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Microsoft no longer ships sample databases with SQL Server, but they do make them available on CodePlex. You can download the full set of sam/www.codeplex.com/ ple SQL Server 2005 and 2008 databases from http:/ MSFTDBProdSamples.

Visual inspectionof Fig 164aindicatesthat the primary disadvantage first-order of splinesis that they are not smoothIn essence, the data points where two splinesmeet at (called a knot), the slopechanges abruptlyIn formal terms,the first derivativeof the function is discontinuousat thesepoints This deficiency is overcomeby using higher-order polynomial splinesthat ensuresmoothness the knots by equatingderivativesat these at points,as will be discussed subsequently Beforedoing that,the following sectionprovides an applicationwhere linear splinesare useful

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in and A table lookup is a common task that is frequentlyencountered engineering science performing repeated interpolations fiorrr a table of computer applicationsIt is useful tbr variablesFor example,suppose that you would like to set up independent and dependent teman M-file that would use linear interpolationto determineair density at a particular peraturebasedon the datafrom Table 1-51 One way to do this would be to passtlreM-file to the temperature which you want the interpolation be performedalong with thetwoadat joining values more generalapproach would be to passin vectorscontainingall thedata A and have the M-file detenninethe bracketThis is called a table lookup variThus, the M-file would perform two tasksFirst, it would search independent the able vector to find the intervirl containingthe unknorvnThen it would performthelineat in interpolation usingone of the techniques described this chapter in Chap15 or a For ordereddata, there are two simple ways to find the interval The first is called value sequentialsearchAs the name impliesthis methodinvolves comparingthe desired with each elementof the vector in seqnence until the interval is locatedFor datain asbeing cendingorder,this can be doneby testingwhetherthe unknownis lessthanthe value one lf assessed so, we know that the unknown falls betweenthis value and the previous is Here a that we examinedlf not, we move to the next value and repeatthe comparison this simpleM-file that accomplishes objective:

The Products table will contain the new information. The Name and ProductNumber fields will contain the data from the AdventureWorksLT2008 database, while the ItemsInStock and CreatedDate fields will be populated when the data is inserted into the table.

functior-i n if xx error yi = Tablelook(;<, y, rr)

cngrn'X); < r(1) xx > x(n) (' Inter1;,olation outside search range' )

CREATE TABLE Products (Name NVARCHAR(50), ProductNumber NVARCHAR(25), ItemsInStock INT, CreatedDate DATETIME); GO

48 104,514,000 19,378,000 2,200,000 48 121,767,000 21,279,000 4,399,000 48 130,879,718 18,833,000 6,601,000 48 149,188,130 19,387,000 5,725,000

i - r;

The next bit of code creates the stored procedure that receives the TVP with the product name and number data. It uses an INSERT statement to add data to the new Products table, setting ItemsInStock to zero and using the GETDATE() function to insert the current date and time.

while (1) if xx = x(i + 1), break, end i = i + 1; end linear interpolation yr = 1(i) + (y(i+1) y(i))/(x(i+1)

x(i));

CREATE PROCEDURE dkInsertProducts @ProductsTVP ProductsType READONLY AS SET NOCOUNT ON INSERT INTO dbo.Products (Name, ProductNumber, ItemsInStock, CreatedDate) SELECT Name, ProductNumber, 0, GETDATE() FROM @ProductsTVP; GO

variablesare storedin ascending order in the arrayx and the The table's independent variablesstoredin the arrayy Before searching, error trap is included ento an dependent hex breakloop s u r e t h a t t h e d e s i r e d v a l u e x x f a l l s w i t h i n t h e r a ntg e o f' s A r r r [ ] l s whether isless it the compares value at which the interpolationis desired,xx, to determine thanthevalueatthetopoftheinterval,x(i+1)Forcaseswherexxisinthesecondintetval or higher,this will not testtrue at first In this casethe counter i is incremented one by intetso that on the next iteration,xx is comparedwith the value at the top of the second val The loop is repeated until the xx is lessthan or equalto the interval'supperbound,in can as which casethe loop is exitedAt this point, the inter-polation be performedsimply shown sort is inetTicient because For situationsfor which thereare lots of datathe sequential it must searchthrough all the precedingpoints to find values In thesecases, simple a followed alternativeisthe binan- searchHere is an M-file that performsa binary search

The final set of server-side code creates the variable of the TABLE type ProductsType, reads data from the AdventureWorksLT2008.SalesLT.Product table, and passes the TVP to the stored procedure.

by linear interpolation:

f unction n tf = yi = T,rbleLookBrn (x, \', xx)

DECLARE @Prods AS ProductsType; INSERT INTO @Prods (ProductName, ProductNumber) SELECT [Name], ProductNumber FROM AdventureWorksLT2008.SalesLT.Product; EXEC dkInsertProducts @Prods; GO SELECT * FROM Products;

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