In Polaris, the formulas you use in line items can affect the sparsity or density of your models.

Within Polaris, a sparser model is more memory-efficient than a dense one. This means you should design formulas and models to maximize sparsity.

A formula can either increase, decrease, or maintain the current level of sparsity. The Calculation Complexity column within Blueprint can contain one of three values, which explains the effect of a formula upon sparsity. These values are One-to-One, One-to-Many, and All cells:

Calculation complexityDescriptionExample

The most efficient type of formula.

One-to-One formulas maintain sparsity as the results only ever calculate values for the same number or fewer cells than the source data.

A formula that multiplies a set of numeric values by another.

As the result only calculates values for cells that contain a non-zero value, the number of cells calculated in the result is the same as in the source. 

One-to-Many (n)

Less efficient than One-to-One, but more efficient than All cells.

One-to-Many formulas decrease sparsity as they calculate results for a greater number of cells than the source data.

The n in brackets is the multiple of populated source cells that could be populated in the target. This is also known as the fan out factor. The higher this is, the less efficiently the formula scales. 

A formula that aggregates values from a parent time period into child time periods.

This populates child cells with the data from the parent cells, which increases the number of calculations required.

All cells

The least efficient type of formula.

All cells formulas decrease sparsity as they calculate results for all cells within the dimensionality of the result line item.

A formula that adds a constant to all values in a line item.

This means that every cell in the result requires calculation, even those that were originally blank or zero values.

In Polaris, Populated Cell Count and Memory Used columns display in Blueprint. You can also use these to monitor the effect on memory of your line items and formulas.

In Polaris, if you update a formula and it decreases calculation efficiency, the changes may take a long time. If this happens, a banner displays that enables you to cancel the change.


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