spence15

 function for Spencer's 15-point graduation rule.
 set out following Spencer's hand-calculation method,
 which isn't the shortest computer program!

0001 function yhat=spence15(y)
0002 % function for Spencer's 15-point graduation rule.
0003 % set out following Spencer's hand-calculation method,
0004 % which isn't the shortest computer program!
0005 
0006 osev = ones(7,1);
0007 n = length(y);
0008 y = [ osev*y(1); y; osev*y(n) ];
0009 
0010 n = length(y);
0011 k = 3:(n-2);
0012 a3 = y(k-1) + y(k) + y(k+1);
0013 a2 = y(k-2) + y(k+2);
0014 y1 = y(k)+3*(a3-a2);
0015 
0016 n = length(y1);
0017 k = 1:(n-3);
0018 y2 = y1(k)+y1(k+1)+y1(k+2)+y1(k+3);
0019 
0020 n = length(y2);
0021 k = 1:(n-3);
0022 y3 = y2(k)+y2(k+1)+y2(k+2)+y2(k+3);
0023 
0024 n = length(y3);
0025 k = 1:(n-4);
0026 y4 = y3(k)+y3(k+1)+y3(k+2)+y3(k+3)+y3(k+4);
0027 
0028 yhat = y4/320;
0029 return;