MTRIL
Updated: 31 January 2012
Use the scalar function MTRIL to return the lower triangular part of the string representation of a matrix.
MTRIL expects a string representation of the matrix, with columns separated by commas and rows separated by semi-colons.
Syntax
SELECT [wctMath].[wct].[MTRIL](
<@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 lower triangular part.
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.MTRIL(@A) as [L]
This produces the following result.
L
------------------------------------------------------------------------------
79,0,0,0,0,0;68,46,0,0,0,0;83,-25,80,0,0,0;77,40,-24,69,0,0;-17,-72,-9,-72,-6,0;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
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
FROM wctString.wct.SPLIT(';',(SELECT wct.MTRIL(@A))) l
This produces the following result:
L
-----------------------------------------
-79,0,0,0,0,0
68,46,0,0,0,0
83,-25,80,0,0,0
77,40,-24,69,0,0
-17,-72,-9,-72,-6,0
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
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.MTRIL(@A))) l
This produces the following result.
RowNum ColNum ItemValue
----------- ----------- ----------------------
0 0 -79
0 1 0
0 2 0
0 3 0
0 4 0
0 5 0
1 0 68
1 1 46
1 2 0
1 3 0
1 4 0
1 5 0
2 0 83
2 1 -25
2 2 80
2 3 0
2 4 0
2 5 0
3 0 77
3 1 40
3 2 -24
3 3 69
3 4 0
3 5 0
4 0 -17
4 1 -72
4 2 -9
4 3 -72
4 4 -6
4 5 0
5 0 64
5 1 -47
5 2 48
5 3 -54
5 4 18
5 5 11
6 0 -4
6 1 -36
6 2 7
6 3 -56
6 4 -34
6 5 -3
7 0 -41
7 1 90
7 2 78
7 3 -43
7 4 38
7 5 64
8 0 -60
8 1 -85
8 2 -31
8 3 -83
8 4 -96
8 5 -36
9 0 -40
9 1 31
9 2 -93
9 3 -62
9 4 64
9 5 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]
FROM (
SELECT *
FROM wct.MATRIX((SELECT wct.MTRIL(@A)))
) M PIVOT(
MAX(ItemValue)
FOR colnum IN([0],[1],[2],[3],[4],[5])
) 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 MTRIL 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]
FROM (
SELECT *
FROM wct.MATRIX((SELECT wct.MTRIL(wct.MATRIX2STRING('#m','*','',NULL))))
) M PIVOT(
MAX(ItemValue)
FOR colnum IN([0],[1],[2],[3],[4],[5])
) AS pvt
ORDER BY rownum
This produces the following result.
