algebra

variables

   PLOT CONTOUR V

The "V" in this statement is a local variable of the PLOT command which equals the electrostatic potential at a given point.

When using such local variables, you normally don't have to take any precaution.

There are however also cases when you wish to have some variables under your own control. Such variables exist in Garfield and are called global variables, or Globals for short. The name has been chosen to reflect the broader scope of globals, as compared to the local variables mentioned above. Local variables have a scope limited to one command, while global variables can be used across sections.

Since these variables are essentially under your own control, they are for instance not automatically evaluated. It is the purpose of this help topic to explain their correct use. Please be familiar with the contents when using globals !

Global variables can be used for a variety of things:

• you can use them for doing ordinary arithmetic;
• they are used to construct a Do_loop;
• they are used in the conditions of If_blocks and If_lines
• they appear as arguments in Call and Parse;
• you can request substitution of their value in ordinary commands.

Additional information on:

creating	naming
substitution	types
storage	constants
predefined

operators

There are also operators for certain kinds of mixed arithmetic, such as between numbers and histograms and between numbers and matrices. Mixed arithmetic of logicals and numbers is not permitted.

Garfield recognises the following binary operators:

Operator	Acts on	Gives	Effect
+	-N-HM	same	addition
+	--L--	--L--	or
+	S----	S----	commutative concatenation
-	-N-HM	same	subtraction
-	--L--	--L--	exclusive or
*	-N-HM	same	multiplication
*	--L--	--L--	and
/	-N-HM	same	division
/	S----	S----	concatenation
**, ^	-N-HM	same	exponentiation
&	--L--	--L--	and
|	--L--	--L--	or
=	SN-HM	--L--	equality
=	--L--	--L--	equivalence
#, <>, ><	SN-HM	--L--	non-equality
#, <>, ><	--L--	--L--	non-equivalence
>	SN-HM	--L--	greater than
>=, =>	SN-HM	--L--	greater than or equal to
<	SN-HM	--L--	less than
<=, =<	SN-HM	--L--	less than or equal to

Unary operators are treated like functions, and therefore have higher precedence than binary operators. As a result, '-x^2' is always positive. The following unary operators are currently known:

Operator	Acts on	Gives	Effect
+	-N-HM	same	assignment
-	-N-HM	same	negative
^, ~	--L--	--L--	not

Notes:

1. The operators act element by element on variables of type Histogram and Matrix.
2. The sorting sequence for characters in Strings depends on the computer system that is used.
3. Mixed operations between Number and Histograms or between Numbers and Matrices result in Histograms and Matrices respectively.
4. All operators can be applied to type Undefined, the result being Undefined.
5. The equality and non-equality operators have a tolerance of 1E-4 on all computers except Cray where a tolerance of 1E-8 is used.

functions

Function	Acts on	Gives	Effect
ABS	-N-HM	same	absolute value
ARCCOS	-N-HM	same	arc cosine
ARCCOSH	-N-HM	same	arc hyperbolic cosine
ARCSIN	-N-HM	same	arc sine
ARCSINH	-N-HM	same	arc hyperbolic sine
ARCTAN	-N-HM	same	arc tangent
ARCTANH	-N-HM	same	arc hyperbolic tangent
COS	-N-HM	same	cosine
COSH	-N-HM	same	hyperbolic cosine
ENTIER	-N-HM	same	integer part
EXP	-N-HM	same	exponential
GLOBAL	S----	any	global with name of the string
LANDAU	-N-HM	same	Landau density function
LOG	-N-HM	same	logarithm
MAXIMUM	---HM	-N---	maximum of matrix or histogram
MEAN	---HM	-N---	mean of a matrix or histogram
MINIMUM	---HM	-N---	minimum of matrix or histogram
NOT	--L--	--L--	negation of logical value
NUMBER	S---M	-N---	conversion to a number
PRODUCT	---HM	-N---	product of matrix or histogram
REFERENCE	S--HM	-N---	reference of a given string etc
REF_HISTOGRAM	-N---	---H-	histogram with given reference
REF_MATRIX	-N---	----M	matrix with given reference
REF_STRING	-N---	S----	string with given reference
RMS	---HM	-N---	RMS of a matrix or histogram
ROW	-N---	----M	row of number 1 to argument
SIN	-N-HM	same	sine
SINH	-N-HM	same	hyperbolic sine
SQRT	-N-HM	same	square root
STRING	SNLHM	S----	conversion to string
SUM	---HM	-N---	sum of matrix or histogram
TAN	-N-HM	same	tangent
TANH	-N-HM	same	hyperbolic tangent
TRAILING	-N-HM	same	complement of ENTIER
TYPE	SNLHM	S----	type of the argument

In addition, the following random number generators are known:

Function	Argument	Effect
RND_EXPONENTIAL	mean	Exponential distribution with given mean
RND_GAUSS	-	Normal distribution N(0,1)
RND_LANDAU	-	Landau distribution
RND_POISSON	mean	Poisson distribution with given mean
RND_POLYA	theta	Polya distribution with given theta
RND_UNIFORM	scaling	Uniform distribution
RND_FUNCTION	-	Random number according to a function
RND_HISTOGRAM	histogram	Random number according to an histogram

Notes:

1. The functions act element by element on arguments of type Histogram and Matrix.
2. All functions can be applied to type Undefined, the result being Undefined.
3. Further functions and random number generators can be added on request.
4. More elaborate operations are available as procedures Calls.

