Tomislav Piasevoli – BI Blog

Boyan Penev recently blogged about a strange behavior which manifests when ordering two related sets thereby mentioning a thread in SSAS forum answered by Deepak Puri. I found this intriguing and decided to reply directly, but the explanation kept growing, so I finally cut everything out and put it as an article on my blog instead. After all, this way my chances of being enlisted in his blog roll should increase 8-).

Here’s the problem in short. The first query works, the second doesn’t. The difference? The second query has related hierarchies while the first one doesn’t.

WITH
SET [RowSet]    AS [Product].[Subcategory].Levels(1).Members
SET [ColumnSet] AS [Date].[Calendar].Levels(1).Members
SELECT
     Order( [RowSet], [ColumnSet].Item(0), BDESC ) ON ROWS,
     [ColumnSet]                                   ON COLUMNS
FROM [Adventure Works]

WITH
SET [RowSet]    AS [Product].[Subcategory].Levels(1).Members
SET [ColumnSet] AS [Product].[Category].Levels(1).Members
SELECT
     Order( [RowSet], [ColumnSet].Item(0), BDESC ) ON ROWS,
     [ColumnSet]                                   ON COLUMNS
FROM [Adventure Works]

Now, some of you may have already guessed this has to be a case of attribute relations and yes, I admit you’re right. Nevertheless, I think an analysis would be beneficial, after all Boyan asked for it.

First, let’s make a small but important distinction. Those queries look like they have been written by a T-SQL developer. Why am I saying it? Because in T-SQL, ORDER is typically (although not necessarily) based on a column, be it numeric, date or string. A set being returned is ordered based on the values of that column.

In MDX, ORDER() is based on an expression which means that the second argument is automatically converted to a tuple (ColumnSet.Item(0)), and then a value of it: (ColumnSet.Item(0)).Value. Let’s see how those two MDX queries might look like in T-SQL.

use AdventureWorksDW2008;

with
t as
(
select
    SubCategory = s.EnglishProductSubcategoryName,
    CalendarYear = d.CalendarYear,
    ResellerSales = sum(f.SalesAmount)
from dbo.DimProductSubcategory s
    join dbo.DimProduct p
        on p.ProductSubcategoryKey = s.ProductSubcategoryKey
    join dbo.FactResellerSales f
        on f.ProductKey = p.ProductKey
    join dbo.DimDate d
        on d.DateKey = f.OrderDateKey
group by
    s.EnglishProductSubcategoryName,
    d.CalendarYear
)
, pvt as
(
select * from t
pivot( sum(ResellerSales)
       for CalendarYear in ( [2001], [2002], [2003], [2004], [2006] ) ) as pvt
)
select * from pvt
order by
— sort A
[2001] desc;
— sort B
/*
(select sum(ResellerSales) from t
        where t.SubCategory = pvt.SubCategory and
              t.CalendarYear = 2001) desc;
*/

with
t as
(
select
    SubCategory = s.EnglishProductSubcategoryName,
    Category = c.EnglishProductCategoryName,
    ResellerSales = sum(f.SalesAmount)
from dbo.DimProductSubcategory s
    join dbo.DimProduct p
        on p.ProductSubcategoryKey = s.ProductSubcategoryKey
    join dbo.FactResellerSales f
        on f.ProductKey = p.ProductKey
    join dbo.DimProductCategory c
        on c.ProductCategoryKey = s.ProductCategoryKey
group by
    s.EnglishProductSubcategoryName,
    c.EnglishProductCategoryName
)
, pvt as
(
select * from t
pivot( sum(ResellerSales)
       for Category in ( [Bikes], [Components], [Clothes], [Accessories] ) ) AS pvt
)
select * from pvt
order by (select sum(ResellerSales) from t
          where –t.SubCategory = pvt.SubCategory and
                t.Category = ‘Accessories’
         ) desc;

They return exactly the same result as those two MDX queries. Btw, who says MDX is not elegant and easy?

Now, let’s analyze them.

The first query is ordered by column [2001]. We said that MDX uses expressions when sorting, so we’ll try to do the same using an expression. We can comment [2001] DESC and un-comment what’s below “sort B”, but the result won’t change.

In the second query I deliberately skipped sorting by a column (ORDER BY [Accessories] DESC) and used the version with an expression in order to get the false result. The column version would yield the correct, expected result. While we might have thought sorting in MDX behaves that way, the truth is it doesn’t. MDX has some specifics and we need to use the expression version in order to show them.

Important thing to notice is that in both queries there’s a join which binds subcategories (disregard it being commented in the second query at the moment, act like it’s still there). We can imagine this as being the first phase in setting the condition of those correlated sub-queries.

The next phase would be to expand this by specifying the argument of the Order() statement in MDX. In case of a Date dimension, that was year 2001. Since that is a different dimension, nothing has changed in our initial condition.

In the second query, there was a related hierarchy (same dimension) which came after the initial phase, so it forced everything so far to adjust to it (which btw might be seen as a third phase). You can imagine this third phase as limiting the join further by adding conditions like this:

and exists (select ProductCategoryKey from dbo.DimProductCategory
            where EnglishProductCategoryName = pvt.SubCategory)

When the related hierarchy is “below” the current one, the initial join could be considered as removed (instead of bringing this extra EXISTS which makes no sense if you analyze what’s inside). Therefore I commented it in the query. In fact, I manually did what SSAS engine implicitly does to joins from the initial phase when a related hierarchy comes in the second phase and when the relation is 1:N, or in OLAP terms – below granularity.

