tailieunhanh - Lecture note Data visualization - Chapter 29

The main contents of the chapter consist of the following: The relational algebra, unary relational operations, relational algebra operations from set theory, binary relational operations, ER-to-Relational mapping algorithm, mapping EER model constructs to relations. | Lecture note Data visualization - Chapter 29 Lecture 29 Recap Summary of Chapter 6 Interpolation Linear Interpolation Cubic Spline Interpolation Connecting data points with straight lines probably isn t the best way to estimate intermediate values although it is surely the simplest A smoother curve can be created by using the cubic spline interpolation technique included in the interp1 function. This approach uses a third order polynomial to model the behavior of the data To call the cubic spline we need to add a fourth field to interp1 interp1 x y spline This command returns an improved estimate of y at x Multidimensional Interpolation Suppose there is a set of data z that depends on two variables x and y . For example Continued . In order to determine the value of z at y 3 and x two interpolations have to performed One approach would be to find the values of z at y 3 and all the given x values by using interp1 and then do a second interpolation in new chart First let s define x y and z in MATLAB y 2 2 6 x 1 4 z 7 15 22 30 54 109 164 218 Continued . Although the previous approach works performing the calculations in two steps is awkward MATLAB includes a two dimensional linear interpolation function interp2 that can solve the problem in a single step interp2 x y z 3 ans The first field in the interp2 function must be a vector defining the value associated with each column in this case x and the second field must be a vector defining Continued . MATLAB also includes a function interp3 for three dimensional interpolation Consult the help feature for the details on how to use this function and interpn which allows you to perform n dimensional interpolation All these functions default to the linear interpolation technique but will accept any of the other techniques Curve Fitting Although interpolation techniques can be used to find values of y between measured x values it would be more convenient if we could model experimental data as y f x Then