Power BI: Working with Visual Calculations (Part II: Simple Tables with Square Numbers as Example)

Introduction

The records behind a visual can be mentally represented as a matrix, the visual calculations allowing to tap into this structure intuitively and simplify many of the visualizations used. After a general test drive of the functionality, it makes sense to dive deeper into the topic to understand more about the limitations, functions behavior and what it takes to fill the gaps. This post focuses on simple tables, following in a next post to focus on matrices and a few other topics. 

For exemplification, it makes sense to use a simple set of small numbers that are easy to work with, and magic squares seem to match this profile. A magic square is a matrix of positive sequential numbers in which each row, each column, and both main diagonals are the same [1]. Thus, a square of order N has N*N numbers from 1 to N*N, the non-trivial case being order 3. However, from the case of non-trivial squares, the one of order 5 provides a low order and allows hopefully the minimum needed for exemplification:

18	25	2	9	11
4	6	13	20	22
15	17	24	1	8
21	3	10	12	19
7	14	16	23	5
1	7	13	19	25

Data Modeling

One magic square should be enough to exemplify the various operations, though for testing purposes it makes sense to have a few more squares readily available. Each square has an [Id], [C1] to [C5] corresponds to matrix's columns, while [R] stores a row identifier which allows to sort the values the way they are stored in the matrix:

let
    Source = #table({"Id","C1","C2","C3","C4","C5","R"}
, {
{1,18,25,2,9,11,"R1"},
{1,4,6,13,20,22,"R2"},
{1,15,17,24,1,8,"R3"},
{1,21,3,10,12,19,"R4"},
{1,7,14,16,23,5,"R5"},
{2,1,7,13,19,25,"R1"},
{2,14,20,21,2,5,"R2"},
{2,22,3,9,15,16,"R3"},
{2,10,11,17,23,4,"R4"},
{2,18,24,5,6,12,"R5"},
{3,1,2,22,25,15,"R1"},
{3,9,10,16,11,19,"R2"},
{3,17,23,13,5,7,"R3"},
{3,24,12,6,20,3,"R4"},
{3,14,18,8,4,21,"R5"},
{4,22,6,3,18,16,"R1"},
{4,4,14,11,15,21,"R2"},
{4,5,8,12,23,17,"R3"},
{4,25,13,19,7,1,"R4"},
{4,9,24,20,2,10,"R5"},
{5,5,9,20,25,6,"R1"},
{5,13,15,2,11,24,"R2"},
{5,21,1,23,3,17,"R3"},
{5,19,18,4,14,10,"R4"},
{5,7,22,16,12,8,"R5"}
}
),
    #"Changed Type to Number" = Table.TransformColumnTypes(Source,{{"C1", Int64.Type}, {"C2", Int64.Type}, {"C3", Int64.Type}, {"C4", Int64.Type}, {"C5", Int64.Type}}),
    #"Sorted Rows" = Table.Sort(#"Changed Type to Number",{{"Id", Order.Ascending}, {"R", Order.Ascending}}),
    #"Added Index" = Table.AddIndexColumn(#"Sorted Rows", "Index", 0, 1, Int64.Type)
in
    #"Added Index"

The column names and the row identifier could have been numeric values from 1 to 5, though it could have been confounded with the actual numeric values.

In addition, the columns [C1] to [C5] were formatted as integers and an index was added after sorting the values after [Id] and [R]. Copy the above code as a Blank Query in Power BI and change the name to Magic5. 

Prerequisites

For the further steps you'll need to enable visual calculations in Power BI Developer via:
File >> Options and settings >> Options >> Preview features >> Visual calculations >> (check)

Into a Table visual drag and drop [R], [C1] to [C5] as column and make sure that the records are sorted ascending by [R]. To select only a square, add a filter based on the [Id] and select the first square. Use further copies of this visual for further tests. 

Some basic notions of Algebra are recommended but not a must. If you worked with formulas in Excel, then you are set to go. 

In Mathematics a matrix starts from the top left side and one moves on the rows (e.g. 18, 25, 2, ...) and then on the columns. With a few exceptions in which the reference is based on the latest value from a series (see Exchange rates), this is the direction that will be followed. 

Basic Operations

Same as in Excel [C1] + [C2] creates a third column in the matrix that stores the sum of the two. The sum can be further applies to all the columns:

Sum(C) = [C1] + [C2] + [C3] + [C4] + [C5] -- sum of all columns (should amount to 65)

The column can be called "Sum", "Sum(C)" or any other allowed unique name, though the names should be meaningful, useful, and succinct, when possible.