When it is “above”, the initial join is just more limited (now it makes sense to use EXISTS).

In DAX it would be something like the ALL() function (for analogies between MDX, T-SQL and DAX I suggest reading my previous blog article).

Err, one more thing, the join is based on keys rather than names, but for simplicity reasons I haven’t included them in queries.

Now let’s get back to OLAP and it’s multidimensional space.

Cube’s space is N-dimensional which means each coordinate should be N-di
mensional too. SSAS formula engine fills the missing parts using the current members of non-mentioned hierarchies. But who are they?

Based on members explicitly specified in a coordinate, the engine implicitly (the way a trigger fires in T-SQL) finds members on related hierarchies. They become current members of those hierarchies. For non-mentioned dimensions (not hierarchies), the engine picks current members which again are “current” because of some previous context set by an expression, function, slicer or the cube itself.

In the first example year 2001 sets the context of that expression. All the hierarchies of Date dimension implicitly shift their current members accordingly (which is not important in this case, but let it be known). Since the Product and others dimension were not mentioned in that expression, we traverse to previous contexts (backwards) in order to find their current members. The Filter() function sets the immediate previous context. For Product dimension, Product.Subcategory hierarchy to be precise. – How come? – Well, Filter() is sort of a loop, which means we iterate over members in its set (the first argument) which in turn become “current” in that expression, one by one. Other dimensions are not important in this case but the process of identifying current members might be visualized likewise.

In the second example Accessories category sets the context. Its presence automatically shifts Product.Subcategory current member to a related position. – Where? – To its root member. – Why? – Because relation is 1:N. If it were N:1, it would shift to a single related member. Since it can’t find one, it shifts to its root member which is a way of saying “I can not find a direct relation to a single member, therefore I’ll move to a place where I don’t stand in a way, a neutral position that doesn’t change the (explicit) coordinate, though complies to the obligation of me being present in the coordinate”.  – Let me think it through a bit … OK, I see. But how come the current member of Product.Subcategory hierarchy didn’t stay too? I mean, he was in Filter() function too, as the first argument. – Correct, but they are not treated the same. – Why’s that? – Layers! – What? – Calculation layers. In form of a stack. On top there’s only Accessories because only that was explicitly there in the expression and that expression is the last thing evaluated in the Filter() function. – Why is that the last thing? – Well, first you need to set a loop. Then you evaluate the expression for each member, right? As you would do in programming, loop is outside, assignments and calculations are inside the loop. Therefore, Product.Subcategory set (and its current members in a loop) is one layer below in this stack. Whoever is NOT on top, or shall we say BELOW the layer being currently evaluated might be implicitly shifted. Might, because it depends whether he’s related or not. If he is, as in the second example, he will shift, but if he isn’t as in the first example, nothing will happen. He’ll come unchanged. In turn, he might determine who’ll be shifted among his “relatives” in layers below his. And so on. The winner takes it all approach among “relatives” and the winner is the “relative” being explicitly in the coordinate, on top of the others. – Oh, I see. Current and lower layers you say … Wait, I got an idea! In order to make them equal, we should bring them on the same layer, right? – Exactly! – And how do you suggest we should do that? – The expression. That determines the top layer in this case so both of them should be there. – Ok, but how? – Simple, by providing a tuple. We should expand the existing condition with .CurrentMember of the first set.

Here are both the false and the correct MDX for the second query, to emphasize their differences.

WITH
SET [RowSet]    AS [Product].[Subcategory].Levels(1).Members
SET [ColumnSet] AS [Product].[Category].Levels(1).Members
SELECT
     Order( [RowSet], [ColumnSet].Item(0), BDESC ) ON ROWS,
     [ColumnSet]                                   ON COLUMNS
FROM [Adventure Works] 

WITH
SET [RowSet]    AS [Product].[Subcategory].Levels(1).Members
SET [ColumnSet] AS [Product].[Category].Levels(1).Members
SELECT
     Order( [RowSet], ( [ColumnSet].Item(0),
                       [RowSet].CurrentMember ), BDESC ) ON ROWS,
     [ColumnSet]                                          ON COLUMNS
FROM [Adventure Works]

Forcing the current member is like saying “I want my current member to stay and not get implicitly converted to other members. I’m forcing this coordinate and I know what I’m doing, return me the value of this explicitly requested intersection (aka coordinate)!”.

Now, return to the second T-SQL query and un-comment the join. You’ll get the correct result because this time you explicitly forced the join. Or shall we say you prevented this join from disappearing in T-SQL just as you prevented the current member in MDX from changing because of attributes relations in that dimension. Interesting?

Finally, it wouldn’t hurt to specify the same tuple in the first MDX query too. I mean, the result would not change, they would stay correct. So, if you, the reader of this article, are searching for the expression which works in any scenario, use the one with the tuple.

