4.3.1.2 Operators and Functions

AMI supports several mathematical operators as well as built-in functions. The supported functions and operators are listed in Table 4.1 and Table 4.2.

Table 4.1: Operators supported by the Analytical Model Interface Language

Operator	Function	Syntax
+	addition	<any datatype> + <any datatype>
-	subtraction	<any datatype> - <any datatype>
*	multiplication	<any datatype> * <any datatype>
/	division	<any datatype> / <scalar datatype>
**	power	<any datatype> ** <scalar datatype>
^T	transpose	<any datatype>^T
D	derive	D(<any datatype>,<user function>(<any datatype>)
Sum	sum	Sum{i=x..y}(<user function>(i))

Table 4.2: Built-in functions supported by the Analytical Model and its ability for auto derivative option

Operator	Function	Syntax	derive
sin	sinus	sin( <scalar datatype> )	yes
cos	cosinus	cos( <scalar datatype> )	yes
tan	tangens	tan( <scalar datatype> )	yes
asin	arcus sinus	asin( <scalar datatype> )	yes
acos	arcus cosinus	acos( <scalar datatype> )	yes
atan	arcus tangens	atan( <scalar datatype> )	yes
asinh	area sinus hyperb.	asinh( <scalar datatype> )	yes
acosh	area cosinus hyperb.	acosh( <scalar datatype> )	yes
atanh	area tangens hyperb.	atanh( <scalar datatype> )	yes
exp	exponential	exp( <scalar datatype> )	yes
sqrt	square root	sqrt( <positive scalar datatype> )	yes
ln	natural logarithm	ln( <positive scalar datatype> )	yes
bernoulli	bernoulli function	bernoulli( <scalar datatype> )	yes
sigma	sigma function	sigma( <scalar datatype> )	no
abs	absolute value	abs( <scalar datatype> )	no

In addition to these functions AMI has implemented two types of user definable functions. The first can be used internally and will be resolved and optimized automatically by the interpreter whenever possible. The analytical derive operator can be used on this type of function, too.

f(x1,x2,...,xn) = <any mathematical expression using x1,x2,...,xn
                   as function parameters>

The second is a so called external function that can neither be resolved nor optimized nor derived by the analytical input interface, but it is a means to submit more complex functions that can not be handled with the model definition language. It's syntax looks like

<<r1[n1,m1]>,<r2[n2,m2]>,...,<rn[nn,mn]>> = 
           <name of C-function>(<var1>,<var2>,...,<varn>)

The variables r₁,r₂,...,r_n with optional dimension definition [n₁, m₁],[n₂, m₂],...,[n_n, m_m] are accessible within AMI like any other variable. During runtime the C-function with the defined name in the analytical model is evaluated using var₁,var₂,...,var_n as its input and the variables r₁,r₂,...,r_n are replaced with the resulting output parameters of the function. Implementing external functions is the only situation where a compilation process is necessary in order to link the external function to the existing executable.