Similarly, one can work with constants, linear or nonlinear transformations (each formula is a distinct calculation):

constant = 1 -- constant value
linear = 2*[C1] + 1 -- linear translation: 2*x+1

linear2 = 2*[C1] + [constant] -- linear translation: 2*x+1
quadratic = Power([C1],2) + 2*[C1] + 1 -- quadratic translation: x^2+2*x+1
quadratic2 = Power([C1],2) + [linear] -- quadratic translation: x^2+2*x+1

Output:

R	C1	constant	linear	linear2	quadratic	quadratic2
R1	18	1	37	37	361	361
R2	4	1	9	9	25	25
R3	15	1	31	31	256	256
R4	21	1	43	43	484	484
R5	7	1	15	15	64	64

Please note that the output was duplicated in Excel (instead of making screenshots).

Similarly, can be build any type of formulas based on one or more columns.

With a simple trick, one can use DAX functions like SUMX, PRODUCTX, MINX or MAXX as well:

Sum2(C) = SUMX({[C1], [C2], [C3], [C4], [C5]}, [Value]) -- sum of all columns

Prod(C) = PRODUCTX({[C1], [C2], [C3], [C4], [C5]}, [Value]) -- product of all columns

Avg(C) = AVERAGEX({[C1], [C2], [C3], [C4], [C5]}, [Value]) -- average of all columns

Min(C) = MINX({[C1], [C2], [C3], [C4], [C5]}, [Value]) -- minimum value of all columns

Max(C) = MAXX({[C1], [C2], [C3], [C4], [C5]}, [Value]) -- maximum value of all columns
Count(C) = COUNTX({[C1], [C2], [C3], [C4], [C5]},[Value]) -- counts the number of columns

Output:

C1	C2	C3	C4	C5	Sum(C)	Avg(C)	Prod(C)	Min(C)	Max(C)	Count(C)
18	25	2	9	11	65	13	89100	2	25	5
4	6	13	20	22	65	13	137280	4	22	5
15	17	24	1	8	65	13	48960	1	24	5
21	3	10	12	19	65	13	143640	3	21	5
7	14	16	23	5	65	13	180320	5	23	5

Unfortunately, currently there seems to be no way available for applying such calculations without referencing the individual columns. 

Working across Rows

ROWNUMBER and RANK allow to rank a cell within a column independently, respectively dependently of its value:

Ranking = ROWNUMBER() -- returns the rank in the column (independently of the value)
RankA(C) = RANK(DENSE, ORDERBY([C1], ASC)) -- ranking of the value (ascending) 

RankD(C) = RANK(DENSE, ORDERBY([C1], DESC)) -- ranking of the value (descending) 

Output:

R	C1	Ranking	RankA(C)	RankD(C)
R1	18	1	4	2
R2	4	2	1	5
R3	15	3	3	3
R4	21	4	5	1
R5	7	5	2	4

PREVIOUS, NEXT, LAST and FIRST allow to refer to the values of other cells within the same column:

Prev(C) = PREVIOUS([C1]) -- previous cell
Next(C) = NEXT([C1])  -- next cell

First(C) = FIRST([C1]) -- first cell
Last(C) = LAST([C1]) -- last cell

Output:

R	C1	Prev(C)	NextC)	First(C)	Last(C)
R1	18		4	18	7
R2	4	18	15	18	7
R3	15	4	21	18	7
R4	21	15	7	18	7
R5	7	21		18	7

OFFSET is a generalization of these functions

offset(2) = calculate([C1], offset(2)) -- 
offset(-2) = calculate([C1], offset(-2))
Ind = ROWNUMBER() -- index
inverse = calculate([C1], offset(6-2*[Ind])) -- inversing the values based on index

Output:

R	C1	offset(2)	offset(-2)	ind	inverse
R1	18	15		1	7
R2	4	21		2	21
R3	15	7	18	3	15
R4	21		4	4	4
R5	7		15	5	18

The same functions allow to calculate the differences for consecutive values:

DiffToPrev(C) = [C1] - PREVIOUS([C1]) -- difference to previous 
DiffToNext(C) = [C1] - PREVIOUS([C1]) -- difference to next 
DiffTtoFirst(C) = [C1] - FIRST([C1]) -- difference to first
DiffToLast(C) = [C1] - LAST([C1]) -- difference to last

Output:

R	C1	DiffToPrev(C)	DiffToNextC)	DiffToFirst(C)	DiffToLast(C)
R1	18	18	14	0	11
R2	4	-14	-11	-14	-3
R3	15	11	-6	-3	8
R4	21	6	14	3	14
R5	7	-14	7	-11	0