Important thing to remember. In MDX you can almost always omit current members in your expressions. Yet, when dealing with related hierarchies, as in this example, specifying them or not makes a world of difference.

The question remains – why there is this attribute relations mechanism in OLAP? Well, that might be a topic for some other article. For now let’s just say that it keeps the multidimensional space smaller and consistent. And although it behaves like a wormhole, it’s here to help. Without it, we might get lost out there.

Creating a Bit array (also known as Bitmap) is an useful technique when analyzing data. Especially (but not necessarily) in case of low cardinality (small number of distinct values in column compared to the number of records in a table). For example, a column having two distinct values (male/female or yes/no status) could be optimized in storage and represented using values 0 and 1 only (bits).

A collection of such bits forms a bit array or a bitmap. Bitmap indexes use those arrays performing bitwise operations on them.

Almost all DSS and analytical systems use bitmap indexes, and so does Analysis Services. An example where it can be seen is SQL Server Profiler. Query Subcube event represents the bitmap of hierarchies and attributes being used in a query. Yet, what’s fine for computers might not be for humans, hence there’s also Query Subcube Verbose event which explains that in plain English. Kind of.

Although SSAS engine intensively uses them, bitwise operations in MDX are in short supplies. In spite of that, the same idea can be borrowed and turned in action using string functions. After all, an alternate name for bit array is bitstring.

Recently I’ve participated in a case where a measure was expected to return the percentage of parent no matter which hierarchy is placed on an axis and no matter how many of them are there. Actually, a similar problem appeared on MSDN SSAS forum a year ago too. While the initial problem in this latter case was solved using special solution, general solutions emerged also. The offer ranged from heavy string manipulation to recursion and stored procedure. Taking a look at it now, from the perspective of this case, I believe bitmap indexes might have been an alternate MDX solution, a relatively fast approach that doesn’t require anything but a query and few calculated members aside.

Here’s a case study featuring the bitmap index as the key point in obtaining the general solution.

SITUATION

The idea was to have a general solution for percentage (ratio to parent). One calculated measure covering all scenarios, meaning, whatever combination of hierarchies appears in OWC (cube browser).

The problem that soon appeared was this – no matter how much improved the calculation in each iteration I posted in forum was (a previous thread and my blog article on that subject), there was always a case where it didn’t fit. Therefore I started focusing on getting as detailed explanation as possible. When I finally got it (as an Excel sheet) and analyze it, deduced the algorithm and describe it like this (as in integrams):

•  
  • if there was a non-root member in the rightmost hierarchy, show ratio to parent
  • root member in the rightmost hierarchy combined with all non-root members from other hierarchies to the left should result in 100%
  • if all hierarchies were on root member, the result should be 100%
  • in all other situations, ratio to parent for non-root member should be the result

The idea in integrams (I couldn’t link for them in English, it’s an enigmatic game) is to mark certain events that hold true and other that can never be such. By doing so in iterations (reading the initial text over and over again, every time in new context), one should be able to deduce the final combination of entities in a puzzle and thereby solve it. The idea here was to list all possible combinations using a bitmap, where 0 represents non-root member, 1 root member and their sequence, well, …the sequence of hierarchies on axis. Translated, that would look like this (asterisk being any value):

Now, see how this looks more like a solvable case? And so it was. The only thing necessary at this stage is to code it using MDX expressions in the most optimized way.

SOLUTION

A general MDX for this could be far more simpler than the one below. However, the requirement was that it should work in OWC and OWC has its specifics when it comes to MDX, about which I blogged here. Therefore, I had to make a lot of additional things, like testing where OWC put measures and everything related to that in later calculations. Nevertheless, I managed to make it work as required.

Create Member CurrentCube.[Measures].[Where are measures in OWC] AS
case
when NOT IsError(Extract( Axis(0), Measures ).Count) then 0
        when NOT IsError(Extract( Axis(1), Measures ).Count) then 1
        when NOT IsError(Extract( Axis(2), Measures ).Count) then 2
        else -1  -- should not be possible
end
    , Visible = 0
;

Create Member CurrentCube.[Measures].[Ratio measure] AS
-- specify a measure you want to have a ratio for, or
-- use default measure, or
-- use dynamic expression, that selects    -- either first measure on an axis or
-- the default measure in case no measure is selected

    /* -- option 1 */
    [Measures].[Sales Amount]
    /* -- option 2
    [Measures].DefaultMember
    */
    /* -- option 3
      iif(Extract( Axis( [Measures].[Where are measures in OWC] ),
                   Measures ).Item(0).Item(0).UniqueName =
          '[Measures].[Universal ratio %]',
          [Measures].DefaultMember,
          Extract( Axis([Measures].[Where are measures in OWC]),                   Measures ).Item(0)
         )
    */
    , Visible = 0
;

Create Member CurrentCube.[Measures].[Test Empty] AS
    IsEmpty( [Measures].[Ratio measure] )
    , Visible = 0
;

Create Member CurrentCube.[Measures].[Count of columns] AS
    iif( IsError( Axis(1).Count ),
         0,
         iif( [Measures].[Where are measures in OWC] = 1,
              Axis(0).Item(0).Count,
              Axis(1).Item(0).Count )
       )
    , Visible = 0
;

