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DIAG

Updated 2023-10-19 13:24:11.957000

Syntax

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

Description

Use the scalar function DIAG to return the vector of the diagonal of the string representation of a matrix. The diagonal is all the values in the matrix where the row number is equal to the column number.

DIAG 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 diagonal.

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.DIAG(@A) as [Diagonal];

This produces the following result.

{"columns":[{"field":"Diagonal"}],"rows":[{"Diagonal":"-79;46;80;69;-6;11"}]}

The matrix does not have to be assigned to a variable before passed into the DIAG function; the string can be passed in directly.

SELECT wct.DIAG('-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') 

          as [Diagonal];

This produces the following result.

{"columns":[{"field":"Diagonal"}],"rows":[{"Diagonal":"-79;46;80;69;-6;11"}]}