DAX makes available several functions for working across the rows of the same column. Two of the useful functions are RUNNINGSUM and MOVINGAVERAGE:

Run Sum(C) = RUNNINGSUM([C1]) -- running sum

Moving Avg3(C) = MOVINGAVERAGE([C1], 3) -- moving average for the past 3 values

Moving Avg2(C) = MOVINGAVERAGE([C1], 2) -- moving average for the past 2 values

Unfortunately, one can use only the default sorting of the table with the functions that don't support the ORDERBY parameter. Therefore, when the table needs to be sorted descending and the RUNNINGSUM calculated ascending, for the moment there's no solution to achieve this behavior. However, it appears that Microsoft is planning to implement a solution for this issue.

RUNNINGSUM together with ROWNUMBER can be used to calculate a running average:

Run Avg(C) = DIVIDE(RUNNINGSUM([C1]), ROWNUMBER()) -- running average

Output:

R	C1	Run Sum(C)	Moving Avg3(C)	Moving Avg2(C)	Run Avg(C)
R1	18	18	18	18	18
R2	4	22	11	11	11
R3	15	37	12.33	9.5	12.33
R4	21	58	13.33	18	14.5
R5	7	65	14.33	14	13

With a mathematical trick that allows to transform a product into a sum of elements by applying the Exp (exponential) and Log (logarithm) functions (see the solution in SQL), one can run the PRODUCT across rows, though the values must be small enough to allow their multiplication without running into issues:

Ln(C) = IFERROR(LN([C1]), Blank()) -- applying the natural logarithm
Sum(Ln(C)) = RUNNINGSUM([Ln(C)]) -- running sum
Run Prod(C) = IF(NOT(ISBLANK([Sum(Ln(C))])), Exp([Sum(Ln(C))])) -- product across rows

Output:

R	C1	Ln(C)	Sum(Ln(C))	Run Prod(C)
R1	18	2.89	2.89	18
R2	4	1.39	4.28	72
R3	15	2.71	6.98	1080
R4	21	3.04	10.03	22680
R5	7	1.95	11.98	158760

These three calculations could be brought into a single formula, though the result could be more difficult to troubleshoot. The test via IsBlank is necessary because otherwise the exponential for the total raises an error. 

Considering that when traversing a column it's enough to remember the previous value, one can build MIN and MAX functionality across a column: 

Run Min = IF(OR(Previous([C1]) > [C1], IsBlank(Previous([C1]))), [C1], Previous([C1])) -- minimum value across rows
Run Max = IF(OR(Previous([C1]) < [C1], IsBlank(Previous([C1]))), [C1], Previous([C1])) -- maximum across rows

Happy coding!

Previous Post <<||>> Next Post

References:
[1] Wikipedia (2024) Magic Squares (online)
[2] Microsoft Learn (2024) Power BI: Using visual calculations [preview] (link)

Power BI: Working with Visual Calculations (Part I: Test Drive) [new feature]

Introduction

I recently watched a webcast with Jeroen (Jay) ter Heerdt (see [2]) in which he introduces visual calculations, a type of DAX calculation that's defined and executed directly on a visual [1]. Visual calculations provide an approach of treating a set of data much like an Excel table, allowing to refer to any field available on a visual and write formulas, which simplifies considerably the solutions used currently for ranking records, running averages and other windowing functions. 

The records behind a visual can be mentally represented as a matrix, while the visual calculations can refer to any column from the matrix, allowing to add new columns and include the respective columns in further calculations. Moreover, if a column is used in a formula, it's not recalculated as is the case of measures, which should improve the performance of DAX formulas considerably. 

Currently, one can copy a formula between visuals and if the formula contains fields not available in the targeted visual, they are added as well. Conversely, it's possible to build such a visual, copy it and then replace the dimension on which the analysis is made (e.g. Customer with Product), without being needed to make further changes. Unfortunately, there are also downsides: (1) the calculations are visible only within the visual in which were defined; (2) currently, the visual's data can't be exported if a visual calculation is added; (3) no formatting is supported, etc.