Create Member CurrentCube.[Measures].[Bitmap Index as String] AS
    iif( [Measures].[Where are measures in OWC] = 1,
        Generate( Head(Measures.AllMembers,                       [Measures].[Count of columns] ) AS L,
                  -(Axis(0).Item(0).Item(L.CurrentOrdinal - 1)                    .Hierarchy.CurrentMember.Level.Ordinal = 0)
              ),
        Generate( Head(Measures.AllMembers,                       [Measures].[Count of columns] ) AS L,
                  -(Axis(1).Item(0).Item(L.CurrentOrdinal - 1)                    .Hierarchy.CurrentMember.Level.Ordinal = 0)
          )
     )
    , Visible = 0
;

Create Member CurrentCube.[Measures].[Reversed Bitmap Index as String] AS
    iif( [Measures].[Where are measures in OWC] = 1,
        Generate( Head(Measures.AllMembers,                       [Measures].[Count of columns] ) AS L,
                  -(Axis(0).Item(0).Item([Measures].[Count of columns] -
                     L.CurrentOrdinal)                    .Hierarchy.CurrentMember.Level.Ordinal = 0)
              ),
        Generate( Head(Measures.AllMembers,                       [Measures].[Count of columns] ) AS L,
                  -(Axis(1).Item(0).Item([Measures].[Count of columns] -
                     L.CurrentOrdinal)                    .Hierarchy.CurrentMember.Level.Ordinal = 0)
              )
       )
    , Visible = 0
;

Create Member CurrentCube.[Measures].[Rightmost non root position] AS
    InStr([Measures].[Reversed Bitmap Index as String], '0')
    , Visible = 0
;

Create Member CurrentCube.[Measures].[Inner 100%] AS
    CInt([Measures].[Bitmap Index as String]) = 1
    , Visible = 0
;

Create Member CurrentCube.[Measures].[Universal ratio %] AS
    iif( [Measures].[Test Empty],
         null,
         iif( [Measures].[Rightmost non root position] = 0 OR
              [Measures].[Inner 100%],
              1,
              iif( [Measures].[Where are measures in OWC] = 1,
                   -- check division by zero
                   iif( ( Axis(0).Item(0)                          .Item([Measures].[Count of columns] -
                           [Measures].[Rightmost non root position])                          .Hierarchy.CurrentMember.Parent,
                          [Measures].[Ratio measure] ) = 0,
                        0,
                        [Measures].[Ratio measure]
                        /
                        ( Axis(0).Item(0)                          .Item([Measures].[Count of columns] -
                           [Measures].[Rightmost non root position])                          .Hierarchy.CurrentMember.Parent,
                          [Measures].[Ratio measure] )),
                    -- check division by zero
                    iif( ( Axis(1).Item(0)                           .Item([Measures].[Count of columns] -
                            [Measures].[Rightmost non root position])                           .Hierarchy.CurrentMember.Parent,
                           [Measures].[Ratio measure] ) = 0,
                           0,
                           [Measures].[Ratio measure]
                           /
                           ( Axis(1).Item(0)                             .Item([Measures].[Count of columns] -
                              [Measures].[Rightmost non root position])                             .Hierarchy.CurrentMember.Parent,
                             [Measures].[Ratio measure] ) )
                 )
            )
       ),
    FORMAT_STRING = "percent"
;

The first measure detects axis that has measures when using OWC.

The second measure is our ratio measure. That is, the measure we want to calculate the ratio for. I provided the syntax for several scenarios. The first one, of course, is the obvious and easiest one – using any measure we want and hard-coding it there. The second option is more general one – the use of cube’s default measure. Meaning, it could work for any cube. Finally, the third and the most complex option is to use the first measure on axis, whatever it might be. That’s even more general solution. In that scenario, it is up to an end-user to put a measure of his choice as the first measure and to see ratios based on that measure. It should work in any cube/report/query. The calculation features a handle for no measures at all (except that ratio measure) in which case the default measure is taken.

Next we test whether the original, ratio measure is empty. We’ll use the result of this in the following calculations, in order to preserve empty rows.

Count of columns gives us count of hierarchies being placed on an axis of interest (that is rows or columns, depending on where measures are not).

Next thing we do is generate a bitmap, and right next to it – a reversed bitmap. Innermost logical test returns either –1 or 0 (True or False), while minus in front of it turns -1 into 1. Looping is performed on a set of measures (which might be a week point – it is up to BI designer to provide something better in case there are only few measures). From which axis is bitmap formed? Depends on measures position in OWC. Additionally, in the reversed bitmap, the reversed order is obtained as it is usually being done in MDX – using a combination of two MDX functions: Count and CurrentOrdinal.

Why do we needed reversed bitmap? It becomes obvious once we come to the next calculated measure – Rightmost non root position. Analysis should be performed backwards, from right to left. That is the order in which we search patterns in bitmaps and therefore we needed reversed bitmap (string search is left based). This new measure returns us the position of the first zero value. In the table featuring 5 distinct cases, those positions are: 1, 2, 3, 2, 0.

Next measure is a Boolean type measure that detects a special case (see the table above) and that special case is 001 combination, where, per request, the value should be 100%.

