MUPDATE
Updated: 10 May 2016
Use the scalar function MUPDATE to change the values in the string representation of a matrix or to perform element-wise operations on a matrix or some portion of a matrix. A new string representation is returned.
Syntax
SELECT [wct].[MUPDATE](
<@A, nvarchar(max),>
,<@start_row_A, int,>
,<@end_row_A, int,>
,<@start_col_A, int,>
,<@end_col_A, int,>
,<@EOperator, nvarchar(4000),>
,<@B, nvarchar(max),>
,<@start_row_B, int,>
,<@end_row_B, int,>
,<@start_col_B, int,>
,<@end_col_B, int,>)
Arguments
@A
A string representation of the A matrix.
@start_row_A
The first row of @A to be included in the result. @start_row_A must be of a type int or of a type that implicitly converts to int.
@end_row_A
The last row of @A to be included in the result. @end_row_A must be of a type int or of a type that implicitly converts to int.
@start_col_A
The first column of @A to be included in the result. @start_col_A must be of a type int or of a type that implicitly converts to int.
@end_col_A
The last column of @A to be included in the result. @end_col_A must be of a type int or of a type that implicitly converts to int.
@EOperator
Identifies the elementwise operation to be performed. The eligible values are '+', '-', '*', '/', and '='.
@B
A string representation of a B matrix.
@start_row_B
The first row of @B to be included in the result. @start_row_B must be of a type int or of a type that implicitly converts to int.
@end_row_B
The last row of @B to be included in the result. @end_row_B must be of a type int or of a type that implicitly converts to int.
@start_col_B
The first column of @B to be included in the result. @start_col_B must be of a type int or of a type that implicitly converts to int.
@end_col_B
The last column of @B to be included in the result. @end_col_B must be of a type int or of a type that implicitly converts to int.
Return Types
nvarchar(max)
Remarks
· The string representations of @A and/or @B 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-numeric data between semi-colons will generate an error.
· To convert the string result to a table, us the table-valued function MATRIX.
· If @B is NULL then the returned matrix is @A or a subset of @A.
· If @A is NULL then the returned matrix is @B or a subset of @B.
· If @start_row_A is NULL then @start_row_A equals 1.
· If @start_col_A is NULL then @start_col_A equals 1.
· If @start_row_B is NULL then @start_row_B equals 1.
· If @start_col_B is NULL then @start_col_B equals 1.
· If @end_row_A is NULL then @end_row_A equals the last row in in @A.
· If @end_col_A is NULL then @end_col_A equals the last row in in @A.
· If @end_row_B is NULL then @end_row_B equals the last row in in @B.
· If @end_col_B is NULL then @end_col_B equals the last row in in @B.
Examples
Example #1
In this example we want to create a 3-by-3 matrix with each element set to the square root of 2.
SELECT wct.MUPDATE(wct.ZERO(3,3),NULL,NULL,NULL,NULL,'=',1.4142135623731,NULL,NULL,NULL,NULL) as M
--Only run this SQL to automatically PIVOT the results into the
--traditional row/column matrix presentation
--SELECT [0],[1],[2]
--FROM wct.MATRIX(wct.MUPDATE(wct.ZERO(3,3),NULL,NULL,NULL,NULL,'=',1.4142135623731,NULL,NULL,NULL,NULL))d
--PIVOT (MAX(ItemValue) FOR ColNum in ([0],[1],[2]))pvt
--ORDER BY RowNum
This produces the following result.
Here are the results formatted as a table.
Example #2
In this example we only want to update the matrix such that the lower right-hand corner is equal the square root of 2; in other words the first column and the first row will still contain zeroes.
SELECT wct.MUPDATE(wct.ZERO(3,3),2,3,2,3,'=',1.4142135623731,NULL,NULL,NULL,NULL) as M
--Only run this SQL to automatically PIVOT the results into the
--traditional row/column matrix presentation
--SELECT [0],[1],[2]
--FROM wct.MATRIX(wct.MUPDATE(wct.ZERO(3,3),2,3,2,3,'=',1.4142135623731,NULL,NULL,NULL,NULL))d
--PIVOT (MAX(ItemValue) FOR ColNum in ([0],[1],[2]))pvt
--ORDER BY RowNum
This produces the following result.
Here are the results formatted as a table.
Example #3
In this example we add 2 to every value in the matrix @A.
DECLARE @A as varchar(max) = '1,1,1,1,1;1,2,4,8,16;1,3,9,27,81;1,4,16,64,256;1,5,25,125,625'
DECLARE @C as varchar(max)
SET @C = wct.MUPDATE(@A,NULL,NULL,NULL,NULL,'+',2,NULL,NULL,NULL,NULL)
SELECT @C as C
--Only run this SQL to automatically PIVOT the results into the
--traditional row/column matrix presentation
--DECLARE @M as nvarchar(max) = N'SELECT @cols FROM wct.Matrix(@C) d PIVOT(MAX(ItemValue) FOR ColNum in (@cols))p ORDER BY RowNum'
--DECLARE @cols as nvarchar(max)
--SET @cols = (SELECT '[' + cast(ColNum as varchar(max)) + ']' FROM wct.MATRIX(@C) WHERE RowNum = 0 ORDER BY colnum FOR XML PATH(''))
--SET @cols = REPLACE(@cols,'][','],[')
--SET @M = REPLACE(REPLACE(@M,'@cols',@cols),'@C','''' + @C + '''')
--EXECUTE(@M)
This produces the following result.
Here are the results formatted as a table.
Example #4
In this example we return the reciprocal of every element in the @A matrix.
