Cardinality (cardn)
Contents
Cardinality. Number of absolute values of scaled components of a vector exceeding some threshold
Syntax
cardn(w, matrix) |
short call |
cardn_name(w, matrix) |
call with optional name |
Parameters
matrix is a PSG matrix:
where the header row contains names of variables. Other rows contain numerical data, 
, 
.
The 2-4-th numerical rows are optional. 
and 
define point for right cardinality “jump” for every variable. 
and 
define point for left cardinality “jump” for every variable.
If matrix includes only one numerical row, then, by default, the the second numerical row is assumed equal to the first one.
If the 3-th and 4-th rows are absent, then, they are assumed to be zero. If 4-th rows is absent, then, it is assumed to be equal to the 3-th one.
The scenario_benchmark column is optional. If scenario_benchmark column is not present, then, by default, 
.
The coefficients 
are dummy and not used for calculation.
 | is a threshold value. |
and 
define “jump steepness“.
Mathematical Definition
Cardinality function is calculated as follows
,
where
is small threshold value,
is an argument of Cardinality function.
for 
.
Remarks
It is recommended to select the multiplier (the second and the third) rows equal to the unit vectors and 
. For instance if decision variables are measured in thousands than 
.
Example
Case Studies with Cardinality
See also
Cardinality Positive, Cardinality Negative, Buyin Positive, Buyin Negative, Buyin, Fixed Charge Positive, Fixed Charge Negative, Fixed Charge