Finally, we come to the last and the only visible measure – Universal Ratio %. There, the first thing we should do is test for emptiness of original ratio measure. Then only we handle the cases in our table. After covering cases with 100% result, based on where the measures are, we enter one branch and there test denominator for zero. Finally, we perform the ratio calculation. Only by now it is in utmost relative form, covering wide varieties of cases withonly one expression (notice the use of Rightmost non root position measure inside the innermost calculation). That’s the power and beauty of having and using bitmap indexes.

BENEFITS

It’s worth reminding again that the final formula looks complicated only because of two reasons: OWC is being used as a front-end and, there were special cases in the bitmap table. Without them, the calculation would come down to always necessary checks for emptiness and division by zero, following by the core ratio expression. In case you’re using a client that keeps measures on the axis you’ve dropped them on in your pivot, you can consider stripping down all unnecessary calculations or part of it, as mentioned in the beginning of this article.

I also made tests with real bitmaps. Meaning, I tried to use numbers, 2 powered to N, where N was the number of hierarchies on axis. Yet that turned out to be not only a dead-end (because the reverse operation is not easy), but also time consuming, prolonging the query time significantly. String operations on the other hand were very fast and manipulations with them very easy. Relatively, of course.

All in all, bitmaps and their power in being flexible pointers proved to be an interesting approach in providing universal MDX solutions, calculations that, did I mention it before, work in any cube.

Recently, I was asked to write a calculation that calculates the ratio to parent on rows that doesn’t depend on cube structure and that also works in OWC. The first part I managed to dig somewhere from the past, the second proved to be much more demanding task. Having bypassed several obstacles and spent significant portion of time on this subject, I decided to pass the knowledge in form of a blog article. Here’s the calculation:

CREATE MEMBER CURRENTCUBE.
[Measures].[Universal share percent for OWC in BIDS %] AS

   iif( IsError( Extract( Axis(0), Measures ).Item(0) ),
   iif( IsError( Extract( Axis(1), Measures ).Item(0) ),
   iif( Axis(1).Item(0).Item(
 Axis(1).Item(0).Count - 1
)
.Hierarchy.CurrentMember.Level.Ordinal = 0,
1,
Extract( Axis(2), Measures ).Item(0)
/
(
Axis(1).Item(0).Item(
Axis(1).Item(0).Count - 1
).Hierarchy.CurrentMember.Parent,
Extract( Axis(2), Measures ).Item(0)
)
),
iif( Axis(0).Item(0).Item(
Axis(0).Item(0).Count - 1
)
.Hierarchy.CurrentMember.Level.Ordinal = 0,
1,
Extract( Axis(1), Measures ).Item(0)
/
(
Axis(0).Item(0).Item(
Axis(0).Item(0).Count - 1
).Hierarchy.CurrentMember.Parent,
Extract( Axis(1), Measures ).Item(0)
)
)
),
iif( IsError( Axis(1).Item(0) ),
1,
iif( Axis(1).Item(0).Item(
Axis(1).Item(0).Count - 1
)
.Hierarchy.CurrentMember.Level.Ordinal = 0,
1,
Extract( Axis(0), Measures ).Item(0) /
(
Axis(1).Item(0).Item(
Axis(1).Item(0).Count - 1
).Hierarchy.CurrentMember.Parent,
Extract( Axis(0), Measures ).Item(0)
)
)
)
),FORMAT_STRING = "Percent",
VISIBLE = 1;

What’s good about it is that it can be used in any project.

I also enhanced it a bit, to support other clients/controls as well (SSMS included).

Finally, it can be used as a template for other calculations that use Axis() function and are intended to work in Cube Browser.

ATTENTION: The improved variant of the same calculation can be found in a more recent blog article here.

“I made a trojan in MDX script!”

Although I deliberately timed this post to be published on my blog on 1st of April, this is far from a joke. And that trojan is a good one, for the benefit of all, as you’ll see soon.

While preparing my presentation about the potential use of Axis() function in calculated measures, I came up to a very interesting discovery: I wrote an MDX expression that allows the use of Axis() function inside dynamic sets in MDX script! Since the use of Axis() function is not supported in dynamic sets, I named the expression Trojan horse for dynamic sets, because of how it tricks the engine and makes Axis() function pass through.

Lets say a few about dynamic sets. Their name suggest they are evaluated dynamically. Furthermore, MSDN definition says they are evaluated everytime they are used in a query. But all that is simply not so. They are actually less powerful (about what I just googled one post from Chris Webb) because they get evaluated only once, before evaluation of cells (where all the fun is usually happening).

Dynamic sets are evaluated much sooner in query execution phases – after (which means in the context of) slicer and subselect. And that brings us to a final conclusion. As opposed to static sets that are static all the time, dynamic sets are just fine-tuned according to slicer and subselect of a query, but are pretty much static when it comes to evaluation of cells on the intersection of axis. In short, they behave just like query defined sets. And I consider them static. Get the idea of problematic name?

I don’t know where I’ve read it, so I made a short search on the net in order to present some proof for that. The best article on that subject that I come upon in a relatively short time is one older post from Mosha (of course). Since I haven’t read it yet and it looks very related to the thing I’m about to show you, I’ll read it now in order not to repeat things here.

