size(x)>1))>1 
 25   error(message(‘MATLAB:chckxy:XNotVector‘)) 
 26 end
 27 
 28 % ensure X is real
 29 if any(~isreal(x)) 
 30   error(message(‘MATLAB:chckxy:XComplex‘)) 
 31 end
 32 
 33 % deal with NaN‘s among the sites:
 34 nanx = find(isnan(x));
 35 if ~isempty(nanx)
 36    x(nanx) = [];
 37    warning(message(‘MATLAB:chckxy:nan‘))
 38 end
 39 
 40 n=length(x);
 41 if n<2 
 42   error(message(‘MATLAB:chckxy:NotEnoughPts‘)) 
 43 end
 44 
 45 % re-sort, if needed, to ensure strictly increasing site sequence:
 46 x=x(:).‘; 
 47 dx = diff(x);
 48 
 49 if any(dx<0), [x,ind] = sort(x); dx = diff(x); else ind=1:n; end
 50 
 51 if ~all(dx), error(message(‘MATLAB:chckxy:RepeatedSites‘)), end
 52 
 53 % if Y is ND, reshape it to a matrix by combining all dimensions but the last:
 54 sizey = size(y);
 55 
 56 
 57 while length(sizey)>2&&sizey(end)==1, sizey(end) = []; end
 58 
 59 
 60 yn = sizey(end); 
 61 sizey(end)=[]; 
 62 yd = prod(sizey);
 63 
 64 if length(sizey)>1
 65    y = reshape(y,yd,yn);
 66 else
 67    % if Y happens to be a column matrix, change it to the expected row matrix.
 68    if yn==1
 69        yn = yd;
 70        y = reshape(y,1,yn); 
 71        yd = 1; 
 72        sizey = yd;
 73    end
 74 end
 75 
 76 % determine whether not-a-knot or clamped end conditions are to be used:
 77 nstart = n+length(nanx);
 78 if yn==nstart
 79    endslopes = [];
 80 elseif nargout==4&&yn==nstart+2
 81    endslopes = y(:,[1 n+2]); y(:,[1 n+2])=[];
 82    if any(isnan(endslopes))
 83       error(message(‘MATLAB:chckxy:EndslopeNaN‘))
 84    end
 85    if any(isinf(endslopes))
 86        error(message(‘MATLAB:chckxy:EndslopeInf‘))
 87    end
 88 else
 89    error(message(‘MATLAB:chckxy:NumSitesMismatchValues‘,nstart, yn))
 90 end
 91 
 92 % deal with NaN‘s among the values:
 93 if ~isempty(nanx)
 94     y(:,nanx) = [];
 95 end
 96 
 97 y=y(:,ind);
 98 nany = find(sum(isnan(y),1));
 99 if ~isempty(nany)
100    y(:,nany) = []; x(nany) = [];
101    warning(message(‘MATLAB:chckxy:IgnoreNaN‘))
102    n = length(x);
103    if n<2 
104      error(message(‘MATLAB:chckxy:NotEnoughPts‘)) 
105    end
106 end