## Appendix III

## AFGEN function

**AFGEN** stands for **A**rbitrary **F**unction **GEN**erator
(Subroutine AFGen).
It is a function which is used for linear interpolation
in a one-dimensional array with paired data. Uneven places
in the array represent the X-values, whereas the Y-values are
represented by the even places. Such an array can
describe the dependency of variable Y on variable X
when no mathematical description is available or is too cumbersome.
A plotted example is depicted in Figure AIII_1:

**Figure AIII_1** Linear interpolation

The array belonging to this example has to be filled as:

Place | (1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) |

Value | X_{1} | Y_{1} | X_{2} | Y_{2}
| X_{3} | Y_{3} | X_{4} | Y_{4
} |

Arguments of the AFGEN function in order of their place in
the argument list are: name of the table, number of pairs, X value
to be interpolated. The X-values have to be arranged from low
to high values and are not allowed to be interchanged. Every X-value
has to precede its connected Y-value.

Three situations for interpolation can occur:

1) The argument *x* at which interpolation should take place
is less or equal to the first X-value in the array. The Y-value
is set to the first Y-value in the array.

2) The argument *x* value at which interpolation should take
place is between the first and the last X-value in the array.
The Y-value can now be found via linear interpolation. First the
X values left and right from the argument *x* have to be
detected, then the Y-value can be calculated:
3) The argument *x* at which interpolation should take place
is equal to or larger then the last X-value in the array. The
Y-value is set to the last Y-value in the array.

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