Mathematical Functions

Various trigonometric, Bessel and miscellaneous functions are built into Feko to help construct geometry, expressions and calculate parameters.

Trigonometric Functions

The following trigonometric functions are supported:

Table 1. Trigonometric functions
SIN	sine (argument in radians)
COS	cosine (argument in radians)
TAN	tangent (argument in radians)
COT	cotangent (argument in radians)
ARCSIN	arcsine (argument in radians)
ARCCOS	arccosine (argument in radians)
ARCTAN	arctangent (in radians)
ATAN2	This function has two arguments atan2(#y,#x) - it yields arctan(#y/#x) in the range $- π ... π$
ARCCOT	arccotangent
SINH	hyperbolic sine
COSH	hyperbolic cosine
TANH	hyperbolic tangent

Bessel Functions

The following Bessel functions are supported:


BESJ(n,x)	Bessel function J_n(x) of integer order $n \geq 0$ and real argument x.
BESY(n,x)	Neumann function Y_n(x) of integer order $n \geq 0$ and real argument x
BESI(n,x)	Modified Bessel function of the first kind I_n(x) of integer order $n \geq 0$ and real argument x
BESK(n,x)	Modified Bessel function of the second kind K_n(x) of integer order $n \geq 0$ and real argument x

Miscellaneous Functions

The following miscellaneous functions are supported:

Table 2. Miscellaneous functions
SQRT	Square root
LOG	Logarithm to base 10.
LN	Natural logarithm
EXP	Exponential function
ABS	Absolute value
DEG	Convert radians into degrees.
RAD	Convert degrees into radians.
STEP	Step function, `STEP(x) = 0` for $x \leq 0$ and `STEP(x) = 1` for x > 0.
CEIL	Smallest integer value that is equal to or greater than the argument.
FLOOR	Largest integer value that is equal to or smaller than the argument.
MAX	Returns the largest of the two arguments — called as `max(#a,#b)`.
MIN	Returns the smallest of the two arguments — called as `min(#a,#b)`.
FMOD	This function has two arguments `fmod(#a,#b)` and returns the remainder of the division `#a/#b`.
RANDOM	This function returns a random value in the range 0 . . . 1. If the argument `X` of RANDOM() is -1, then a random number is returned. For any other argument `X` in the range 0 . . . 1 this value is used to set the seed, and then a random number is created using this seed. (Using the same seed allows one to create a deterministic and reproducible random number series). If `RANDOM(-1)` is called before any seed is set in the .pre file, then the returned values are random and not reproducible. (The internal seed is used based on the time when PREFEKO is executed).

Coordinate functions provide access to the individual X coordinate, Y coordinate and Z coordinate of a Cartesian coordinate in 3D space.

Coordinate Functions

The following coordinate functions are supported:

Table 3. Coordinate functions
X_COORD	This function returns the X coordinate of a point previously defined by a DP card.
Y_COORD	This function returns the Y coordinate of a point previously defined by a DP card.
Z_COORD	This function returns the Z coordinate of a point previously defined by a DP card.

The X_COORD, Y_COORD and Z_COORD functions are used by passing the name of the point, in quotation marks, as an argument to the function. For example, the following code sets the parameter #x equal to 1.234.

DP   PNT01                    1.234     0.4567    #z
#x = x_coord("PNT01")