MTRIU

Updated 2023-10-17 14:41:18.787000

Syntax

SELECT [westclintech].[wct].[MTRIU](
   <@Matrix, nvarchar(max),>)

Description

Use the scalar function MTRIU to return the upper triangular part of the string representation of a matrix.

MTRIU expects a string representation of the matrix, with columns separated by commas and rows separated by semi-colons.

Arguments

@Matrix

a string representation of a matrix.

Return Type

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 upper 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.MTRIU(@A) as [U];

This produces the following result.

{"columns":[{"field":"U"}],"rows":[{"U":"-79,-45,9,9,-91,-5;0,46,9,81,-61,35;0,0,80,-67,-22,-38;0,0,0,69,73,-20;0,0,0,0,-6,-34;0,0,0,0,0,11;0,0,0,0,0,0;0,0,0,0,0,0;0,0,0,0,0,0;0,0,0,0,0,0"}]}

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 item as [U]
FROM wct.SPLIT(wct.MTRIU(@A), ';') l;

This produces the following result:

{"columns":[{"field":"U"}],"rows":[{"U":"-79,-45,9,9,-91,-5"},{"U":"0,46,9,81,-61,35"},{"U":"0,0,80,-67,-22,-38"},{"U":"0,0,0,69,73,-20"},{"U":"0,0,0,0,-6,-34"},{"U":"0,0,0,0,0,11"},{"U":"0,0,0,0,0,0"},{"U":"0,0,0,0,0,0"},{"U":"0,0,0,0,0,0"},{"U":"0,0,0,0,0,0"}]}

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(wct.MTRIU(@A)) l;

This produces the following result.

{"columns":[{"field":"RowNum","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"},{"field":"ColNum","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"},{"field":"ItemValue","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"}],"rows":[{"RowNum":"0","ColNum":"0","ItemValue":"-79"},{"RowNum":"0","ColNum":"1","ItemValue":"-45"},{"RowNum":"0","ColNum":"2","ItemValue":"9"},{"RowNum":"0","ColNum":"3","ItemValue":"9"},{"RowNum":"0","ColNum":"4","ItemValue":"-91"},{"RowNum":"0","ColNum":"5","ItemValue":"-5"},{"RowNum":"1","ColNum":"0","ItemValue":"0"},{"RowNum":"1","ColNum":"1","ItemValue":"46"},{"RowNum":"1","ColNum":"2","ItemValue":"9"},{"RowNum":"1","ColNum":"3","ItemValue":"81"},{"RowNum":"1","ColNum":"4","ItemValue":"-61"},{"RowNum":"1","ColNum":"5","ItemValue":"35"},{"RowNum":"2","ColNum":"0","ItemValue":"0"},{"RowNum":"2","ColNum":"1","ItemValue":"0"},{"RowNum":"2","ColNum":"2","ItemValue":"80"},{"RowNum":"2","ColNum":"3","ItemValue":"-67"},{"RowNum":"2","ColNum":"4","ItemValue":"-22"},{"RowNum":"2","ColNum":"5","ItemValue":"-38"},{"RowNum":"3","ColNum":"0","ItemValue":"0"},{"RowNum":"3","ColNum":"1","ItemValue":"0"},{"RowNum":"3","ColNum":"2","ItemValue":"0"},{"RowNum":"3","ColNum":"3","ItemValue":"69"},{"RowNum":"3","ColNum":"4","ItemValue":"73"},{"RowNum":"3","ColNum":"5","ItemValue":"-20"},{"RowNum":"4","ColNum":"0","ItemValue":"0"},{"RowNum":"4","ColNum":"1","ItemValue":"0"},{"RowNum":"4","ColNum":"2","ItemValue":"0"},{"RowNum":"4","ColNum":"3","ItemValue":"0"},{"RowNum":"4","ColNum":"4","ItemValue":"-6"},{"RowNum":"4","ColNum":"5","ItemValue":"-34"},{"RowNum":"5","ColNum":"0","ItemValue":"0"},{"RowNum":"5","ColNum":"1","ItemValue":"0"},{"RowNum":"5","ColNum":"2","ItemValue":"0"},{"RowNum":"5","ColNum":"3","ItemValue":"0"},{"RowNum":"5","ColNum":"4","ItemValue":"0"},{"RowNum":"5","ColNum":"5","ItemValue":"11"},{"RowNum":"6","ColNum":"0","ItemValue":"0"},{"RowNum":"6","ColNum":"1","ItemValue":"0"},{"RowNum":"6","ColNum":"2","ItemValue":"0"},{"RowNum":"6","ColNum":"3","ItemValue":"0"},{"RowNum":"6","ColNum":"4","ItemValue":"0"},{"RowNum":"6","ColNum":"5","ItemValue":"0"},{"RowNum":"7","ColNum":"0","ItemValue":"0"},{"RowNum":"7","ColNum":"1","ItemValue":"0"},{"RowNum":"7","ColNum":"2","ItemValue":"0"},{"RowNum":"7","ColNum":"3","ItemValue":"0"},{"RowNum":"7","ColNum":"4","ItemValue":"0"},{"RowNum":"7","ColNum":"5","ItemValue":"0"},{"RowNum":"8","ColNum":"0","ItemValue":"0"},{"RowNum":"8","ColNum":"1","ItemValue":"0"},{"RowNum":"8","ColNum":"2","ItemValue":"0"},{"RowNum":"8","ColNum":"3","ItemValue":"0"},{"RowNum":"8","ColNum":"4","ItemValue":"0"},{"RowNum":"8","ColNum":"5","ItemValue":"0"},{"RowNum":"9","ColNum":"0","ItemValue":"0"},{"RowNum":"9","ColNum":"1","ItemValue":"0"},{"RowNum":"9","ColNum":"2","ItemValue":"0"},{"RowNum":"9","ColNum":"3","ItemValue":"0"},{"RowNum":"9","ColNum":"4","ItemValue":"0"},{"RowNum":"9","ColNum":"5","ItemValue":"0"}]}

