SQL Server MRORTHO Function

Updated 2023-10-20 15:07:32.743000

Description

Use the scalar function MRORTHO to generate an m-by-m random orthogonal matrix.

Syntax

SELECT [westclintech].[wct].[MRORTHO](
   <@m, int,>)

Arguments

@m

the number of rows and columns in returned matrix. @m must be of the type int or of a type that implicitly converts to int.

Return Type

nvarchar(max)

Remarks

m must be greater than zero.

Examples

Example #1

In this example we generate a random 4-by-4 random orthogonal matrix. The returned matrix is a string where the columns are separated by commas and the rows are separated by semicolons. Your results will be different.

SELECT wct.MRORTHO(4) as [Random Ortho];

This produces the following result.

Example #2

In this example we generate a 5-by-5 random orthogonal matrix and use the MATRIX function to convert the output to 3^rd normal form. Your results will be different.

SELECT *
FROM wct.MATRIX(wct.MRORTHO(5));

This produces the following result.

Example #3

In this example we generate the 5-by-5 random orthogonal matrix and pivot the MATRIX output into 'spreadsheet' format. Your results will be different.

SELECT [0],
       [1],
       [2],
       [3],
       [4]
FROM wct.MATRIX(wct.MRORTHO(5)) d
    PIVOT
    (
        MAX(ItemValue)
        FOR ColNum IN ([0], [1], [2], [3], [4])
    ) pvt
ORDER BY RowNum;

This produces the following result.

See Also

SVD - Economy-sized singular value decomposition using a formatted matrix as input