If the error variance is known, it should be supplied to the routine in 'var'. The degree of smoothing is then determined by minimizing an unbiased estimate of the true mean square error. On the other hand, if the error variance is not known, 'var' should be set to -1.0. The routine then determines the degree of smoothing by minimizing the generalized cross validation. This is asymptotically the same as minimizing the true mean square error (see reference 1). In this case, an estimate of the error variance is returned in 'var' which may be compared with any a priori approximate estimates. In either case, an estimate of the true mean square error is returned in 'wk[4]'. This estimate, however, depends on the error variance estimate, and should only be accepted if the error variance estimate is reckoned to be correct. Bayesian estimates of the standard error of each smoothed data value are returned in the array 'se' (if a non null vector is given for the paramenter 'se' - use (double*)0 if you don't want estimates). These also depend on the error variance estimate and should only be accepted if the error variance estimate is reckoned to be correct. See reference 4. The number of arithmetic operations and the amount of storage required by the routine are both proportional to 'n', so that very large data sets may be analysed. The data points do not have to be equally spaced or uniformly weighted. The residual and the spline coefficients are calculated in the manner described in reference 3, while the trace and various statistics, including the generalized cross validation, are calculated in the manner described in reference 2. When 'var' is known, any value of 'n' greater than 2 is acceptable. It is advisable, however, for 'n' to be greater than about 20 when 'var' is unknown. If the degree of smoothing done by this function when 'var' is unknown is not satisfactory, the user should try specifying the degree of smoothing by setting 'var' to a reasonable value.

             Notes:
            
             Algorithm 642, "cubgcv", collected algorithms from ACM.
             Algorithm appeared in ACM-Trans. Math. Software, Vol.12, No. 2,
             Jun., 1986, p. 150.
            
             Originally written by M.F.Hutchinson, CSIRO Division of Mathematics
             and Statistics, P.O. Box 1965, Canberra, Act 2601, Australia.
             Latest revision 15 august 1985.
            
             References:
            
             1.  Craven, Peter and Wahba, Grace, "Smoothing noisy data with spline
                 functions", Numer. Math. 31, 377-403 (1979).
             2.  Hutchinson, M.F. and de Hoog, F.R., "Smoothing noisy data with spline
                 functions", Numer. Math. 47, 99-106 (1985).
             3.  Reinsch, C.H., "Smoothing by spline functions", Numer. Math. 10,
                 177-183 (1967).
             4.  Wahba, Grace, "Bayesian 'confidence intervals' for the cross-validated
                 smoothing spline", J.R.Statist. Soc. B 45, 133-150 (1983).
            
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