time   calls  line
                  1 function pp=mkpp(breaks,coefs,d)
                  2 %MKPP Make piecewise polynomial.  
                  3 %   PP = MKPP(BREAKS,COEFS) puts together a piecewise polynomial PP from its
                  4 %   breaks and coefficients.  BREAKS must be a vector of length L+1 with
                  5 %   strictly increasing elements representing the start and end of each of L
                  6 %   intervals.  The matrix COEFS must be L-by-K, with the i-th row, 
                  7 %   COEFS(i,:), representing the local coefficients of the order K polynomial
                  8 %   on the interval [BREAKS(i) ... BREAKS(i+1)], i.e., the polynomial                 
                  9 %   COEFS(i,1)*(X-BREAKS(i))^(K-1) + COEFS(i,2)*(X-BREAKS(i))^(K-2) + ... 
                 10 %   COEFS(i,K-1)*(X-BREAKS(i)) + COEFS(i,K)
                 11 %   Note: A K-th order polynomial uses K coefficients in its description:
                 12 %      C(1)*X^(K-1) + C(2)*X^(K-2) + ... + C(K-1)*X + C(K)
                 13 %   hence is of degree < K.  For example, a cubic polynomial is usually
                 14 %   written as a vector with 4 elements.
                 15 %
                 16 %   PP = MKPP(BREAKS,COEFS,D) denotes that the piecewise polynomial PP has
                 17 %   values of size D, with D either a scalar or an integer vector.
                 18 %   BREAKS must be an increasing vector of length L+1.
                 19 %   Whatever the size of COEFS may be, its last dimension is taken to be the
                 20 %   polynomial order, K, hence the product of the remaining dimensions must
                 21 %   equal prod(D)*L. If we take COEFS to be of size [prod(D),L,K], then
                 22 %   COEFS(r,i,:) are the K coefficients of the r-th component of the i-th
                 23 %   polynomial piece.
                 24 %   Internally, COEFS is stored as a matrix, of size [prod(D)*L,K].
                 25 %
                 26 %   Examples:
                 27 %   These first two plots show the quadratic 1-(x/2-1)^2 = -x^2/4 + x 
                 28 %   shifted from the interval [-2 .. 2] to the interval [-8 .. -4], and the
                 29 %   negative of that quadratic, namely the quadratic (x/2-1)^2-1 = x^2/4 - x,
                 30 %   but shifted from [-2 .. 2] to the interval [-4 .. 0].
                 31 %      subplot(2,2,1)
                 32 %      cc = [-1/4 1 0];
                 33 %      pp1 = mkpp([-8 -4],cc); xx1 = -8:0.1:-4;
                 34 %      plot(xx1,ppval(pp1,xx1),'k-')
                 35 %      subplot(2,2,2)
                 36 %      pp2 = mkpp([-4 -0],-cc); xx2 = -4:0.1:0;
                 37 %      plot(xx2,ppval(pp2,xx2),'k-')
                 38 %      subplot(2,1,2)
                 39 %      pp = mkpp([-8 -4 0 4 8],[cc; -cc; cc; -cc]);
                 40 %      xx = -8:0.1:8;
                 41 %      plot(xx,ppval(pp,xx),'k-')
                 42 %      [breaks,coefs,l,k,d] = unmkpp(pp);
                 43 %      dpp = mkpp(breaks,repmat(k-1:-1:1,d*l,1).*coefs(:,1:k-1),d);
                 44 %      hold on, plot(xx,ppval(dpp,xx),'r-'), hold off
                 45 %   This last plot shows a piecewise polynomial constructed by alternating the
                 46 %   first two quadratic pieces over 4 intervals.  To stress the piecewise
                 47 %   polynomial character, also shown is its first derivative, as constructed 
                 48 %   from information about the piecewise polynomial obtained via UNMKPP.
                 49 %
                 50 %   Class support for inputs BREAKS,COEFS:
                 51 %      float: double, single
                 52 %
                 53 %   See also UNMKPP, PPVAL, SPLINE.
                 54 
                 55 %   Carl de Boor 7-2-86
                 56 %   Copyright 1984-2010 The MathWorks, Inc.
                 57 %   $Revision: 5.17.4.5 $  $Date: 2010/11/22 02:46:40 $
                 58 
            25   59 if nargin==2, d = 1; else d = d(:).'; end 
            25   60 dlk=numel(coefs); l=length(breaks)-1; dl=prod(d)*l; k=fix(dlk/dl+100*eps); 
            25   61 if (k<=0)||(dl*k~=dlk) 
                 62    error(message('MATLAB:mkpp:PPNumberMismatchCoeffs',...
                 63        int2str(l),int2str(d),int2str(dlk)))
                 64 end
                 65 
            25   66 pp.form = 'pp'; 
            25   67 pp.breaks = reshape(breaks,1,l+1); 
            25   68 pp.coefs = reshape(coefs,dl,k); 
            25   69 pp.pieces = l; 
            25   70 pp.order = k; 
            25   71 pp.dim = d;