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MDX – Multid imensional E xpressions

Microsofts proposal for a

multidimensional query and

presentation language

for OLE DB for OLAP

Robert Fenk

March 11, 1999

Robert Fenk February 17, 2000, mdx-vortrag.tex

Contents� MDX Overview

– Data Cube

– MDX Syntax

– Data Set

� MDX and Range Queries

� MDX Summary

� Implementing MDX

� Processing of two Example Queries


MDX Overview

Data Set

Data Cube

MDXquery


MDX Data Cube

The MDX view of a multidimensional data cube:

Dimension: a set of elements of the same type

Member: elements of a dimension

Hierarchy: groups members of a dimension

Member–Properties: additional information


Example MDX Data Cube

4 Dimensions: Salesperson, Time, Measures, Product

Salesperson –dim: . . . , Netz, . . . , Venkatrao, . . .

Time –dim:. . . , 1998, Qtr1 1998, Jan 1998,

1/1/1998, . . . , 1999, . . .

Measures –dim: Sales, Turnover, . . .

Product –dim: . . . , TV, Color–TV, . . .

Member–Props of

Salesperson –dim:Name, Phone, . . .


Hierarchy–Schemata over the Time –dimension

Level: Weeks

Level: Days

Level: Year

Level: Quarter

Level: Month

Level: Day

Level: All Level: All

Hierarchy: WeeksHierarchy: Quarters

Dimension:Time

Level: Year

in different hierarchies

contained in one hierarchyA dimension member only

A dimension member contained


Example Hierarchy over the Time –dimension

... ...

1998.Qtr41998.Qtr2

1998.Qtr1.Mar

1998.Qtr1

19981985

1998.Qtr3

1998.Qtr1.Jan

Level: Month

Level: Year

Hierarchy: Quarters

Level: Day

Level: Quarter

Level: All

Dimension:Time

All

1998.Qtr1.Jan.311998.Qtr1.Jan.1 1998.Qtr1.Dec.1 1998.Qtr1.Dec.31

1998.Qtr4.Nov 1998.Qtr4.Dec1998.Qtr4.Oct1998.Qtr1.Feb


Example Fact Table according to ROLAP

dimensions / key attributes measures

Salesperson Time Product Cost Sales Turnover

Venkatrao 1998 TV 50000 10023 190000

Netz 1998 TV 56789 90023 100000

. . . . . . . . . . . . . . . . . .


Example Fact Table for an MDX Data Cube

dimensions / key attributes one data–cell

Salesperson Time Product Measures Value

Venkatrao 1998 TV Cost 50000

Venkatrao 1998 TV Sales 10023

Venkatrao 1998 TV Turnover 190000

Netz 1998 TV Cost 56789

Netz 1998 TV Sales 90023

Netz 1998 TV Turnover 100000

. . . . . . . . . . . . . . .


MDX Rowsets storing meta data

CATALOG_NAMESCHEMA_NAME

CUBE Rowset

CUBE_NAMECUBE_TYPECUBE_GUIDCREATED_ONLAST_SCHEMA_UPDATESCHEMA_UPDATED_BYLAST_DATA_UPDATEDATA_UPDATED_BYDESCRIPTION

CATALOG_NAMESCHEMA_NAMECUBE_NAMEDIMENSION_UNIQUE_NAME

HIERARCHY_UNIQUE_NAMEHIERARCHY_NAME

HIERACHY_GUIDHIERACHY_CAPTIONDIMENSION_NAMEHIERACHY_CARINALITYDEFAULT_MEMBERALL_MEMBERDESCRIPTION

HIERACHIES Rowset LEVELS Rowset

LEVEL_NAMELEVEL_UNIQUE_NAMELEVEL_GUIDLEVEL_CAPTIONLEVEL_NUMBERLEVEL_CARDINALITYLEVEL_TYPEDESCRIPTION

HIERARCHY_UNIQUE_NAMEHIERARCHY_NAMEDIMENSION_UNIQUE_NAME

CATALOG_NAMESCHEMA_NAMECUBE_NAME

MEMBERS RowsetCATALOG_NAMESCHEMA_NAMECUBE_NAMEDIMENSION_UNIQUE_NAMEHIERACHY_UNIQUE_NAMELEVEL_UNIQUE_NAMELEVEL_NUMBERMEMBER_ORDINALMEMBER_NAMEMEMBER_UNIQUE_NAMEMEMBER_TYPEMEMBER_GUIDMEMBER_CAPTIONCHILDREN_CARDINALITYPARENT_LEVELPARENT_UNIQUE_NAMEPARENT_COUNTDESCRIPTION

