Working with Multidimensional Data

The result of a query on multidimensional data is called a Cellset. A Cellset consists of a collection of axes, usually no more than four axes and typically only two or three. Points along an axis are called positions. For an axis consisting of a single dimension, these positions are a subset of the dimension members. If an axis consists of more than one dimension, then each position is a compound entity, which has n parts where n is the number of dimensions oriented along that axis. Each part of the position is a member from one constituent dimension.

For example, if the Geography and Product dimensions from the Sales Data cube are oriented along the x-axis of a Cellset, a position along this axis may contain the members "USA" and "Computers." In this example, determining a position along the x-axis requires that members from each dimension are oriented along the axis.

The objects positioned at the intersection of axis coordinates are called cells. Each cell has multiple pieces of information associated with it, including the data itself, a formatted string (the displayable form of cell data), and the cell ordinal value. (Each cell is a unique ordinal value in the Cellset. The ordinal value of the first cell in the Cellset is zero, while the leftmost cell in the second row of a Cellset with eight columns would be eight.)

For example, consider a Sales Data cube that has the following six dimensions:

Salesperson
Geography (natural hierarchy)—Continents, Countries, States, and so on
Quarters—Quarters, Months, Days
Years
Measures—Sales, PercentChange, BudgetedSales
Products

Consider the following Cellset:

Sales for 1991, All Products

		Venkatrao				Netz
		USA			Japan	USA			Japan
		USA_ North		USA_ South		USA_ North		USA_ South
		Seattle	Boston			Seattle	Boston
	Jan	00	10	20	30	40	50	60	70
Qtr1	Feb	01	11	21	31	41	51	61	71
	Mar	02	12	22	32	42	52	62	72
Qtr2		03	13	23	33	43	53	63	73
Qtr3		04	14	24	34	44	54	64	74
	Oct	05	15	25	35	45	55	65	75
Qtr4	Nov	06	16	26	36	46	56	66	76
	Dec	07	17	27	37	47	57	67	77

Note The cell values in the example can be viewed as ordered pairs of axis position ordinals where the first digit represents the x-axis position and the second digit the y-axis position.

The characteristics of this Cellset are as follows:

Axis dimensions: Quarters, Salesperson, Geography
Filter dimensions: Measures, Years, Products
Two axes: COLUMN (x, or Axis 0) and ROW (y, or Axis 1)
x-axis: two nested dimensions, Salesperson and Geography
y-axis: Quarters dimension

The x-axis has two nested dimensions: Salesperson and Geography. From Geography, four members are selected: Seattle, Boston, USA_South, and Japan. Two members are selected from Salesperson: Venkatrao and Netz. This yields a total of eight positions on this axis (8 = 4*2).

Each coordinate is represented as a position with two members—one from the Salesperson dimension and another from the Geography dimension:

(Venkatrao, Seattle), (Venkatrao, Boston), (Venkatrao, USA_North), (Venkatrao, Japan), (Netz, Seattle), (Netz, Boston), (Netz, USA_North), (Netz, Japan)

The y-axis has only one dimension. It contains the following eight positions:

Jan, Feb, Mar, Qtr2, Qtr3, Oct, Nov, Dec