QUADOSC
Updated: 31 March 2014
Use the scalar function QUADOSC to evaluate an infinite integral. QUADOSC calculates the integral of the given function f(x) over the interval (-Infinity, Infinity) using Double Exponential Quadrature for Periodic functions.
Syntax
SELECT [wctMath].[wct].[QUADOSC](
<@Func, nvarchar(max),>
,<@VarName, nvarchar(4000),>
,<@A, sql_variant,>
,<@B, sql_variant,>
,<@Omega, float,>)
Arguments
@Func
the function to be integrated. @Func is a string containing any valid TSQL statement which includes a single variable that is the object of the integration. The variable name is defined in @VarName. @Func is of a type nvarchar or of any type which implicitly converts to nvarchar.
@VarName
the TSQL variable name. The variable name must start with '@'. @VarName must be of a type nvarchar of a type which implicitly converts to nvarchar.
@A
the lower limit of integration.
@B
the upper limit of integration.
@Omega
the periodicity of the function. @Omega must be of the type float or of a type that implicitly converts to float.
Return Types
float
Remarks
· If @A is not '-Inf' and @B is not 'Inf' then NULL will be returned.
· If @A is '-Inf' then the function will be integrate from –8 to @B.
· If @A is not '-Inf' then the function will be integrated from @A to 8.
· If @Omega is NULL then @Omega is set to 1.
· @Omega cannot be equal to zero.
· @A can be any floating point number or '-Inf'.
· @B can be any floating point number or 'Inf'.
· If @Func contains an undeclared SQL variable and it is not defined in @VarName a NULL will be returned.
· For best results you should only periodic functions. For non-periodic functions use QUADDE instead.
Example
In this example we want to evaluate the integral:
SELECT dbo.QUADOSC(
'SELECT (SIN(@x)-@x*COS(@x))/POWER(@x,2)', --@Func
'@x', --@VarName
0, --@A
'Inf', --@B
1 --@Omega
) as Integral
This produces the following result.
Integral
----------------------
0.99999999999999
In this example we want to evaluate the integral:
SELECT dbo.QUADOSC(
'SELECT (SIN(@x)-@x*COS(@x))/POWER(@x,2)', --@Func
'@x', --@VarName
'-Inf', --@A
0, --@B
1 --@Omega
) as Integral
This produces the following result.
Integral
----------------------
-0.99999999999999
In this example we want to evaluate the integral:
SELECT dbo.QUADOSC(
'SELECT EXP(-16*POWER(@x,2))*COS(3*(@x+5))', --@Func
'@x', --@VarName
'-Inf', --@A
'Inf', --@B
NULL --@Omega
) as Integral
This produces the following result.
Integral
----------------------
3.14159265358979
See Also