Tabulated function definition

@TABULATED_FUNCTION_DEFINITION {
@TABULATED_FUNCTION_NAME {TblFunName} {
@FUNCTION_1D_TYPE {Fun1DType}
@TABLE_ENTRIES {
@X_ENTRY {xi}
@Y_ENTRY {Fi}
@X_ENTRY {xj}
@Y_ENTRY {Fj}
}
@NUMBER_OF_CHEBYSHEV_COEFFICIENTS {N}
@COMMENTS {CommentText}
}
}

Introduction

A tabulated function is a single entry table that lists the values of a function at discrete points. It describes a function of a single variable, F = F(x), where x is the independent variable and F the value of the function. For some applications, a continuous description of function F = F(x) is required. In that case, the discrete function must be approximated by its expansion in terms of Chebyshev polynomials. Tabulated function are used in conjunction with 1D functions. A plot of the function will be generated if plotting control parameters are defined.

NOTES

  1. The nature of the data entered in the tabulated function is determined by parameter Fun1DType.
    • Possible values of parameter Fun1DType are listed for the associated function 1D.
    • Parameters Fun1DType defined for the tabulated function and associated function 1D must match.
    • Parameter Fun1DType defines the units of the xi and Fi entries of the tabulated function.
  2. Keyword @TABLE_ENTRIES introduces the list of tabulated function values. Any number of entries can be defined. @X_ENTRY values xi must appear in a non-decreasing sequence. Each table entry is defined by two keywords.
    • Keyword @X_ENTRY defines a discrete value of the independent variable, xi.
    • Keyword @Y_ENTRY defines the corresponding discrete value of the function Fi = F (xi) of the table.
  3. If keyword @NUMBER_OF_CHEBYSHEV_COEFFICIENTS appears, the tabulated data will be approximated by means of a Chebyshev expansion using N Chebyshev polynomials.
  4. It is possible to attach comments to the definition of the object; these comments have no effect on its definition.

Interpolation in tabulated functions

Tabulated functions are defined by a non-decreasing sequence of independent variable values xi and corresponding function values Fi. For an arbitrary value of the independent variable, table values are interpolated linearly. Let an arbitrary entry be defined as
xi + α = (1 - α) xi + α xi + 1, 0 ≤ α ≤ 1,
where xi and xi + 1 are two consecutive entries in the table. The interpolated function values are then
Fi + α = (1 - α) Fi + α Fi + 1.