MEASURES RowsetCATALOG_NAMESCHEMA_NAMECUBE_NAMEMEASURE_NAMEMEASURE_UNIQUE_NAMEMEASURE_CAPTIONMEASURE_GUID

DATA_TYPENUMERIC_PRECISIONNUMERIC_SCALENUMERIC_UNITSDESCRIPTION

MEASURE_AGGREGATOR

CATALOG_NAMESCHEMA_NAME

DIMENSION_NAMEDIMENSION_UNIQUE_NAME

DIMENSION_CAPTIONDIMENSION_ORDINAL

DIMENSIONS Rowset

DIMENSION_GUID

DIMENSION_TYPEDIMENSION_CARDINALITYDEFAULT_HIERARCHYDESCRIPTION

CUBE_NAME

PROPERTIES Rowset

MEMBER_UNIQUE_NAMEPROPERTY_TYPEPROPERTY_NAMEPROPERTY_CAPTIONDATA_TYPECHARACTER_MAXIMUM_LENGTHCHARACTER_OCTET_LENGTHNUMERIC_PRECISIONNUMERIC_SCALEDESCRIPTION

CATALOG_NAMESCHEMA_NAMECUBE_NAMEDIMENSION_UNIQUE_NAMEHIERACHY_UNIQUE_NAMELEVEL_UNIQUE_NAME


MDX “Syntax”

[WITH <formula_spec>]

SELECT <axis_spec> [, <axis_spec>, ...]

FROM <cube_spec> [, <cube_spec>, ...]

WHERE <slicer_spec> [cell_properties]


MDX “Syntax” Description� WITHclause: creation of a new dimension member, which lives

in the context of the expression.e.g.:

WITH MEMBER Measures.[% Change from Last Year’s Sales] AS

Sales / (Sales, Year.PREVMEMBER)

� axis spec : maps dimensions to axes and gives restrictions.

e.g.: f1998, 1999 g ON COLUMNS

� cube spec : determines the data cube (usually a single data

cube)

� slicer spec : restricts to dimensions not given in the

axis spec (meaning of the cell contents)


MDX–Query Example

SELECT CROSSJOIN({Venkatrao, Netz},

{USA_North.CHILDREN,

USA_South, Japan})

ON COLUMNS

{Qtr1.CHILDREN, Qtr2,

Qtr3, Qtr4.CHILDREN}

ON ROWS

FROM SalesCube

WHERE (Sales, [1998], Products.All)


MDX Data Set

The result of an MDX–query is called a data set.

Dataset: a multidimensional cube / a set of Excel tables

Axis: dimensions are mapped to axes

Coordinate: elements of an axis

Cell: element of the dataset specified by its axis–coordinates

Cell–Properties: additional information


Example Data SetSum of all product sales for 1998:

Venkatrao Netz

USA

Japan

USA

JapanUSA NorthUSA South

USA NorthUSA South

Boston Seattle Boston Seattle

Qtr1

Jan � � � � � � � � � � � � � � � � � � � � � � � �

Feb � � � � � � � � � � � � � � � � � � � � � � � �

Mar � � � � � � � � � � � � � � � � � � � � � � � �

Qtr2 � � � � � � � � � � � � � � � � � � � � � � � �

Qtr3 � � � � � � � � � � � � � � � � � � � � � � � �

Qtr4

Oct � � � � � � � � � � � � � � � � � � � � � � � �

Nov � � � � � � � � � � � � � � � � � � � � � � � �

Dec � � � � � � � � � � � � � � � � � � � � � � � �


MDX Summary� Data Cube: “contains” also aggregated measures

– contains the measures (a single value)

– the type of the measure is given by the Measure–dimension

� Restriction: given by sets of members

– sets of members are ordered (! data set)

– axis spec and slicer spec

� Projection:

– members given in the axis spec are mapped to axes

– the order of the members defines the order of the coordinates


Restrictions resulting in intervals

� <member>:<member> (range)

� <dimension>.MEMBERS

� <hierarchy>.MEMBERS

� <level>.MEMBERS

� <member>.CHILDREN

� DESCENDANTS(<member>, <level>)


Examples Restrictions resulting in a Range Queries

Restriction: fHuber, 1998, Sales, TVg

! MDX: a point query resulting in a single measure.

