Operators

# match_funct_1d_trans (Operator)

## Name

match_funct_1d_trans — Calculate transformation parameters between two functions.

## Signature

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

## Description

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

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

Note that in case that there is no unique solution for the transformation parameters, match_funct_1d_trans either returns one selected single solution or returns the error 9205 (Matrix is singular).

## Parallelization

• Multithreading type: reentrant (runs in parallel with non-exclusive operators).
• Processed without parallelization.

## Parameters

Function1 (input_control)  function_1d (real / integer)

Function 1.

Function2 (input_control)  function_1d (real / integer)

Function 2.

Border (input_control)  string (string)

Border treatment for function 2.

Default value: 'constant'

List of values: 'constant', 'cyclic', 'mirror', 'zero'

ParamsConst (input_control)  number-array (real)

Values of the parameters to remain constant.

Number of elements: 4

Default value: [1.0,0.0,1.0,0.0]

UseParams (input_control)  string-array (string)

Should a parameter be adapted for it?

Number of elements: 4

Default value: ['true','true','true','true']

List of values: 'false', 'true'

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