SQL Server SYMMEIG Function

Updated 2024-03-07 15:35:35.977000

Description

Use the table-valued function SYMMEIG to return the D and V matrices representing the eigenvalues and eigenvectors of a real symmetric matrix. The input into the function is an SQL statement having a resultant table which is a real, symmetric matrix. The resultant table can be in either 3rd-normal or 'spreadsheet' form. SYMMEIG returns a table in third normal form containing the D and V matrices such that:

\textbf{A}=\textbf{VDV}^T

Syntax

SELECT * FROM [westclintech].[wct].[SYMMEIG](
  <@MatrixQuery, nvarchar(max),>
 ,<@Is3N, bit,>)

Arguments

@MatrixQuery

An SQL statement which upon execution returns a real symmetric matrix or the string representation of the matrix with the columns separated by commas and the rows separated by semicolons.

@Is3N

A bit value which indicates whether the resultant table returned by @MatrixQuery is in 3^rd normal form. Enter TRUE for a resultant table in 3^rd normal form.

Return Type

table

Remarks

If @Is3N is NULL then @Is3N = FALSE.

Type is either 'D' or 'V'.

Examples

Example #1

In this example we supply @A as a real symmetric matrix and return the D and V matrices.

DECLARE @A as varchar(max) = '5,15,55,225;15,55,225,979;55,225,979,4425;225,979,
          4425,20515';
SELECT *
FROM wct.SYMMEIG(@A, NULL);

This produces the following result.

Example #2

Using the same values, with the matrix passed in as SQL which produces a resultant table not in 3 ^rd -normal form.

SELECT *
FROM wct.SYMMEIG(
                    'SELECT * FROM (VALUES (5,15,55,225),(15,55,225,979),(55,225,
                              979,4425),(225,979,4425,20515))n(x1,x2,x3,x4)',
                    'False'
                );

This produces the following result.

Example #3

Using the same values, with the matrix passed in as SQL which produces a result in 3^rd normal form.

SELECT *
INTO #t
FROM
(
    VALUES
        (0, 0, 5),
        (0, 1, 15),
        (0, 2, 55),
        (0, 3, 225),
        (1, 0, 15),
        (1, 1, 55),
        (1, 2, 225),
        (1, 3, 979),
        (2, 0, 55),
        (2, 1, 225),
        (2, 2, 979),
        (2, 3, 4425),
        (3, 0, 225),
        (3, 1, 979),
        (3, 2, 4425),
        (3, 3, 20515)
) n (r, c, x);
SELECT *
FROM wct.SYMMEIG('SELECT * FROM #t', 'True');

This produces the following result.

See Also

MUPDATE - perform elementwise operations on a matrix