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ddmat


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 -- Function File: D = ddmat (X, O)
     Compute divided differencing matrix of order O

          Input
               X: vector of sampling positions
               O: order of diffferences
          Output
               D: the matrix; D * Y gives divided differences of order O

     References: Anal.  Chem.  (2003) 75, 3631.


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Compute divided differencing matrix of order O



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regdatasmooth


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 -- Function File: [YHAT, LAMBDA] = regdatasmooth (X, Y, [OPTIONS])

     Smooths the Y vs.  X values of 1D data by Tikhonov regularization.  The
     smooth y-values are returned as YHAT.  The regularization parameter LAMBDA
     that was used for the smoothing may also be returned.

     Note: the options have changed!  Currently supported input options are
     (multiple options are allowed):

     ‘"d", VALUE’
          the smoothing derivative to use (default = 2)
     ‘"lambda", VALUE’
          the regularization paramater to use
     ‘"stdev", VALUE’
          the standard deviation of the measurement of Y; an optimal value for
          lambda will be determined by matching the provided VALUE with the
          standard devation of YHAT-Y; if the option "relative" is also used,
          then a relative standard deviation is inferred
     ‘"gcv"’
          use generalized cross-validation to determine the optimal value for
          lambda; if neither "lambda" nor "stdev" options are given, this option
          is implied
     ‘"lguess", VALUE’
          the initial value for lambda to use in the iterative minimization
          algorithm to find the optimal value (default = 1)
     ‘"xhat", VECTOR’
          A vector of x-values to use for the smooth curve; must be
          monotonically increasing and must at least span the data
     ‘"weights", VECTOR’
          A vector of weighting values for fitting each point in the data.
     ‘"relative"’
          use relative differences for the goodnes of fit term.  Conflicts with
          the "weights" option.
     ‘"midpointrule"’
          use the midpoint rule for the integration terms rather than a direct
          sum; this option conflicts with the option "xhat"

     Please run the demos for example usage.

     References: Anal.  Chem.  (2003) 75, 3631; AIChE J. (2006) 52, 325

     See also: rgdtsmcorewrap, rgdtsmcore.


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Smooths the Y vs.



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rgdtsmcore


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 -- Function File: [YHAT, V] = rgdtsmcore (X, Y, D, LAMBDA, [OPTIONS])

     Smooths Y vs.  X values by Tikhonov regularization.  Although this function
     can be used directly, the more feature rich function "regdatasmooth" should
     be used instead.  In addition to X and Y, required input includes the
     smoothing derivative D and the regularization parameter LAMBDA.  The smooth
     y-values are returned as YHAT.  The generalized cross validation variance V
     may also be returned.

     Note: the options have changed!  Currently supported input options are
     (multiple options are allowed):

     ‘"xhat", VECTOR’
          A vector of x-values to use for the smooth curve; must be
          monotonically increasing and must at least span the data
     ‘"weights", VECTOR’
          A vector of weighting values for fitting each point in the data.
     ‘"relative"’
          use relative differences for the goodnes of fit term.  Conflicts with
          the "weights" option.
     ‘"midpointrule"’
          use the midpoint rule for the integration terms rather than a direct
          sum; this option conflicts with the option "xhat"

     References: Anal.  Chem.  (2003) 75, 3631; AIChE J. (2006) 52, 325

     See also: regdatasmooth.


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Smooths Y vs.



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rgdtsmcorewrap


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 -- Function File: CVE = rgdtsmcorewrap (LOG10LAMBDA, X, Y, D, MINCELL, OPTIONS)
 -- Function File: STDEVDIF = rgdtsmcorewrap (LOG10LAMBDA, X, Y, D, MINCELL,
          OPTIONS)

     Wrapper function for rgdtsmcore in order to minimize over LAMBDA w.r.t.
     cross-validation error OR the squared difference between the standard
     deviation of (Y-YHAT) and the given standard deviation.  This function is
     called from regdatasmooth.

     See also: regdatasmooth.


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Wrapper function for rgdtsmcore in order to minimize over LAMBDA w.r.t.
cross...





