Cumulate

Cumulate(X,I)

Returns an array with each element being the sum of all of the elements of X along dimension I up to, and including, the corresponding element of X.

Declaration

Cumulate(X:Array[I] ; I : Index)

Library

Array Functions

Examples

I →	1	2	3	4	5	6
X →	8	2	0	5	-3	7
Cumulate(X,I) →	8	10	10	15	12	19

Library

Array Functions

Optional Parameters

PassNull

Cumulate(X,I,passNull:true)

When the optional «passNull» is omitted or false, Cumulate ignores Null values. In that case they have essentially the same effect as a zero, unless they happen to be the first value in «X», in which case they are passed since no numeric values are yet obtained.

When «passNull» is explicitly set to true, then Null values are passed through as Null in the result.

X →	«null»	«null»	4	1	«null»	«null»	1	9	3	2	«null»
Cumulate(X,I) →	«null»	«null»	4	5	5	5	6	15	18	20	20
Cumulate(X,I,passNull:false) →	«null»	«null»	4	5	5	5	6	15	18	20	20
Cumulate(X,I,passNull:true) →	«null»	«null»	4	5	«null»	«null»	6	15	18	20	«null»

Reset

Cumulate(X,I,reset:R)

New to Analytica 4.3

The optional «reset» parameter accepts an array of boolean values indexed by «I». At the positions where «reset» is true, Cumulate starts over. This sets the sum of all previous values to zero, so that the value at that position will be the same as the value in «X».

I →	1	2	3	4	5	6	7
X →	8	2	0	5	-3	7	5
R →	0	0	1	0	0	1	0
Cumulate(X,I,reset:R) →	8	10	0	5	2	7	12

«Reset» can be used to restart the cumulation each time some state change occurs. In such a scenario, the «reset» parameter is set to True at the first instant (along «I») that the system is in the new state.

Suppose State is a state designator, indexed by I. The following would compute how long the system has been in the same state for:

Cumulate(1,I,State[@I=@I-1]<>State)

Notes

Recumulate

In Analytica 4.2 and earlier, the functionality of the «reset» parameter can be obtained using the Recumulate library function, which resets the total to zero at selected points. This usage is:

Recumulate(x,b,I)

where b is an array of booleans indexed by I, having 1 at each point where the cumulation is to be reset to zero. Recumulate is implemented as a User-Defined Function in the example Recumulate example.ana. A clever usage of this function computes the number of time steps that the system has been in the same state (see the example).

See Also

• Uncumulate
• Sum
• CumProduct
• Recumulate example.ana