Ranking and Differences

I started to build a solution based on publicly available sales data, which offers a good basis for testing the use of visual calculations. Based on a Power BI visual table made of [Customer Name], [Sales Amount], [Revenue] and [Total Discount], I've added several calculations:

-- percentages
Sales % = 100*DIVIDE([Sales Amount], COLLAPSE([Sales Amount], ROWS))
Revenue % = 100*DIVIDE([Revenue],[Sales Amount])
Discount % = 100*DIVIDE([Total  Discount], [Total  Discount]+[Sales Amount])

-- rankings 
Rank Sales = Rank(DENSE, ORDERBY([Sales Amount], DESC))
Rank Revenue = Rank(DENSE, ORDERBY([Revenue], DESC))

-- differences between consecutive values
Diff. to Prev. Sales = IF([Rank Sales]>1, INDEX([Rank Sales]-1, , ORDERBY([Sales Amount], DESC)) - [Sales Amount] , BLANK())
Diff. to Prev. Rev. = IF([Rank Revenue]>1, INDEX([Rank Revenue]-1, , ORDERBY([Revenue], DESC)) - [Revenue] , BLANK())

Here's the output considered only for the first 10 records sorted by [Sales Amount]:

Customer Name	Sales Amount	Sales %	Revenue	Revenue %	Total Discount	Discount %	Rank Sales	Diff. to Prev. Sales.	Rank Rev.	Diff. to Prev. Rev.
Medline	1058923.78	3.76	307761.99	3.75	126601.02	10.68	1		1
Ei	707663.21	2.51	229866.98	2.8	95124.09	11.85	2	351260.57	2	77895.01
Elorac, Corp	702911.91	2.49	209078.76	2.55	83192.39	10.58	3	4751.3	6	20788.22
Sundial	694918.98	2.47	213362.1	2.6	78401.72	10.14	4	7992.93	4	-4283.34
OUR Ltd	691687.4	2.45	196396.26	2.4	78732.2	10.22	5	3231.58	10	16965.84
Eminence Corp	681612.78	2.42	213002.78	2.6	86904.03	11.31	6	10074.62	5	-16606.52
Apotheca, Ltd	667283.99	2.37	157435.56	1.92	101453.91	13.2	7	14328.79	31	55567.22
Rochester Ltd	662943.9	2.35	224918.2	2.74	81158.11	10.91	8	4340.09	3	-67482.64
ETUDE Ltd	658370.48	2.34	205432.79	2.51	89322.72	11.95	9	4573.42	9	19485.41
Llorens Ltd	646779.31	2.29	206567.4	2.52	82897.59	11.36	10	11591.17	8	-1134.61

Comments:
1) One could use [Total Amount] = [Total  Discount]+[Sales Amount] as a separate column.
2) The [Rank Sales] is different from the [Rank Rev.] because of the discount applied.
3) In the last two formulas a blank was considered for the first item from the ranking.
4) It's not possible to control when the totals should be displayed, however one can change the color for the not needed total to match the background.

Visualizing Differences 

Once the formulas are added, one can hide the basis columns and visualize the data as needed. To obtain the below chart I copied the visual and changed the column as follows:

Diff. to Prev. Rev. = IF([Rank Revenue]>1, [Revenue]- INDEX([Rank Revenue]-1, , ORDERBY([Revenue], DESC)) , [Revenue]) -- modified column

Comments:

1) Instead of showing the full revenue, the chart shows only the differences from the highest revenue, where the column in green is the highest revenue, while the columns in red are the differences of the current customer's revenue to the previous customer, as the data are sorted by the highest revenue. At least in this case it results in a lower data-ink ratio (see Tufte).

2) The values are sorted by the [Revenue] descending. 

3) Unfortunately, it's not possible to change the names from the legend.

Simple Moving Averages (SMAs)

Based on the [Sales Amount], [Revenue] and [Month] one can add the following DAX formulas to the table for calculating the SMA:

Sales Amount (SMA) = MOVINGAVERAGE([Sales Amount],6)
Revenue (SMA) = MOVINGAVERAGE([Revenue],6)

The chart becomes:

Comments:

1) Unfortunately, the formula can't project the values into the feature, at least not without the proper dates.
2) "Show items with not data" feature seems to be disabled when visual calculations are used.

3) The SMA was created via a template formula. Similarly, calculating a running sum is reduced to applying a formula:

Running Sales Amount = RUNNINGSUM([Sales Amount])

Wrap Up

It's easier to start with a table for the visual, construct the needed formulas and then use the proper visual while eliminating the not needed fields. 

The feature is still in public preview and changes can still occur. Unfortunately, there's still no information available on the general availability date. From the first tests, it provides considerable power with a minimum of effort, which is great! I don't want to think how long I would have needed to obtain the same results without it!

Happy coding!

Previous Post <<||>> Next Post

References: 
[1] Microsoft Learn (2024) Power BI: Using visual calculations [preview] (link)
[2] SSBI Central (2024) Visual Calculations - Making DAX easier, with Jeroen ter Heerdt (link)