Additional information on:

ABS	ARCCOS
ARCCOSH	ARCSIN
ARCSINH	ARCTAN
ARCTANH	COS
COSH	ENTIER
EXP	GLOBAL
LANDAU	LOG
MAXIMUM	MEAN
MINIMUM	NOT
NUMBER	PRODUCT
REFERENCE	REF_HISTOGRAM
REF_MATRIX	REF_STRING
RMS	RND_EXPONENTIAL
RND_FUNCTION	RND_GAUSS
RND_LANDAU	RND_HISTOGRAM
RND_POISSON	RND_POLYA
RND_UNIFORM	ROW
SIN	SINH
SQRT	STRING
SUM	TAN
TANH	TRAILING
TYPE

instruction_list

The instruction list usually contains many pieces, identified by entry_points which can be executed independently.

The instruction list consists, as the name says, of a list of instructions.

Each instruction is made up of 4 integers:

1. either a function specification code or an index in the array R;
2. code for the operation;
3. an index in the array R;
4. the index for the outcome, in R for intermediate results, in the result list for final results

Additional information on:

argument	arithmetic
call	functions
goto	results
return

entry_points

Each time you ask a function to be translated, this will be done in a new entry point. Similarly, when you enter the editor, you are assigned an entry point to store your instructions in. The entry point description for en edited entry point is updated when leaving the editor.

You can not change the description of an entry point but you can delete entry points, add new ones and see the description of one.

ADD-ENTRY-POINT

Format:

ADD-ENTRY-POINT

CLEAR-ENTRY-POINT

Format:

CL-ENTRY [entry_reference]

Examples:

CL-ENTRY
CL-ENTRY 5

In the first example, the current entry point (the one you are editing) is dropped. You may continue to modify it etc. and it can also be executed as long as no garbage collect is done.

In the second example, the entry point with reference number 5 is dropped. The reference number can be obtained from the MEMORY command, details about an entry point are provided by the DISPLAY-ENTRY-POINT command.

DELETE

Format:

DELETE [from [to|LAST]]

Example:

DEL
DEL 1 LAST

(Both examples delete all instructions.)

DISPLAY-ENTRY-POINT

Note that the description of an entry point that is being edited is not always entirely up to date.

Format:

DISPLAY-ENTRY-POINT [entry_reference]

Example:

DISP-ENTRY

Shows details about your current entry point.

EXECUTE

Format:

EXECUTE [from [to|LAST]]

Example:

EXEC

(Execute the whole instruction list, skipping branching statements.)

EXIT

Format:

EXIT

FUNCTION

Format:

FUNCTION function

Example:

F ARCTAN (EX/EY)

GARBAGE-COLLECT

Format:

GARBAGE-COLLECT

INSERT

Format:

INSERT before

LIST

Format:

LIST [from [to|LAST]]

Example:

LIST 5

(Lists line 5 only.)

MEMORY

Format:

MEMORY

OPTIONS

Format:

OPTIONS [NO-SYNTAX-CHECK | ALGEBRA-SYNTAX-CHECK | ...
         PROCEDURE-SYNTAX-CHECK] ...
        [SIGNAL-UNDERFLOW | IGNORE-UNDERFLOW]

Examples:

&SIGNAL
(avalanche, time resolution and other settings)
Global phi0=10*pi/180
@
opt ignore-underflow
exit
signal ion-tail cross-induced noelectron-pulse ...
   ion-angles 20 angular-spread exp(-((phi/{phi0})**2))

Avalanches are spread around the wire with a standard deviation of 10 degrees. This would lead to many underflows in the calculation and the spread would be rejected as a result. This is why the IGNORE-UNDERFLOW option is used.

OPTION NO-SYNTAX-CHECK DEBUG

(If you are confident you won't make typing errors ...)

Additional information on:

SYNTAX-CHECK	IGNORE-UNDERFLOW

PRINT

Format:

PRINT [from [to|LAST]]

Example:

PRINT 2 10

(Prints lines 2 through 10.)

REGISTER

You have access to the entire storage area, constant elements included.

Format:

REGISTER array_index value

Examples:

REG 5 10
REG 5

(First assign the value 10 to R(5), then check the value.)

RESET

Format:

RESET

RESULTS

Format:

RESULTS

SIMPLIFY

During the simplification, constants are evaluated, complementary operations are cancelled, assignments are propagated and removed, equal subexpressions are identified and stored and unexecutable steps are dropped from the instruction list.

Some of these simplifications are skipped if the instruction list contains (un)conditional jumps since the jump address can not a priori be assumed to be known.

Format:

SIMPLIFY

TEST

This instruction differs from EXECUTE in that goto is executed. Loops, jumps and if's therefore work as usual.

Format:

TEST var1 var2 ...

Example:

TEST 2 3 6 10

(Execute the instruction list after substituting 2 for R(1), 3 for R(2), 6 for R(3) and 10 for R(4).)

VARIABLES

Format:

VARIABLES

Formatted on 15/01/01 at 23:07.