Ok, I read it. That thing about subselect is nice.

Now let’s get back to what I ment to present you.

While being active on MSDN SSAS forum, I came up to this thread, where Bryan C. Smith nicely pointed out to me that my advice about the use of Axis() function simply doesn’t hold since it’s not allowed in MDX script. I played with it for a while, but encountered some problems, so I quit and concured with him.

But, being persistant (not to say stubborn) as I am, I took another chance as soon as I saw the first opportunity for that, a time when I was deeply into that issue – preparing a session about Axis() function. And I succeeded! Yes!

If you need a reason for it, I mean, reason why I wanted to do it, just take a look at that thread – making dynamic sets evaluate according to a measure placed on the opposite axis. Isn’t that great possibility? I mean, people ask for it, yet it isn’t supported. So, what do we do? Wait for the next release, for the new Extra Dynamic Sets? Yeah, right.

Why not think of something magical and use it now. This same moment. Why wait? All we need is some kind of expression that will evaluate differently when in MDX script as opposed to query context. But how? What differs those two environment?

When query executes, there are axis. When MDX script is evaluated, we have default measure in context. And iif function is optimized in various program languages not to evaluate on both paths, for performance reasons. Could it be my gate for trojan? Can I somehow make a trojan horse in MDX script that will pass the Axis() function hidden inside various iifs or other constructs and at the same time trigger properly when in context of a query?

Yes! It can be done. Here it is.

Create Dynamic Set CurrentCube.[Query measures evaluated] As
— aka Trojan for Dynamic Sets
        iif(Measures.CurrentMember Is Measures.DefaultMember,
            iif(IsError(Axis(1).Count),
                iif(IsError(Axis(0).Count),
                    {Measures.CurrentMember},
                    iif(IsError(Extract(Axis(0), Measures).Count),
                        {Measures.CurrentMember},
                        Extract(Axis(0), Measures)
                        )
                   ),
                iif(IsError(Extract(Axis(1), Measures).Count),
                    {Measures.CurrentMember},
                    Extract(Axis(1), Measures)
                   )
               ),
            {Measures.CurrentMember}
           )
      , Display_Folder = ‘Universal dynamic sets’;

Although it referes to Axis() function, this dynamic set evaluates correctly inside MDX script, yet returns a set of measures that are relevant for the query being executed when triggered from that same query. What does that mean?

If the query doesn’t contain any measure, a default one is returned. If the query contains a measure on slicer, that measure is returned. If a query contains measure in subselect, (only) first measure inside is returned (a default for that subcube). Here’s a possibility for improvement, for eager ones. If a query contains measures on columns, they are returned. If the query contains measures on rows, they are returned. All in all, it collects measures from query, wherever they are.

How is it achieved?

First, let’s get one thing straight. Everything you write in MDX script of a cube needs to be evaluated and checked for errors before it is deployed. Meaning, if you naively reference Axis() inside it, withouth cloaking it properly, you’ll see an error that it is not allowed to use the Axis() function and you won’t be able to deploy. So we need to cloak it somehow. And here’s how.

When that expression is evaluated/checked in MDX script, the first condition (always) evaluates as False. That’s the main trick. Why? The CurrentMember doesn’t exist yet, it exists only in query! Which means that the whole expression results as an empty set ({Measures.CurrentMember} in False part evaluates to null set). SSAS engine doesn’t check the construct in True part (performance optimization, luckily for us) and treats it as a deterministic expression – an empty set. In other words, this {}.

Everything’s clean and fine. We’re in (whisper men in the horse)!

Now, we could have put anything that will evaluate to False in the first condition but we didn’t. We carefully constructed that condition, because we need it to evaluate differently once it is called from a query. CurrentMember is a valid expression in the context of query. On the other hand, current member might or might not be default member. And that means we got ourselves a perfect condition, the one that evaluates either as True or False when triggered from query (which is ok, our condition is therefore not static, but a dynamic, smart one) and the one that is always False (static, which is ok) when evaluated/checked inside MDX script for deployment.

If the set is evaluated in a query, then depending on where the measures are placed in that query, a different path will be chosen. The first condition will be True in most cases. Only in situations when there is some other measure, not a default one, placed in slicer or subselect it will also evaluate to False. How come? Remember that dynamic set is evaluated in context of slicer and subselect, so that first expression catches scenarios when we have something there. In case it is False, we will grab the current member. That means a measure in slicer or the first measure in subselect (since when you make a subselect, the first measure inside becomes a default one automatically for that subcube). And that is exactly what we need.

In other words, the first condition will evaluate as False and take that path only for MDX script evaluation AND for measure in slicer/subselect other than a default one. Two flies, one stroke!

In all other cases the first condition will evaluate as True which means we don’t have measures in slicer or subselect. If that is so, they might be on axis. We test Axis(1) first, then Axis(0). If by some chance there are no measures on either of axes (a query without measures was executed), default measure is implicitely in slicer and that is taken as currentmember.

If measures are on axis, they will be extracted carefully.

That’s basically the operating mode of this trojan.

The explaination above was corrected and enriched 8 hours after the initial post, after a revision and after my memory about all the tips and tricks concerning this issue was refreshed. The key parts that were changed are evaluation paths.

