functions

The following are real functions:

ABS(-2.3) = 2.3	absolute value
EXP(1.5) = 4.48	inverse of natural log
LOG10(10) = 1	log base 10
LOGE(4.48) = 1.5	natural log
MAX(2.1,3.3) = 3.3	maximum of two
MIN(2.1,3.3) = 2.1	minimum of two
NORMAL, CUMNORMAL	normal distribution functions
LOGNORMAL, CUMLOGNORMAL	normal distribution functions new for GEMPACK 10
GPERF and GPERFC	normal distribution functions new for GEMPACK 10
RANDOM(1,100)	random real number uniform between 1 and 100
SQRT(60) = 7.75	square root
ID01(3.4) = 3.4 ID01(0) = 1	maps nonzero X to X, else 1
ID0V(3.4,7) = 3.4 ID0V(0,7) = 7	maps nonzero X to X, else 2nd arg

Example of ID01

Equation E_p3_s (all,c,COM)

ID01(Sum{s,SRC, V3PUR(c,s)})*p3_s(c)

= Sum{s,SRC, V3PUR(c,s)*p3(c,s)};

The ID01 ensures a non-zero coefficient on p3_s in all cases.

These three functions turn real numbers into integers (can be used for mappings):

ROUND(x) is the nearest integer to the real number x.

ROUND(3.1)=3, ROUND(3.6)=4, ROUND(-3.1)=-3, ROUND(-3.6)=-4.

TRUNC0(x) truncates the real number x to the nearest integer towards 0.

TRUNC0(3.1)=3, TRUNC0(3.0)=3, TRUNC0(3.6)=3, TRUNC0(-3.1)=-3, TRUNC0(-3.6)=-3.

TRUNCB(x) truncates the real number x to the nearest integer which is below x.

TRUNCB(3.1)=3, TRUNCB(3.0)=3, TRUNCB(3.6)=3, TRUNCB(-3.1)=-4, TRUNCB(-3.6)=-4.

MINS and MAXS functions find minimum or maximum of a vector:

(all,r,REG)(all,d,REG)

DISTANCE2(r,d) = MINS[q,REG,DISTANCE(r,q)+DISTANCE(q,d)];

(all,r,REG: AREA(r) >3) COST(r) = MAXS[q,REG, DISTANCE(r,q)];

NB: MINS over an empty set is a very large positive number, about 10^38 !

URL of this topic: www.copsmodels.com/webhelp/tabmate/hc_functions.htm