# Created by Octave 3.6.1, Thu Mar 22 19:35:12 2012 UTC <root@brouzouf>
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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.