Now, typical dynamic set looks like this.

Create Dynamic Set CurrentCube.[Top 10 Products for slicer measure] As
        TopCount(
                 [Product].[Product].[Product].Members,
                 10,
                 Measures.CurrentMember
                )
      , Display_Folder = ‘My demo sets’; 

It operates only on slicer and subselect, as we stated before.

However, this new dynamic set, an improved version of previous example, uses the first measure in trojan no matter where it is (as long as it is not on the same axis – it can be on opposite axis or slicer/subselect).

 Create Dynamic Set CurrentCube.[Top 10 Products for first measure] As
        TopCount(
                 [Product].[Product].[Product].Members,
                 10,
                 [Query measures evaluated].Item(0).Item(0)
                )
      , Display_Folder = ‘My demo sets’; 

And finally, in order to test all this, you would need to add those definitions into your Adventure Works 2008 database (in the end of MDX script), and fire the following queries (or your variants of it).

SELECT
NON EMPTY
    {
        [Measures].CurrentMember
    }
ON AXIS(0),
    NON EMPTY
    {
        [Top 10 Products for first measure]
    }
ON AXIS(1)
FROM
    [Adventure Works]

SELECT
NON EMPTY
    {
        [Measures].[Order Quantity],
        [Measures].[Reseller Sales Amount]
    }
ON AXIS(0),
    NON EMPTY
    {
        [Top 10 Products for first measure]
    }
ON AXIS(1)
FROM 
    [Adventure Works]

SELECT
NON EMPTY
    {
        [Measures].[Reseller Sales Amount],
        [Measures].[Order Quantity]
    }
ON AXIS(0),
    NON EMPTY
    {
        [Top 10 Products for first measure]
    }
ON AXIS(1)
FROM 
    [Adventure Works]

SELECT
NON EMPTY
    {
        [Measures].CurrentMember
    }
ON AXIS(0),
    NON EMPTY
    {
        [Top 10 Products for first measure]
    }
ON AXIS(1)
FROM
   (SELECT [Measures].[Order Quantity] ON 0 FROM [Adventure Works])

SELECT
NON EMPTY
    {
        [Date].[Calendar].[All Periods]
    }
ON AXIS(0),
    NON EMPTY
    {
        [Top 10 Products for first measure]
    }
ON AXIS(1)
FROM
    [Adventure Works]
WHERE
    ([Measures].[Order Quantity])

In case you have any doubts about results, feel free to make another query, the one where you’ll precisely write what do you want, so that you can verify whether Top 10 Products dynamic set calculates correctly or not.

Once you cast your fears aside, feel free to use it in any of your projects in case you need it.

Oh, one more thing. Excel 2007 and OWC are immune to it, they can not profit from this discovery. Only those OLAP clients/tools that generate clean MDX (no fancy stuff in subselect) and respect sets in general as a valid and powerful entity in OLAP (or let you at least edit the MDX if nothing else) are candidates for exploiting this trick. MDX Studio and CubePlayer are some of them known (and available) to me. Any information about other front-ends/tools?

More advanced MDX stuff coming soon :-).

Few months ago, while on vacation, I saw an interesting post on MSDN forum where a user asked for rank of members placed on rows, irrespective of hierarchy. Furthermore, that was supposed to be achieved using only one calculated measure, nothing else. Intrigued by this puzzle, I made an example of such calculated measure on Adventure Works database using Axis() function. Here it is:

WITH
MEMBER [Measures].[Sales Amount Rank] AS
     iif(
         IsEmpty([Measures].[Sales Amount]),
         null,
         Rank(
              Axis(1).Item(0).Item(Axis(1).Item(0).Count – 1
                                  ).Hierarchy.CurrentMember,
              Order(
                    Extract(
                            Axis(1),
                            Axis(1).Item(0).Item(
                                            Axis(1).Item(0).Count – 1
                                                ).Hierarchy
                           ),
                   [Measures].[Sales Amount],
                    BDESC
                   )
             )
        )
SELECT
{
    [Measures].[Sales Amount],
    [Measures].[Sales Amount Rank]
}
ON AXIS(0),
NON EMPTY
    [Product].[Category].[Category].MEMBERS *
    [Sales Territory].[Sales Territory Country].
                      [Sales Territory Country].MEMBERS
ON AXIS(1)
FROM
    [Adventure Works] 

Here’s how it works.

We should test for empty values first. Empty values of the measure on which we do ranking (Sales Amount in this example). This is done in order not to influence the original result, the one without the rank measure. Why? Because Rank() function returns numbers, never nulls. Normally, NON EMPTY serves to filter rows for which Sales Amount in the above example is null.  If we introduce the second measure that is never null, those rows will suddenly appear too. And this is not a wanted behavior.

Rank is made by using current member of the last hierarchy on rows, as requested. Ordered set is made by extracting that hierarchy and ordering its members by measure Sales Amount. The trick is that Order() function returns a different set of members for each row. In other words, current context (tuple) influences ordering of members. On each Category (first hierarchy), another ordered set of Countries (last hierarchy) might appear, because countries will be ordered per current product category. The same would work for any number of hierarchies on rows.

