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Description:
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           This function is used to compute pairwise distances for
           sparsely observed functional trajectories. The output
           distance is the estimated conditional expection of the L2
           distance on observed data.


           References: Yao, F., M\"{u}ller, H.G., Wang, J.L. (2005). Functional
           data analysis for sparse longitudinal data.  J. American
           Statistical Association 100, 577--590.
           Peng, J., M\"{u}ller, H.G. (2008). Distance-based clustering of sparsely
           observed stochastic processes, with applications to online auctions.
           Annals of Applied Statistics 2, 1056--1077.

 
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Usage:
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function [D1,D2,Y] = spadis(X)

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Input: 
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     X:          a cell array containing the original data or the output
                 of FPCA; if the original data are given, X{1} should be
                 y, X{2} should be t and X{3} should be p as in the FPCA
                 function; if user already used PACE, X should be a cell
                 array containing all the outputs of the FPCA function.

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Output:  
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     D1:         n*n matrix where D1(i,j) is the estimated
                 conditional expection of the L2 distance between subject
                 i and j.  
     D2:         n*n matrix where D2(i,j) is the Euclidean distance
                 between estimated functional principal component socres
                 of subject i and j.  
     Y:          a cell array available when the original data are
                 given, recording the output of PACE from the FPACE
                 function.