match_funct_1d

match_funct_1d_trans ( : : Function1, Function2, Border, ParamsConst, UseParams : Params, ChiSquare, Covar )

Calculate transformation parameters between two functions.

match_funct_1d_trans calculates the transformation parameters between two functions given as the tuples Function1 and Function2 (see create_funct_1d_array und create_funct_1d_pairs). The following model is used for the transformation between the two functions:

    y1(x) = a1*y2(a3*x+a4)+a2 .

The transformation parameters are determined by a least-squares minimization of the following function:

    n-1
    ----
    \                                  2
    /   (y1(x[i])-a1*y2(a3*x[i]+a4)+a2)  .
    ----
    i=0

The values of the function y2 are obtained by linear interpolation. The parameter Border determines the values of the function Function2 outside of its domain. For Border='zero' these values are set to 0, for Border='constant' they are set to the corresponding value at the border, for Border='mirror' they are mirrored at the border, and for Border='cyclic' they are continued cyclically. The calculated transformation parameters are returned as a 4-tuple in Params. If some of the parameter values are known, the respective parameters can be excluded from the least-squares adjustment by setting the corresponding value in the tuple UseParams to the value 'false'. In this case, the tuple ParamsConst must contain the known value of the respective parameter. If a parameter is used for the adjustment (UseParams = 'true'), the corresponding parameter in ParamsConst is ignored. On output, match_funct_1d_trans additionally returns the sum of the squared errors ChiSquare of the resulting function, i.e., the function obtained by transforming the input function with the transformation parameters, as well as the covariance matrix Covar of the transformation parameters Params. These parameters can be used to decide whether a successful matching of the functions was possible.

Parameters

`Function1` (input_control)	function_1d-array `->` real / integer
Function 1.

`Function2` (input_control)	function_1d-array `->` real / integer
Function 2.

`Border` (input_control)	string `->` string
Border treatment for function 2.
Default value: 'constant'
List of values: 'zero', 'constant', 'mirror', 'cyclic'

`ParamsConst` (input_control)	number-array `->` real
Values of the parameters to remain constant.
Default value: '[1.0,0.0,1.0,0.0]'
Number of elements: 4

`UseParams` (input_control)	string-array `->` string
Should a parameter be adapted for it?
Default value: '['true','true','true','true']'
List of values: 'true', 'false'
Number of elements: 4

`Params` (output_control)	number-array `->` real
Transformation parameters between the functions.
Number of elements: 4

`ChiSquare` (output_control)	number `->` real
Quadratic error of the output function.

`Covar` (output_control)	number-array `->` real
Covariance Matrix of the transformation parameters.
Number of elements: 16

Parallelization Information

match_funct_1d_trans is reentrant and processed without parallelization.

Possible Predecessors

create_funct_1d_array, create_funct_1d_pairs

See also

gray_projections

Module

Tools