DECLARE @A as varchar(max) = '1,1,1,1,1;1,2,4,8,16;1,3,9,27,81;1,4,16,64,256;1,5,25,125,625'
DECLARE @C as varchar(max)
SET @C = wct.MUPDATE(1,NULL,NULL,NULL,NULL,'/',@A,NULL,NULL,NULL,NULL)
SELECT @C as C
--Only run this SQL to automatically PIVOT the results into the
--traditional row/column matrix presentation
--DECLARE @M as nvarchar(max) = N'SELECT @cols FROM wct.Matrix(@C) d PIVOT(MAX(ItemValue) FOR ColNum in (@cols))p ORDER BY RowNum'
--DECLARE @cols as nvarchar(max)
--SET @cols = (SELECT '[' + cast(ColNum as varchar(max)) + ']' FROM wct.MATRIX(@C) WHERE RowNum = 0 ORDER BY colnum FOR XML PATH(''))
--SET @cols = REPLACE(@cols,'][','],[')
--SET @M = REPLACE(REPLACE(@M,'@cols',@cols),'@C','''' + @C + '''')
--EXECUTE(@M)
This produces the following result.
Here are the results formatted as a table.
Example #5
In this example we subtract the @B matrix from the @A matrix.
DECLARE @A as varchar(max) = wct.EYE(5,5)
DECLARE @B as varchar(max) = '1,1,1,1,1;1,2,4,8,16;1,3,9,27,81;1,4,16,64,256;1,5,25,125,625'
SET @B = wct.MUPDATE(1,NULL,NULL,NULL,NULL,'/',@B,NULL,NULL,NULL,NULL)
DECLARE @C as varchar(max)
SET @C = wct.MUPDATE(@A,NULL,NULL,NULL,NULL,'-',@B,NULL,NULL,NULL,NULL)
SELECT @C as C
--Only run this SQL to automatically PIVOT the results into the
--traditional row/column matrix presentation
--DECLARE @M as nvarchar(max) = N'SELECT @cols FROM wct.Matrix(@C) d PIVOT(MAX(ItemValue) FOR ColNum in (@cols))p ORDER BY RowNum'
--DECLARE @cols as nvarchar(max)
--SET @cols = (SELECT '[' + cast(ColNum as varchar(max)) + ']' FROM wct.MATRIX(@C) WHERE RowNum = 0 ORDER BY colnum FOR XML PATH(''))
--SET @cols = REPLACE(@cols,'][','],[')
--SET @M = REPLACE(REPLACE(@M,'@cols',@cols),'@C','''' + @C + '''')
--EXECUTE(@M)
This produces the following result.
Here are the results formatted as a table.
Example #6
In this example we subtract @B from @A excluding the first row and the first column.
DECLARE @A as varchar(max) = wct.EYE(5,5)
DECLARE @B as varchar(max) = '1,1,1,1,1;1,2,4,8,16;1,3,9,27,81;1,4,16,64,256;1,5,25,125,625'
SET @B = wct.MUPDATE(1,NULL,NULL,NULL,NULL,'/',@B,NULL,NULL,NULL,NULL)
DECLARE @C as varchar(max)
SET @C = wct.MUPDATE(@A,2,5,2,5,'-',@B,2,5,2,5)
SELECT @C as C
--Only run this SQL to automatically PIVOT the results into the
--traditional row/column matrix presentation
--DECLARE @M as nvarchar(max) = N'SELECT @cols FROM wct.Matrix(@C) d PIVOT(MAX(ItemValue) FOR ColNum in (@cols))p ORDER BY RowNum'
--DECLARE @cols as nvarchar(max)
--SET @cols = (SELECT '[' + cast(ColNum as varchar(max)) + ']' FROM wct.MATRIX(@C) WHERE RowNum = 0 ORDER BY colnum FOR XML PATH(''))
--SET @cols = REPLACE(@cols,'][','],[')
--SET @M = REPLACE(REPLACE(@M,'@cols',@cols),'@C','''' + @C + '''')
--EXECUTE(@M)
This produces the following result.
Here are the results formatted as a table.
Example #7
In this example we subtract @B from @A, excluding the first row and the first column where we want to retain the original @A values.
DECLARE @A as varchar(max) = wct.EYE(5,5)
DECLARE @B as varchar(max) = '1,1,1,1,1;1,2,4,8,16;1,3,9,27,81;1,4,16,64,256;1,5,25,125,625'
SET @B = wct.MUPDATE(1,NULL,NULL,NULL,NULL,'/',@B,NULL,NULL,NULL,NULL)
DECLARE @C as varchar(max)
SET @C = wct.MUPDATE(@A,2,5,2,5,'=',wct.MUPDATE(@A,2,5,2,5,'-',@B,2,5,2,5),NULL,NULL,NULL,NULL)
SELECT @C as C
--Only run this SQL to automatically PIVOT the results into the
--traditional row/column matrix presentation
--DECLARE @M as nvarchar(max) = N'SELECT @cols FROM wct.Matrix(@C) d PIVOT(MAX(ItemValue) FOR ColNum in (@cols))p ORDER BY RowNum'
--DECLARE @cols as nvarchar(max)
--SET @cols = (SELECT '[' + cast(ColNum as varchar(max)) + ']' FROM wct.MATRIX(@C) WHERE RowNum = 0 ORDER BY colnum FOR XML PATH(''))
--SET @cols = REPLACE(@cols,'][','],[')
--SET @M = REPLACE(REPLACE(@M,'@cols',@cols),'@C','''' + @C + '''')
--EXECUTE(@M)
This produces the following result.
Here are the results formatted as a table.
See Also