Recently, I was asked to make it even more universal (general) in a way to avoid ranking of members from different hierarchy levels at the same time. Meaning, if we place .ALLMEMBER, we don’t want [All] member to be ranked as 1, while all the others as second, third, and so on.

Another puzzle, another solution. This time I named it Goldfish Rank since it fulfills any wishes you might have about ranking in general. Here it is:

WITH
MEMBER [Measures].[Goldfish Rank] AS
    iif(
        IsEmpty(Axis(0).Item(0).Item(0))
        — making it absolutely general
        — using first measure on columns

        /*
        — un-comment this block if you want to get rank
        — only for lowest level members in you last column
        OR
        Axis(1).Item(0).Item(Axis(1).Item(0).Count – 1
                            ).Hierarchy.CurrentMember.Level.Ordinal <
        Max(
            Extract(
                    Axis(1),
                    Axis(1).Item(0).Item( Axis(1).Item(0).Count – 1
                                        ).Hierarchy
                   ),
            Axis(1).Item(0).Item(Axis(1).Item(0).Count – 1
                                ).Hierarchy.CurrentMember.Level.Ordinal
           )
        */
        ,
        null,

        Rank(
             Axis(1).Item(0).Item(Axis(1).Item(0).Count – 1
                                 ).Hierarchy.CurrentMember,
             Intersect(
                       Order(
                             Extract(
                                     Axis(1),
                                     Axis(1).Item(0).Item(
                                             Axis(1).Item(0).Count – 1
                                                         ).Hierarchy
                                    ),
                             Axis(0).Item(0).Item(0),
                             — making it absolutely general
                             DESC
                             — BDESC would be redundant,
                             — since we work per level
                            ),
                       iif(
                           Axis(1).Item(0).Item(
                                                Axis(1).Item(0).Count – 1
                                               ).Hierarchy.CurrentMember
                                                .Level.Ordinal = 0,
                           Axis(1).Item(0).Item(
                                                Axis(1).Item(0).Count – 1
                                               ).Hierarchy.CurrentMember,
                           NonEmpty(
                                    Axis(1).Item(0).Item(
                                            Axis(1).Item(0).Count – 1
                                                        ).Hierarchy.CurrentMember
                                                         .SIBLINGS,
                                  { Axis(0).Item(0).Item(0) }
                                    — making it absolutely fast
                                   )
                          )
                       */

                       — /*
                       — this is the second block, referred above
                       — comment NonEmpty() function
                       — if you un-comment the block above
                       NonEmpty(
                                Axis(1).Item(0).Item(
                                                Axis(1).Item(0).Count – 1
                                                    ).Hierarchy.CurrentMember
                                                     .Level.MEMBERS,
                              { Axis(0).Item(0).Item(0) }
                                — making it absolutely fast
                               )
                       — end of second block
                       — */

                      )
            )
       )
SELECT
{
    [Measures].[Sales Amount],
    [Measures].[Goldfish Rank]
}
ON AXIS(0),
NON EMPTY
{
    [Product].[Category].ALLMEMBERS
    * [Sales Territory].[Sales Territory].ALLMEMBERS
}
    — un-comment lower part and comment the line above
    — if you find it difficult to compare results
    — when the last column is hierarchized
    — and when applying rank on level members, not siblings
/*
*
{
    [Sales Territory].[All],
    [Sales Territory].[Group].MEMBERS,
    [Sales Territory].[Country].MEMBERS,
    [Sales Territory].[Region].MEMBERS
}
*/
ON AXIS(1)
FROM
    [Adventure Works] 

This query has [All] members on rows. From both hierarchies. That serves for testing purposes of newly created calculated measure for rank.

Calculated measure used in previous example was enhanced in a way that it sorts only members that have the same level (or parent) as current one (current member from the last hierarchy). This is achieved using Intersect() function. Members on each level (or siblings, depends on the switch you make with blocks of code) will be ranked only according to equal to themselves. By the term equal, I assume those from the same level (or of the same parent). Metaphorically, having the same chance to be ranked as 1.

Second argument of Intersect() function should have been simple .MEMBERS from particular level (or .SIBLINGS), but that was optimized using NonEmpty() function and the same measure we rank by. Optimization means we reduce potentially large set of members by applying NonEmpty() function on them, so that only those having result for that measure will survive.

Goldfish Rank has several options how to deal with higher levels.

     

First commented block enables user to rank only on lowest level members, while providing nulls for the rest. The second block enables user to avoid ranking the [All] member, since it will most probably always have rank 1. And finally, if you find it hard to match members from different levels in the example above, I provided commented block of several levels for the second user hierarchy on axis 1. This way results will not be hierarchized, so it will be easier for you to compare them and see them in action.

Another way of ranking is to rank among siblings. For that purpose, I provided a commented block inside Intersect() function. Using that instead of the block below (un-commented) will give us results as in right picture.

While there can be other variations of ranking, I assume the code above will suffice as a template for each of those variations. If you encounter any problems during that, remember to ask the Goldfish!

In the end, it’s worth saying that the forum user’s wish was fulfilled.

– If you like this post, be sure to drop by occasionally, since there will be more interesting MDX queries in the days to come.