! UB–Tree: two ranges (Time– and Product–dimension),

+ aggregation

Restriction: fHuber, 1998.CHILDREN, Sales, TVg

Restriction: fHuber:Maier, 1998.CHILDREN, Sales, TV.MEMBERSg


Implementing MDX

1. Get an MDX–Parser

2. Map the data cube in a useful way to a DBMS

e.g. a star schema of a RDBMS or a UB–Tree

3. Transform the MDXs to the query–language of the used DBMS

e.g. MDX ! SQLs

4. Build up a data set with the results of the DBMS–query

e.g. aggregations, reordering, folding

5. Provide the data set to the application


Implementing a MDX Data Cube (SalesCubeRelation)

create a fact table with

one column per hierarchy level of each dimension

Salesperson Year Month Day Product SalesVenkatrao 1998 Jan 1 TV 4Venkatrao 1998 Feb 2 TV 16Venkatrao 1998 Mar 3 TV 68Venkatrao 1999 Jan 1 TV 71Venkatrao 1999 Feb 2 TV 41Venkatrao 1999 Mar 3 TV 30Netz 1998 Jan 1 TV 86Netz 1998 Feb 2 TV 68Netz 1998 Mar 3 TV 89Netz 1999 Jan 1 TV 40Netz 1999 Feb 2 TV 32Netz 1999 Mar 3 TV 82


Implementing MDX Queries

Query Transformation:

� extract the restrictions on dimensions given in the axis specand slicer spec

� determine by the slicer spec over which dimensions weaggregate and get the aggregation type from the meta date

Query Execution:

� recognize ranges in the restrictions on the dimensions

� execute the transformed query

Transformation of the Result Relation to a Data Set:

� reordering of the result relation according to the axis spec

� folding of the result relation according to the axis spec


COGNOS like MDX Example (1/4)

SELECT { Salesperson.All.Venkatrao,

Salesperson.All.Netz }

ON AXIS(0)

{ Time.All.1998,

Time.All.1999 }

ON AXIS(1)

FROM SalesCube

WHERE { Product.All.TV, Measures.All.Sales }


COGNOS like MDX Example (2/4)The dimensions are restricted to:

Salesperson: fVenkatrao, Netzg

Time: f1998, 1999g

Product: fTVg

Measures: fSalesg

Aggregation is done over:

Saleperson–dimensionYear–dimension



fold(tG;F (��(R)))

where

R = SalesCubeRelation

� = Salesperson 2 fVenkatrao;Netzg ^

Year 2 f1998; 1999g ^

Product 2 fTVg ^

Measures 2 fSalesg

G = ffSalesperson; Yeargg

F = f�Salesg



Result Relation:

Salesperson Year Product Sales

Venkatrao 1998 TV 88

Venkatrao 1999 TV 142

Netz 1998 TV 243

Netz 1999 TV 154

Data Set: By folding the result relation according to the axisspecification we get the following data set:

Sum of the TV Sales

Venkatrao Netz

1998 88 243

1999 142 154


More general Example (1/4)

SELECT CROSSJOIN({Venkatrao, Netz},

{1998.Jan, 1998.Feb,

1998.Mar, 1998})

ON AXIS(0)

{TV, Computer, Product.ALL}

ON AXIS(1)

FROM SalesCube

WHERE {Sales}



fold(��2(tG;F (��1(R))))

�1 = Salesperson 2 fVenkatrao;Netzg ^

Year 2 f1998g ^ Product 2 fTV;Computerg ^

Measures 2 fSalesg

G = ffSalesperson; Year;Month; Productg

fSalesperson; Year; Productg

fSalesperson; Year;Monthg

fSalesperson; Yeargg

F = f�Salesg

�2 = Month 2 fJan, Feb, Marg _

(Year 2 f1998g ^ Month = ALL) Robert Fenk February 17, 2000, mdx-vortrag.tex

More general Example (3/4)Result Relation:

Salesperson Year Month Product SalesNetz 1998 Jan TV . . .Netz 1998 Feb TV . . .Netz 1998 Mar TV . . .. . . . . . . . . . . . . . .Netz 1998 ALL TV 243. . . . . . . . . . . . . . .Netz 1998 ALL Computer 417. . . . . . . . . . . . . . .Netz 1998 ALL ALL 660. . . . . . . . . . . . . . .Venkatrao 1998 ALL TV 150. . . . . . . . . . . . . . .Venkatrao 1998 Jan Computer . . .Venkatrao 1998 Feb Computer . . .Venkatrao 1998 Mar Computer . . .. . . . . . . . . . . . . . .Venkatrao 1998 ALL Computer 350. . . . . . . . . . . . . . .Venkatrao 1998 ALL ALL 500



Data Set:

Venkatrao Netz1998

19981998

1998Jan Feb Mar Jan Feb Mar

TV . . . . . . . . . 150 . . . . . . . . . 243Computer . . . . . . . . . 350 . . . . . . . . . 417ALL . . . . . . . . . 500 . . . . . . . . . 660


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