TRANSPOSE
Updated: 31 January 2012
Use the scalar function TRANSPOSE to return the transposed matrix.
TRANSPOSE expects a string representation of the matrix, with columns separated by commas and rows separated by semi-colons.
Syntax
SELECT [wctMath].[wct].[TRANSPOSE](
<@Matrix, nvarchar(max),>)
Arguments
@Matrix
a string representation of a matrix.
Return Types
[nvarchar](max)
Remarks
· The string representations of @Matrix must only contain numbers, commas (to separate the columns), and semi-colons to separate the rows.
· Consecutive commas will generate an error.
· Consecutive semi-colons will generate an error.
· Non-numeric data between commas will generate an error
· Non-number data between semi-colons will generate an error
· To convert non-normalized data to a string format, use the Matrix2String or the Matrix2String_q function.
· To convert normalized data to a string format, use the NMatrix2String or the NMatrix2String_q function.
Examples
Let’s assume that we had the following matrix, A, and we want to return the transposed matrix A’.
A = [-79,-45,9,9,-91,-5;68,46,9,81,-61,35;83,-25,80,-67,-22,-38;77,40,-24,69,73,-20;-17,-72,-9,-72,-6,-34;64,-47,48,-54,18,11;-4,-36,7,-56,-34,-3;-41,90,78,-43,38,64;-60,-85,-31,-83,-96,-36;-40,31,-93,-62,64,10]
We could enter the following SQL to perform the calculation.
DECLARE @A as varchar(max)
SET @A = '-79,-45,9,9,-91,-5;68,46,9,81,-61,35;83,-25,80,-67,-22,-38;77,40,-24,69,73,-20;-17,-72,-9,-72,-6,-34;64,-47,48,-54,18,11;-4,-36,7,-56,-34,-3;-41,90,78,-43,38,64;-60,-85,-31,-83,-96,-36;-40,31,-93,-62,64,10'
SELECT wct.TRANSPOSE(@A) as [A']
This produces the following result.
A'
-----------------------------------------------------------------------------
-79,68,83,77,-17,64,-4,-41,-60,-40;-45,46,-25,40,-72,-47,-36,90,-85,31;9,9,80,-24,-9,48,7,78,-31,-93;9,81,-67,69,-72,-54,-56,-43,-83,-62;-91,-61,-22,73,-6,18,-34,38,-96,64;-5,35,-38,-20,-34,11,-3,64,-36,10
Of course, this is a little hard to read. Since the result is a string, we can reformat the solution to make it easier to read. Simply by changing the SELECT statement:
SELECT l.StringSegment as [A']
FROM wctString.wct.SPLIT(';',(SELECT wct.TRANSPOSE(@A))) l
This produces the following result:
A'
------------------------------------
-79,68,83,77,-17,64,-4,-41,-60,-40
-45,46,-25,40,-72,-47,-36,90,-85,31
9,9,80,-24,-9,48,7,78,-31,-93
9,81,-67,69,-72,-54,-56,-43,-83,-62
-91,-61,-22,73,-6,18,-34,38,-96,64
-5,35,-38,-20,-34,11,-3,64,-36,10
Which is a little bit easier to follow
However, we can use the table-valued function MATRIX, to format the result in third-normal form where it is even easier to see the output.
SELECT *
FROM wct.MATRIX((SELECT wct.TRANSPOSE(@A))) l
This produces the following result.
RowNum ColNum ItemValue
----------- ----------- ----------------------
0 0 -79
0 1 68
0 2 83
0 3 77
0 4 -17
0 5 64
0 6 -4
0 7 -41
0 8 -60
0 9 -40
1 0 -45
1 1 46
1 2 -25
1 3 40
1 4 -72
1 5 -47
1 6 -36
1 7 90
1 8 -85
1 9 31
2 0 9
2 1 9
2 2 80
2 3 -24
2 4 -9
2 5 48
2 6 7
2 7 78
2 8 -31
2 9 -93
3 0 9
3 1 81
3 2 -67
3 3 69
3 4 -72
3 5 -54
3 6 -56
3 7 -43
3 8 -83
3 9 -62
4 0 -91
4 1 -61
4 2 -22
4 3 73
4 4 -6
4 5 18
4 6 -34
4 7 38
4 8 -96
4 9 64
5 0 -5
5 1 35
5 2 -38
5 3 -20
5 4 -34
5 5 11
5 6 -3
5 7 64
5 8 -36
5 9 10
And, if we wanted to see the result in a row/column presentation, we could use the following SQL.
SELECT [0],[1],[2],[3],[4],[5],[6],[7],[8],[9]
FROM (
SELECT *
FROM wct.MATRIX((SELECT wct.TRANSPOSE(@A)))
) M PIVOT(
MAX(ItemValue)
FOR colnum IN([0],[1],[2],[3],[4],[5],[6],[7],[8],[9])
) AS pvt
ORDER BY rownum
This produces the following result.
The matrix does not have to be assigned to a variable before passed into the TRANSPOSE function; the string can be passed in directly.
SELECT [0],[1],[2],[3],[4],[5],[6],[7],[8],[9]
FROM (
SELECT *
FROM wct.MATRIX((SELECT wct.TRANSPOSE('-79,-45,9,9,-91,-5;68,46,9,81,-61,35;83,-25,80,-67,-22,-38;77,40,-24,69,73,-20;-17,-72,-9,-72,-6,-34;64,-47,48,-54,18,11;-4,-36,7,-56,-34,-3;-41,90,78,-43,38,64;-60,-85,-31,-83,-96,-36;-40,31,-93,-62,64,10')))
) M PIVOT(
MAX(ItemValue)
FOR colnum IN([0],[1],[2],[3],[4],[5],[6],[7],[8],[9])
) AS pvt
ORDER BY rownum
This produces the following result.
In this example, we insert the matrix values into a table, #m, which is in ‘spreadsheet’ format, and we use the MATRIX2SRTING function to convert the table values into a string format to be used by the TRANSPOSE function.
SELECT *
INTO #m
FROM (
SELECT -79,-45, 9, 9,-91, -5 UNION ALL
SELECT 68, 46, 9, 81,-61, 35 UNION ALL
SELECT 83,-25, 80,-67,-22,-38 UNION ALL
SELECT 77, 40,-24, 69, 73,-20 UNION ALL
SELECT -17,-72, -9,-72, -6,-34 UNION ALL
SELECT 64,-47, 48,-54, 18, 11 UNION ALL
SELECT -4,-36, 7,-56,-34, -3 UNION ALL
SELECT -41, 90, 78,-43, 38, 64 UNION ALL
SELECT -60,-85,-31,-83,-96,-36 UNION ALL
SELECT -40, 31,-93,-62, 64, 10
) n(x0,x1,x2,x3,x4,x5)
SELECT [0],[1],[2],[3],[4],[5],[6],[7],[8],[9]
FROM (
SELECT *
FROM wct.MATRIX((SELECT wct.TRANSPOSE(wct.MATRIX2STRING('#m','*','',NULL))))
) M PIVOT(
MAX(ItemValue)
FOR colnum IN([0],[1],[2],[3],[4],[5],[6],[7],[8],[9])
) AS pvt
ORDER BY rownum
This produces the following result.