1 # Created by Octave 3.6.1, Thu Mar 22 19:35:12 2012 UTC <root@brouzouf>
13 # name: <cell-element>
17 -- Function File: D = ddmat (X, O)
18 Compute divided differencing matrix of order O
21 X: vector of sampling positions
23 O: order of diffferences
26 D: the matrix; D * Y gives divided differences of order
29 References: Anal. Chem. (2003) 75, 3631.
35 # name: <cell-element>
39 Compute divided differencing matrix of order O
44 # name: <cell-element>
51 # name: <cell-element>
55 -- Function File: [YHAT, LAMBDA] = regdatasmooth (X, Y, [OPTIONS])
56 Smooths the Y vs. X values of 1D data by Tikhonov regularization.
57 The smooth y-values are returned as YHAT. The regularization
58 parameter LAMBDA that was used for the smoothing may also be
61 Note: the options have changed! Currently supported input
62 options are (multiple options are allowed):
65 the smoothing derivative to use (default = 2)
68 the regularization paramater to use
71 the standard deviation of the measurement of Y; an optimal
72 value for lambda will be determined by matching the provided
73 VALUE with the standard devation of YHAT-Y; if the option
74 "relative" is also used, then a relative standard deviation
78 use generalized cross-validation to determine the optimal
79 value for lambda; if neither "lambda" nor "stdev" options are
80 given, this option is implied
83 the initial value for lambda to use in the iterative
84 minimization algorithm to find the optimal value (default = 1)
87 A vector of x-values to use for the smooth curve; must be
88 monotonically increasing and must at least span the data
91 A vector of weighting values for fitting each point in the
95 use relative differences for the goodnes of fit term.
96 Conflicts with the "weights" option.
99 use the midpoint rule for the integration terms rather than a
100 direct sum; this option conflicts with the option "xhat"
102 Please run the demos for example usage.
104 References: Anal. Chem. (2003) 75, 3631; AIChE J. (2006) 52, 325
106 See also: rgdtsmcorewrap, rgdtsmcore
112 # name: <cell-element>
120 # name: <cell-element>
127 # name: <cell-element>
131 -- Function File: [YHAT, V] = rgdtsmcore (X, Y, D, LAMBDA, [OPTIONS])
132 Smooths Y vs. X values by Tikhonov regularization. Although this
133 function can be used directly, the more feature rich function
134 "regdatasmooth" should be used instead. In addition to X and Y,
135 required input includes the smoothing derivative D and the
136 regularization parameter LAMBDA. The smooth y-values are returned
137 as YHAT. The generalized cross validation variance V may also be
140 Note: the options have changed! Currently supported input
141 options are (multiple options are allowed):
144 A vector of x-values to use for the smooth curve; must be
145 monotonically increasing and must at least span the data
148 A vector of weighting values for fitting each point in the
152 use relative differences for the goodnes of fit term.
153 Conflicts with the "weights" option.
156 use the midpoint rule for the integration terms rather than a
157 direct sum; this option conflicts with the option "xhat"
159 References: Anal. Chem. (2003) 75, 3631; AIChE J. (2006) 52, 325
161 See also: regdatasmooth
167 # name: <cell-element>
175 # name: <cell-element>
182 # name: <cell-element>
186 -- Function File: CVE = rgdtsmcorewrap (LOG10LAMBDA, X, Y, D, MINCELL,
188 -- Function File: STDEVDIF = rgdtsmcorewrap (LOG10LAMBDA, X, Y, D,
190 Wrapper function for rgdtsmcore in order to minimize over LAMBDA
191 w.r.t. cross-validation error OR the squared difference between
192 the standard deviation of (Y-YHAT) and the given standard
193 deviation. This function is called from regdatasmooth.
195 See also: regdatasmooth
201 # name: <cell-element>
205 Wrapper function for rgdtsmcore in order to minimize over LAMBDA