SECANT

Updated 2023-10-18 21:03:29.767000

Syntax

SELECT [westclintech].[wct].[SECANT] (
   <@Func, nvarchar(max),>
  ,<@VarName, nvarchar(4000),>
  ,<@A, float,>
  ,<@B, float,>
  ,<@MaxIter, int,>
  ,<@tol, float,>)

Description

Use the scalar function SECANT to find the root of a univariate function.

Arguments

@tol

Absolute tolerance.

@A

One of the 2 starting values.

@B

Another starting value.

@VarName

The name of the variable.

@MaxIter

Maximum number of iterations.

@Func

The function to be evaluated, as a string. The function must be in the form of a SELECT statement.

Return Type

float

Remarks

If Func returns a NULL then NULL is returned.

If Func is not a valid SELECT statement then NULL is returned.

If no solution is found then NULL is returned.

The solution must be bound by A and B.

If A is NULL then A = 0.

If B is NULL then B = 0.

If MaxIter is NULL then MaxIter = 100.

If tol is NULL then tol = 0.

If tol <= 0 then tol = 0.0000000149011612.

Examples

Example #1

Let’s find the root of the Legendre polynomial of degree 5.

SELECT wct.SECANT('SELECT (63 * POWER(@x,5) - 70 * POWER(@x,3) + 15 * @x)/8e+00',

          '@x', 0.9, 1.0, NULL, NULL) as SECANT;

This produces the following result.

{"columns":[{"field":"SECANT","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"}],"rows":[{"SECANT":"0.906179845936973"}]}

Example #2In this example we call the PRICE function to calculate the yield on a bond using the SECANT function and compare that with value returned by the YIELD function.

SELECT wct.SECANT(

                     'SELECT wct.PRICE(

             ''2018-04-25''

          ,''2025-05-15''

            ,.04

            ,@Y

            ,100

          ,2

            ,0) - 98.25',

                     '@Y',

                     .04,

                     .12,

                     NULL,

                     1E-08

                 ) as secant,

       wct.YIELD('2018-04-25', '2025-05-15', .04, 98.25, 100, 2, 0) as yield;