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(wct.MTRIU(@A)) ) M
PIVOT
(
    MAX(ItemValue)
    FOR colnum IN ([0], [1], [2], [3], [4], [5])
) AS pvt
ORDER BY rownum;

This produces the following result.

{"columns":[{"field":"0","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"},{"field":"1","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"},{"field":"2","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"},{"field":"3","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"},{"field":"4","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"},{"field":"5","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"}],"rows":[{"0":"-79","1":"-45","2":"9","3":"9","4":"-91","5":"-5"},{"0":"0","1":"46","2":"9","3":"81","4":"-61","5":"35"},{"0":"0","1":"0","2":"80","3":"-67","4":"-22","5":"-38"},{"0":"0","1":"0","2":"0","3":"69","4":"73","5":"-20"},{"0":"0","1":"0","2":"0","3":"0","4":"-6","5":"-34"},{"0":"0","1":"0","2":"0","3":"0","4":"0","5":"11"},{"0":"0","1":"0","2":"0","3":"0","4":"0","5":"0"},{"0":"0","1":"0","2":"0","3":"0","4":"0","5":"0"},{"0":"0","1":"0","2":"0","3":"0","4":"0","5":"0"},{"0":"0","1":"0","2":"0","3":"0","4":"0","5":"0"}]}

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 MTRIU 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(wct.MTRIU(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.

{"columns":[{"field":"0","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"},{"field":"1","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"},{"field":"2","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"},{"field":"3","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"},{"field":"4","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"},{"field":"5","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"}],"rows":[{"0":"-79","1":"-45","2":"9","3":"9","4":"-91","5":"-5"},{"0":"0","1":"46","2":"9","3":"81","4":"-61","5":"35"},{"0":"0","1":"0","2":"80","3":"-67","4":"-22","5":"-38"},{"0":"0","1":"0","2":"0","3":"69","4":"73","5":"-20"},{"0":"0","1":"0","2":"0","3":"0","4":"-6","5":"-34"},{"0":"0","1":"0","2":"0","3":"0","4":"0","5":"11"},{"0":"0","1":"0","2":"0","3":"0","4":"0","5":"0"},{"0":"0","1":"0","2":"0","3":"0","4":"0","5":"0"},{"0":"0","1":"0","2":"0","3":"0","4":"0","5":"0"},{"0":"0","1":"0","2":"0","3":"0","4":"0","5":"0"}]}